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Technical ManualMTS 006 Iss. B
Outhouse distribution authorised
Documentresponsibility
Dept. code : BTE/CC/SC Validation Name : JF. IMBERT
Name : P. CIAVALDINI Function: Deputy DepartmentGroup Manager
Dept. code : BTE/CC/ADate : 06/05/99Signature
This document belongs to AEROSPATIALE and cannot be given to third parties and/or be copied withoutprior authorisation from AEROSPATIALE and its contents cannot be disclosed.
This issue is incomplete and existing chapters are liable to change.All allowable values and coefficients related to the various materials described in chapter Zare updated with each issue of the manual. This means that different values may be found inthe stress dossiers prior to latest issue.The data processing tools are given for information purposes only.
Assuming that allnormal load Ny apthe whole cross-se
ε =+b EMi e Ei(
This elongation th
- in the lower ski
- in the core, a s
- in the upper sk
The equivalent meby the relationship
Remark: In the casEmc ec <
ε ≈+
N
b EMi ei(
pagenumber
reference(s) ofsubchapter(s)title of chapter
reference of chaptertitle(s) of subchapter(s)
ror
Ems
Emc
Emi
SANDWICHt of normal load Ny
N 4.2.11/2
ormal load Ny
layers are in a pure tension or compression condition, aplied at the neutral line results in a constant elongation overction. This elongation may be formulated as follows:
+Ny
Mc e Ems ec s)
eferencefelation
MTS 006 Iss. A
is unduces:
n, a stress σi = Emi ε,
tress σc = Emc ε,
in, a stress σs = Ems ε.
mbrane modulus of the sandwich beam may be determined m14.
e of a sandwich beam in which< Emi ei and Emc ec << Ems es, the relationship becomes:
4 . Inspection of damage4.1 . Minimum damage detectable by a Special Detailed Inspection4.2 . Minimum damage detectable by a Detailed Visual Inspection4.3 . Minimum damage detectable by a General Visual Inspection4.4 . Minimum damage detectable by a Walk Around Check4.5 . Classification of accidental damage by detectability ranges
5 . Effects of flaws/damage on mechanical characteristics5.1 . Health flaws
5.1.2.2 . Delaminations in stiffener area of an integrally-stiffened panel5.1.3 . Delamination in spar radii5.1.4 . Delamination on spar flange edges5.1.5 . Foreign bodies5.1.6 . Translaminar cracks5.1.7 . Delaminations consecutive to a shock
6 . Justification of permissible manufacturing flaws7 . Justification of in-service damage
7.1 . Justification philosophy7.1.1 . Undetectable damage7.1.2 . Readily and obvious detectable damage7.1.3 . Damage susceptible to be detected during scheduled in-service inspections
7.1.3.1 . Aerospatiale semi-probabilistic method7.1.3.1.1 . Process for determining inspection intervals7.1.3.1.2 . Inspection interval calculation software7.1.3.1.3 . Load level K to be demonstrated in the presence of large VID
L . MONOLITHIC PLATE - FASTENER HOLE1 . Notations2 . General - Failure modes
2.1 . Bearing failure2.2 . Net cross-section failure2.3 . Plane shear failure2.4 . Cleavage failure2.5 . Cleavage and net cross-section failure2.6 . Fastener shear failure
3 . Single hole with fastener3.1 . Pitch p definition3.2 . Membrane design - Short cut method
3.2.1 . Theory3.2.2 . EDP computing program PSG33
3.3 . Bending design - Short cut method3.4 . Justifications3.5 . Nominal deviations on a single hole
3.5.1 . Changing to a larger diameter3.5.2 . Pitch decrease3.5.3 . Edge distance decrease
3.6 . "Point stress" finite element method3.6.1 . Description of the method3.6.2 . Justifications
4 . Multiple holes4.1 . Independent holes4.2 . Interfering holes4.3 . Very close holes
5 . Examples
M . MONOLITHIC PLATE - SPECIAL ANALYSIS1 . Stiffener run-out2 . Bending on border3 . Effect of "stepping"4 . Edge effects
N . SANDWICH - MEMBRANE/BENDING/SHEAR/ANALYSIS1 . Notations2 . Specificity3 . Construction principle4 . Design principle
4.1 . Sandwich plate4.2 . Sandwich beam
4.2.1 . Effect of a normal load Ny4.2.2 . Effect of a shear load Tx4.2.3 . Effect of a shear load Tz - Honeycomb shear4.2.4 . Effect of a bending moment Mx4.2.5 . Effect of a bending moment Mz4.2.6 . Equivalent properties
Q . SANDWICH - BUCKLING ANALYSIS1 . Local buckling
1.1 . Dimpling1.2 . Wrinkling
2 . General buckling2.1 . Bending2.2 . Shear load
R . SANDWICH - SPECIAL DESIGNS1 . Densified zones2 . Slopes/ramps
S . BONDED JOINTS1 . Notations2 . Bonded single lap joint
2.1 . Elastic behavior of materials and adhesive2.1.1 . Highly flexible adhesive2.1.2 . General case (without cleavage effect)2.1.3 . General case (with cleavage effect)2.1.4 . Scarf joint
2.2 . Elastic-plastic behavior of adhesive and elastic behavior of materials3 . Bonded double lap joint4 . Bonded stepped joint5 . Software6 . Examples
6 . Assessment of mechanical distributed in-plane forces on the doubler6.1 . Distribution of flow Nx6.2 . Distribution of flow Ny6.3 . Distribution of shear flow Nxy
7 . Assessment of thermal in-plane forces on the doubler ?8 . Assessment of flows in the panel9 . Assessment of loads per fastener
9.1 . Repair with 1 row of fasteners9.2 . Repair with 2 rows of fasteners9.3 . Repair with 3 rows of fasteners9.4 . Repair with 4 rows of fasteners9.5 . Repair with a number of rows of fasteners greater than 49.6 . General resolution method for direction x
10 . Assessment of loads per fastener due to the transfer of shear loads Nxy11 . Justifications12 . Summary flowchart13 . Examples
V . THERMAL CALCULATIONS1 . Notations2 . Introduction3 . Hooke - Duhamel law4 . Behavior of unidirectional fibre5 . Behavior of a free monolithic plate
6 . Theory of the bimetallic strip6.1 . Determining stresses of thermal origin6.2 . Study of the link between two parts
6.2.1 . Bolted or riveted joints6.2.1.1 . Force F taken by one fastener6.2.1.2 . Force F taken by two fasteners6.2.1.3 . Force F taken by three fasteners6.2.1.4 . Force F taken by four or more fasteners
6.2.2 . Bonded joints7 . Influence of temperature on aircraft structures
7.1 . General7.2 . Temperature of ambient air
7.2.1 . Temperature envelope7.2.2 . Variation of ambient air temperature
7.2.2.1 . Ambient temperature on ground7.2.2.2 . Ambient temperature in flight
7.3 . Wall temperature7.3.1 . Influence of solar radiation
7.3.1.1 . Maximum solar radiation7.3.1.2 . Solar radiation during the day
7.3.2 . Influence of aircraft speed7.3.3 . Temperature of structure
7.3.3.1 . Calculation method7.3.3.2 . Thermal characteristics of the materials7.3.3.3 . Temperatures of structure on ground7.3.3.4 . Temperatures of structure in flight
The importance of using composite materials in aeronautical construction, and specificallywithin the Aerospatiale group, has initiated the need to prepare a document the interest ofpreparing a document gathering all the design methods and mechanical properties of themain composite materials used and/or developed by the composite material DesignOffice.
Each one of these two subjects shall make up one volume of the composite materialdesign manual.
Composite materials result from the association of at least two chemically andgeometrically different materials.
"Composite material" commonly means arrangements of fibres - continuous or not - of aresistant material (reinforcing material) which are embedded in a material with a muchlower strength (matrix), and stiffness.
The bond between the reinforcing material and the matrix is created during thepreparation phase of the composite material and this bond shall have a fundamentaleffect on the mechanical properties of the final material.
Their purpose is to ensure the mechanical function of the composite material. Fibres canbe of very different chemical and geometrical types, and the following properties shall bespecifically searched for:
- high mechanical properties.
- physico-chemical compatibility with the matrix.
- easy to use.
- good repeatability of the properties.
- low density.
- low cost.
They are made up of several thousand filaments (the number of filaments being indicatedby 3K: 3000 filaments, 6K: 6000 filaments or 12K: 12000 filaments) with a diameterbetween 5 and 15 µm, and they are commercialised in two different forms:
- short fibres (a few centimeters long): they are felt, pylons (fabrics in which fibres arelaid out randomly) and injected short fibres,
- long fibres: they are cut during manufacture of the composite material, used as suchor woven,
- metal matrices (aluminium, titanium and nickel alloys).
3 . PROCESSING METHOD
The reinforcing fibre/resin mix becomes a genuinely resistant composite material onlyupon completion of the last manufacturing phase, i.e; curing of the matrix.
This cycle is achieved following the chemical reaction between the various components -this is the crosslinking phase.
The chemical reaction is initiated as soon as products are in contact, and it is oftenaccelerated by heat: the higher the temperature, the quicker and more explosive is thereaction:
There are two types of chemical reactions:
- the polyaddition reaction for epoxy resins where the weight of reactants is equal tothe weight of the compound,
- the condensation reaction (polycondensation) for phenolic resins where twocompounds are formed (a solid one and a gaseous one).
The curing cycle consist of a number of temperature levels of variable duration:
- a gel level which allows getting a consistent temperature gradient throughout thematerial before full gelation to limit internal stresses,
- a curing level which allows hardening,
- a post-curing level which allows internal stresses to be relieved, and additional curingfor a better temperature resistance.
Note: the glass transition point is the temperature value at which all material propertieschange. This important property must be measured, before and after wet aging.
There are several types of manufacturing facilities and processes:
- Manufacturing facilities:
• Autoclave: parts are produced under pressure and at high temperature.
• Oven: parts are vacuum produced and at high temperature.
• Hot press: pressure is applied by a mechanical device or by hydraulic jacks.
- Manufacturing processes:
• Multiple shots process: laminate are cured separately, then bonding oflaminates to the substructure (ribs, honeycombs, etc.) is performed as asecond operation.
• Semi-cocuring process: the external skin is cured separately, the substructure(rib, or honeycomb + internal skin and stiffeners) is then cocured on theexternal skin with an adhesive film spread, if necessary.
• Single phase process: or "cocuring", skins are cured and bonded to thesubstructure (ribs or honeycomb or stiffeners) in one single operation.
After being manufactured, the different composite (and metal) elements must beconnected to one another to allow load transfer.
The two most commonly used techniques are bonding and bolting (or riveting).
Bonding techniques are tricky to implement (preparation of surfaces to be bonded)because they are sensitive to environmental conditions: hygrometry, temperature, curedate of adhesives.
They are also difficult to control because even a sound adhesive film is a barrier toultrasounds.
More repetitive and reliable bolting techniques may generate:
- stress concentration at fastener holes,
- delamination during drilling or assembly operations,
- corrosion of fasteners or of metal parts assembled with composite parts.
6 . ADVANTAGES - DISADVANTAGES OF COMPOSITE MATERIALS
The use of composite materials has four major advantages:
- a weight gain which is reflected by fuel saving and, therefore, by a payload increase,
- the capacity to control stiffness and strength according to the areas of the structure,thanks to the different types of layered materials. Composite materials naturally offermembrane-bending coupling or plane coupling possibilities, which can have importantapplications in the field of aero-elasticity,
- a good fatigue strength, which increases the life of aircraft parts concerned andlightens the maintenance program considerably,
- absence of corrosion, which also lightens the maintenance program.
However, composite materials remain sensitive to environmental conditions. Theirmechanical properties change, due to:
- humidity,
- temperature,
- the various aeronautical fluids such as Skydrol (hydraulic fluid), oils or solvents (MEK)and fuels,
- radiation (ultraviolet).
On the other hand, the effects of lightning strikes (temperature rise, melting, impacts,electronic damages) and shocks (delamination, separation, punctures) must be taken intoaccount in the design and justification of composite parts.
INTRODUCTIONMetal/composite material similitudes - System equilibrium A 7
7.11/4
7 . COMPARISON BETWEEN COMPOSITE STRUCTURES AND METALSTRUCTURES
Composite material and metal material structures obey the same basic rules of structuralmechanics.
On the other hand, composite material behavior laws are slightly different from those formetals.
The purpose of this sub-chapter is to specify the similitudes between metal materials andcomposite materials for the structural justification of structures.
Composite parts and metal parts have the same behavior with respect to:
- static equilibrium.
- load distribution rules among several elements.
- basic rules of structural mechanics.
- general instability problems (buckling).
7.1 . System equilibrium
Whatever the type of system or element under study (metal, composite or combined), it issubject to a set of external loads which may be of several types:
- Solid loads: distributed in the volume of the solid and of gravity (selfweight), dynamic(inertial forces), electrical or magnetic origin.
- Areal loads: distributed over the external surface of the solid, such as normalpressures due to a fluid or tangential loads due to friction phenomena.
- Line loads: distributed over a line and which are, in fact, an idealized density ofsurface load with a much smaller application width than length.
- Concentrated loads (P): acting in one point and which are, in fact, an idealizeddensity of surface load acting on a surface with smaller dimensions with respect tothe dimensions of the solid under study.
- Concentrated moments (M): acting in one point and which are, in fact, an idealizedconcentrated moment.
To reach the equilibrium of the solid, all these external loads (C) must be equilibrated byreactions at the bearing surfaces (R).
If the system is isostatic, the solving alone of these six equations allows all reactions atthe bearing surfaces to be found.
If the system is slightly hyperstatic and consisting of a simple geometry, it is necessary tointroduce new equations (the number depends on the degree of redundancy) of thedeformation compatibility type that take element stiffness into account.
If the system is complex or if the degree of redundancy is high, only a point stress or amatrix analysis makes it possible to find reactions at the bearing surfaces and the internalloads they generate.
Whatever the case and whatever the type of structure (composite or metal), the threefollowing rules must always be applied before any stress and deformation calculation:
INTRODUCTIONLoad distribution - Normal load N A 7.2.1
7.2 . Distribution of loads among several closely bound structural elements
7.2.1 . Normal load N
If a system made up of several parts which are connected together, is subject to a normalload N, then, the load distribution within the different elements (whether metal orcomposite) is as follows:
we have:
ε = NE S
NE S
NE S
N
E SNE S
kk
k kk k kk
1
1 1
2
2 2
3
3 3
1
3
1
3
1
3= = = ==
= =
�
� �
a1 hence Ni = N E SE Si i
k kk =� 1
3
a2 we may deduce Eeq. memb. (1 + 2 + 3) = E S
S
k kk
kk
=
=
�
�
1
3
1
3
where Ni: load transferred by layer (i)Ei: layer (i) elasticity modulusSi: layer (i) section
INTRODUCTIONLoad distribution - Bending moment M A 7.2.2
7.2.2 . Bending moment M
A bending moment M applied to the neutral axis of the system is picked up in each layerin proportion to its bending stiffness.
The moment M breaks down, in each layer (i), into a bending moment Mi and a normalload Ni, so that:
a3 N M E S vE l
ii i i
k kk
==� 1
3
a4 M M EE l
ii i
k kk
==�
ι
1
3
a5 we may deduce E eq. flex. (1 + 2 + 3) = E l
l
k kk
kk
=
=
�
�
1
3
1
3
where Ni: normal load applied to layer (i)Mi: moment applied to layer (i)li: layer (i) inertia with relation to the system neutral axisι i: layer inertia of layer (i)Si: layer (i) sectionvi: distance between layer (i) neutral axis and system neutral axisEi: layer (i) elasticity modulus
INTRODUCTIONMaterial strength laws - Behavior laws A 7.3
7.3 . Material strength laws - Behavior laws
Composite materials obey the general rules of structural mechanics.
Stress - deformation relationship for a two-dimensional analysis: Hooke's law applies(σ) = (Aij) (ε), the matrix (Aij) is more complex for composite materials as described inchapter C.
The equation of the elastic line of a bent metal beam ∂∂
2
2y
xMEI
= becomes
∂∂
2
2
1
yx
ME lk kk
n==�
for a composite structure.
Normal stress - normal load relationship: for a stressed or compressed metal beam, the
expression σ = NS
becomes σi = N EE S
i
k kk
n
=� 1
for each layer of a composite beam.
Normal stress - bending moment relationship: for a bent metal beam,
σ = M vl
becomes σi = M E vE li i
k kk
n
=� 1
for each layer of the composite beam.
Shear stress - shear load relationship: for a sheared metal beam, τ = T Wl b
For a beam, Euler's law which associates the general instability critical compression loadwith the geometrical and mechanical properties of the beam remains valid, whatever thematerial used (metal/isotropic or composite/orthotropic).
Indeed, the critical load is formulated as follows:
Fc = π2
2E l
l for metal beams,
Fc = π2
12
E l
lk kk
n
=� for composite beams,
where l is the buckling length.
Regarding plates, the approach is more complex for composite materials, although basesare identical.
The differential equation which governs composite plate instability is formulated in itsmost general form:
C wx
C C wx y
C wy
N wx
N wy
N wx yx y xy11
4
4 12 33
4
2 2 22
4
4
2
2
2
2
2
2 2 2∂∂
∂∂ ∂
∂∂
∂∂
∂∂
∂∂ ∂
+ + + = + +( )
where C11, C12, C33 and C22 are the temps of the matrix (Cij) binding the rotation tensorand the bending load tensor (see chapter D).
For isotropic materials such as metals, the relationship is simplified:
INTRODUCTIONMetal/composite material differences A 8
1/3
8 . DIFFERENCES BETWEEN METAL AND COMPOSITE MATERIALS
These differences are actually covered by the composite material manual. A fewexamples are given below:
- Metal material isotropic/composite material anisotropic duality
If metal and composite materials are both macroscopically homogeneous, compositematerials are generally anisotropic. This means that their properties depend on thedirection (see drawing below) along which they are measured.
This difference may be an advantage. Through an optimization of the orientation of fibres,it allows a greater freedom to choose element rigidity and, therefore, a more accuratecontrol of load routing.
INTRODUCTIONMetal/composite material differences A 8
2/3
- Failure criteria
Because of their microscopic heterogeneity, composite materials do not obeycovariant failure criteria (independent from the coordinate system direction) like metalmaterials. Generally, they must be applied to each layer and are applicable only in apreferential direction (the direction of the fibre to be justified).
- Effect of holes
Sizing of holes in composite materials not only takes into account the net cross-section coefficient (as for metal materials) due to material removal, but also adecrease of the intrinsic material strength.
- Effect of bearing
The presence of bearing due to load transfer at a fastener in a laminate causesmembrane stresses to be artificially increased by part of the bearing stresses and, asa result, residual strength to be decreased.
- Damage tolerance
The presence of impact or manufacturing damages causes a significant decrease tothe laminate static strength.
- Effect of fatigue/damage tolerance
Corrosion and fatigue are the overriding factors of the limited life of metal structures.Metal fatigue is controlled by the number of cycles required, on the one hand, toinitiate a crack and, on the other hand, bring it to its critical length (growth phase).Influent factors of this phenomena are stress concentrations and tension loads.
As a general rule, fatigue is not a design factor for composite elements of civil aircraftwith thin thicknesses and no structural irregularities. More specifically, mechanicalproperties are such that static design requirements naturally "cover" fatigue designrequirements. Wohler curves are relatively flat and damaging loads are of thecompression type (R = - 1).
(Impact or manufacturing) Damage growth under mechanical fatigue is not allowedbecause of the high rate of delamination growth. The current inability to controlthrough analysis the damage growth rate in composite materials does not allow adamage tolerance justification based on slow growth. For this reason, allowabledamage tolerance values are low; this makes it possible to avoid any explosiveevolution during the aircraft life.
- Metal material plasticity/composite material "brittleness" duality
Metal materials have an elastic range and a plastic range, in their behavior, whichlead to breaking, breaking occurs in carbon composite materials without plasticizing.
- A material is so-called homogeneous when its properties are independent from the pointconsidered.
- A material is isotropic if it has the same properties in all directions.
- A material is anisotropic if there is no property symmetry, i.e. properties depend on thedirection and on the point considered.
- A material is orthotropic if its properties are symmetrical with relation to twoperpendicular planes. Axes of symmetry are so-called axes of orthotropy.
2.2 . Coupling phenomenon
2.2.1 . Plane coupling
In the case of an orthotropic material, there is a “plane coupling” if the loading axis is notcoincident with one of its axes of orthotropy. In that case, normal loading (σ) generatesshear (γ) and shear loading (τ) generates elongation (ε).
2.2.2 . Mirror symmetry
The laminate must be such that each layer has an identical symmetrical layer with relationto the neutral plane.
This symmetry allows the membrane-bending coupling to be eliminated, i.e. theoccurrence of plate bending, when a tension load is applied in its plane.
The design method for a flat plate consists in assessing stresses in each ply and indetermining the corresponding Hill’s criterion (see § G.3).
Let’s assume that all plies are made up of the same material, and that the laminate isprovided with the mirror symmetry property.
That is to say the central plane of the laminate (for example: (0°/45°/135°/90°) s =(0°/45°/135°/90°/90°/135°/45°/0°). This property implies that there is no coupling betweenthe membrane effects and the bending effects.
Which means that the membrane flux tensor (Nx, Ny, Nxy) induces εx, εy, and γxy typeelongations only and that, on the other hand, the moment flux tensor (Mx, My, Mxy) inducesχx, χy and χxy type rotations only.
In other words, in the case of a laminate with the mirror symmetry property, therelationship which binds loading and elongation may be formulated as follows:
2nd step: Design of the stiffness matrix for the unidirectional layer in direction θ in thereference coordinate system (x, y). This matrix shall be called (Qx, y,θ).
c2 (Qx, y,θ) = (Tθ) x (Ql, t) x (T'θ)-1
with:
(Tθ) =
(cos ) (sin ) sin cos
(sin ) (cos ) sin cos
sin cos sin cos (cos ) (sin )
θ θ θ θ
θ θ θ θ
θ θ θ θ θ θ
2 2
2 2
2 2
2
2
−
− −
x x
x x
x x
(T'θ) =
(cos ) (sin ) sin cos
(sin ) (cos ) sin cos
sin cos sin cos (cos ) (sin )
θ θ θ θ
θ θ θ θ
θ θ θ θ θ θ
2 2
2 2
2 22 2
−
− −
x
x
x x x x
Matrix (Tθ) corresponding to the basic transformation matrix for stress condition.
Matrix (T'θ) corresponding to the basic transformation matrix for elongation condition.
Remark: the stiffness matrix (Qx, y, θ) also allows determination of the mechanicalproperties of the unidirectional layer in direction θ in the reference coordinatesystem (o, x, y). For the unidirectional layer, we have:
(σx, y) = (Qx, y, θ) x (εx, y) hence (εx, y) = (Qx, y, θ)-1 x (σx, y)
3rd step: Knowing the stiffness matrix of each layer (Qx, y, θ) with relation to the referencecoordinate system (x, y), the laminate stiffness matrix can be calculated in this samecoordinate system: (Rx, y).
For this, the mixture law shall be applied.
c3 (Rx, y) = (Q ), ,x yk
n
k
nθ=� 1 or (Rx, y) =
ep
ex yk
n
k(Q ), , θ=� 1
4th step: Determination of the laminate elongation tensor in the reference coordinatesystem.
c4 (εx, y) = 1e
x (Rx, y)-1 x (Nx, y)
ε
ε
γ
x
y
xy
= 1e
(Rx, y)-1
N
N
N
x
y
xy
or
N
N
N
x
y
xy
= (A)
ε
ε
γ
x
y
xy
where (A) is the laminate membrane stiffness matrix: (A) = e x (Rx, y).
Matrix (A) is the stiffness matrix which binds the stress flux tensor (N) with the elongationtensor (ε).
MONOLITHIC PLATE - MEMBRANEEquivalent properties C 4
4 . DEFORMATIONS AND EQUIVALENT MECHANICAL PROPERTIES
Monolithic plates are microscopically heterogeneous. It is sometimes necessary to findtheir equivalent membrane stiffness properties in order to determine the passing loadsand resulting deformations.
Equivalent membrane young's moduli are directly derived from the laminate stiffnessmatrix (A):
c9 (A)-1 = 1e
1
1
1
E Ex
E Ex
x xG
xx
yx
yy
xy
xx yy
xy
memb equi
memb equi
memb equi
memb equi
memb equi memb equi
memb equi
. .
. .
. .
. .
. . . .
. .
−
−
ν
ν
If reference axes (o, x, y) are coincident with the axes of orthotropy of the laminate, weobtain:
Let a laminate be made up of plies in the same material and described as follows:
- overall thickness e,
- percentage of plies at 0°,
- percentage of plies at 45°,
- percentage of plies at 135°,
- percentage of plies at 90°.
If membrane fluxes Nx, Ny and Nxy, are applied to the laminate, so that Nx2 + Ny
2 + Nxy2 = 1,
the design method outlined above allows loads inside each layer to be determined and theoverall plate margin (m) to be found (see § G "Failure criteria").
It can be represented in a two-dimensional space (Nx, Ny) in the form of graphs (eachcurve corresponding to the intersection S' with an equation plane Nxy = Nxyi).
If this set of curves is projected onto the plane (o, Nx, Ny), a network of curves is obtainedwhich constitutes the breaking graph of the laminate.
This graph (corresponding to a given material and a specific lay-up) allows the laminatemargin (Hill's criterion) to be determined graphically.
MONOLITHIC PLATE - MEMBRANEGraphs - Mechanical properties C 5.2
In practice, curves are represented in stress and not in flux values. This makes it possibleto group together some laminates per lay-up class (for example: 3/2/2/1 ≡ 6/4/4/2 ≡
9/6/6/3).
A number of orthotropic laminate failure envelopes in carbon T300/914 layers shall befound in chapter Z “material properties”.
5.2 . Mechanical properties
For a given material, a set of graphs may be created giving the mechanical properties(strength and elasticity moduli) of an orthotropic laminate described by its percentages ofplies in each direction (see drawing below).
A number of those graphs associated with carbon T300/914 layer shall be found inchapter Z “material properties”.
The purpose of this example is to search for stresses applied to each ply (0°, 45°, 135°,90°) knowing that the laminate is globally subject to the three following load fluxes in thereference coordinate system (x, y):
(o, x, y): reference coordinate system(o, l, t): coordinate system specific to the unidirectional fibre
u, v, w: displacement from any point on the beamuo, vo, wo: displacement from the beam neutral planeβ: beam curvature at a given pointR: beam radius of curvature at a given point
εx, εy, γxy: strains at any pointεox, εoy, γoxy: strains neutral plane
(M): bending moment tensor
(χ): rotation tensor(α): tensor of angles formed by the deformation diagram(C): inertia matrix of laminate
k: fibre coordinate system
θ: fibre orientation
El: longitudinal young's modulus of unidirectional plyEt: transversal young's modulus of unidirectional plyνlt: longitudinal/transversal poisson coefficient
νtl = νlt EE
t
l: transversal/longitudinal poisson coefficient
Glt: shear modulus of unidirectional plyep: ply thickness
MONOLITHIC PLATE - BENDINGIntroduction - Design method D 2
31/4
2 . INTRODUCTION
In chapter C, we examined the case of a laminate provided with mirror symmetry subjectto membrane type loading. In the paragraph below, we shall examine the case of alaminate with the same properties but, this time, subject to pure bending type loads.
By convention, we shall consider that any positive moment compresses the laminateupper fibre.
Let’s assume that bending moment flows Mx, My and Mxy generate εx, εy and γxy typestrains.
Let’s assume also (Kirchoff) that the neutral plane is coincident with the neutral line.
If the tensor of angles formed by the strain diagram in each direction is defined by (α):(αx, αy, αxy) we may write in a simplified form the relationship:
d6 (χ) = tg (α)
By convention, we shall assume that (α) is negative when the upper fibre is in tension. Wehave:
d7 (ε)z = - (χ) x z
This relationship makes it possible to determine each ply strain and, therefore, to find(using chapter C) stresses applied to it.
Remark: The terms Cij must be determined with relation to the laminate neutral line(Kirchoff’s assumption). In this case, the neutral plane shall also be used as areference for the overall load pattern.
MONOLITHIC PLATE - BENDINGEquivalent mechanical properties D 4
4 . DEFORMATIONS AND EQUIVALENT MECHANICAL PROPERTIES
Monolithic plates are microscopically heterogeneous. It is sometimes necessary to findtheir equivalent bending stiffness properties in order to determine the passing loads andresulting deformations.
Equivalent bending elasticity moduli are directly derived from the laminate stiffness matrix(C):
d8 (C)-1 = 123e
1
1
1
Ex x
xE
x
x xG
xxbending equi
yybending equi
xybending equi
.
.
.
If reference axes (o, x, y) are coincident with the axes of orthotropy of the laminate, weobtain:
Let a T300/BSL914 laminate (new) be laid up as follows:
0°: 2 plies45°: 2 plies135°: 2 plies90°: 2 plies
Stacking from the external surface being as follows: 0°/45°/135°/90°/90°/135°/ 45°/0°.
Mechanical properties of the unidirectional ply are the following:
El = 13000 hbEt = 465 hbνlt = 0.35νtl = 0.0125Glt = 465 hbep = 0.13 mm
The purpose of this example is to search for elongations at the laminate external surface,knowing that the laminate is globally subject to the three following moment fluxes in thereference coordinate system (x, y):
3rd step: Calculation of laminate inertia matrix (C) coefficients Cij expressed in daN mm.
The laminate being provided with the mirror symmetry property, coefficients Cij shall becalculated for the laminate upper half, then they shall be multiplied by 2.
MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSISIntroduction E 2
2 . INTRODUCTION
We have seen in chapter C that there is a relationship which binds membrane strains andloading of the same type.
This relationship may be formulated as follows: (N) = (A) x (ε).
We also saw in chapter D that there is a relationship which binds the curvature tensor andthe moment tensor.
This relationship may be formulated as follows: (M) = (C) x (χ).
If lay-up has the mirror symmetry property, then both phenomena are dissociated andindependent. In other words, the overall relationship which binds the set of strains and theset of loadings may be formulated as follows:
N
N
N
M
M
M
x
y
xy
x
y
xy
=
A A A
A A A
A A A
C C C
C C C
C C C
11 12 13
21 22 23
31 32 33
11 12 13
21 22 23
31 32 33
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
ε
ε
γ
∂∂
∂∂∂∂ ∂
x
y
xy
o
o
o
wxwyw
x y
2
2
2
2
2
2
where coefficients Aij and Cij are defined in chapters C and D.
MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSISAnalysis method E 3
1/2
3 . ANALYSIS METHOD
If lay-up is non-symmetrical, then all zero terms of the previous matrix become non-zeroand there is a membrane/bending coupling. Both phenomena become dependent. Therelationship between loadings and strains is thus:
Ε13(θ) = Ε31(θ) = c s {c2 Εl - s2 Εt - (c2 - s2) (νtl Εl + 2 Glt)}Ε23(θ) = Ε32(θ) = c s {s2 Εl - c2 Εt + (c2 - s2) (νtl Εl + 2 Glt)}
where
c ≡ cos(θ) where θ is the fibre direction in the reference coordinate system (o, x, y).
s ≡ sin(θ) where θ is the fibre direction in the reference coordinate system (o, x, y).
with
e4 Εl = El
tl lt1 − ν ν
Εt = Et
tl lt1 − ν ν
Remark: The terms Bij and Cij must be determined with relation to the laminate neutralline (Kirchoff’s assumption). In this case, the neutral plane shall also be used asa reference for the overall load pattern.
MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSISExample E 4
2/9
The purpose of this example is to search for strains at the laminate internal and externalsurfaces, knowing that the laminate is globally subject to the following fluxes in thereference coordinate system (x, y):
Nx = 5 daN/mmNy = 0 daN/mmNxy = 0 daN/mm
Mx = 0 daN
My = - 0.15 daN mm daNmm
���
���
Mxy = 0 daN
1st step: calculation of stiffness coefficients for the unidirectional fibre:
90° 135° 45° 0°A11 = (467 x 0.13 + 3925 x 0.13 + 3925 x 0.13 + 13057 x 0.13)A12 = (163 x 0.13 + 2995 x 0.13 + 2995 x 0.13 + 163 x 0.13)A13 = (0 x 0.13 - 3146 x 0.13 + 3146 x 0.13 + 0 x 0.13)A21 = (163 x 0.13 + 2995 x 0.13 + 2995 x 0.13 + 163 x 0.13)A22 = (13057 x 0.13 + 3925 x 0.13 + 3925 x 0.13 + 467 x 0.13)A23 = (0 x 0.13 - 3146 x 0.13 + 3146 x 0.13 + 0 x 0.13)A31 = (0 x 0.13 - 3146 x 0.13 + 3146 x 0.13 + 0 x 0.13)A32 = (0 x 0.13 - 3146 x 0.13 + 3146 x 0.13 + 0 x 0.13)A33 = (465 x 0.13 + 3297 x 0.13 + 3297 x 0.13 + 465 x 0.13)
MONOLITHIC PLATE - TRANSVERSAL SHEARIntroduction - Analysis method F 2
31/5
We shall assume that shear load Txz (direction z load shearing a plane perpendicular to x-axis) creates stress τxz and, based on the reciprocity principle, stress τzx.
Similarly, we shall assume that shear load Tyz (direction z load shearing a planeperpendicular to y-axis) creates stress τyz and, based on the reciprocity principle, stressτzy.
These shear stresses are called interlaminar stresses.
3 . ANALYSIS METHOD
To calculate interlaminar stresses τxz (τzx) generated by shear load Txz (Tyz), use thefollowing methodology.
We shall only consider the case of a laminate subject to shear load Txz. The analysisprinciple is the same for Tyz.
In this case, inertias (El) and static moments (E Wk) are measured with relation to y-axis.Elasticity moduli (Ek) are measured with relation to x-axis.
MONOLITHIC PLATE - TRANSVERSAL SHEARAnalysis method F 3
2/5
1st step: The position of the laminate neutral axis is determined. If the laminate lower fibreis used as a reference, then the neutral axis is defined by dimension zg, so that:
f2 zg = ( )( )
E z z
E z z
k k kk
n
k k kk
n
21
21
112
−
−
−=
−=
�
�
2nd step: The (moduli weighted) bending stiffness of laminate El is determined with relationto the lay-up neutral axis
MONOLITHIC PLATE - TRANSVERSAL SHEARAnalysis method F 3
3/5
3rd step: Then the (elasticity moduli weighted) static moment E Wk (of the material surfacelocated above the line where interlaminar stress is to be calculated), is determined. Thisstatic moment shall be calculated with relation to the plate neutral axis.
If the line is a fibre interface surface (z = zk - 1), then we have the following relationship:
f4 E Wk = ( )E z zz z
zii k
ni i
i ig= −
−� −
+−
�
��
�
��1
1
2
If the line is situated at the centre of a fibre at z = z zk k+ − 1
MONOLITHIC PLATE - TRANSVERSAL SHEARAnalysis method F 3
4/5
4th step: Shear stress τxzk is determined, so that:
f6 τxzk = T E WE
xz k
l
.
where Txz is the shear load applied to the laminate.
By using this analysis method for each ply interface (or at the center of each ply forgreater accuracy), it is possible to plot the interlaminar shear stress diagram over theentire plate width.
The previous relationship shows that the shear stress is maximum when the staticmoment is maximum as well, i.e. at the neutral axis (z = zg).
Remark: The previous analysis is based on a shear load flux Txz applied to a sectionperpendicular to x-axis.
In the case of any section forming an angle β in the coordinate system (o, x, y), the shearload flux in this new section may be expressed as a function of Txz and Tyz.
MONOLITHIC PLATE - TRANSVERSAL SHEARAnalysis method F 3
5/5
As shown in the drawing above, the z equilibrium of the hatched material element leads tothe following relationship:
T(β) ds - Txz ds cos(β) - Tyz ds sin(β) = 0
hence:
T(β) = cos(β) Txz + sin(β) Tyz
It is easy to show that for β = Arctg TT
yz
xz
�
��
�
�� , a modulus extremum T(β) (called main shear
load flux) is reached that is equal to:
f7 l T(β) l = Txz Tyz2 2+
Example: if shear load fluxes Txz and Tyz are equal, then the maximum shear load flux islocated in the plane with a direction β = 45°. Its modulus equals 2 Txy (or 2 Tyz).
4th step: calculation of maximum interlaminar shear stress
In the example given, it is located at the point where the static moment is maximum, i.e. atthe base of the ply at 0°. Its value equals at E W0 = 59.15 daN, which gives stress τxz0:
{f6}
τxz0 = 0 7 591519 67
. ..
x = 2.1 hb (21 MPa)
If these interlaminar shear stresses are analysed for each fibre, stresses are distributedalong the laminate thickness as follows:
This criterion is the one used by Aerospatiale. In order to avoid having a prematuretheoretical failure in the resin, the transversal modulus Et was considerably reduced (by acoefficient 2 approximately) with relation to the average values measured.
This "design" value is determined so that the transversal strain is greater than thelongitudinal one.
The allowable plane shear value S of the unidirectional fibre was determined for having, agood test/calculation correlation and significant tension and compression failures ofnotched or unnotched laminates.
Hill's criterion shall be applied to the example considered in the chapter "plain plate -membrane". Stresses applied to fibres are calculated and presented in the correspondingchapter (C.6) and quoted in the following pages.
Let a T300/BSL914 laminate (new) be laid up as follows:
0°: 6 plies45°: 4 plies135°: 4 plies90°: 6 plies
Mechanical properties of the unidirectional fibre are the following:
MONOLITHIC PLATE - DAMAGE TOLERANCEIntroduction I 2
2 . INTRODUCTION
The regulatory requirements in terms of structural justification concern, on the one hand,the static strength JAR § 25.305 and, on the other hand, fatigue + damage tolerance JAR§ 25.571. For the latter, three cases are to be considered:
For the static strength evaluation, Acceptable Means of Compliance ACJ 25.603 § 5.8requests resistance to ultimate loads with "realistic" impact damage susceptible to beproduced in production and in service. This damage must be at the limit of thedetectability threshold defined by the selected inspection procedure. Also, static strengthmust be demonstrated after application of mechanical fatigue (§ 5.2) and test specimensmust have minimum quality level, that is, containing the permissible manufacturing flaws(§ 5.5) and "realistic" impact damage.
The static strength range is defined therefore for a detection threshold and by a "realistic"cut-off energy leading to "realistic" impacts.
The damage tolerance range is outside the static range.
MONOLITHIC PLATE - DAMAGE TOLERANCEIntroduction I 2
33.1
Distinction is made between the range above the detectability threshold where all damagewill be detectable and the range above the static cut-off energy and below the detectabilitythreshold where the damage will never be detected.
In this "Damage tolerance" section, we shall discuss both manufacturing defects andimpact damage for the static justification and the fatigue-damage tolerance justification.
The basic assumption to be retained is the fatigue damage no-growth concept.
3 . DAMAGE SOURCES AND CLASSIFICATION
Distinction is made between damage which may occur during manufacture and that whichoccurs in service.
3.1 . Manufacturing damage of flaws
Manufacturing damage or flaws include porosities, microcracks and delaminationsresulting from anomalies, during the manufacturing process and also edge cuts, unwantedrouting, surface scratches, surface folds, damage attachment holes and impact damage(see § 3.2.3).
Damage, outside of the curing process, can occur a detail part or component level duringthe assembly phases or during transport or on flight line before delivery to the customer.
If manufacturing damage/flaws are beyond permissible limits, they must be detected byroutine quality inspections.
For all composite parts, the acceptance/scrapping criteria must be defined by the DesignOffice. Acceptable damage/flaws are incorporated into the ultimate load justification byanalysis and into the test specimens to demonstrate the tolerance of the structure to thisdamage throughout the life of the aircraft.
MONOLITHIC PLATE - DAMAGE TOLERANCEFatigue damage I 3.2
3.2.1
3.2 . In-service damage
This damage occurs in service in a random manner. Distinction is made between threetypes of damage:
- fatigue,- corrosion and environmental effects,- accidental.
3.2.1 . Fatigue damage
Composite materials are said to be insensitive to fatigue; more exactly, their mechanicalproperties are such that the static dimensioning requirements naturally cover the fatiguedimensioning requirements. This is valid for a laminate submitted to plane loads, less than60 % of ultimate load. However, complex areas or areas with a sudden variation in rigiditymay favour the appearance of delaminations under triaxial loads.
Today, it is very difficult to (analytically or numerically) model the growth rate of a possibleflaw. This is why a "safe-life" justification philosophy has been adopted. It is based on twoprinciples which must be underpinned by experimental results:
- non-creation of fatigue damage (endurance),- no-growth of damage of tolerable size.
On account of the dispersion proper to composites and the form of the "Wohler" curvesassociated with them (relatively flat curve with low gradient), the factor 5 normally used onmetallic structures for the number of lives to be simulated during a fatigue test, wasreplaced by a load factor.
All these points will be discussed in detail in section O (MONOLITHIC PLATE -FATIGUE).
3.2.2 . Corrosion damage and environmental effects
a) Corrosion
Composites are insensitive to corrosion. Nevertheless, their association with certainmetallic materials can cause galvanic coupling liable to damage certain metal alloys.
For information purposes, the table below shows various carbon/metal pairs over a scaleranging from A to E.
We consider that type A and B couplings are correct and that those of types C, D and Eare not.
A Anodised titanium, protected titanium fasteners
A Titanium and gold, platinium and rhodium alloys
B Chromiums, chrome-plated parts
B Passivated austenitic stainless steels
B Monel, inconel
B Martensitic stainless steels
C Ordinary steels, low alloys steels, cast irons
D Anodic or chemically oxidised aluminium and light alloys
D Cadmium and cadmium-plated parts
D Aluminium and aluminium-magnesium alloys
D Aluminium-copper and aluminium-zinc alloys
b) Environmental effects
At high temperatures, aggressions by hydraulic fluids may cause damage such asseparation, delamination, translaminar cracks, etc.
Rain can cause damage by erosion, etc.
All these points will be discussed in detail in section W (INFLUENCE OF THEENVIRONMENT).
MONOLITHIC PLATE - DAMAGE TOLERANCEAccidental damage - Inspection of damage I 3.2.3
4
3.2.3 . Accidental damage
This is the most important type of damage and the damage most liable to call intoquestion the structural strength of the part. It can occur during the manufacture of the item(drilling delamination) or in service (drop of a maintenance tool, hail or bird strikes).
4 . INSPECTION OF DAMAGE
One of the main preoccupations concerning the damage tolerance of composites isdamage detection. This is true both during manufacture and in service. In service, thedetectability threshold depends on the type of scheduled in-service inspection. There arefour types of inspections:
Inspection - Special detailed (ref: Maintenance Program Development: MPD):
An intensive examination of a specific location similar to the detailed inspection exceptfor the following differences. The examination requires some special technique such asnon-destructive test techniques, dye penetrant, high-powered magnification, etc., andmay required disassembly procedures.
This type of inspection is mainly conducted during production but can be usedexceptionally in service.
Inspection - Visual Detailed (ref: Maintenance Program Development: MPD):
An intensive visual examination of a specified detail, assembly, or installation. Itsearches for evidence of irregularity using adequate lighting and, where necessary,inspection aids such as mirrors, hand lens, etc. Surface cleaning and elaborate accessprocedures may be required.
This type of inspection enables BVID (Barely Visible Impact Damage) to be detected.
MONOLITHIC PLATE - DAMAGE TOLERANCEInspection of damage I 4
4.14.2
Inspection - General Visual (ref: Maintenance Program Development: MPD):
A visual examination that will detect obvious unsatisfactory conditions/discrepancies.This type of inspection may require removal of fillets, fairings, access panels/doors, etc.Workstands, ladders, etc. may be required to gain access.
Inspection - Walk Around Check (ref: Maintenance Review Board Document: MRB):
A visual check conducted from ground level to detect obvious discrepancies.
In general, the Walk Around check is considered as a general daily visual inspection.
4.1. Minimum damage detectable by a Special Detailed Inspection
These inspections are conducted with bulky facilities: ultrasonic, thermographic, X-rays,etc. Minimum detectable sizes are related to the size of the U.S. probes and the accuracyof the tools used, etc.
4.2 . Minimum damage detectable by a Detailed Visual Inspection
This type of damage is called BVID (Barely Visible Impact Damage). The geometricaldetectability criteria are as follows (cf. ref. 22S 002 10504):
MONOLITHIC PLATE - DAMAGE TOLERANCEInspection of damage I 4.3
4.4
4.3 . Minimum damage detectable by a General Visual Inspection
This type of damage is called Minor VID (Minor Visible Impact Damage). The geometricaldetectability criteria are as follows (cf. ref. 22S 002 10504):
Depth of flaw "δδδδ" Size of perforation
2 mmor thickness of structure
if < 2 mm20 mm ∅
4.4 . Minimum damage detectable by a Walk Around Check
This type of damage is called Large VID (Large Visible Impact Damage). The geometricaldetectability criteria are not explicitly defined but the damage must be detectable withoutambiguities during a Walk Around Check.
We generally use a 50/60 mm ∅ perforation as criterion.
The diagram below summarises these four detectability levels according the size of thedamage.
Depth of indent δ = 0.3 mm δ = 2 mmdiameter 20 mm ∅ 50/60 mm ∅
In the remainder of this document, we will consider only visual inspections.
MONOLITHIC PLATE - DAMAGE TOLERANCEClassification of damage I 4.5
4.5 . Classification of accidental damage by detectability ranges
Depending on the type of visual inspection considered during the maintenance phases(general or detailed), we will define three clearly separate detectability ranges:
a) Damage undetectable by visual means used in service.
b) Damage susceptible to be detected during in-service inspections.
c) Damage "inevitably" detectable that can be placed into two categories:
MONOLITHIC PLATE - DAMAGE TOLERANCEInfluence of damage - Porosity I
4.555.15.1.1
Remark: Note that certain authors define the BVID notion according to the type ofinspection selected.In this case, for a general inspection: MINOR VID ≡ BVIDIn our document, we will conserve the initial definition related to the visualdetailed inspection.
5 . EFFECT OF FLAWS/DAMAGE ON MECHANICAL CHARACTERISTICS
5.1 . Health flaws
5.1.1 . Porosity
→ Description
By "porosity", we mean a heterogeneity of the matrix leading, more often than not, to lackof inter- or intra-layer cohesion, generally small in size, but distributed uniformly or almostthroughout the complete thickness of the laminate. Note that for unidirectional tapes theporosities have a tendency to be located between the layers whereas, for fabrics, they aremore generally located where the weft and warp threads cross. The porosity ratio given isa surface porosity ratio measured by the ultrasonic attenuation method. The permissibleabsorption level is fixed at 12 dB irrespective of the thickness inspected (cf. note440.241/90 issue 2 - SIAM curve). All absorption areas above this limit will be consideredas a delamination and meet therefore the same criteria as a delamination.
However, only T300/N5208, more fluid than T300/BSL914 has a higher tendency to beporous.
MONOLITHIC PLATE - DAMAGE TOLERANCEPorosity I 5.1.1
→ Loss of mechanical characteristics due to porosity
The test results were interpolated, for the V10F wing, on T300/N5208 with variousporosity ratios distributed in all interply areas to determine the influence on the mechanicalcharacteristics for a 3 % ratio considered as the acceptable limit. This ratio combined withthe fatigue, ageing and residual test effects at 80° C, led to the following losses inmechanical characteristics:
The 3 % acceptance criterion appears therefore as being non-conservative forinterlaminar shear. However, let us recall:
- that the spar boxes of the wings, movable surfaces or fin are subjected to very lowinterlaminar stresses,
- only T300/N5208 had porosities,
- that the 3 % porosity criterion distributed at all interply areas is today no longerapplied to primary structures. The permissible porosity ratio depends on the thicknessof the laminate.
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations outside stiffener I 5.1.2
5.1.2.11/5
5.1.2 . Delaminations
A delamination is a lack of cohesion between the layers caused by a shear or transversetensile failure of the resin or, more simply, by forgetting a foreign body.
5 1.2.1 . Delaminations outside stiffener
���� Skin bottom areas
→ Description
A skin bottom delamination is a lack of cohesion between two well-defined plies. Naturaldelaminations appear during manufacture (surface contamination). A foreign body left inthe laminate (separator) will be considered as a delamination.
→ Loss of characteristics due to a delamination
For the V10F wing, a lack of interlayer cohesion up to 400 mm2 leads to a loss ofcompression strength of around 10 % for the two materials (T300/N5208 andT300/BSL914) tested in new condition at θ = 80° C. In aged/fatigue condition the drop instrength is 20 % for T300/N5208 and 13 % for T300/BSL914 in relation to the newstate/80° C reference. Fatigue leads to no growth of the flaw.
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations outside stiffener I 5.1.2.1
2/5
���� Fastener areas
→ Description
As for the skin bottom delaminations, the lack of cohesion in these areas occurs betweentwo well-defined plies, sometimes at several levels but generally adjacent. These flawscome through to the bore. They are created during the drilling operations. The ultrasonicinspections conducted after each test case showed no evolution of existing flaws.
The parameter representing the size of the damage is the number given by: φ = ∅∅
fastenerdamage
The parameter representing the drop in characteristics is the number given by: ν = VcVb
where Vb represents the "B value" (see section Y) relevant to all tests characterising thematerial and where Vc is the calculation value used. Provided that the calculation value islower than the "B value", the integrity of the item is ensured. For safety reasons, we willimpose a minimum margin of 10 % between the calculated value and the "b value".
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations outside stiffener I 5.1.2.1
3/5
Two cases can occur:
- if ν ≥ 1.1: no reduction will be made on the initial reserve factor RF,
- if ν < 1.1: after reduction, the new reserve factor is equal to RF’ = RF 1.1ν
The values of ν are given by the graphs in section Z for the prepreg epoxy carbon fibreT300/914.
Generally speaking, the graphs gives the values of ν for the flaw (delamination) but alsofor repairs which may be made on it (injection of resin, NAS cup). They enable you to findtherefore:
- whether the flaw is acceptable as such,- what type of repair is to be chosen.
→ Examples of acceptance and concession criteria
- in standard area, the delamination must be covered by a concession if its surfacearea is greater than:
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations in stiffener area I 5.1.2.2
1/5
5.1.2.2 . Delaminations in stiffener area of an integrally-stiffened panel
❏ Stiffener runouts
Stiffener runouts represent a critical point for dimensioning. When these stiffener runoutsare made during moulding without later machining operations, these fairly tortured areasmay include lacks of cohesion either in the base, or in the stiffener itself.
���� Crater
→ Description
This flaw is consecutive to too short a wedge which gives, after machining of the stiffenerrunout, a crater at the end of the stiffener.
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations in stiffener area I 5.1.2.2
2/5
→ Loss of characteristics due to crater
Size of flaw Test conducted ConditionsLoss of
characteristicsdue to flaw
TensileCompression
(stiffener runoutsnot protected)
Newθ = 20° C - 28 %ATR 72
T300/914L = 10 mml = 4 mme = 1 mm
TensileCompression
(stiffener runoutsprotected)
Newθ = 20° C 0 %
Compression(with reinforcement) - 4 %
ATR 72HTA/EH25 Compression
(withoutreinforcement)
Agedθ = 70° C
- 12 %
For unprotected stiffener runouts (that is, when it was impossible to thicken the skin tomake structure relatively simple to manufacture), this flaw must be covered by aconcession. When it is located at protected stiffener runouts (that is with a significant skinoverthickness at stiffener runout), this flaw will be covered by a concession only if its sizeis greater than the following values:
L = 10 mm l = 2 mm e = 0.5 mm
���� Punching
→ Description
This flaw is due to an imperfect Mosite cut leading to flaws at stiffener ends.
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations in stiffener area I 5.1.2.2
3/5
→ Loss of characteristics due to punching
Size of flaw Test conducted ConditionsLoss of
characteristicsdue to flaw
TensileCompression
(stiffener runoutsnot protected)
Newθ = 20° C - 20 %
ATR 72T300/914
L = 10 mme = 1 mm
TensileCompression
(stiffener runoutsprotected)
Newθ = 20° C 0 %
Must be covered by a concession when located at unprotected stiffener runouts. Whenlocated at protected stiffener runouts, it will be covered by a concession only if it size isgreater than the following values:
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations in stiffener area I 5.1.2.2
5/5
� Loss of characteristics due to flaw
Type of flaw Test conducted ConditionsLoss of
characteristicsdue to flaw
V10FT300/N5208
200 mm2
(flaw B)
Tensile(between wedgeand base skin)
Newθ = 20° C - 17 %
ATR 72T300/914(flaw BC)
Tensile(unprotected
stiffener runouts)
Wet ageingθ = 50° C - 20 %
ATR 72T300/914(flaw BC)
Compression(unprotected
stiffener runouts)
Wet ageingθ = 50° C 0 %
❏ Stiffener top
Lack of interlayer cohesion at top of stiffener between the U-section and the wedge doesnot seem to modify the mechanical characteristics.
❏ Stiffener base
Lack of interlayer cohesion in stiffener base hardly modifies the mechanicalcharacteristics. Within the scope of the V10F programme, the greatest drop is less than10 % in standard stiffener compression case with a type BC flaw.
Same criteria as given for delaminations (cf. § 5.1.2.1).
5.1.6 . Translaminar cracks
Translaminar cracks have been detected on the ATR 72 outer wing spar box, the A340aileron, the 2000 fin, the A300/A310 (cf. note 494.048/91); however there are none on theflight V10F (cf. note 494.007/91).
These are elongated flaws due to the use of a corrosive stripper (MEK, Methyl EthylKetone). Currently, baltane is used. T300/914 and G803/914 have these flaws; the testsconducted on IM7/977-2 and HTA/EH25 showed no translaminar cracks (cf. note494.056/91).
These cracks are detected by ultrasonic inspection in the fastener areas (the back surfaceecho totally disappears). They concern all ply directions but do not touch between twoplies with different orientations. It is in the high crack density area that the ultrasonic signalis totally damped. There a transition zone between this area and the healthy part of thelaminate where crack density decreases and the ultrasonic back surface echo reappears.
These cracks are parallel to the fibres leaving the holes. They first affect the plies at 0°,then the plies at ± 45°. Some cracks are observed in the central plies at 90°. The axes ofthese crack networks correspond approximately to the hole diameters.
They do not lead to a drop in the mechanical characteristics (cf. note 437.115/91).
The existence of flaws at fasteners can be masked by high density translaminar cracks.Therefore, the threshold of the surface areas of the translaminar cracks which must beplotted is coherent with the size of acceptable delaminations.
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations consecutive to a shock I 5.1.7
1/4
5.1.7 . Delaminations consecutive to a shock (during production and in service)
→ Description
An impact causes lack of interlayer cohesion at several levels depending on the energy ofthe impact.
→ Loss of characteristics due to a delamination
Generally speaking, a composite material with a non-through delamination is much moresensitive from a structural strength viewpoint to compression or shear loads (resin) than totensile loads (fibre).
The drops in characteristics within the scope of the V10F programme are:
- 18 % in tensile strength for a maximum invisible impact,
- 36 % in compression strength for a maximum invisible impact.
All points of the tests conducted on the V10F test specimens were plotted on the graphbelow (the points of the static and fatigue test specimens are combined on this curve as ithas been demonstrated that the ageing effect is not significant for damage tolerance).
The curve used at Aerospatiale for the new states/residual test at ambient temperatureand aged/fatigue states/residual test at ambient temperature is shown on the curve belowby comparison at static test specimen and fatigue test specimen points.
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations consecutive to a shock I 5.1.7
2/4
Behaviour to impact damage V10FStatic test specimen (CES)
Fatigue test specimen (CEF)
Delaminated surface area (mm2)
→ Ultimate strength of a delaminated laminate
The problem is generally posed as follows: we take a laminate consisting of a set of tapes(or fabrics) that we will assume to be made of the same material, each one of them havinga specific orientation in relation to the reference frame (o, x, y).
The laminate is submitted to shear forces (of membrane type) Nx, Ny and Nxy. In thepresence of a delamination (without ply failure) in surface area Sd, what is the strength ofthe plain composite plate?
Today, there are three methods for evaluating the residual strength in the presence of adelamination (established from experimental results) which call on the stresses and/orstrains of the unidirectional fibre and not those of the laminate considered as ahomogeneous plate. Each fibre direction must therefore be justified.
0 500 1000 1500 2000 2500- 1000
- 1500
- 2000
- 2500
- 3000
- 3500
- 4000
- 4500
- 5000
CES
CEF
i22 - (- 3108 µd)Rupture CES
COURBE ACTUELLE VALEURS DE CALCULEtat neuf/température ambiante ou
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations consecutive to a shock I 5.1.7
3/4
We will describe here these three methods in chronological order.
1st method:
This first method consists in calculating a failure criterion determined from the strains ofeach fibre in relation to their intrinsic frame (o, l, t).
By referring to the "plain plate - calculation method" section, it is possible to calculate thestrains in the various layers of the composite from the global flows Nx, Ny and Nxy appliedto the laminate and from the characteristics of the material used.
For layer "i" defined by its orientation α i, the strains of the fibre "i" in its own frame aredefined by the following strain tensor: (εli, εti, γlti).
We can define the following failure criterion C1 for each layer "i":
i1 C1 = 2
adm
lt2
adm
l ii
��
�
�
��
�
�
γγ
+��
�
���
�
�
εε
where εadm and γadm are the permissible strains (longitudinal and shear) of theunidirectional fibre (equivalent).
These values (obtained from the test results) depend on the material and the surface areaSd of the delamination considered and the types of loads.
They are given in section Z (sheets giving calculation values and coefficients used).
This criterion was used for the dimensioning of the ATR 72 wing panels (dossier22S00210460).
2nd method:
This second method consists in calculating a failure criterion C2 (Hill type criterion in whichthe permissible stresses are reduced by coefficients κR and κS) calculated from thestresses in each fibre in relation to their intrinsic frames (o, l, t).
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations consecutive to a shock I 5.1.7
4/4
By referring to the "plain plate - calculation method" section, it is possible to calculate thestrains in the various layers of the composite from the global flows Nx, Ny and Nxy appliedto the laminate and from the characteristics of the material used.
For layer "i" defined by its orientation α1, the stresses of the fibre "i" in its own frame aredefined by the following stress tensor: (σli, σti, τlti).
We can define the following failure criterion C2 for each layer "i":
i2 C2 = ( )2
lR
tl2
s
lt2
t
t2
lR
l
RSRRiiiii
κ
σσ−�
�
�
���
�
�
κτ
+��
�
���
�
� σ+�
�
�
���
�
�
κσ
where Rl, Rt and S are the permissible longitudinal, transverse and shear stresses of theunidirectional fibre respectively (equivalent) and where κR and κs are the reductioncoefficients for these permissible stresses.
These coefficients depend on the material used and the surface area of the delaminationconsidered and are determined from the test results.
They are given in section V (sheets giving calculation values and coefficients used).
This criterion was used for the sizing of the A330/340 inboard and outboard aileronpanels.
3rd method:
This method consists in calculating a failure criterion C3 (similar to the one of method 1)calculated from the strains of each fibre in relation to their intrinsic farmes (o, l, t).
For layer "i" defined by its orientation αi, the strains of the fibre "i" in its own frame aredefined by the following strain tensor: (εli, εti, γlti).
We can define the following failure criterion C3 for each layer "i" :
MONOLITHIC PLATE - DAMAGE TOLERANCEDelaminations consecutive to a shock
Visual flaws - Sharp scratchesI 5.1.7
5.25.2.1
i4 εa =
( ) ( )2adm
2adm
22
31
γ−
ε
i5 εab =
( ) ( )2adm
2adm
62
31
γ−
ε
else
εa = εadm
εab = + ∞
The particularity of this method is that it takes into account (in a significant manner) theload transverse to the fibre.
Tests have shown that presence of a tensile force perpendicular to the fibre directioncompression increases the ultimate strength of the laminate.
Criterion C3 takes this phenomenon into account. Indeed, if εti is of tensile type and εli ofcompression type, the third term of the criterion C3 becomes negative and tends toincrease the reserve factor and therefore the margin (RF = 1/C3).
Today, it is recommended to use this third finer method based on a high number ofexperimental results.
5.2 . Visual flaws
5.2.1. Sharp scratches
→ Description
Sharp scratches are made by scalpels or cutting tools. Sharp scratches lead to drops intensile characteristics of around 15 %; for compression, we assume that there is no dropin characteristics.
MONOLITHIC PLATE - DAMAGE TOLERANCESharp scratches I 5.2.1
→ Examples of acceptance criteria for sharp scratches
A long anomaly is acceptable without concession within following limits:
� On the ATR 72 outer wing carbon box structure,
→ In standard areas: permissible scratches are defined as follows:- maximum length: 100 mm,- maximum depth: 1 ply irrespective of the thickness.
→ in designated areas: the acceptance criteria are as follows:- maximum length: 100 mm,- maximum depth: 1 ply irrespective of the thickness,- all scratches though to a hole, an hedge or stopping less than 5 mm away must be
covered by a concession.
Any scratch concentrations must be covered by a concessions if the flaws are less than20 mm apart.
� On A330/A340 inboard and outboard ailerons, if length of scratch is less than 100 mmand if its depth is less than 0.15 mm for tapes and 0.3 mm for fabrics, sealing withHysol 9321 will be performed.
� On A330/A340, A320, A319, A321 nose landing gear doors (carbon fabrics G803/914),
→ at fittings, the permissible scratches are defined as follows:- maximum length: 10 mm,- maximum depth: 1 ply irrespective of the thickness.
→ outside fittings: the acceptance criteria are as follows :- maximum length: 250 mm,- maximum depth: 1 ply irrespective of the thickness.
MONOLITHIC PLATE - DAMAGE TOLERANCEIndents - Scaling I 5.2.1
5.2.25.2.3 1/3
� On A330/A340, A320, A319, A321 main landing gear doors (carbon fabrics G803/914),
→ at fittings, the acceptance criteria as follows:
- maximum length: 10 mm,- maximum depth: 1 ply irrespective of the thickness.
→ outside fittings: the acceptance criteria area as follows :
- maximum length: 100 mm,- maximum depth: 1 ply irrespective of the thickness.
5.2.2 . Indents
"Indent" type flaws due, for instance, to abrasion of skin by a rototest are permissible if:
- surface area of indent is ≤ 20 mm2 (∅ 5),
- only the 1st ply is totally damaged, that is 2nd ply visible.
Any flaw concentrations must be covered by a concession if two indents are less than100 mm apart.
5.2.3 . Scaling
→ Description
By "scaling", we mean separation or removal of several fibres (locally) altering only thefirst surface ply on monolith edge or on outgoing side of drilled holes.
→ Examples of scaling acceptance criteria
� On ATR 72 outer wing carbon box structure,
→ in standard areas: the permissible scaling flaws are defined as follows:
Maximum surface area = 30 mm2
Maximum depth: 1 ply for th < 20 plies2 plies for th ≥ 20 plies
MONOLITHIC PLATE - DAMAGE TOLERANCEScaling I 5.2.3
2/3
For scaled hole concentrations, this flaw must be covered by a concession if, for alignedfasteners, more than 20 % of the holes are scaled and/or two flaws are less than5 fastener pitches apart.
→ in designated area: permissible scaling flaws are defined as follows:
Maximum surface area = 20 mm2,Maximum depth: 1 ply irrespective of the thickness.
For scaled hole concentrations, this flaw must be covered by a concession if:
- for aligned fasteners, more than 10 % of the holes are scaled and/or two flaws areless than 5 fastener pitches apart,
- for areas with several fasteners rows (e.g. piano area)
• for fasteners on same row: same as above,
• for flaws on several rows; must be covered by a concession if they are less than175 mm apart.
Flaw 1 Flaw 2
Flaw 1 Flaw 2
Flaw 1175 mm
Flaw 2
Flaw 3
For flaws 1 and 3:to be covered by a
concession
For flaws 1 and 2:if S1 and S2 ≤ permissiblesurface area permissible
MONOLITHIC PLATE - DAMAGE TOLERANCEScaling I 5.2.3
3/3
All scaled areas will be sealed with Hysol 9321 to restore flat surface and avoid scalingdeveloping during later operations.
� On A330/A340 inboard and outboard ailerons, scaling on 1 ply of skin will be sealedwith Hysol 9321. Permissible scaling flaws are defined as follows:
→ panels (delaminations at fasteners)
Maximum surface area = 30 mm2
For flaw concentrations at fasteners, two flaws on same row must be separated by 9fasteners.
Areas with several fastener rows:
- on same row: see above,- between different fastener rows
minimum distance = 175 mm
→ panels (leading edge joints), ribs, spar
Maximum surface area = 30 mm2
Maximum depth: 0.2 mm
For flaw concentrations, 5 flaws maximum on 10 consecutive fasteners.
→ panels (other areas) (scaling at fasteners)
Maximum surface area = 30 mm2
Maximum depth: 0.2 mm
For flaw concentrations, two flaws on a given row must be separated by 9 fasteners.
This is a fold of one or more skin plies which may occur between two (spar support)blocks or on a sandwich skin during co-curing or in spar webs.
→ Examples of acceptance criteria
� On ATR 72 outer wing carbon box structure
→ On bearing surfaces (spar, rib passage)
- Standard areas: steps on spar and rib passage areas are acceptable within a limit of0.3 mm. This type of flaw will be compensated for by Filleralu over a width of 50 mmon either side of the step.
- Designated areas: this flaw must be covered by a concession irrespective of itsgeometry.
→ On stiffeners
- standard areas: steps on stiffener flanges are acceptable within a height limit of0.3 mm provided that:
• there are no flaws in stiffener radius,• two flaws are at least 400 mm apart in Y-direction (wing frame),• two adjacent stiffeners are not affected in the same section,• an ultrasonic inspection demonstrates absence of "delamination" type flaws.
- designated areas: steps on stiffener flanges must be covered by a concession.
MONOLITHIC PLATE - DAMAGE TOLERANCESteps - Justification of permissible manufacturing flaws I 5.2.4
2/2
� On A330/A340 inboard and outboard ailerons under spar and rib bearing surfaces,steps lower than or equal to 0.2 mm and with a width lower than or equal to 3 mm willbe accepted, but:
- they must never be trimmed,- they will be compensated for by Filleralu,- in other areas, acceptable height is 0.4 mm.
� On A330 Pratt et Whitney thrust reverser sandwich skins mainly in areas with highcurvatures, steps with a height less than 0.5 mm are accepted in production. Stepsgreater than 0.5 mm will be examined case by case.
6 . JUSTIFICATION OF PERMISSIBLE MANUFACTURING FLAWS
MONOLITHIC PLATE - DAMAGE TOLERANCEJustification of in-service damage I 7
7.17.1.1
7 . JUSTIFICATION OF IN-SERVICE DAMAGE
7.1. Justification philosophy
A justification philosophy in agreement with European regulations (JAR) is associated witheach damage detectability range § 4.5 (undetectable damage; damage susceptible to bedetected [during inspection]; readily and obvious detectable damage).
7.1.1. Justification philosophy for undetectable damage
ACJ 25.603 § 5.1 :The static strength of the composite design should be demonstrated through aprogramme of component ultimate load tests in the appropriate environment, unlessexperience with similar design, material systems and loadings is available todemonstrate the adequacy of the analysis supported by subcomponent tests, orcomponent tests to agreed lower levels.
ACJ 25.603 § 5.2 :The effect of repeated loading and environmental exposure which may result in materialproperty degradation should be addressed in the static strength evaluation…
ACJ 25.603 § 5.5 :The static test articles should be fabricated and assembled in accordance withproduction specifications and processes so that the test articles are representative ofproduction structure.
ACJ 25.603 § 5.8 :It should be shown that impact damage that can be realistically expected frommanufacturing and service, but not more than established threshold of detectability forthe selected inspection procedure, will not reduce the structural strength below ultimateload capability. This can be shown by analysis supported by test evidence, or by test atthe coupon, element or subcomponent level.
MONOLITHIC PLATE - DAMAGE TOLERANCEJustification of in-service damage I 7.1.2
7.1.31/3
Undetectable damage, whether due to accidental impacts (in-service damageundetectable by a detailed visual inspection and therefore corresponding to BVID) ormanufacturing flaws must be covered by a static justification at ultimate load under themost severe environmental conditions (humidity and temperature) and at end of aircraftlife. During the certification tests, this damage will be introduced into minimum marginareas
7.1.2 . Justification philosophy for readily and obvious detectable damage
As laid down in the regulations, any damage which cannot withstand the limit loads mustbe readily detectable during any general visual inspection (50 flights) or obvious.
� Damage readily detectable within an interval of 50 flights must withstand 0.85 LL.� Obvious damage (engine burst) which occurs in flight with crew being aware of it must
withstand 0.7 LL (get-home loads capability).
7.1.3 . Justification philosophy for damage susceptible to be detected duringscheduled in-service inspections
� Regulatory aspects
ACJ 25.603 § 6.2.1 :Structural details, elements, and subcomponents of critical structural areas should betested under repeated loads to define the sensitivity of the structure to damage growth.This testing can form the basis for validating a no-growth approach to the damagetolerance requirements…
ACJ 25.603 § 6.2.3 :...The evaluation should demonstrate that the residual strength of the structure is equalto or greater than the strength required for the design loads (considered as ultimate)...
ACJ 25.603 § 6.2.4 :...For the case of no-growth design concept, inspection intervals should be establishedas part of the maintenance programme. In selecting such intervals the residual strengthlevel associated with the assumed damage should be considered.
MONOLITHIC PLATE - DAMAGE TOLERANCEJustification of in-service damage I 7.1.3
2/3
� General
For metallic structures, the two fundamental damage tolerance parameters are theinitiation of the damage and its growth before detection. Many tests have been conductedtherefore to evaluate the growth speed of the damage and the time required to reach itscritical size and therefore its residual strength (limit load).
The critical loading mode is mainly tensile loading.
In contrast, impact damage to the composite structure of perforation/delamination typecause, when it occurs, a very substantial drop in the mechanical strength but it does notgrow under the fatigue load levels on civil aircraft.
The critical loading mode is mainly compression (and shear) loading
MONOLITHIC PLATE - DAMAGE TOLERANCEJustification of in-service damage I 7.1.3
3/3
Several methods are used for demonstrating conformity with regulations:
a) Semi-probabilistic methods
If the no-growth concept of the flaw is demonstrated (by fatigue test), the size of thedamage no longer depends on an evolving phenomenon but on a random event(accidental).
For the damage range between BVID and VID, the aim of the (analytical) justification willbe to determine an inspection interval so that the probability (Re) of simultaneously havinga flaw and a load greater than its residual load will be a highly improbable event(probability per flight hour less than 10-9).
This probabilistic damage occurrence versus time aspect therefore replaces thedeterministic concept for metallic materials where the occurrence of a flaw depends eitheron fatigue initiation, or, for certain areas, on an accidental impact; the effect of the latterbeing a modification in the threshold.
The complete philosophy can be summarised by the curve below. It expresses the loadlevel to be demonstrated and the type of justification versus the damage rangeconsidered.The portion of the curve between the BVID and the VID depends on the results of theprobabilistic analysis.
7.1.3.1.1 . Process for determining inspection intervals
As stated above and in § 4.5, certain damage is susceptible to be detected duringinspections which implies that the aircraft may possibly fly between two inspections withdamage in a structure the residual strength of which may be lower than the ultimate loads.
In order not to design composite structures less reliable than metallic ones, an inspectionprogramme has been defined so that the probability of simultaneously having a flaw and aload greater than its residual strength will be a highly improbable event (probability perflight hour less than 10-9).
In mathematical form, this requirement can be written:
probability of occurrence of an impact with given energy (Pat)x
probability of not detecting the resulting flaw (1- Pdat)x
probability of occurrence of loads greater than the residual strength of the damage(Prat) ≤ 10-9/fh
or again:
i6 Pat x (1 - Pdat) x Prat ≤ 10-9/fh
This condition involves several notions that we will specify in the following sections.
MONOLITHIC PLATE - DAMAGE TOLERANCEDetermining inspection intervals I 7.1.3.1.1
2/6
❑ Pdat: probability of detecting the damage.
We defined, in § 4.2 to 4.4, the visual detection criteria for "A" value and "B" valuedamage and the mean value for various types of in-service inspections. Knowing that the"A" values correspond to a detection probability of 99 %, the "B" values to a probability of90 % and the mean values to a probability of 50 %, we can deduce the curve below whichshows the probability of detection versus the depth of the indent and the type ofinspection.
❑ Pat: probability of occurrence of an impact with given energy.
Several sources of impacts can be considered (this list is not restrictive):
- projection of gravel,- removal of the item,- dropping of tools or removable items,- shock with maintenance vehicle.
Each impact source will be defined by its incident energy.
As for detection, we will define an impact source by a statistical distribution (in this case,the Log-normal distribution).
We will therefore speak of the impact probability (or, more precisely, the impact energyrange) that we will call (Pat) and which will be characterised by mean energy Em and astandard deviation (according to Sikorsky, the standard deviation σ has a constant valueequal to 0.217).
The probability of having an impact energy between E et E+2 Joules is equal to
�+
=2E
E
dEx)E(fPat
0,3
0,52
0 0.5
5
0.99 1
Depth of indent(mm)
General visual inspection: *Detailed visual inspection: **
MONOLITHIC PLATE - DAMAGE TOLERANCEDetermining inspection intervals I 7.1.3.1.1
3/6
We also obtain 1dEx)E(f0
=�∞
The impact energy will generally be limited to 50 J (cut-off energy), except for THS root:140 J corresponding to the energy of a tool box failing from the top of the fin.
Now that the impact has been defined, we must find the relation between the incidentenergy (E), the size of the damage (Sd) and its indentation (f).
Generally, we have :
Sd = Ksd e
E
f = Kf 3.3
eE��
���
�
Test campaigns are however necessary to determine the coefficients Ksd and Kf whichdepends on the types of materials, their thickness and the item bearing conditions.
❑ Prat: probability of having a loading case greater than the residual strength of theimpacted laminate.
As we saw in paragraph § 5.1.7, the residual strength of a laminate with a delaminationdefined by its surface area Sd can be determined by the numbers C1, C2 and C3 that wewill call more generally C in the remainder of this section.
The need to have three variables to characterise the number C (εl, εt, γlt ou σl, σt, τlt)makes all theoretical exploitations of the item loads (or deformations) difficult.
MONOLITHIC PLATE - DAMAGE TOLERANCEDetermining inspection intervals I 7.1.3.1.1
4/6
We will therefore define a number εresidual = C
admissibleε which represents the permissible
strain of damage of size Sd under a single compression load.
This residual deformation depends of course on the size of the damage Sd. The generalform of this relation can be represented by the following curve:
It is therefore possible to determine, for each point on the item studied, the probability ofoccurrence of the load leading to the failure of the laminate with a delamination of size Sd
Knowing that the following gust occurrence probabilities are generally admitted:
- 2 x 10-5 for limit loads,- 1 x 10-9 for ultimate loads,
We can plot the curve below associating a probability of occurrence Prat with all residualstrength levels (εresidual = k x εL.L.) such that:
MONOLITHIC PLATE - DAMAGE TOLERANCEDetermining and calculating inspection intervals I 7.1.3.1.1
7.1.3.1.21/4
This curve, like all statistical distribution curves, is characterised by a mean value and astandard deviation. A simple calculation enables us to obtain the following expressions:
εmean = 10(Log (εU.L.) - 0.5554)
σ = 0.0928
To sum up, it is clear that by choosing a given impact energy range, the values of Pat, f,Pdat, Sd, εresidual and Prat are implicitly determined.
The drawing above shows the links between these various quantities.
The calculation tool is based on the fundamental principle described above: all damagesusceptible to be detected during an inspection must have a probability of encountering aload greater than its residual strength lower than 10-9 per flight hour (maximum value atend of aircraft life or before last inspection).
This principle involves three probabilities:
❑ Pat: probability of occurrence of an impact with a given energy.
❑ Pdat: probability of detecting the damage.
❑ Prat: probability of occurrence of a loading case greater than the residual strength ofthe impacted laminate.
MONOLITHIC PLATE - DAMAGE TOLERANCECalculating inspection intervals I 7.1.3.1.2
2/4
This principle can be stated in a more useable form:
The probability of having damage susceptible to encounter a load greater than its residualstrength is equivalent to the sum of the probabilities of having:
- damage relevant to an incident energy between 0 and 2 J susceptible to encounter aload greater than its residual strength
and- damage relevant to an incident energy between 2 and 4 J susceptible to encounter a
load greater than its residual strengthand
- damage relevant to an incident energy between 48 and 50 J susceptible to encountera load greater than its residual strength.
By discretizing the incident energy and therefore the type of the damage, each flaw rangecan be dealt with independently of the others.
We can therefore apply the fundamental principle to each energy interval then add theresults.
First of all we will consider an incident energy range between E and E+2 Joules.
The trickiest bit is to determine the probability of existence of damage of a well-definedsize versus time knowing that its probability of occurrence is equal to Pat (per flight hour)and its probability of non-detection during inspections is equal to (1 - Pdat).
MONOLITHIC PLATE - DAMAGE TOLERANCECalculating inspection intervals I 7.1.3.1.2
3/4
If Pat is the probability of occurrence of the flaw per flight hour at time t1 (before firstinspection for instance) the probability of existence of the flaw is equal to: 1 - (1 - Pat)t1
.
After the first inspection, the probability of occurrence of the flaw is therefore reduced to:[1 - (1 - Pat)t1] (1 - Pdat) then increases according to same curve as before but with a timeshift as initial probability is no longer zero. We repeat this operation up until the lastinspection.
The form of the function makes the calculations difficult; it is for this reason that wecompare the curve to its tangent: 1 - (1 - Pat)t ≈ t x Pat. This approximation remains validas long as the term t x Pat is small in comparison with 1.
This therefore gives the following configuration:
tIT1 t1 t2IT2 t3IT3 IT4 t4
1
Probability ofoccurrence
of a flaw
1 - (1 - Pat) ̂t1[1 - (1 - Pat) ̂t1] (1 - Pdat)
The curve [1 - (1 - Pat) ^ t] will be comparedto its limited development: t x Pat
MONOLITHIC PLATE - DAMAGE TOLERANCELoad level K I 7.1.3.1.2
7.1.3.1.31/5
E f Sd εεεεresidual Prat Pdat Pat Rd Rr
0 - 2 J2 - 4 J4 - 6 J
.
.
.
.
.
.
.
.
.
.44 - 46 J46 - 48 J48 - 50 J
i8
i9
7.1.3.1.3 . Load level K to be demonstrated in the presence of Large VID
The previous analysis can be substantiated by a static test with VID and a load level k.CL(1 ≤ k ≤ 1.5).
❑ First method:
This method consists in initially evaluating the reduction coefficient α on the permissiblestrengths of the material so that the final calculated risk Re is equal to 10-9 per flight hour(this determination can only be done by successive approximations).
This means that we can suppose that the damage tolerance behaviour of the material isdegraded in relation to that really used, that is a material whose strength (undercompression loading after impact) will be equal to a certain percentage, called α, of that ofthe real material.
MONOLITHIC PLATE - DAMAGE TOLERANCELoad level K I 7.1.3.1.3
2/5
In this case, the (εresidual; Sd) is submitted to a homothety in relation to the x-axis.
The number α1 can therefore legitimately be compared to a reserve factor.
We will thus define a static test with VID (Visible Impact Damage) such that the margin inrelation to the residual strain ε (VID) of the flaw is the one defined above.
We obtain:
.L.LxK)VID(1
εε=
α
hence:
i11 K = α )VID(kx)VID(.L.L
α=ε
ε
value representing the load level K to be demonstrated with VID.
❑ Second method:
Another method would consist in directly considering the probability and load notions.
MONOLITHIC PLATE - DAMAGE TOLERANCELoad level K I 7.1.3.1.3
3/5
It is clear that for a static test, we can consider that the probabilities of occurrence of theflaw (Pat) and the probabilities of detecting (Pat) and not detecting (1 - Pdat) the flaw areequal to 1 as we are sure that it is present in the item.
If we write the equivalence between the test and the maximum risk per flight hour from aprobabilistic viewpoint, we obtain: Re = Prat x PatVID x (1 - PdatVID) = Prat.
The method consists therefore in determining a fictive ultimate load level such that theprobability of the flaw residual load level is equal to Re.
The drawing below shows that we must randomly subject the curve (strain level ε; Prat) to
a homothety with a factor η1
so as to move point A to point B level. In this case, it appears
that the permissible load level of the VID has a probability of occurrence Re.
We see that this transformation also moves point A' to point B' which corresponds to thefictive ultimate load level that must be applied to the structure.
By zooming in onto the part of the graph which concerns us and imposing a logarithmicscale on the y-axis, we obtain the following representation:
MONOLITHIC PLATE - DAMAGE TOLERANCELoad level K I 7.1.3.1.3
4/5
We obtain:
)VID(kx6.89.3)Re(Log
)B(axis)A(axis +−==η
We can deduce the fictive ultimate load level to be demonstrated in the presence of VID
i129.3)Re(Log
)VID(kx9.12K+−
=
Load level K must always be between 1 and 1.5.
The graph below represents the previous relation (the maximum risk Re per flight hour onthe x-axis and the load level K to be demonstrated on the y-axis). Each curve is relevantto a residual load level of the flaw K.
MONOLITHIC PLATE - HOLE WITHOUT FASTENERNotations K 1
1 . NOTATIONS
(o, x, y): reference coordinate system of panel(o, 1, 2): orthotropic axis of laminate
φ: angle formed by loading with the orthotropic axisα: angular position of point to be calculated with the orthotropic coordinate system
Ex: longitudinal modulus of laminate in the reference coordinate systemEy: transversal modulus of laminate in the reference coordinate systemGxy: shear modulus of laminate in the reference coordinate systemνxy: Poisson coefficient of laminate in the reference coordinate system
E1: longitudinal modulus of laminate in the orthotropic coordinate systemE2: transversal modulus of laminate in the orthotropic coordinate systemG12: shear modulus of laminate in the orthotropic coordinate systemν12: Poisson's ratio of the laminate in the orthotropic coordinate system
σ x∞ : stress to infinity
σx (y): stress along y-axisσt (α): tangential stress around circular hole
K T∞ : hole coefficient for an infinite plate width
MONOLITHIC PLATE - HOLE WITHOUT FASTENERIntroduction - Theory - First method K 2
3.11/3
2 . INTRODUCTION
The purpose of this chapter is to assess stresses at the edge of a hole without fastener onan axially loaded composite plate and to anticipate failure of a notched laminate.
3 . GENERAL THEORY
3.1 . First method (Withney and Nuismer)
From a theoretical point of view, the problem is formulated as follows: let an infinite platebe subjected to stress flux σ x
∞ and with the diameter hole: ∅ .
The method is valid only if the x-axis is the laminate orthotropic axis. What is the stress σx
MONOLITHIC PLATE - HOLE WITHOUT FASTENERTheory - Second method K 3.2
2/3
The first step consists in searching for the orthotropic axes (o, 1, 2) of the material. Anglesφ and α are thus determined (α being the angular coordinate of the point to be consideredwith relation to the orthotropic coordinate system).
The hole coefficient expression is the following:
k8
[ ]{K t EE
k n k n kTx
∞∞= = − + + + + − −σ α
σα φ φ α φ φ α( ) ( cos ( ) sin ) cos ( ) cos sin sin1
2 2 2 2 2 21
}n k n( ) sin cos sin cos1 + + φ φ α α
with
k9 k = EE
1
2
k10 EE E
EEG
α
α α ν α1 4 1
2
4 1
1212
2
114
2 2=
+ + −�
��
�
��sin cos sin
K11 n = 12
112
2
1
GE
EE2 +��
�
����
�ν−
where E1, E2, G12 and ν12 are the mechanical properties of the laminate in the orthotropiccoordinate system (o, 1, 2).
MONOLITHIC PLATE - HOLE WITHOUT FASTENERTheory - Third method K 3.3
3.3 . Third method (isotropic plate theory)
If the material is isotropic (or nearly-isotropic) and if the plate is infinitely large, then thestress tensor may be formulated for any point P (identified by its coordinates r and α) onthe plate as follows:
MONOLITHIC PLATE - HOLE WITHOUT FASTENERTheory - Fourth method K 3.4
1/2
3.4 . Fourth method (empirical)
This method is simple, fast but conservative. For more details, refer to chapter L(MONOLITHIC PLATE - FASTENER HOLE) by considering the bearing load as zero.
Let a plate of length L be subjected to stress triplet σ x∞ , σ y
∞ , and τ xy∞ .
The first step consists in calculating the principal stresses σ p∞ and σ p'
∞ and in weighting
them with the net cross-section coefficient LL − ∅
.
Thus, the main net stresses σ pN and σ p
N' are obtained.
Both stresses are then divided by coefficients Kt (K tc or K t
MONOLITHIC PLATE - HOLE WITHOUT FASTENERTheory - Fourth method K 3.4
2/2
These coefficients (smaller than 1) are a function of the material, the elasticity moduli inthe direction considered (p or p'), the hole diameter (∅ ) and the type of load (tension "t" orcompression "c"). They are found in the form of graphs (for carbon T300/914 layer inparticular) in chapter Z (sheets 3 and 4 T300/914).
The two following final stresses are obtained :
σ pF =
σpN
tK
σ pF
' = σp
N
tK'
'
Both stresses are expressed in the main coordinate system (o, p, p').
MONOLITHIC PLATE - HOLE WITHOUT FASTENER"Point stress" - Failure criterion K 4.1
1/2
4 . ASSOCIATED FAILURE CRITERIA
4.1 . Failure criterion associated with the "point stress" method (Whitney andNuismer)
To determine the failure of a notched laminate, it is generally allowed (for compositematerials) to search for edge stresses at a certain distance do from the hole edge. Indeed,edge distance stress release through microdamages causes them to be analyzed at theedge distance do in practice. This distance depends on the type of load of the fibreconsidered (compression or tension), on the hole diameter and on the material (seechapter Z sheets 9 and 10 for T300/914).
At the composite material stress office of the Aerospatiale Design Office, one considers("point stress" method) that there is a failure in the laminate when the longitudinal stressof the most highly loaded fibre (located at the edge distance do) tangent to the hole isgreater than the longitudinal stress allowable for the fibre.
k13 There is a failure if: σl (y = R + do) > Rl
σl: longitudinal stress of the fibre tangent to the hole
MONOLITHIC PLATE - HOLE WITHOUT FASTENER"Point stress" - Failure criterion K 4.1
2/2
For complex loads, there is a software (PSH2 on mx4) which automatically models a finiteelement mesh and finds loads in fibres that are tangent to the hole.
Longitudinal stress analysis is performed in a circle of elements, its center of gravity beinglocated at the hole edge distance do.
MONOLITHIC PLATE - HOLE WITHOUT FASTENER"Average stress" - Failure criterion K 4.2
4.2 . Failure criterion associated with the "average stress" method (Whitney andNuismer)
This method consists in determining the average stress average σx average (ao) betweencoordinate points (0, R) and (0, R + ao). It is assumed that the plate is infinitely large andthe loading uniaxial.
Based on the previous theory (see K 3.1), the following may be formulated as:
MONOLITHIC PLATE - HOLE WITHOUT FASTENEREmpirical method - Failure criterion K 4.3
It is possible to choose ao so that:
σx average (ao) ≈ σx (R + do)
This condition allows the "point stress" and the "average stress" method to becomeequivalent.
The "average stress" method is rarely used at Aerospatiale, the same failure criterion asfor the "point stress" method may be applied: one considers that there is a failure in thelaminate when the longitudinal stress of the most highly loaded fibre tangent to the hole isgreater than the longitudinal stress allowable for the fibre.
4.3 . Failure criterion associated with the empirical method
After determining stresses σ pF and σ p
F' , a smooth calculation must be performed (see
chapter C) in order to assess longitudinal stresses in fibres tangent to the hole.
The Hill's failure criterion shall be used to each single ply (see chapter G3).
It may be noted that this method is relatively conservative because both coefficients Kt
and K't are assessed for different points, each one being the most critical with relation todirections p and p'.
On the other hand, coefficient Kt and K't values were determined only for diametersbetween ∅ 3.2 to ∅ 11.1. It is, therefore, necessary to use the theory for large diameters.
If one determines the flux at a hole edge distance do = 1 mm (see do in tension for theT300/914), one gets: Nx (y = 20 + 1) = 32.47 daN/mm.
A smooth plate calculation (chapter C) with this flux makes it possible to determine thelongitudinal stress of the most highly loaded fibre (fibre at 0°): σl = 32.41 hb.
On the other hand, as the allowable longitudinal tension stress of the same fibre is equalto Rl = 120 hb, based on the "point stress" failure criterion, we obtain:
Margin: ��
���
� −141.32
120 100 = 270 %
At a hole edge distance do = 1 mm (see tension do for fibre T300/914 in chapter Z), flux Nx
is now only 32.47 daN/mm.
A smooth plate calculation makes it possible to find that fibres with a 0° direction aresubjected to a 32.41 hb longitudinal stress at this particular hole edge distance.
The longitudinal tensile strength of fibre T300/914 being 120 hb, the targeted margin isthus:
Let's determine the normal stress fluxes of the hole edge at point P (fibre at 0° tangent tohole). To do this, we shall use the second method
First of all, (in order to eliminate the shear flux), let's be positioned in the main coordinatesystem (o, p, p') which forms a 22.5° angle with the reference coordinate system (o, x, y).Stress fluxes then become N p
∞ = 5 daN/mm, N p'∞ = - 10 daN/mm.
Orthotropic axes (o, 1, 2) are coincident with the reference coordinate system (o, x, y).
The plate and its loading may then be described as follows:
In the coordinate system (o, p, p'), the mechanical properties of the laminate are thefollowing:
MONOLITHIC PLATE - HOLE WITHOUT FASTENERReferences K
BARRAU - LAROZE, Design of composite material structures, 1987
GAY, Composite materials, 1991
VALLAT, Résistance des matériaux
S.C. TAN, Finite width correction factors for anisotropic plate containing a central opening,1988
J. Rocker, Composite material parts: Design methods at fastener holes 3 ≤ φ ≤ 100 mm.Extrapolation to damage tolerance evaluation, 1998, 581.0162/98
W.L. KO, Stress concentration around a small circular hole in a composite plate, 1985,NSA TM 86038
WHITNEY - NUISMER, Uniaxial failure of composite laminates containing stressconcentration, American Society for testing materials STP 593, 1975
ERICKSON - DURELLI, Stress distribution around a circular hole in square plate, loadeduniformly in the plane, on two opposite sides of the square, Journal of applied mechanics,vol. 48, 1981
(o, x, y): initial coordinate system(o, M, M'): coordinate system specific to the bearing load(o, P, P'): stress main coordinate system
F: bearing load∅ : fastener diameterSf: countersink surface of fastenere: actual thickness of laminatee*: thickness taken into account in bearing calculationsp: fastener pitch
σ tN : net cross-section stress at the hole
σm: bearing stressσR: allowable stress of material (general designation)
σxa: allowable normal stress of material in direction xσya: allowable normal stress of material in direction yτxya: allowable shear stress of materialτvisa: allowable shear stress of screw
N xB
N yB gross fluxes in panel
N xyB
N xN
N yN net cross-section fluxes
N xyN
N MN
N MN
' net cross-section fluxes in the coordinate system specific to the bearing loadN MM
N'
N Mm additional flux due to the bearing load
β: bearing load angle with relation to the initial coordinate system
σxa is the allowable normal stress of the notched material in direction xσya is the allowable normal stress of the notched material in direction yτxya is the allowable shear stress of the notched materialσRm is the allowable bearing stress of the materialτvisa is the allowable shear stress of the screw
3 . SINGLE HOLE WITH FASTENER
The purpose of this sub-chapter is to outline the justification method of a hole with afastener to which is applied a bearing load in any direction, the laminate being subjectedto membrane type surrounding load fluxes and/or bending moment fluxes. The failuremode associated with this method is a combined net cross-section failure mode in thepresence of bearing (see 2.1 and 2.2).
3.1 . Pitch p definition
If the main loading is in the F1 direction, the pitch taken into account in the calculations
MONOLITHIC PLATE - FASTENER HOLEMembrane analysis - Short cut method - Theory L 3.2.1
1/8
If the main loading is direction F2, the pitch (which is more commonly called edgedistance) taken into account in the designs shall be equal to: p = 2 p3.
For complex loading (or for simplification purposes), the following pitch value may beused: p = mini (p1; p2; 2 p3).
It should be noted that for membrane or membrane and bending loading, pitch p is limitedto k ∅ where k depends on the material used. The value of k is generally between 4.5 and5. For pure bending loading, this limitation does not apply.
3.2 . Membrane analysis - Short cut method
3.2.1 . Theory
Generally speaking, a failure is reached at a fastener hole when:
l1 σ tN + Km σm ≥ Kt σR
In the case of a membrane loaded single hole with fastener, the various justification(broadly summed up by relationship I1) steps must be followed:
MONOLITHIC PLATE - FASTENER HOLEMembrane analysis - Short cut method - Theory L 3.2.1
2/8
1st step: For load introduction zones (fittings, splices), the membrane gross flux NB to betaken into account at fasteners is deduced from the constant flux to infinity N∞ by thefollowing relationship:
l2 NB = p5 ∅
N∞ if p > 5 ∅ NB = N∞ if p ≤ 5 ∅
If the zone to be justified is a typical zone (ribs, spars), then:
NB = N∞
The drawing above shows the difference between the flux to infinity and the actual flux atfasteners for a load introduction zone and highlights the existence of a working strip ateach fastener of a width equivalent to 5 Ø. This phenomenon is comparable to the onedescribed in chapter M.1.
MONOLITHIC PLATE - FASTENER HOLEMembrane analysis - Short cut method - Theory L 3.2.1
4/8
where the countersink surface is equal to:
Sf = b h = h2 tgθ
3rd step: It consists in transforming the previously designed fluxes in the coordinatesystem specific to the bearing load:
l4
N
N
N
MN
MN
MMN
'
'
=
22
22
22
)(sin)(coscosxsincosxsin
cosxsinx2)(cos)(sin
cosxsinx2)(sin)(cos
β−βββ−ββ
ββββ
ββ−ββ
N
N
N
xN
yN
xyN
Angle β is, in the trigonometric coordinate system, the angle leading from the M-axis(bearing coordinate system) to the x-axis (reference coordinate system).
MONOLITHIC PLATE - FASTENER HOLEMembrane analysis - Short cut method - Theory L 3.2.1
7/8
Angle α is, in the trigonometric coordinate system, the angle leading from the M-axis(bearing coordinate system) to the P-axis (main coordinate system).
6th step: Fluxes are maximized by coefficient 1Kt
where Kt is the hole coefficient.
Kt values depend on the type of loading (tension or compression), the fastener diameter,the mechanical properties and the material used (see chapter Z).
It should be noted that to each of both main fluxes is associated a hole coefficient whichmay be different. This is why their notation differs from the sign*.
MONOLITHIC PLATE - FASTENER HOLEMembrane analysis - Short cut method - Theory L 3.2.1
8/8
7th step: Fluxes so maximized are recalculated in the initial coordinate system (o, x, y).
l9
N
N
N
xF
yF
xyF
= 2))(sin(2))(cos()cos(x)sin()cos(x)sin(
)cos(x)sin(x22))(cos(2))(sin(
)cos(x)sin(x22))(sin(2))(cos(
α−β−α−βα−βα−βα−βα−β−
α−βα−β−α−βα−β
α−βα−βα−βα−β
NKNK
PN
t
PN
t
'*
0
Angle (α - β) are, in the trigonometric coordinate system, the angle leading from the x-axis(reference coordinate system) to the p-axis (main coordinate system).
8th step: A smooth plate calculation is made with fluxes NF previously determined (seechapter C) to obtain the margin.
MONOLITHIC PLATE - FASTENER HOLEEDP computing program PSG33 L 3.2.2
3.2.2 . Computing program PSG33
This software, which can be used on mx4 or PC, is simply the digital application of thetheory presented above, the eight steps being integrated into the calculation.
Let input data relating to the example covered further in this chapter be as follows.
The software gives the design margin for each value of Km, as well as all intermediateresults. To allow a quick check of loading, it represents the bearing load and main netfluxes in the reference coordinate system.
Note the bearing load direction (β = - 30°).
^90I
N2 = -20.19 I N1 = 22.19* I ** I ** I ** I * /* I * /* I * /*I*/ FM = 77.
MONOLITHIC PLATE - FASTENER HOLEBending analysis L 3.3
1/5
3.3 . Bending analysis - Short cut method
If the notched plate is subjected to bending moment fluxes Mx, My and Mxy, follow theadditional steps described hereafter:
1st step: Determine stresses on the external and internal surfaces corresponding tobending loads only.
As a first approximation, these stresses may be assessed by the general relationship
σ ≈ M vl
Me
≈6
2 . In that case, the material shall be considered as homogeneous.
It is nevertheless recommended to determine these stresses with the computing softwarePSD48 (stacking homogenizing and analysis) which takes into account stiffness variationswithin the laminate or to refer to chapter D.
Thus, for each design direction (x, y and xy), the following stresses are obtained:
MONOLITHIC PLATE - FASTENER HOLEBending analysis L 3.3
2/5
2nd step: From these stresses, "equivalent" membrane gross fluxes are evaluated.
l10
∆
∆
∆
∆
∆
∆
n
n
n
n
n
n
exB
eyB
exyB
ixB
iyB
ixyB
= e
σ
σ
τ
σ
σ
τ
exB
eyB
exyB
ixB
iyB
ixyB
surfaceernalintfor
surfaceexternalfor
3rd step: On the contrary of membrane analysis, no majoration between fluxes to infinityN∞ and gross fluxes NB will be taken into account at load introduction areas.
NB = N∞
4th step: "Equivalent" membrane net fluxes are evaluated from "equivalent" membranegross fluxes.
MONOLITHIC PLATE - FASTENER HOLEBending analysis L 3.3
3/5
∆ni xN = ∆ni x
B pp − ∅
∆ni yN = ∆ni y
B pp − ∅
for internal surface (no countersunk fastener head)
∆ni xyN = ∆ni xy
B pp − ∅
Confer to sub-chapter L.3.1 to determine fastener pitch.
5th step: "Equivalent" membrane net fluxes are divided by the coefficient Kf (bending holecoefficient) which depends on the material (in general Kf = 0.9).
Hence, we get the (majorated) "equivalent" membrane net fluxes:
MONOLITHIC PLATE - FASTENER HOLEJustifications - Nominal deviations L 3.4
3.5.1
3.4 . Justifications
Whatever the type of load (membrane or membrane + bending), make sure that:
- the plain monolithic plate subject to "equivalent" membrane load fluxes (NF + ∆neF) or
(NF + ∆niF) is acceptable from a structural strength point of view (refer to chapter C),
- the allowable bearing stress of material σm (which depends on the material, thefastener diameter and the thickness to be clamped - see chapter Z) is greater orequal to the bearing stress applied corresponding to a laminate thickness that issmaller or equal to 1.3 ∅ for single shear or 2.6 ∅ for double shear (see sub-chapterL.2.1 - 4th step):
3.5 . Nominal deviations on a single hole
This sub-chapter is directly related to concession processing. Here, simple rules areoutlined, that shall allow the stressman to assess the effect of a geometrical deviation,such as a fastener diameter, its pitch or edge distance, on an initial margin.
The following paragraphs are valid only for a hole with fastener subject to membranefluxes.
However, for greater accuracy, it is recommended to redo the calculation or use thesoftware psg33.
3.5.1 . Changing to a larger diameter
Following a drilling fault, it is sometimes necessary to change to a repair size or tooversize the fastener.
Based on the theory we have just presented, any diameter change (∅ changes to ∅ ')shall have an effect on:
- the net cross-section coefficient: the resulting reduction shall be equal to:
l14 k = p Sf
ep Sf
e
− ∅ −
− ∅ −
' '
- the bearing stress: we shall assume that there is no effect on the bearing stress, evenif it tends to decrease (this assumption is conservative),
- the hole coefficient: if we assume that the hole coefficient value is in the mostunfavorable case Kt = 0.003684 ∅ 2 - 0.08806 ∅ + 0.886 (see corresponding curve inchapter Z - material T300/914), the resulting reduction shall be equal to:
k' = '89.0088.00037.0
89.0'088.0'0037.02
2
∅∅≈
+∅−∅+∅−∅
Thus, the general relationship may be given as follows:
l15 RF' ≈ RF k k' ≈ RF ∅∅
− ∅ −
− ∅ −'
' 'p Sfe
p Sfe
3.5.2 . Pitch decrease
If loads are parallel to the free edge, no reduction is necessary on the reserve factor:
MONOLITHIC PLATE - FASTENER HOLE"Point stress" finite element method - Description L 3.6.1
3.6 . "Point stress" finite element method (membrane analysis)
3.6.1 . Description of the method
Procedure PSH2 allows the calculation of stresses in fibres around a circular hole withfastener in a multilayer composite plate subjected to membrane type surrounding fluxes. Itis based on a finite element display of a drilled plate. Mapping calls for two separate parts:
- the bolt (rivet/screw/bolt),
- the drilled plate.
The drilled hole is modeled by 8-junction quadrangular elements and 6-junction triangularelements. The area adjacent to the hole is modeled by two rings of elements. The ringnearest to the hole is thin and is not utilized directly on issued sheets. Issues arepresented on the second ring, the center of gravity of elements being at a design distancefrom the hole corresponding to the point stress theory (do).
Contact elements between the plate and the bolt (which also simulate clearance betweenthe fastener and the edge distance) are of the variable stiffness type. Their stiffness isvery low when there is no contact with the plate, their stiffness is very high if there is acontact.
Loading is achieved by (normal and shear) fluxes on plate edges.
MONOLITHIC PLATE - FASTENER HOLE"Point stress" finite element method - Justifications L 3.6.2
3.6.2 . Justifications
Make sure that:
- longitudinal stresses in fibres tangent to the hole edge distance (and located at adistance do) are smaller than the longitudinal stress allowable for fibre Rl,
Fibre a
t 45°
Fibre at 135°
Fib r
e at
90°
do
σlσl
Fibre at 0°
- The allowable bearing stress of the material σm is greater or equal to the bearingstress applied corresponding to a laminate thickness that is smaller or equal to 1.3 ∅for single shear or 2.6 ∅ for double shear (see sub-chapter L.2.1 - 3rd step).
The previous study allowed us to find the structural effect of a single hole with fastener (ordistant enough from others) on a monolithic plate subject to membrane or bending typeloads.
We shall now study the effect of several lined up holes. We shall assume that the plate issubjected to a membrane type uniaxial load flux that is perpendicular to the row offasteners.
If loading is parallel to the row of fasteners, refer to chapter L.3.4.2 calculation.
4.1 . Independent holes
If each fastener pitch is greater of equal to 5 ∅ , each fastener may be considered as asingle hole. Refer to sub-chapter L.3.
4.2 . Interfering holes (0 < d < 3.5 ∅∅∅∅ )
If the distance between two holes is smaller than 5 ∅ , the net cross-section coefficient tobe used changes to:
MONOLITHIC PLATE - FASTENER HOLEFirst example L 5.1
1/7
5.1 . First example
Let a T300/BSL914 (new) laminate be laid up as follows:
0°: 6 plies45°: 4 plies135°: 4 plies90°: 6 plies
Total thickness: e = 20 x 0.13 = 2.6 mm
It is subjected to the three following fluxes in the initial coordinate system (o; x; y):
N xB = 8 daN/mm
N yB = - 6 daN/mm
N xyB = 20 daN/mm
and to the bearing load:
F = 185 daNβ = - 30°
The fastener is a ∅ 4.8 mm countersunk head one (100° countersink angle, whichcorresponds to a 4.91 mm2). The fastener pitch is 21.6 mm.
The purpose of the example is to determine the three final fluxes that shall be used for theequivalent smooth plate design, which shall provide the hole margin looked for (thiscalculation shall be covered in chapter C).
MONOLITHIC PLATE - FASTENER HOLEFirst example L 5.1
7/7
New, let's assume that, as a result of a defective drilling operation, the fastener diameterhad to be changed to a ∅ 6.35 mm with a 8.62 mm2 countersunk surface.
What would be the new margin?
{l15}
RF' = 1.31 x 92.0
6.291.48.46.216.2
62.835.66.21x
35.68.4 =
−−
−−
Which corresponds to a - 8 % margin, thus non allowable. However, a full manual analysis(or using software PSG33) would have made it possible to find a 0 % margin.
If the calculation is conservative, it is due to the fact that the decrease of the bearingstress corresponding to fastener oversizing was not taken into account (see chapterL.3.5.1).
The preceding example shall also be fully covered in the composite material manual part"Calculation programs" (PSG33 instructions).
MONOLITHIC PLATE - FASTENER HOLESecond example L 5.2
4/5
Hole coefficient weighting
{l12}
for the external skin:
∆ne xF =
9.037.13 = 14.86 daN/mm
∆ne yF =
9.002.10− = - 11.13 daN/mm
∆ne xyF =
9.072.16− = - 18.58 daN/mm
for the internal skin:
∆ni xF =
9.087.11− = - 13.19 daN/mm
∆ni yF =
9.09.8 = 9.89 daN/mm
∆ni xyF =
9.084.14 = 16.49 daN/mm
All prior calculations were made in the initial coordinate system (o; x; y). These"equivalent" bending type fluxes are thus to be added to the membrane type fluxes foundin the first example (see summary table on next page).
SANDWICH - MEMBRANE / BENDING / SHEARNotations N 1
1 . NOTATIONS
Ny: normal load fluxMx: moment fluxMz: moment fluxTx: shear load fluxTz: shear load flux
Emi: membrane elasticity modulus of lower skinEfi: bending elasticity modulus of lower skinGi: shear modulus of lower skinei: thickness of lower skin
Emc: membrane elasticity modulus of core materialEfc: bending elasticity modulus of core materialGc: shear modulus of core materialec: thickness of core material
Ems: membrane elasticity modulus of upper skinEfs: bending elasticity modulus of upper skinGs: shear modulus of upper skines: thickness of upper skin
zg: neutral axis position with respect to the lower skin
Σ El: overall inertia of elasticity moduli weighted plate
SANDWICH - MEMBRANE / BENDING / SHEARSpecificity - Construction principle - Design principle N 2
34
2 . SPECIFICITY
A sandwich is a three-phase structure consisting of a core generally made out ofhoneycomb or foam with a low elasticity modulus and two thin and stiff face sheets.
Sandwich structures have a very high specific bending stiffness.
3 . CONSTRUCTION PRINCIPLE
The face sheets and core are assembled by bonding with synthetic adhesives. There areseveral alternative manufacturing processes:
- multiple phase process: face sheets are cured separately, then bonding of facesheets to the honeycomb is performed as a second operation,
- semi-cocuring process: the external face sheet is cured separately, the honeycomband the internal face sheet are then cocured on the external face sheet,
- single phase or "cocuring" process: face sheets and the honeycomb are cured in onesingle operation.
4 . DESIGN PRINCIPLE
The design rules that shall be developed are derived from the classical elasticity (refer to"distribution of load among several closely bound structural elements" in chapter A.7).
First of all, we shall consider that the three materials together are completely ordinary.Then, we shall simplify the relationships obtained by considering that face sheets are thinand stiff and that the sandwich core is thick and flexible.
4.1 . Sandwich plates
Like monolithic metal or composite plates, sandwich plates are under the general plateequation (see § A.7.4).
The determination of matrices (Aij), (Bij) and (Cij) which connect the strain tensor to theload tensor is described in chapters C, D and E.
4.2 . Short cut theory - "Sandwich" beams
Here, we shall outline a short cut method applicable to sandwich beams. This methoddoes not take into account transversal loading, transversal effects so-called "Poisson"effects and membrane-bending coupling. This simplification may lead to an error ofapproximately 10 % on results obtained in cases of complex loading.
From the overall deformation point of view, sandwich plates obey the conventionalequations of classical elasticity theory. Stiffness equivalences (with iso-cross-section) withhomogeneous beams are described by relationships n14 to n18.
Let a sandwich beam be made up of:
- an upper skin of thickness es, of membrane elasticity modulus Ems and of equivalentbending elasticity modulus Efs,
- a core thickness ec, of membrane elasticity modulus Emc and of equivalent bendingelasticity modulus Efc,
- a lower skin of thickness ei, of membrane elasticity modulus Emi and of equivalentbending elasticity modulus Efi.
SANDWICH - MEMBRANE / BENDING / SHEARSandwich beams N 4.2
2/3
The bending modulus concept comes from the fact that lower and upper skins aregenerally (in the case of honeycomb sandwiches) laminates with different membrane andbending moduli (see chapters C and D). Its value depends on ply stacking. This conceptwas extended to all three materials.
First of all, we shall develop the full sandwich beam theory while taking into account facesheet thickness and bending stiffnesses, then we shall outline at the end of each sub-chapter, the simplified relationships in which face sheets shall supposedly be thin andsubject to membrane stress only.
The neutral line of the sandwich beam is defined by dimension zg to that:
n1 zg = Em e Em e e e Em e e e e
Em e Em e Em e
ii
c c ic
s s i cs
i i c c s s
2
2 2 2+ +�
��
��� + + +�
��
���
+ +
Remark: In the case of a beam in which Emc ec << Emi ei and Emc ec << Ems es, therelationship becomes:
SANDWICH - MEMBRANE / BENDING / SHEAREffect of normal load Ny N 4.2.1
2/2
By taking into account the remark assumptions of the previous page (ei << ec, es << ec,Emc << Emi and Emc << Ems), it is possible to oversimplify load distribution in the differentsandwich layers.
We shall assume that load Ny applied at the beam neutral axis is fully picked up by twomembrane type normal loads (Fs and Fi) in both face sheets.
SANDWICH - MEMBRANE / BENDING / SHEAREffect of shear load Tz N 4.2.3
2/3
The equivalent shear modulus with relation to the z-axis may be determined by therelationship n16.
Remark 1: In the case of a sandwich beam in which Emc ec << Emi ei and Emc ec << Emses, τA, τzg and τB take the following simplified from:
n10 τA ≈ τzg ≈ τB ≈ T
b e e ez
ic
s
2 2+ +�
��
���
Remark 2: It should be noted that the equivalent shear modulus of a thin face sheetsandwich beam is on the same order of magnitude as the core for thehoneycomb it consists of, thus very low.
For the assessment of a honeycomb sandwich beam (or plate) deflection, it istherefore important to take into account this significant effect with respect tothe deformation due to the bending moment.
SANDWICH - MEMBRANE / BENDING / SHEAREffect of shear load Tz N 4.2.3
3/3
For example, for a sandwich beam simply supposed, loaded in its center, the deflectedshape due to the shear load may represent approximately 60 % of the overall deflection.
Let an aluminium beam and a sandwich beam with equivalent bending stiffness be, giving:
Aluminium beam: f1 = 0.3041 mm (99.6 %); f2 = 0.0011 mm (0.4 %)
Sandwich beam: f1 = 0.3041 mm (38 %); f2 = 0.5 mm (62 %)
f1: deflection due to the bending moment f P lE l
148
3
=
f2: deflection due to the shear load SG4lP2.12f =
300
1 daN
3
10AluminiumE = 7400 hb, G = 2840 hbEl = 1.85E6 daN mm2
SANDWICH - MEMBRANE / BENDING / SHEAREffect of bending moment Mx N 4.2.4
1/2
4.2.4 . Effect of bending moment Mx
A bending moment Mx applied at the neutral line results in the creation of a lineardistribution of elongations along the cross-section. At the outer surfaces, we have:
n11 εs = M vEl
M e e e zEl
x s x i c s g
Σ Σ=
− + + −( )
εi = M vEl
M zEl
x i x g
Σ Σ=
with:
Σ El = b Ef e b Em e e e e zs ss s i c
sg
3 2
12 2+ + + −�
��
��� +
b Ef e b Em e e e zc cc c i
cg
3 2
12 2+ + −�
��
��� +
b Ef e b Em e e zi ii i
ig
3 2
12 2+ −�
��
���
The equivalent bending modulus of the sandwich beam may be determined by therelationship n17.
SANDWICH - MEMBRANE / BENDING / SHEAREffect of bending moment Mx N 4.2.4
2/2
Remark: In the case of a sandwich beam in which ei << ec, es << ec, Emc << Emi andEmc << Ems, self inertias of both face sheets and honeycomb stiffness may bedisregarded:
Σ El ≈ b Ems es e e e z b Em e e zi cs
g i ii
g+ + −���
��� + −�
��
���
2 2
2 2
We shall assume that moment Mx is fully picked up by two membrane type normal loads(F's and F'i) in both face sheets.
Both loads have the same modulus but are opposite. Their value is equal to:
SANDWICH - MEMBRANE / BENDING / SHEAREffect of bending moment Mz N 4.2.5
4.2.5 . Effect of bending moment Mz
Generally speaking, bending moment Mz is distributed in each of the three materials inproportion to their natural bending stiffness (with relation to the z-axis).
The maximum normal stress in each of the three materials may then be simply formulatedas follows:
n13 σs = ±+ +
62M
b eEm e
Em e Em e Em ez
s
s s
s s c c i i
σc = ±+ +
62M
b eEm e
Em e Em e Em ez
c
c c
s s c c i i
σi = ±+ +
62M
b eEm e
Em e Em e Em ez
i
i i
s s c c i i
The equivalent bending modulus with relation to the z-axis is identical to the equivalentmembrane modulus with relation to the y-axis (see relationships n14 and n18).
4.2.6 . Deformations and equivalent mechanical properties
Sandwiches are microscopically heterogeneous. It is sometimes necessary to find theirequivalent stiffness properties in order to determine the passing loads and resultingdeformations.
For a sandwich beam, equivalences (with iso-cross-section) with respect to typical loadsare the following:
Let a 10 mm wide sandwich beam be defined by the following stacking sequence:
- an upper skin (carbon layers) of thickness es = 1.04 mm and of longitudinal elasticitymodulus Es = 6000 daN/mm2 (the bending modulus being identical),
- a core (honeycomb) of thickness ec = 10 mm and of longitudinal elasticity modulusEc = 15 daN/mm2,
- a lower skin (carbon cloths) of thickness ei = 0.9 mm and of longitudinal elasticitymodulus Ei = 4500 daN/mm2 (the bending modulus being identical).
We shall assume that the beam is subjected to the following two loads and moment:
- at the lower fibre, an elongation of 7612 + 4761 = 12373 µd,
- at the upper fibre, an elongation of 7612 - 3256 = 4356 µd.
The second part of the example consists in calculating the evolution of shear stress due toshear load Tz, at the neutral axis in particular, at point A (upper face sheet - honeycombinterface) and at point B (lower face sheet - honeycomb interface).
1st step: To calculate the inertia of the elasticity moduli weighted beam.
{n7}
Σ El = 2978541 daN mm2
Remark: If the simplified relationship of a sandwich beam is used (see § M.3.2.4), weobtain the value:
- To calculate the elasticity moduli weighted static moment EWzg (static moment with
relation to the neutral axis of part of the material located above it).
{n8}
EWzg = 10 6000 1.04 2
204.1
210
29.0151009.7
204.1109.0 �
�
���
� +++��
���
� −++
EWzg = 275538 daN mm
- To calculate the elasticity moduli weighted static moment EWA (static moment withrelation to the neutral axis at the upper face sheet).
EWA = 10 6000 1.04 ��
���
� −++ 09.7204.1109.0
EWA = 270192 daN mm
- To calculate the elasticity moduli weighted static moment EWB (opposite of the staticmoment with relation to the neutral axis at the lower face sheet).
3rd step: to determine shear stresses at the neutral axis (shear stress in honeycomb), atpoint A and point B.
{n9}
τzg = 250 27553810 2978541
= 2.31 hb (23.1 MPa)
τA = 250 27019210 2978541
= 2.26 hb (22.6 MPa)
τB = 250 26892010 2978541
= 2.25 hb (22.5 MPa)
It should be noted that, between point A and point B, the shear stress is practicallyconstant. It would be totally constant if the honeycomb elasticity modulus were zero(which may be considered as such).
E1: longitudinal elasticity modulus of material 1e1: thickness of material 1E2: longitudinal elasticity modulus of material 2e2: thickness of material 2E: longitudinal elasticity modulus of materials 1 and 2, if they are similare: thickness of materials 1 and 2, if they are similar
Gc: shear modulus of adhesiveEc: longitudinal elasticity modulus of adhesiveec: thickness of adhesive
h: width of adhesively bonded joint
l: length of adhesively bonded joint
lm: minimum length of adhesively bonded joint
t: thickness of cleavage t e e ec= + +���
���1 2
2 2
λ: design constant
k: design constant
D: design constant
τm: average shear stress in adhesively bonded joint
τM: maximum shear stress in adhesively bonded joint
τx: shear stress in adhesively bonded joint at dimension x
τam: allowable average shear stress of adhesive
τaM: allowable maximum shear stress of adhesive
σm: average peel stress in adhesively bonded joint
σM: maximum peel stress in adhesively bonded joint
F1i: normal load passing through material 1 (at center of step No. i)F2i: normal load passing through material 2 (at center of step No. i)∆Fi: normal load transferred by the adhesively bonded joint (in step No. i)
E1i: longitudinal elasticity modulus of material 1 (in step No. i)e1i: thickness of material 1 (in step No. i)E2i: longitudinal elasticity modulus of material 2 (in step No. i)e2i: thickness of material 2 (in step No. i)
li: length of adhesively bonded joint (in step No. i)
τmi: average shear stress in adhesively bonded joint (in step No. i)τMi: maximum shear stress in adhesively bonded joint (in step No. i)
BONDED JOINTSBonded single joint - Highly flexible adhesive S 2.1.1
2 . BONDED SINGLE LAP JOINT
This technique consists in assembling two (or several) elements by molecular adhesion.The adhesive must ensure load transmission.
Bonding of two flat surfaces only shall be considered.
Four cases shall be examined:
- Single joints:• highly flexible adhesive with respect to bonded laminates,• general case (without cleavage effect),• general case (with cleavage effect).
BONDED JOINTSGeneral case - Without cleavage S 2.1.2
1/3
In the case of an adhesive with a very low stiffness as opposed to the stiffness of thelaminates to be assembled, shear stress may be considered as uniform and equal to:
s1 τm = lxh
F
If τa is the allowable shear stress of the adhesive, the minimum length of the adhesivelybonded joint shall be equal to:
lm = maxh
Fτ
The failure load is equal to:
Fr = λ x τam x h
In practice, check that the average stress (which, in this case, is equal to the maximumstress) is smaller or equal to τam.
BONDED JOINTSGeneral case - Without cleavage S 2.1.2
2/3
In the case of any bonded assembly (E1 x e1 > E2 x e2) (see drawing on previous page)subjected to a normal load F, the shear stress in the adhesively bonded joint may beformulated as follows (VOLKERSEN) :
s2 τx = τm ���
����
�
+−
λλ+
λλλ
2211
2211
exEexEexEexEx
)2/lx(cosh)xx(sinh
)2/lx(sinh)xx(coshx
2lx
with:
s3 λ = 2211
2211
c
c
exExexEexEexEx
eG +
and
τm = lxh
F
Remark: If E1 x e1 = E2 x e2 = E x e the joint is so-called equilibratedIf E1 = E2 = E and e1 = e2 = e the joint is so-called symmetrical
In the case of an equilibrated joint, the maximum shear stress may be formulated asfollows:
BONDED JOINTSGeneral case - Without cleavage S 2.1.2
3/3
In practice, check that τM ≤ τaM and that τm ≤ τam
If τa is the allowable shear stress of the adhesive, the minimum length of the adhesivelybonded joint shall be equal to:
lm = Max ��
�
�
��
�
�
τ��
�
�
��
�
�
τλ
λ hxF;
x2xFArcthx2
mM ahxa
The failure load is equal to:
Fr = Min ���
����
�τ
λτ
��
���
� λ hxxl;hxx2
x2
lxthm
Ma
a
The latter relationship makes it possible to establish, for a bonded assembly, the conceptof optimum bonding length. Indeed, the function "th ( )" is asymptotically directed towards1 when "λ x l/2" increases; now, value 1 is practically reached for a value of "λ x l/2" equalto 2.7 (th (2.7) = 0.99).
Thus, we have:
λ x l = 2 x 2.7
hence:
l = c
c
c
c
GexexEx82.3
Gx2exexEx4.54.5 ==
λ
In practice, the following relationship shall be used:
2.2 . Elastic-plastic behavior of adhesive and elastic behavior of laminates
Case of an elastic-plastic behavior of adhesive (see drawing below).
As long as maximum stresses at joint ends (τM) have not reached the critical value τp
(plasticizing stress of adhesive), the bonded joint behaves like a flexible joint and stressevolution follows the rules defined in paragraph 1).
If the load increases, a plasticizing zone (with stress τp) is formed at the most highlyloaded end of the joint.
If loading is yet increased, the shear stress of the adhesive in this plasticizing zonereaches the critical value τr (failure stress of adhesive), which causes the adhesivelybonded joint failure.
The drawing below illustrates, from a quality standpoint, the shear stress evolution in theadhesively bonded joint as the bonding force increases.
Remark: There is no simple theory for the elastic-plastic behavior of a bonded joint. Afinite element model only would allow justification of the structural strength ofsuch a system in this case.
However, in the case of an equilibrated joint and assuming that the adhesive has anelastic-plastic behavior such as described in the drawing below, it is possible to determine(M.J. DAVIS, The development of an engineering standard for composite repairs, AGARDSMP 1994) the length of plasticized adhesive and, of course, the length of adhesive inelastic behavior.
In the case of such behavior, the shear stress diagram in the adhesive is the following:
Lp ≈ pxhx4
Fτ
Le ≈ c
c
Gx2exexE66 ≈
λ
If the joint is equilibrated, the plasticized length is given by the following relationship:
For the case of a bonded double lap joint, shear stress distribution in the adhesive film isgiven by the following formula (in replacement of relationship s2) :
τx = τm x λ x l x ���
����
�λβ−−λ��
�
����
�
λβ+
λβ− )xx(sinh)1()xx(cosh
)lx(sinh)lx(tanh1
where β = 1
11
22
exEexE1
−
���
����
�+
In the general case, the maximum shear stress at the joint ends is formulated as follows:
When the laminates to be bonded are too thick or when the loads to be transmitted aretoo high, the "stepping" or scarfing bonding technique is imperative.
The drawing below shows the general geometry of such a joint (the drawing shows athree-stepped joint (n = 3), a higher number may be considered).
The design method consists in determining, for each adhesively bonded joint portion, theload fraction crossing it, then, in considering each step "i" as elementary.
This so-called "short cut" method is a strictly manual method which gives the order ofmagnitude of average shear stresses per step. For greater accuracy, it is recommendedto use the computing software PSB2 (see § S4 and program PSB2 instructions).
Assumptions: Let's assume that transversal effects are insignificant (εy = 0 or Fy = 0). Let'salso assume that there is no secondary bending (off-centering from the neutral line shallnot be taken into account): joints below are considered as equivalent.
1st step: Determination of loads (F1i et F2i) passing through both laminates (parent material"1" and repair material "2") at the center of each step.
We shall assume that loads are distributed (at the center of each step) in proportion to therigidity of each material:
s11 F1i = F x iiii
ii
2211
11
exEexEexE
+F2i = F - F1i
We shall assume that the load evolution in material 1 (and consequently in material 2) islinear by portions. Which leads to the following configuration:
F
FF1i
F2i
E2i, e2i
E1i, e1i
F
F
F1i
F2i
F11
F21
F1n
F2n
x
F2i
F2i
F2n
F
F2x
Evolution of the load transferred in the repair material
The allowable average shear value of the adhesive being: τam = 0.8 hb.
Assuming that the joint is subjected to load F = 1000 daN and that there is no cleavageeffect.
{s1} τm = 50001000
50x1001000 = = 0.2 hb (2 MPa)
{s5} λ = 1.0x2x5000
400x2 = 0.9
{s4} τM = 0.2 x ��
���
�
250x9.0cothx
250x9.0 = 4.5 hb (45 MPa)
Check that the average stress τm is smaller than the allowable stress τam (0.8 hb; 8 MPa)and that the maximum stress τM is smaller than τaM (8 hb; 80 MPa).
The margin thus obtained is equal to 77 % (RF = 1.77 = 8/4.5). Within the framework ofthe previous example, let's calculate the optimum bonding length from which any increasebecomes useless over the decrease of maximum shear stress in the adhesive.
This result proves that, concerning the maximum shear stress, a change in the bondinglength from 50 mm to 5 mm increases (after calculations) this stress by only 1 %. The gainis thus insignificant.
Concerning the average stress, the minimum length is equal to:
lm = 100x8.0
1000 = 12.5 mm
The drawing below shows the evolution of the actual stress (smooth curve) and the valueof the average stress (dotted curve) in the example quoted.
Let the following three-stepped joint be defined by its geometry and mechanicalproperties:
The allowable average shear value of the adhesive being: τam = 0.8 hb (8 MPa).
The allowable maximum shear value of the adhesive being: τaM = 8 hb (80 MPa).
We shall assume that the joint is subjected to load F = 100 daN and that there is nocleavage effect.The first stage consists in calculating, at the center of each step, loads passing througheach material.Concerning the first step:
The drawing below represents the different loads ∆Fi transferred by each step.
The third stage consists in determining for each step the average and maximum stressesin the adhesively bonded joint, based on ∆Fi calculated previously.
steps 1 and 3 being equivalent for symmetry reasons, only the first two shall be justified.
The fourth stage consists in checking that average stresses are smaller than τam.
0.266 < 0.8 hb
Only a digital analysis (program PSB2) or a finite element analysis (program PSH14) shallbe able to determine with accuracy the shear stress evolution along each step.
It may thus be observed that the short cut method provides (in this example), with respectto the PSB2 method, a difference of:
+ 16 % for external steps- 20 % for the central step
Consequently, it is recommended to use as often as possible the software PSB2, itsanalytical model being "closer" to physical reality. The "short cut" method being mainly amanual method.
When a panel undergoes a damage (hole, delamination, etc.), two types of repair may beconsidered: a bolted repair (see chapter U) or a bonded repair.
Let the damaged (assuming that the damage is a hole) panel (monolithic skin) besubjected to stress fluxes Nx∝ , Ny∝ , Nxy∝ .
We shall assume that the repair is circular and of its stiffness close to that of the skin (noincrease of parent skin fluxes due to load transfer in a repair that is too stiff).
This is an extrapolation of the bonded joint method (see chapter S) and, therefore, it is notsuited for shear flux transfer. Thus, it is necessary to work within the principal coordinatesystem in which stress fluxes are Np∝ and Np'∝ to return to the case of a single joint. Thismethod is conservative.
1st step: Calculation of principal fluxes Np and Np' and of main angle β.
2nd step: For each calculation direction (p and p'), let's consider the repair as a 1 mm widematerial strip.
The drawing below shows that, based on a two-dimensional repair (R), two one-dimensional bonded stepped joints (Jp) and (Jp') are determined (or isolated). Each one ofthese elementary bonded joints must transfer a normal load Fp = 1 Np∝ and Fp' = 1 Np'∝ .
For the determination of flux transfers from the parent material to the repair material, referto the design method for bonded stepped joints (see chapter S) or to the computingsoftware PSB2.
4th step: It consists of a combination of previously determined shear stresses and normalfluxes.
- Average shear stresses in the adhesively bonded joint calculated for both directions pand p' are vertorially combined (although points are different) and the resulting stress foreach step is compared with the allowable average shear value of the adhesiveconsidered.
t4 ( ) ( ' )τ τ τm m ai i m
2 2+ ≤
- Maximum shear stresses in the adhesively bonded joint calculated for both directions pand p' are vectorially combined (although points are different) and the value found foreach step is compared with the allowable maximum shear value of the adhesiveconsidered.
- In a plain plate calculation (see chapter C), normal stress fluxes Nsi and N'si for theparent material are associated (although points are different).
This calculation shall be performed where fluxes are maximum (at the beginning of eachstep).
- In a plain plate calculation (see chapter C), normal stress fluxes Nri and N'ri for the repairmaterial are associated (although points are different).
This calculation shall be performed where fluxes are maximum (at the end of each step).
In the case of a highly loaded bonded repair or with complex loading, the use of finiteelement modeling is preferable.
The software PSH14 has been developed for this purpose. It allows automatic modeling ofa circular bonded repair (see drawing below). This model is subjected to membrane stressonly and does not take cleavage effects into account.
The adhesively bonded joint is represented by type 29 volume elements (with elastic-plastic behavior), the panel and repair by type 80 and 83 elements.
The plotted results represent:
- plane fluxes in the parent material,
- plane fluxes in the repair material,
- shear stresses in the adhesive.
For more information, refer to program instructions.
Let's assume (with a view to simplification) that both materials are nearly-isotropic (theirelasticity modulus being equal to 4417 daN/mm2 in all directions) for each step and thatsteps are 12 and 20 mm long.
The parent panel is only subjected to shear flux Nxy∝ = 4 daN/mm.
After running the software PSB2 (computation of a bonded stepped joint), the followingresults are found for direction p (results may be multiplied by - 1 for direction p'):
• The first check consists of a vectorial combination of average shear stresses for eachstep. In this case, average shear stresses are the same (to the nearest sign) in bothdirections p and p'.
The maximum value is equal to 0.207 daN/mm2 in each direction. We may deduce thevectorial resultant stress:
{t4}
( ) ( ' )τ τm m1 1
2 2 2+ = 0.207 = 0.293 daN/mm2
This value is to be compared to the allowable average shear value of the adhesivelybonded joint that is generally selected equal to 0.8 daN/mm2 (a 173 % margin isobtained).
• The second check consists of a vectorial combination of maximum shear stresses foreach step. In this case, shear stresses are the same (to the nearest sign) in bothdirections p and p'.
The maximum stress is reached at the beginning of the first step. The value reached isequal to 2.20 daN/mm2.
We may deduce the vectorial resultant stress :
{t5}
( ) ( ' )τ τM M1 1
2 2 2+ = 2.20 = 3.11 daN/mm2
This value is to be compared to the allowable maximum shear value of the adhesivelybonded joint: 8 daN/mm2 (a 157 % margin is obtained).
• The third check consists of a plain plate calculation of the parent material for each step(where the flux is maximum: at the beginning of the step).
At the beginning of the first step, the flux in direction p is Ns1 = 4 daN/mm and the flux indirection p' is N's1 = - 4 daN/mm, which corresponds to a shear flux Nxys1 equal to4 daN/mm in the reference coordinate system. At this location, the parent material ismade out of six fabrics (3 fabrics at 0°/90° + 3 fabrics at 45°/135°) G803/914 (supposednew).
A running of the program PSB3 (plain plate computation) makes it possible to find a Hill'scriterion margin equal to 966 %.
At the beginning of the second step, the flux in direction p is Ns2 = 1.512 daN/mm andthe flux in direction p' is N's2 = - 1.512 daN/mm, which corresponds to a shear flux Nxys2
equal to 1.512 daN/mm in the reference coordinate system. At this location, the parentmaterial is made out of two fabrics (1 fabric at 0°/90° + 1 fabric at 45°/135°) G803/914(supposed new).
A running of program PSB3 (smooth plate computation) makes it possible to find a Hill'scriterion margin equal to 843 %.
• The fourth check consists of a smooth plate calculation of the repair material for eachstep (where the flux is maximum: at the end of the step).
At the end of the first step, the flux in direction p is Nr1 = 2.472 daN/mm and the flux indirection p' is N'r1 = - 2.472 daN/mm, which corresponds to a shear flux Nxyr1 equal to2.472 daN/mm in the reference coordinate system. At this location, the repair material ismade out of four fabrics (2 fabrics at 0°/90° + 2 fabrics at 45°/135°) G803/914 (supposednew).
A running of the program PSB3 (plain plate computation) makes it possible to find a Hill'scriterion margin above 1000 %.
At the end of the second step, the flux in direction p is Nr2 = 4 daN/mm and the flux indirection p' is N'r2 = - 4 daN/mm, which corresponds to a shear flux Nxyr2 equal to4 daN/mm in the reference coordinate system. At this location, the repair material is madeout of eight fabrics (4 fabrics at 0°/90° + 4 fabrics at 45°/135°) G803/914 (supposed new).
A running of the program PSB3 (plain plate computation) makes it possible to find a Hill'scriterion margin above 1000 %.
In conclusion, the minimum safety margin is assessed at 157 % under maximum stress inthe adhesively bonded joint.
αxs: coefficient of expansion of panel in direction xαys: coefficient of expansion of panel in direction y
Exr: longitudinal elasticity modulus (direction x) of doublerEyr: transversal elasticity modulus (direction y) of doublerGxyr: shear modulus of doublerer: doubler thickness.αxr: coefficient of expansion of doubler in direction xαyr: coefficient of expansion of doubler in direction y
R sx : stiffness of panel with respect to flux Nx
R sy : stiffness of panel with respect to flux Ny
R sxy : stiffness of panel with respect to flux Nxy
R rx : stiffness of doubler with respect to flux Nx
R ry : stiffness of doubler with respect to flux Ny
R rxy : stiffness of doubler with respect to flux Nxy
η: correcting factor of panel shear stiffness
a and a*: fastener pitchni: number of rows of fasteners on a "unit strip"ri: stiffness of all fasteners on row "i"A: distance between the last load-carrying row of fasteners and the axis of symmetry ofthe repair
Fxi: overall load transferred by row of fasteners "i" in direction xFyi: overall load transferred by row of fasteners "i" in direction yfx/xij: load on fastener identified by rows "i" and "j" due to flux Nx
fy/yij: load on fastener identified by rows "i" and "j" due to flux Ny
fx/xyij: direction x load on fastener identified by rows "i" and "j" due to flux Nxy
fy/xyij: direction y load on fastener identified by rows "i" and "j" to flux Nxy
lxi: position of row of fasteners "i" with relation to the axis of symmetry of the repairlyj: position of row of fasteners "j" with relation to the axis of symmetry of the repair
Remark: Without an exponent, a notation looses its directional nature and thus becomesgeneral and applicable to x and y-axes.
BOLTED REPAIRSStiffness of a fastener in single shear U 2.1
2 . STIFFNESS OF FASTENERS
One of the most important parameters for the justification of a bolted repair is the stiffnessof fasteners which make it up. Their effect on load transfer is direct. The purpose of thissub-chapter is to make an analytical assessment of the stiffness of a fastener.Two cases are considered: single shear (the most common in our case) and doubleshear.
2.1 . Stiffness of a fastener in single shear
Let a fastener of diameter D and longitudinal elasticity modulus E bind two parts ofthickness er and es and of elasticity moduli Er and Es.
The stiffness of the fastener + parts system to be bound may be assessed by one of thethree relationships quoted below.
��
�
�
��
�
�++=
ssrr eE1
eE18.0
ED5
r1 → Mac Donnel Douglas
���
����
�++��
�
����
�+=
E83
E1
e2
E83
E1
e2
r1
ss
De85.0
rr
De85.0 sr
→ Boeing
12
1 1 12
12
2 3
re e
D E e E e e E e Es r
r r s s r s=
+�
��
�
�� + + +
�
��
�
��ξ
/
→ Huth
withξ = 2.2 → rivet on metal jointξ = 3 → screw on metal jointξ = 4.2 → carbon seal
BOLTED REPAIRSStiffness of a fastener in double shear - Assumptions U 2.2
31/2
In the software (Bolted Repairs), the stiffness of the fastener + parts system to be boundis calculated by the Huth method:
u1 ���
����
�+++��
�
����
� +=
Ee21
Ee21
eE1
eE1
D2ee2.4
r1
srssrr
3/2rs
2.2 . Stiffness of a fastener in double shear
For the case of a load-carrying fastener in double shear, let's assume:
rdouble shear ≈ 1.5 rsingle shear
3 . ASSUMPTIONS
Let's have the five following assumptions:
- a delamination type damage shall be considered as a hole if the load flux it issubjected to is a compression or shear flux. In tension, we shall consider that thepanel retains its initial stiffness,
- the panel is subjected to membrane stress. The bending effects cannot be taken intoaccount in this method,
- the panel and doubler have a constant thickness and all fasteners are similar,
BOLTED REPAIRSGeometrical data - Mechanical properties U 4
5
The justification method of such a repair shall first consist in calculating the three loadfluxes crossing the doubler (Nxr meca.
, Nyr meca. and Nxyr meca.
) then in assessing loads applied tothe repair fasteners, based on these results. The set of fluxes at each fastener may bedetermined on a unique basis.
Some geometrical and mechanical parameters of the structure shall be required forconducting this study.
4 . GEOMETRICAL CHARACTERISTICS
Below are represented the general geometrical characteristics describing the repair. Allother geometrical characteristics appearing further in the document may be formulatedaccording to these characteristics.
5 . MECHANICAL PROPERTIES
The mechanical properties required are the following:
For the panel: Longitudinal (direction x) and transversal (direction y) elasticity moduli,shear modulus and thickness: Exs; Eys; Gxys; es.
For the doubler: Longitudinal (direction x) and transversal (direction y) elasticity moduli,shear moduli and thickness: Exr; Eyr; Gxyr; er.
For fasteners: Number of load-carrying fasteners (n) and elementary stiffness in shear (r)of each fastener.
6 . ASSESSMENT OF MECHANICAL ORIGIN FLUXES IN THE DOUBLER
The assessment method of fluxes crossing the doubler (Nxr meca., Nyr meca.
and Nxyr meca.) is
identical for all three fluxes Nx∞
.meca , Ny∞
.meca and Nxy∞
.meca . It consists in calculating for eachone the equivalent stiffness of the panel (Rs) and the equivalent stiffness of the doubler(Rr) and in distributing the flux in proportion to those.
6.1 . Distribution of flux Nx
If Nx∞
.meca is the panel flux "far from the repair", the flux Nxr meca.crossing the doubler is equal
to:
u2 Nxr meca. = Nx x
sxr
xr
.meca RRR+
∞
with
u3 R rx
x r rx
rx
x r rx
rx
E e h n rL
E e hL
n r
r
r
=
+
4
4
and
u4 R sx =
E e hL
x s sx
sx
s without chamfer
R sx = Exs es
aL a
h aLs
xsx
sx
* *−
+−�
��
�
�� with chamfer
where 2 L rx is the distance between the centers of gravity of fasteners located on either
side of the damage (see shaded fasteners on drawing below). The number of columnstaken into account shall never exceed 3.
BOLTED REPAIRSFlux in panel - Loads per fastener due to Nx and Ny U 8
9
Fyr therm. =
( )2
4
∆θ α αys sy
yr ry
ry
r ry
yr
sy
s sy
ys
L L
Le h E
Le h E nr
−
+ +
We may thus deduce the thermal gross fluxes in the doubler:
Nxr therm. =
Fh
x
rx
r therm.
2
Nyr therm. =
F
hy
ry
r therm.
2
8 . ASSESSMENT OF FLUXES IN THE PANEL
Gross fluxes in the panel are deduced immediately form fluxes crossing the doubler:
u13 Nxs meca. = Nx
∞.meca - Nxr meca.
- Nxr therm.
Nys meca. = Ny
∞.meca - Nyr meca.
- Nyr therm.
Nxys meca. = Nxy
∞.meca - Nxyr meca.
9 . ASSESSMENT OF LOAD S PER FASTENER DUE TO THE TRANSFER OFNORMAL LOADS Nx AND Ny
Loads in fasteners are deduced from the geometry and from mechanical and thermalfluxes crossing the doubler and calculated previously.
A half repair may be represented as follows. The analysis being similar for directions xand y, indexes x and y have been removed to make the diagram as general as possible.
There are two possible cases (see drawings on next page):
BOLTED REPAIRSRepair with 1 row of fasteners U 9.1
9.1 . Repair with 1 row of fasteners
If the number of rows of fasteners is equal to 1, the load transmitted in the doubler isequal to loads transmitted by all fasteners on the row (single). The load per fastener isthen deduced immediately by the relationship:
BOLTED REPAIRSwith a number of rows of fasteners greater than 4 U 9.5
9.5 . Repair with a number of rows of fasteners greater than 4
We may easily find the previous equation system type for a number of rows of fastenersgreater than 4.
However, we shall consider that, for a number of rows of fasteners greater than 6, therows greater or equal to 7 have an insignificant effect on load Fr transfer distribution (seediagram below).
BOLTED REPAIRSAssessment of loads per fastener due to Nxy U 10
The fastener is identified by the letter "i" . "i" being the number of the row perpendicular tothe load. By definition, only full lines shall be considered and it shall be assumed that rownumber 1 is located next to the free edge of the doubler.
10 . ASSESSMENT OF LOADS PER FASTENER DUE TO THE TRANSFER OF SHEARLOADS Nxy
Loads in the fasteners are deduced from the geometry and from the mechanical originfluxes crossing the doubler.
Loads on fasteners due to the transfer of Nxyr meca. flux are equal to:
u17 fx/xyij = � =
n
1j
xy
jly
jlyxaxN.mecar
fy/xyij = � =
m
1i
xy
ilx
ilxx*axN.mecar
The fastener is identified by letters "i" and "j". "i" being the number of the row parallel tothe y-axis and "j" being the number of the row parallel to the x-axis. By definition, only fulllines shall be considered and it shall be assumed that row number 1 is located next to thefree edge of the doubler.
The repair justification consists of a notched and loaded plain plate calculation (for theparent skin and for the repair) and a check of the behavior of the existing damage.
The most highly loaded fastener holes (of the four angles) must be justified bysuperposing loads due to fluxes Nx meca.
(fx/x), Ny meca. (fy/y) and to flux Nxy meca.
(fx/xy and fy/xy).
This resulting load (f) must then be combined with fluxes N xs meca., Nys meca.
and Nxys meca. (for
the initial skin) or Nxr meca., Nyr meca.
and Nxyr meca. (for the repair) at the fastener considered.
On the other hand, the damage in the parent skin in the presence of fluxes Nxs meca., Nys meca.
and Nxys meca. at the repair center shall be justified.
General remark: It should be noted that there are two types of fastener arrangements: aso-called "square" arrangement and a so-called "staggered"arrangement. The "square" arrangement is preferred because the holecoefficient is limited.
Assessment of fluxes in the doubler and the panel below the doubler
This example does not include any thermal loads, we shall only cover mechanical fluxes.Therefore, notations shall not have any index.The first calculation step consists in determining both fluxes crossing the doubler (Nyr;Nxyr) which entails assessing panel and doubler stiffnesses with respect to both of theseload types, first of all. The fact that flux Nx∝ is zero has the following consequence Nxr =Nxs = 0.
Determination of doubler and panel stiffnesses
{u6}
mm/daN5138
42000x30
3645x56.1x4008
2000x3036x4
45x56.1x4008
Ryr =
+=
(30 is the total number of load-carrying fasteners in direction y).
{u7}
mm/daN986454
35x12.3x4878Rys ==
{u9}
mm/daN2518
82000x3256.1x2355
82000x32x56.1x2355
Rxyr =
+=
(32 is the total number of load-carrying fasteners in direction xy).
Repair with 3 rows of fasteners: if F1, F2 and F3 corresponds to loads transmitted by therows of fasteners, the system displacement resolution leads to the three followingequations:
+���
����
�++
2000x51
90x12.3x487818
90x56.1x400818F3
+���
����
�+
90x12.3x487818
90x56.1x400818F2
90x12.3x487818xF
90x12.3x487818
90x56.1x400818F1 =��
�
����
�+
+���
����
�+++��
�
����
� −2000x51
90x12.3x487818
90x56.1x400818F
2000x51F 23
90x12.3x487818xF
90x12.3x487818
90x56.1x400818F1 =��
�
����
�+
90x12.3x.487818xF
2000x51
90x12.3x487818
90x56.1x400818F
2000x51F 12 =��
�
����
�+++��
�
����
� −
by assuming F = 1, loads F1, F2 and F3 per row "i" of fasteners are deduced from thematrix resolution.
Assessment of effective load transferred by row "i = 1" of fastener
Fyi = - 4275 x 0.1366 = - 584 daN
{u16}
Assessment of effective loads transferred by each fastener of row "i = 1"
fyi = 5
584x15.1 − = 1.15 x - 116.8 = - 134 daN
Load due to Nxy
{u17}
Loads on fasteners due to transfer of Nxyr flux are equal to:
fx/xyij = 18365454.18x28.6
++− = - 56.56 daN
fy/xyij = 36
36x18x28.6− = - 113.13 daN
The resultant shall be equal to ( )( ) 5.022 13413.11356.56 ++ = 254 daN and the slopeangle of the load shall have the value Arctg (- 247.13/- 56.56) = 77° (- 180°) = - 103°.
Now, let's assume that the carbon reinforcing plate is replaced by an Aluminium plate ofthickness er = 0.84 mm (the thickness was selected so that the doubler stiffness mayremain constant: 0.84 x 7400 = 1.56 x 4008 = 6252 daN/mm) and of coefficient expansionαr = 2.2 E-5/°C.
The expansion factor of the parent skin (isotropic T300/314 laminate) is equal to: αs = 1.4E-6/°C (refer to chapter § V 4.2 for the calculation of equivalent coefficient of expansion ofa laminate).
We shall look for thermal loads for an absolute temperature of + 74° C, which correspondsto a relative temperature with respect to the ambient temperature of ∆T = + 54° C (with aview to simplicity, mechanical loads shall be considered as zero).
By applying the relationship {u12}, we find the thermal loads in the doubler in directions xand y.
{u12}
In direction x :
Fxr therm. =
2000x264
4878x53x12.336
7400x63x84.069.27
)69.27x5E2.236x6E4.1(54x2
++
−−−
Fxr therm. = - 314 daN
(26 is the total number of load-carrying fasteners in direction x)
In direction y :
Fyr therm. =
2000x304
4878x35x12.354
7400x45x84.036
)36x5E2.254x6E4.1(54x2
++
−−−
Fyr therm. = - 260 daN
(30 is the total number of load-carrying fasteners in direction y)
Which allows calculation of thermal loads on the most highly loaded fasteners (those inangles).
In direction x:
Repair with two rows of fasteners: if F1 and F2 correspond to loads transmitted by the rowsof fasteners, the system displacement resolution leads to the two following equations (seechapter § U 9.2) :
+���
����
�++
12.3x126x487818
2000x61
84.0x126x740018F2
12.3x126x487818xF
12.3x126x487818
84.0x126x740018F1 =��
�
����
�+
12.3x126x487818xF
2000x71
12.3x126x487818
84.0x126x740018F
2000x61F 12 =��
�
����
�+++��
�
����
� −
By assuming that F = 1, loads F1 and F2 per row "i" of fasteners are deduced from thematrix resolution:
Assessment of effective load transferred by row "i = 1" of fasteners
Fxi = - 1818 x 0.1271 = - 231 daN
{u16}
Assessment of effective loads transferred by each fastener of row "i = 1"
fxi = daN37)33(x15.17
231x15.1 −=−=−
In direction y:
For calculation in direction y, just use results for the transfer of mechanical origin fluxes(distribution on rows of fasteners being independent from the load value - see § U 13 p.5).
We know that:
mechanical loads:
Nyr meca. = - 10.96 daN/mm → fyi = - 134 daN
therefore:
thermal loads:
Nyr therm. = - 2.89 daN/mm → fyi = daN35
96.1089.2x134 −=
−−−
The resulting load on angle fasteners is equal to:
BARRAU - LAROZE, Design of composite material structures, 1987
GAY, Composite materials, 1991
VALLAT, Strength of materials
ESCANE - CIAVALDINI - TROPIS, Design of a bolted repair on a composite structure -determination of mechanical loads in the reinforcing piece, 1992, 440.192/92
∆T, ∆θ: relative temperature (difference between effective and ambient temperatures)Tather., θather.: athermane temperatureTamb., θamb.: ambient temperatureTstruc., θstruc.: structure temperature
A homogeneous anisotropic solid subjected to a uniform variation of temperature expandsdifferently in different directions. To characterize its behavior, several expansioncoefficients must be defined. In addition, strains and (or) stresses will appear dependingon the boundary conditions and the temperature range inside the solid.
A free composite plate subjected to a uniform variation in temperature will be subjected tostrains and stresses due to the different expansions of the fiber and the resin. Ascomposite plates are generally manufactured by curing at a temperature greater thanutilization θ, residual curing stresses appear in these plates. Although they can be high,they are generally not explicitly calculated but included implicitly into the calculation valuesdetermined on crosswise laminated plates (see § V 5.2).
As well, a variation in temperature applied to an assembly (attached or bonded) of plateswith different expansion coefficients leads to stresses and strains in these plates whichare added to those induced by mechanical loading.
The aim of this chapter is to study the stresses and strains of thermal origin forunidirectional fibers, composite plates, bimetallic strips and, lastly, aircraft structures,submitted to regulation environmental conditions.
If a material is submitted to a mechanical load, the stress - strain relation can be written inits tensorial form:
v1 εij = ηijkl x σkl
ou cf. § V 5σij = λ ijkl x εkl
If a homogeneous, elastic and anisotropic solid which is free to deform is submitted to achange in temperature, the strain - temperature relation can be written in its tensorialform:
v2 εij = αij (T - To)
where
To: original temperature (uniform)T: modified temperature (uniform)
αij is the thermal expansion tensor which is a characteristic of the material.αij is symmetrical.For an orthotropic material in the orthotropy reference frame.
(α) =
α
α
α
l
ll
lll
o o
o o
o o
�
�
�����
�
�
�����
If the material is submitted to a mechanical load, the stress - strain - temperature relationcan be written:
T: absolute temperature appliedTo: reference temperature∆T: relative temperature
4 . BEHAVIOR OF UNIDIRECTIONAL FIBER
Let us take a unidirectional fiber defined by its longitudinal direction (l) and by itstransverse direction (t), it is a transverse isotropic and orthotropic material.
The unidirectional fiber will be characterized by two expansion coefficients in theorthotropic axis:
THERMAL CALCULATIONSBehavior of a monolith plate V 5.1
1/3
The expansion coefficients are different in the two directions l and t:
αl: longitudinal expansion coefficient of unidirectional fiber in x-axis.αt: transverse expansion coefficient of unidirectional fiber (resin) in y- and z-axes.
Generally αl << αt (α) =
α
α
α
l
t
t
o o
o o
o o
�
�
�����
�
�
�����
5 . BEHAVIOR OF A FREE MONOLITHIC PLATE
5.1 . Calculation methodAs we saw in chapter E 3, the general relation between the strain sensor and the loadsensor of a monolith plate can be written in its matrix form (relation to be compared withthe relation v1):
THERMAL CALCULATIONSBehavior of a monolith plate V 5.1
2/3
If the plate is submitted to a relative uniform temperature ∆T = (T - To), the previousexpression becomes (relation which is to be compared with relation v3):
v4
N
N
N
M
M
M
x
y
xy
x
y
xy
=
A B
B C
ε
ε
γ
∂∂
∂∂∂∂ ∂
x
y
xy
o
o
o
wxwyw
x y
2
2
2
2
2
2
- ∆t
α
α
α
α
α
α
Eh
Eh
Eh
Eh
Eh
Eh
x
y
xy
x
y
xy
2
2
2
where the thermoelastic behavior of the laminate is described by vector (αEh) which termsare equal to:
THERMAL CALCULATIONSBehavior of a monolith plate V 5.1
3/3
αα ν α ν α α
ν νEh
z z s E c Ey
k k l l tl t t lt l t
lt tlk
n22
12 2 2
1 2 1= −
− + + +−
�
���
�
���
−
=�( ) ( )
αν α α α ν α
ν νEh
z z c s E c s Exy
k t lt l t l l tl t
lt tlk
n k22 2
11
2 1= −
− + + − +−
�
�
��
�
�
��
−
=�( ) ( )
where:
c ≡ cos(θ) where θ is the orientation of the fiber in the basic reference frame (o, x, y)s ≡ sin(θ) where θ is the orientation of the fiber in the basic reference frame (o, x, y)
El: longitudinal modulus of elasticity of the unidirectional fiber
Et: transverse modulus of elasticity of the unidirectional fiber
νlt: longitudinal/transverse Poisson coefficient of the unidirectional fiber
νtl = νlt EE
t
l: transverse/longitudinal Poisson coefficient of the unidirectional fiber
THERMAL CALCULATIONSCuring stresses - expansion coefficients V 5.2
5.3
5.2 . Residual curing stresses
For thermosetting resin composites, the plates are made by juxtaposing different layerswith different characteristics.
These layers are manufactured simultaneously to the plate. We assume that when theresin cures, each layer is frozen in the state it is in at that time. Let Tp be the curingtemperature; the stresses in the plate can be considered as zero at this temperature.
To obtain the stresses at ambient temperature after cooling, apply relation v4.
If the plate does not have mirror symmetry, the coupling terms, (B) and αEh2 of v4 arenon zero; therefore, a uniform reduction in the temperature (from curing temperature toambient temperature) will create a strain in the plane and a curvature of the neutral plane.
In the same way, if there is in-plane coupling (terms A16, A26 non zero), that is if plies arenot equal in + or - α, angular distortion will occur during cooling after curing, the plate willbe "parallelogram" shaped.
5.3 . Equivalent expansion coefficients
The equivalent expansion coefficient vector αequi. (αx equi., αy equi., αxy equi.) of an orthotropiccomposite plate, with mirror symmetry without in-plane coupling, can be determined bythe following relation:
v6 (αequi.) = (A)- 1 x (αEh)
where terms Aij of the laminate rigidity matrix (A) can be determined by relation c6 ofchapter C.3.
6 . BEHAVIOR OF A SYSTEM CONSISTING OF TWO BEAMS WITH DIFFERENTEXPANSION COEFFICIENTS - BIMETALLIC STRIP THEORY
6.1 . Determining stresses of thermal origin
The aim of this subchapter is to study the mechanical influence of the temperature on asystem consisting of two beam elements with an infinitely rigid connection at their ends.
The following analysis is unidirectional. Furthermore, we shall neglect the secondarybending effects and the Poisson effects.
Let us take, therefore, two long plates (L >> b) with an infinitely rigid connection at theirends and with the following mechanical characteristics:
Initially, let us assume that the two plates are free at their ends. If we submit each one ofthem to a uniform relative temperature ∆T (in relation to the ambient temperature of thesetup), they will expand by the following lengths:
∆L1 = ∆T α1 L
where α1 ≠ α2
∆L2 = ∆T α2 L
Now, as these two plates are rigidly attached at their ends, they will deform by the samelength. Mechanical interaction forces of thermal origin (F1 and F2) are created:
Remark: For two plates with totally different geometries attached at the ends by anelement (one or several fasteners for example) of global rigidity ℜ , the previousrelation is slightly modified.
In practice, the link between two parts is ensured either by fasteners or by bonding.
6.2.1 . Bolted or riveted joints
We shall assume that the plates are sufficiently long so that the thermal expansion cannotbe absorbed by the play (and the rigidity) of the fasteners (see previous remark).
The thermal force, which will have been calculated previously by relation v4, will beexpressed herein by letter F.
Several hypotheses can be put forward concerning the number of fasteners (of rigidity r)likely to take force F.
6.2.1.1 . Force F taken by one fastener
f = F
For information purpose, the table on the next page shows the various forces applied tothe structural elements for a splice and a doubler, these being submitted to tensile orcompression loads and at a positive or negative relative temperature.
We will consider that the expansion coefficient of the upper material (aluminium forinstance) is higher than that of the lower material (isotropic carbon laminate for instance).
It is important to point out that the forces represented on the drawings are those applied tothe structure by the fasteners.
SPLICE DOUBLER
TEN
SIO
NC
OM
PRES
SIO
N ∆∆ ∆∆
T >
0
upper α > lower α upper α > lower α
∆∆ ∆∆T
< 0
upper α > lower α upper α > lower α
0° 0°
0° 0°
Table V6.2.1.1: Transfer of mechanical and thermal forces to the splices and doublers
Remark: Relations v10 to v14 have been established analytically. It is howeverrecommended for a large number of fasteners to solve the problem by a matrixcalculation or a finite element model.
For a bonded link, the (antisymmetrical) loading of the two plates is continuous from oneend of the system to the other; the main part of the loading is however at the start of thebonded link.
The maximum shear stress at the interface of the two plates can be written as follows:
where Gc is the shear modulus of the adhesive and ec its thickness.
This relation has been established by analogy with the bonded joint theory (see chapter S)where the distribution of the shear stresses in the adhesive joint is of the symmetrical typeand where the value of this stress, although negligible, is not zero in the center.
Symmetrical distribution of shear stresses: Bonded splice
Antisymmetrical distribution of shear stresses: Bonded doubler
THERMAL CALCULATIONSInfluence of temperature V 7.1
7.27.2.1
7 . INFLUENCE OF TEMPERATURE ON AIRCRAFT STRUCTURES
7.1 . General
The influence of the temperature on the aircraft structures is twofold:
- thermal stresses induced by the different expansion coefficients per unit length of thecomponents of the composite and metallic structures (spars/skins/rib, etc.) and alsobetween the fibers and the resin,
- reduction of the mechanical properties especially the resin and the adhesives (certainfibers are also sensitive to the temperature).
The demonstration of the resistance to the ultimate loads must be made in the mostpenalizing association case of the ultimate temperatures of the structure combined withselected design-critical mechanical loads.
We shall first of all define the various types of temperatures involved in the proceduredescribed in this chapter.
7.2 . Temperature of ambient air
7.2.1 . Temperature envelope
The static air temperature envelope to be considered on the ground and in flight are givenfor each aircraft (DBD: Data Basis Design); they depend on changes in regulatoryrequirements and aircraft operational limits.
For example, the maximum temperature to be considered on the ground was increased by10° C between the A320 (45°) and the A340 (55°). The minimum temperature on theground is - 54° C (see curves below).
THERMAL CALCULATIONSInfluence of temperature V 7.2.2
7.2.2.1
We must therefore determine the ultimate temperatures of the structure for all aircraftflight phases (static and fatigue). This is dealt with in this subchapter.
7.2.2 . Variation of ambient air temperature
7.2.2.1 . Ambient temperature on ground
The ambient temperature on the ground changes during the day. We will assume that itsvariation is homothetic to the quantity of heat Qϕ received by the ground (see chapter §V 7.3.1.2).
It therefore depends on the time of the day and the geographical location on earth(latitude ζ/type of atmosphere).
The table and curves below show change of ambient temperature on ground for a tropicalatmosphere (55° C at 12 h ≡ ISA + 40° C) and for a polar atmosphere (regulatory lowerlimit of - 54° C).
THERMAL CALCULATIONSInfluence of temperature V 7.2.2.2
We consider however that heat builds up during the day which explains why the "night"temperature (32° C for the tropical atmosphere) starts at 20 h and not at 18 h.
Time 6 h 7 h 8 h 9 h 10 h 11 h 12 h 13 hTamb. (° C) 32 38 43.5 48.3 51.9 54.2 55 54.5
Time 13 h 14 h 15 h 16 h 17 h 18 h 19 h 20 hTamb. (° C) 54.5 52.9 50.5 47.3 43.6 39.7 35.7 32
7.2.2.2 . Ambient temperature in flight
The ambient temperature in flight depends on the ambient temperature on the ground(see previous chapter) and the altitude z. From 0 to 40000 fts (troposphere), we generallyconsider that the temperature decreases on average 0.5° C for every 328 fts increase inaltitude with a lower limit of - 54° C.
The diagram below gives the ambient temperature at a given altitude for all ambienttemperatures on the ground.
Tamb. z ≈ - 2 E-3 x z + Tamb. gnd where ∀ z Tamb. z ≥ - 54° C
The combined effects of the solar radiation in flight (optional effect) and the speed of theaircraft (Mach number M) lead to a significant increase in the wall temperatures whencompared with the temperature of the ambient air in flight.
THERMAL CALCULATIONSInfluence of solar radiation V 7.3.1.1
7.3.1.21/3
7.3.1 . Influence of solar radiation
7.3.1.1 . Maximum solar radiation
It is maximum outside the atmosphere (z ≥ 36000 fts) and is equal to 1360 w/m2. Thisradiation is lower on earth due to the influence of the ozone layer, humidity and otherfactors.
At sea level (z = 0) and at 12-o-clock, Qs ≈ 1010 w/m2 in tropical areas.
Between these two points, we assume that Qs varies in a linear manner as a function ofthe altitude: Qsz ≈ 9.72 E-3 x z + 1010 (see curve below).
Remark: These values are unchanged between ISA + 35° C and ISA + 40° C.
7.3.1.2 . Solar radiation during the day
The quantity of heat Qϕ received by the ground depends on the quantity of heat Qsemitted by the sun and passing through the atmosphere (Qs = 1010 w/m2) and the angleof incidence ϕ between the light rays and the ground.
THERMAL CALCULATIONSInfluence of solar radiation V 7.3.1.2
2/3
This angle of incidence ϕ itself depends on time t (represented by angle ω on the drawing)and on the latitude ζ of the point under study.
ϕ = Arc (cos ζ x cos ω) = Arc (cos ζ x cos (15 t - 180)) for 18 h ≤ t ≤ 6 h
In tropical atmosphere (ζ ≈ 0°), this expression is simplified and becomes:
ϕ = Arc (cos 0° x cos ω) = 15 t - 180 for 18 h ≤ t ≤ 6 h
The diagram below shows, between 6 h and 18 h the "theoretical" change in the quantityof heat Qϕ that the ground receives for different types of atmospheres.
THERMAL CALCULATIONSInfluence of solar radiation V 7.3.1.2
3/3
Nevertheless, we will assume that during the night (from 18 h to 6 h), a certain quantity ofheat (≈ 280 W/m2 for a tropical atmosphere) is exchanged between the outside mediumand the structure ("night irradiation").
The table and curve below show the "regulatory" change in the quantity of heat Qϕ duringthe day in tropical atmosphere and at sea level.
The curve Qϕ = Qs x cosϕ has therefore been (arbitrarily) offset at 280 w/m2 for 6 h and18 h.
THERMAL CALCULATIONSInfluence of speed - Temperature of structure V 7.3.2
7.3.3
7.3.2 . Influence of aircraft speed
The effect of the speed of the aircraft (friction of the air) increases the ambienttemperature in flight to a level called the athermane temperature.
The athermane temperature (or friction temperature) is the temperature at which thethermal flow exchange between the wall of the structure and the outside medium is zero.
To find the athermane temperature at structure stagnation point, the ambient temperatureat an altitude z must be multiplied by a coefficient which depends on the speed of theaircraft:
Tath. z = Tam. z x 1 1 2+−�
��
�
��
γγ
Mach
where γ = CpCv
= 1.4 γ: ratio between molar heat capacities (perfect gas constant).
where Cp and Cv are the heat capacities of the gas (in this case, of the air at the altitudeconcerned) at constant pressure and volume.
7.3.3 . Temperature of the structure
In the previous subchapters, we defined the various temperatures outside the structure(ambient temperature on ground, ambient temperature in flight, wall temperature andathermane temperature).
The aim of the next chapter is to determine the temperature of the various structuralelements.
The temperature of each structural element depends on:
- the change of the athermane temperature which itself depends on the time, thealtitude, the speed of the aircraft and the type of atmosphere,
- the solar radiation at the altitude in question (generally not taken into account),
- the geometrical and thermal characteristics of the various elements comprising thestructure,
- the color of the exterior paint.
The calculation method consists in breaking down the structure into elements assumed tobe at a uniform temperature at time t and in writing the thermal equilibrium of each ofthese elements assuming that at time t = 0 all the structure has a uniform temperatureequal to the temperature of the ambient air.
A finite difference calculation enables the problem to be solved including in transientphase.The quantity of heat required to vary the temperature of each element by ∆T in the timeinterval ∆t is:
C x V x ∆T = Qa + Qc + Qi + (Qϕ - Qr)
where:
C = heat capacity of the materialV = volume of the elementQc = quantity of heat exchanged with the boundary layer by convectionQa = quantity of heat exchanged by conduction with adjacent elementsQi = quantity of heat exchanged with the inside medium (kerosene)Qϕ = quantity of heat received by solar radiationQr = quantity of heat lost by radiation
THERMAL CALCULATIONSCalculation method - Thermal characteristics V 7.3.3.1
7.3.3.22/2
For "tank" structures, three kerosene levels can be studied:
- all internal elements are in contact with the kerosene,- only the lower surface elements and a section of the spars are in contact with the
kerosene,- only the upper surface elements are not in contact with the kerosene.
This method enables us to find at time t the temperature of each element and therefore todeduce the forces and thermal stresses required for the fatigue and static justification.
Remark: The effects of the radiation of a section of the structure to another section neednot be taken into account in the calculations as this effect tends to make thetemperatures uniform.
7.3.3.2 . Thermal characteristics of the materials
THERMAL CALCULATIONSTemperatures of structure on ground V 7.3.3.3
- Paints
To calculate the temperatures on the ground (or optionally in flight), the absorptivity andemissivity coefficients of the paint must be defined.
The emissivity coefficient ε is generally taken as equal to 0.85 or 0.9.
The absoptivity coefficient α is related to the color of the paint.
Color white lightgray
lightyellow
darkgray
navyblue
α 0.2 0.5 0.5 0.65 0.8
7.3.3.3 . Temperatures of structure on ground
The first step consists in determining, with software PST2, change in the temperature ofthe structure on the ground during the day in order to evaluate the most critical initial flightconditions.
The study is generally conducted over a complete day from 0 h to 24 h but can beextended over two or three days in order to minimize the influence of the initil conditions(ambient temperature at 0 h: 32° C at ISA + 40° C).
Several sections of the structure with different thermal and geometrical characteristics willbe modeled.
As the absoptivity coefficient corresponds to the color of the paint used and the groundambient temperature and insolation curves, we calculate the maximum temperature onthe ground for each structural item during a day (see drawing below).
THERMAL CALCULATIONSTemperatures of structure in flight V 7.3.3.4
1/3
7.3.3.4 . Temperatures of structure in flight
As we saw previously, software PST2 enables us to define the changes in thetemperatures of the structural elements on the ground. We shall apply the same methodto find the changes of these elements in flight.
For this, we must define the aircraft operating scenarios. These scenarios depend on:
- typical aircraft mission (change of speed M and altitude z versus time),
- distribution of the missions during the day (generally not taken into account for thestatic justification),
- type of atmosphere,
- initial conditions defined previously (see chapter V 7.3.3.3).
- Typical mission
Several flight configurations or "missions" can be taken into account depending on theway in which the aircraft is used.
THERMAL CALCULATIONSTemperatures of structure in flight V 7.3.3.4
2/3
Generally, a typical "mission" can be described as follows (A300-600):
- Daily use of the aircraft
A mean "typical" use is determined. For instance: for the A340, five 75' flights have beenconsidered distributed over 1 day as shown below:
Remark: For the static justification, we will not take into account the influence of theprevious flight on the initial conditions of the mission under study. Each flight willbe considered as isolated during the day. We shall therefore choose the mostpenalizing time for the start of the mission (generally 12 h for positivetemperatures).
THERMAL CALCULATIONSTemperatures of structure in flight V 7.3.3.4
3/3
- Definitions of atmospheres
Three types of atmospheres are to be considered in the analyses:
- standard,
- tropical,
- polar.
Remark: For the fatigue analysis, it is sometimes necessary (if we do not want to be tooconservative) to use a random distribution of the type of atmosphereencountered during one year in service. The "standard" operating time can forinstance be broken down as follows:
- ¼ of operation in polar atmosphere,
- ¼ of operation in standard atmosphere,
- ½ of operation in tropical atmosphere.
For the static justification, we shall choose the most penalizing atmosphere (tropical orpolar).
For complex structures, there are three software programs to determine, on the one hand,the temperature ranges in the various structural elements and, on the other hand, theresulting thermal stresses and strains.
Software PST2:
It is used to determine the map of the temperatures of the structure over time versuschanges in external conditions and the speed of the aircraft (during a mission forexample).It is assumed that the temperature of the walls is equal to the athermane temperature, thatis the ambient temperature multiplied by the following factor: ��
�
����
�
γ−γ− 2Machx11 .
Knowledge of the thermal conductivity characteristics of the various materials (and thefluids contained in the structure: air, kerosene, etc.) is required together with the heattransfer coefficients between the various elements in order to evaluate the temperaturemap of the structure and its changes.
Remark: We can, for simplification reasons, consider that the complete structure has auniform temperature equal to the outside temperature or to the athermanetemperature.
Once the temperature range within the part has been determined, we must evaluate thestresses and strains of thermal origin. For this, in addition to the "manual" methodpreviously described (§ V 6), this can be done by two computing software programs.
Software PST1:
It is used to determine for a long structure of the dissimilar beam type (several differentmetals) submitted to any temperature field (uniform or not) the stresses of thermal originand the resulting longitudinal strains (x-direction).
The part will be described by its current section which will be broken down into elementaryparts defined by their positions (center of gravity) and their geometrical and mechanicalcharacteristics (cross-section, inertia, modulus of elasticity, expansion coefficient, etc.).
Software PST4:
This calculation sequence is used to determine the thermoelastic stresses of a structureschematized by finite elements for any temperature range (a temperature is associatedwith each node of the structure).
If there are no loads of mechanical origin, what are the forces on the fasteners and theflows at the center of the doubler and the panel if the panel and its repair are heated to anabsolute temperature of 70° C (∆T = 50° C) ?The fasteners subjected to the highest loads are the ones located in the corners of therepair. We shall therefore study fastener A.
As the thermal load (relevant to a strip of material of width b = 15 mm that we will consideras a bimetallic strip) is (in first approximation) independent of the length (relation v7), thecomponents in the x- and y-directions are equal.
We can therefore deduce the global shear stress at point A:
τMax. = hb54.975.675.6 22 =+
This value is to be compared with the permissible value for the adhesive which generallyis equal to 8 hb. If the plastic adaptation of the adhesive is not taken into account, therepair will unstick.
The terms Aij of the rigidity matrix of the laminate (in daN/mm) were calculated in chapterE 4:
A11 = 2779 x 2 = 5558A12 = 821 x 2 = 1642A13 = 0A21 = 821 x 2 = 1642A22 = 2779 x 2 = 5558A23 = A31 = A32 = 0A33 = 978 x 2 = 1956
As external loads are zero, the relation v1 can be written as follows:
{v4}
5558 1642 0
1642 5558 0
0 0 1956
ε
ε
γ
x
y
xy
= -160
0
3E232.6
3E232.6
−
−
We can deduce the thermal expansions (in mm/mm) of the laminate in the referenceframe (x, y):
ε
ε
γ
x
y
xy
=
0
5E85.13
5E85.13
−−
−−
The results above are the apparent thermal expansions of the plate in the reference frame(x, y) and the expansions of the fiber at 0° in its own reference frame (l, t):
To determine the internal stresses applied to the fiber at 0°, we must find what theexpansions of this fiber would be if it was isolated and free from all strains:
The thermoelastic coefficients of the unidirectional fiber at 0° in its reference frame (l, t)are equal to:
Under the influence of a ∆T = - 160° C, the thermal expansions (in mm/mm) of an isolatedfiber would satisfy the following relation:
45.6000
071.6019.21
019.211697
ε
ε
γ
l
t
lt
= -160
0
3E407.2
4E487.8
−
−
We therefore obtain:
ε
ε
γ
l
t
lt
=
0
3E4.6
5E16
−−
−
It is important to specify that in this case, the fiber is submitted to no internal thermalstresses as free from all strains.
By simply calculating the difference, we find the "expansions" (in mm/mm) of the fiber at0° if it was submitted to the stresses of thermal origin alone:
ε'fiber thermal stresses 0° = εthermal of plate - εthermal of 0° fiber alone
These three types of expansions must be determined in the same reference frame. Forthe fiber at 0°, no change of reference frame is required. If we had wanted to study forinstance the internal stresses in the fiber at 45°, we would have had to determine theexpansions of the plate in a frame oriented at 45° in relation to the reference frame(relation c7).
We therefore obtain the expansions (in mm/mm) of the fiber at 0° due only to the thermalstresses which are applied to it:
We can determine, by relation c8, the stresses (in hb) of thermal origin applied to the fiberat 0° (and therefore to all fibers as all directions are equivalent):
{c8}
σ
σ
τ
'
'
'
l
t
lt
=
13057 163 0
163 467 0
0 0 465
0
3E259.6
5E85.29
−
−−
=
0
88.2
88.2−
In fact, these stresses are not to be taken into account in the justification of the laminateas they are indirectly taken into account when determining the permissible values for theunidirectional fiber of the material.
It is also possible, by relation v6, to determine the equivalent membrane expansioncoefficients of the laminate (in mm/mm/° C):
Calculation of the temperatures associated with a typical A340 mission on a section of anA340 aileron at bearing 1 (see note 440.092/92).
In agreement with ACJ 25.603, we must, for the structural justification, associate the mostpenalizing environmental conditions (temperature and humidity) with the calculationcases. Here, we shall deal only with the temperature case. The atmosphere chosen willbe tropical.
The Loop 1A calculation cases corresponding to the various aircraft configurations isgiven in the table below:
We shall choose to study case Vc/Vd for an altitude z ≈ 29500 fts (cases 13, 14, 15, 18,and 19) the typical mission of which can be represented by the following diagram (time,speed, altitude):
First step: Consists in determining, from the meteorological data, the change in ambienttemperature on the ground for a tropical atmosphere. This temperature depends on thequantity of heat due to the solar radiation Qϕ.
By considering the change in the angle of incidence of the rays during the day, we find avariation of Qϕ versus the angle of incidence ϕ and therefore versus the time (Qϕ beingtaken as equal to 280 between 18 h and 6 h)
t 6 h 6 h 45 7 h 7 h 20 8 h 9 h 10 h 10 h 20 11 h 11 h 30 12 h
Second step: We will deduce the maximum ambient temperatures on the ground (z = 0)throughout the day (ISA + 40° C) which corresponds to a maximum temperature at 55° Cat midday in a tropical atmosphere (the non-symmetry of the curve in relation to 12 h isexplained by taking into account the buildup of heat during the day):
t 6 h 6 h 45 7 h 7 h 20 8 h 9 h 10 h 10 h 20 11 h 11 h 30 12 h
Third step: Consists in evaluating the temperature on the ground of the various structuralitems during a day in order to determine the most penalizing departure time. Thiscalculation was done with software PST2 over three days so as to eliminate the effects ofthe initial conditions.
The calculation method consists in dividing the structure into elementary sections (uppersurface panel, lower surface panel, spar, leading edge, fittings) which initially have auniform temperature (temperature of the ambient air) and in determining their changesbefore takeoff according to the three following phenomena:
- conduction with adjacent elements,- convection with surrounding media (turbulences, kerosene),- solar radiation (α = 0.5; ε = 0.85)
By integrating all these data, we obtain the curve below which represents, over a period of24 hours, the change in the temperature of the various structural elements.
We find (as was predictable) that the most unfavorable time for high temperatures is 12 h.We will therefore consider that the aircraft's mission starts at this time.
Fourth step: consists, again with software PST2, in determining the change in temperatureof each part during the mission itself by putting forward the (conservative) hypothesis thatthe ambient temperature on the ground is constant and equal to 55° C throughout themission (ISA + 40° C) and by taking as initial values for the structural elements thepreviously defined temperatures at 12 o'clock.
The curves below represent the change in temperature of each element of the part duringthe mission considered.
We can see that all the temperatures of the structural elements tend asymptotically to theathermane temperature (skin temperature) which depends on:
- the ambient temperature on the ground (considered as being independent of time): 55° C,- the speed of the aircraft expressed in Mach number: M,- the altitude z.
Tather. ≈ Tamb. x (- 1.88 E-3 x z + 55) x (1 + 0.18 M2)
Fifth step: Consists in combining throughout the mission, the loads of mechanical origin(aerodynamic) and the loads of thermal origin. This analysis (not covered by this chapter)gave two design-critical cases (see previous curve):
- point �: VCM = 0.86t = 3426 s
- point �: VDM = 0.92t = 3510 s
Remark: We could have also conducted a study on the negative temperature range werelower limit imposed by regulations is - 54° C.
We however observed that the effect of the speed of the aircraft on theathermane temperature (1 + 0.18 M2) implied high temperatures in flight. Wetherefore limited the justification to - 54° C.
Definitions of the main characteristics of honeycomb
Ec (daN/mm2) Compressive modulus direction T
Rc (hb) Compressive strength direction T
Gl (daN/mm2) Shearing modulus direction L
Gw (daN/mm2) Shearing modulus direction W
sl (hb) Shear strength direction L
sw (hb) Shear strength direction w
* Preliminary values are obtained from testing one or two blocks of honeycomb type and often only oneor two specimens for each point or condition tested.
** Predicted values indicate that no mechanical tests have been performed.