Mechanical Testing of Composites and their Constituents Tests done to determine intrinsic material properties such as modulus and strength for use in design.

Mechanical Testing of Composites and their Constituents

• Tests done to determine intrinsic material properties such as modulus and strength for use in design and analysis (major emphasis here)

• Tests done to determine quality or acceptability of specific components during manufacturing (minor emphasis here)

American Society for Testing and Materials (ASTM) Standards

• Test standards for polymer matrix and metal matrix composites - ASTM Vol. 15.03 Space Simulation; Aerospace and Aircraft; Composite Materials

• Test standards for ceramic matrix composites – ASTM Vol. 15.01 – Refractories; Activated Carbon; Advanced Ceramics

HI-NICALONTM Type SCERAMIC FIBER

Direct measurement of fiber longitudinal properties Ef1 and Sf1

(+)

Different ways of mounting fiber specimens on backing strip. (From ASTM Standard C 1557-03R08. Copyright ASTM International. With permission.)

Different failure modes for resin-impregnated strand test specimens. (From ASTM Standard D4018-99(2008). Copyright ASTM International. Reprinted with permission.)

P = load

Δ = deflection

P

Δ

Diametral compression of fiber for measurement of fiber transverse Young’s modulus. (From Kawabata, S. 1989. In Vinson, J.R. ed., Proceedings of the 4th Japan–U.S. Conference on Composite Materials, pp. 253–262. CRC Press, Boca Raton, FL. With permission.)

Indirect measurement of fiber transverse modulus Ef2

Experimental data

Prediction

Tensile measurement of neat resin properties Em and Sm1

(+)

ASTM D638-10 Type I, II, III, IV and V neat resin tensile specimen geometries. (From ASTM Standard D638-10. Copyright ASTM International. Reprinted with permission).

ASTM 618-05 Conditioning Plastics and Electrical Insulating Materials for Testing

Standard Laboratory Atmosphere:

Temperature of 23C (73.4F) and relative humidity of 50%

Specimen for measurement of neat resin compressive properties Em and Sm1

(-)

Neat resin compressive test specimen. (From ASTM Standard D695-10. Copyright ASTM International. Reprinted with permission.)

Neat resin compression specimen support jig

Support jig for D695-10 compressive test specimen. (From ASTM Standard D695-02a. Copyright ASTM International. Reprinted with permission.)

Compression test fixture for neat resin specimen

Compression fixture with ball-and-socket joint to minimize bending. (From ASTM Standard D695-10. Copyright ASTM International. Reprinted with permission.)

Three-point bending specimen for flexural properties of neat resin or composite. (From ASTM Standard D790-10. Copyright ASTM International. Reprinted with permission.)

M

Bending moment diagram

Constituent Volume Fraction Measurement

• Removal of resin matrix from composite sample by either chemical digestion with acids or other chemicals (carbon fiber composites), or resin burn-off in a furnace (glass fiber composites) according to ASTM Standard D3171-09

• Computer-aided image analysis of digital photomicrographs to determine fiber area fractions of polished composite specimens

Composite tensile specimen for measurement of longitudinal properties E1 and SL

(+)

Width

Overall Length

Tab Length

Specimen Thickness

Tab Thickness

Tab Bevel Angle

Specimen geometry for ASTM D3039/D3039M-08 standard tensile test. (Dimensions from ASTM D3039/D3039M-08. Copyright ASTM International. Reprinted with permission.)

Typical stress-strain curves from D3039 specimen

Longitudinal and transverse strain data at different stresses for [0]8 graphite/epoxy tensile specimen. (From Carlsson, L.A. and Pipes, R.B. 1989. Experimental Characterization of Advanced Composite Materials. Prentice-Hall, Inc., Englewood Cliffs, NJ. Reprinted by permission of Prentice-Hall, Englewood Cliffs, NJ.)

End constraints can cause bending of off-axis tensile specimens due to shear coupling

Effect of end conditions on deformation of an off-axis tensile specimen exhibiting shear coupling. (From Pagano, N.J. and Halpin, J.C 1968. Journal of Composite Materials, 2, 18–31. With permission.)

Importance of specimen length-to-width ratio

xxEx

xyy

0

xQx

xyy

11

0

!!!!!11

QxE

xE

0

20

40

60

80

100

120

140

0 20 40 60 80 100

"App

aren

t" M

odul

us (G

Pa)

θ (Degrees)

Series1

Series2

xE

11Q

Variation of “apparent moduli” and with fiber orientation for off-axis tensile test of a unidirectional T300/934 carbon/epoxy lamina. Lamina engineering constants are taken from Table 2.2. Conclusion: except at 11xE Q 0 and 90o o

Lamina tensile strength can be “backed out” from laminate tensile test data

“Backed out” tensile strength data from seven different laminates of IM7G/8551-7 graphite/epoxy. (From Rawlinson, R.A. 1991. Proceedings of the 36th International SAMPE Symposium and Exhibition, Book 1, pp. 1058–1068. Reprinted by permission of the Society for the Advancement of Material and Process Engineering.)

Compression test specimen for ASTM D3410/D3410M-03

D3410 fixtures produce side-loading rather than end-loading as in D695

Geometry for tabbed compression test specimen. (From ASTM Standard D3410/D3410M-03 (Reapproved 2008). Copyright ASTM International. Reprinted with permission.)

Cutaway view of compression test fixture for ASTM D3410/D3410M-03

Cross-section view of ASTM D3410/D3410M-03 (Reapproved 2008) compression test fixture. (From ASTM Standard D3410/D3410M-03 (Reapproved 2008). Copyright ASTM International. Reprinted with permission.)

Sandwich beam specimen for face sheet compression

ASTM D5467/D5467M-97 (Reapproved 2004) sandwich beam specimen for face sheet compression. (From ASTM Standard D5467/D5467M-97 (Reapproved 2004). Copyright ASTM International. Reprinted with permission.)

Test fixture for ASTM D 6641/D 6641M- 09combined loading compression (CLC) test method

Test fixture for ASTM D6641/D6641M-09 CLC test method. (From ASTM Standard D6641/D6641M-09. Copyright ASTM International. Reprinted with permission.)

Test fixture for compressive residual strength of polymer composite plates. (From ASTM D 7137/D 7137M-07)

Test fixture for compressive residual strength of polymer composite plates. (From ASTM D7137/D7137M-07. Copyright ASTM International. Reprinted with permission.)

Comparison of shear test methods for composites. (From Adams, D.F., 2005 High Performance Composites, 13(5), pp. 9–10)

Iosipescu test fixture for shear strength and stiffness in all three shear stress states

(ASTM D5379)

Test fixture for V-notched rail shear test

Test fixture for V-notched rail shear test. (From ASTM Standard D7078/D7078M-05. Copyright ASTM International. Reprinted with permission.)

Different test specimen arrangements for V-notched rail shear test. (From ASTM Standard D7078/D7078M-05. Copyright ASTM International. Reprinted with permission.)

Rail shear test fixtures, ASTM D4255/D4255M-01 (Methods A and B)

Rail shear test fixtures. (From ASTM Standard D4255/D4255M-01(2007). Copyright ASTM. Reprinted with permission.)

xy

PLt

Analysis of Rail Shear Test Procedure A

(10.8)

Shear stress along loading axes x,y)

Strain transformation from normal strain along strain gage axis x’ oriented at 45o from x to shear strain along(x,y) axes

'2xy x (10.10)

Therefore the shear modulus along loading axes is

'2xy

xyxy x

PG

Lt

where P, L, t, and εx’ are all measured quantities.

If the specimen is unidirectional, and (x,y) are alignedwith (1,2), then and if this specimen isloaded to failure

12xyG G

xy LTS

Laminate test for in-plane shear modulus G12045

Shear stress from applied stress: 212x

Shear strain from measured normal strains:

oy

ox

12

Shear modulus: 1212

12

G

Off-axis tensile test for indirect measurement of G12

Young’s modulus, Ex

2

1

y

x

x

x

xxE

When ,0x 0 xyy

1111

1

SSE

x

xx

or

4

2

22

121

124

1

1121

1

sE

scGE

vc

E

Ex

(2.39)

(2.40)

Off-axis tensile test for indirect measurement of G12

• Conduct off-axis tensile test to measure Ex at some fiber orientation θ

• Conduct longitudinal tension test to measure E1 and υ12

• Conduct transverse tension test to measure E2

• Use above results in Eq. 2.40 to calculate G12

Limitation of the off-axis tensile test for measurement of shear properties of an orthotropic lamina

The off-axis tensile test of the orthotropic lamina shown below can be used to determine the shear modulus, 𝐺12, by using the first of the transformation equations for elastic constants (Equations (2.40)) if the properties E1, E2, and ν12 are known from separate tensile tests along the 1 and 2 axes, and Ex is determined from the off-axis test at angle θ. y 1 x Alternatively, 𝐺12can be determined from the off-axis tensile test data by using the definition 𝐺12 = 𝜏12𝛾12

where the shear stress 𝜏12 and the shear strain 𝛾12 can be determined from applied stress, x, along with the measured strains from the strain gages and the stress and strain transformation equations. This is true even though there is a biaxial stress state (𝜎1,𝜎2,𝜏12) acting along the 1,2 axes.

strain gages

45o

2 x

Limitation of the off-axis tensile test for measurement of

shear properties of an orthotropic lamina (continued) Usually, however, the purpose of such a mechanical test is to determine not only the slope of the linear part of the stress-strain curve (in this case, the shear modulus, 𝐺12), but the failure stress, or strength (in this case, the shear strength, 𝑆𝐿𝑇). The off-axis tensile test cannot be expected to yield accurate measurement of 𝑆𝐿𝑇 because of the biaxial stress state (𝜎1,𝜎2,𝜏12). For example, if we apply the Tsai-Hill failure criterion for the biaxial stress state along the 1,2 axes, the failure condition is given by

𝜎12𝑆𝐿2 - 𝜎1𝜎2𝑆𝐿2 + 𝜎22𝑆𝑇2 + 𝜏122𝑆𝐿𝑇2 =1

Clearly, the failure here is due to all three stress components (𝜎1,𝜎2,𝜏12), and we can only have an accurate measurement of the shear strength 𝑆𝐿𝑇 when we have the pure shear condition 𝜎1 = 𝜎2 = 0,𝜏12 ≠ 0, in which case the Tsai-Hill criterion reduces to 𝜏12 = 𝑆𝐿𝑇. Such a pure shear condition is not possible with the off-axis tensile test.

ASTM D2344/D2344M-00 Short beam shear test for interlaminar strength (parallel fibers only)

Note: not recommended for measurement of intrinsic properties, only for quality control and specification

L

P

d

b

Short beam test specimen with shear and moment diagrams

Shear stress

Bending stress

Mechanics ofmaterials stresses

xy

VQ

Ib

xyy

Mz

I

Short beam shear test

• Short beam fails due to interlaminar shear stress• Long beam fails due to either tensile or

compressive normal stress on bottom or top of beam, respectively

• Questions about accuracy of mechanics of materials beam theory equations for stresses in short beams where support effects may not be negligible (Whitney’s theory of elasticity analysis)

Whitney’s conclusion: Stress distributions from mechanics of materials beam theory are only accurate far away from loads and supports

Comparison of predicted interlaminar shear stress distributions from theory of elasticity (solid curves) and beam theory (dotted curve) for a 50 ply short beam shear specimen with length-to-depth ratio of 4. Differences are particularly large near loading point (section C) and support points (section A). (From Whitney, J. M. 1985. Composites Science and Technology, 22, 167-184. With permission)

Interlaminar Fracture Tests

DCB analysis – treat one half of DCB as cantilever beam(ASTM D5528-01 (2007)e3)

Mode I strain energy release rate

2 2 2

2 3f

962

Ix

P s P aG

t a E t h

(10.16)

Mixed mode bending (MMB) test for Mode Iand Mode II delamination testing

(ASTM Standard D6671)

Test fixture for MMB test. (From ASTM Standard D6671/D6671M-06. Copyright ASTM International. Reprinted with permission.)

Single fiber fragmentation specimen for measurement of fiber/matrix interfacial

shear strength

Test procedure: Load specimen until fiber starts to break up into fragments, then measure “critical lengths” of fragments, then calculate interfacial shear strength from theory of discontinuous fiber composites developed in Chap. 6

Single-fiber fragmentation specimen developed by Drzal et al. (From Drzal, L.T., Rich, M.J., and Lloyd, P.F. 1982. Journal of Adhesion, 16, 1–30.; Drzal, L.T., Rich, M.J., Koenig, M.F., and Lloyd, P.F. 1983. Journal of Adhesion 16, 133–152. With permission.)

Microindenter test for fiber/matrix interfacial shear strength

Test procedure: Load end of fiber in compression with microindenter probe until fiber slips with respect to matrix, then use finite element analysis of specimen to estimatefiber/matrix interfacial shear strength

Microindenter test for fiber/matrix interfacial strength. (From Mandell, J.F., Grande, D.H., Tsiang, T.H., and McGarry, F.J. 1986. Composite Materials: Testing and Design (Seventh Conference), ASTM STP 893, pp. 87–108. American Society for Testing and Materials, Philadelphia, PA. Copyright ASTM. Reprinted with permission.)

Microbond test for fiber/matrix interfacial shear strength

applied tensile force

fiber embedded in resin dropletresin droplet

Problem: Difficult to reproduce the composite resin matrix cure condition in a small droplet.

Source: From McDonough, W.G., Herrera-Franco, P.J., Wu, W.L., Drzal, L.T., and Hunston, D.L. 1991. In Advanced Materials/Affordable Processes, Proceedings of 23rd International SAMPE Technical Conference, Kiamesha Lake, NY, pp. 247–258. Society for Advancement of Material and Process Engineering, Covina, CA. Reprinted by permission of the Society for the Advancement of Material and Process Engineering.

(a)

(b) (c) (d)

ASTM D5766 open hole tension test – similar to ASTM D3039 tensile test, but with central hole

Acceptable test failure modes for ASTM D 5766/D 5766M-07 standard test method for open hole tensile strength (a) failure mode codes (b) LGM (c) AGM (d) MGM. (From ASTM D5766/D5766M-07. 2009. Copyright ASTM International. Reprinted with permission.)

Fixture assembly for ASTM D5961/D5961M-08 (Procedure A) double shear test method for bearing response of polymer matrix composite laminates. (From ASTM D5961/D5961M-08. 2009. Copyright ASTM International. Reprinted with permission.)

ASTM D5961 bearing test – Procedure A

Test fixture and specimen for ASTM standard test method for measuring the fastener pull-through resistance of a fiber-reinforced polymer matrix composite, Procedure B. (From ASTM D 7332/D 7332M-07e1. Copyright ASTM International. Reprinted with permission.)

ASTM D7332 fastener pull-through test

Measurement of Viscoelastic and Dynamic Properties

Strain, ε

Time, t

Constant applied stress, σo

Initial elastic strain, εo

Creep strain, ε(t)

Creep test parameters

Elastic compliance = εo/ σo

Creep compliance = ε(t)/σo

Testspecimen

Total strain = εo+ε(t)

Straingage

Measurement of orthotropic creep compliances

Measurement of orthotropic creep compliances

Apply constant stresses and measure time-dependent strains for applied longitudinal stress, 1 :

111

1

( )( )

tS t

where strain 1( )t is measured

221

1

( )( )

tS t

where strain 2 ( )t is measured

For applied transverse stress 2 :

222

2

( )( )

tS t

where strain 2 ( )t is measured

112

2

( )( )

tS t

where strain 1( )t is measured

For off-axis creep test with applied stress x and measured

strains and at 45ox y

Stress transformation equation:

12 cos( 45 )sin( 45 ) 0.5o ox x

Strain transformation equation:

12 cos( 45 )sin( 45 ) cos( 45 )sin( 45 )2

2

o o o ox y

x y

Therefore for time-dependent strains: 12 ( ) ( ) ( )x yt t t

and the measured shear creep compliance is

1266

12

[ ( ) ( )]( )( ) 2 x y

x

t ttS t

S(t)S0 S1tn

Empirical power law for creep compliance

where S(t) is the creep compliance, S0 the initial elastic compliance, and S1 and n the empirically determined parameters

Important modes of specimen deformation for vibration tests

Flexural

Torsional

Longitudinal

Response

Frequency

Flexural and torsional modes

Longitudinalmodes

Range of typical excitation frequencies

Natural frequencies of flexural and torsional modes of vibration are usually in the range of typical excitation frequencies, but longitudinal modes are usually well above this range. Automated Dynamic Mechanical Analyzers (DMA) typically operate in the flexural mode.

Storage Modulus, E’

Loss Modulus, E”

Loss Factor, η = tan δ

Temperature

Representation of automated DMA plot showing storage modulus, loss modulus and loss factor (tan δ) vs. temperature.

Material Damping

• Energy dissipation within a material under cyclic or oscillatory stress

• Characterized by stress-strain hysteresis loop under steady-state vibration and decaying oscillation under free vibration

• Area enclosed by hysteresis loop and rate of decay are proportional to damping factor

• Damping is linear if it is independent of oscillation amplitude

Hysteresis loop insteady state vibration

Free vibration decay

Complex modulus of linear viscoelastic material from stress-strain hysteresis loop ( assuming perfectly elliptical loop)

Energy dissipated per cycle

cosacdD2

Energy stored at maximumdisplacement

cosdbU22

1

Loss factor

ba

cosdbcosad

UD

221222

Storage Modulus

cosdb

cosd

b'E

22

Free vibration decay method

Logarithmic decrement

Loss factor (for light damping)

nxox

lnn1

Impulse-frequency response apparatus forflexural vibration of cantilever beam specimens

Impulse-frequency response method

-100

-80

-60

-40

-20

0

0 400 800 1200 1600 2000Frequency (Hz)

FRF

Modal frequencies and loss factors found by curve-fitting to frequency response curve at peak frequencies

Modal frequencies

Single Degree of Freedom Curve Fit to Peak in Frequency Response Curve by Half Power Bandwidth Method

Damping Loss Factor

nf

f

Amplitude

Frequencynf

X

0.707 X

f

= natural frequency of nth mode

= bandwidth at half power points

nf

f

Peak fornth mode

(10.36)

Measurement of Hygrothermal Properties

A

B DMA Tg

E’

Temperature

ASTM D7028-07e1 test for determination of DMA Tg from storage modulus vs. temperature plot

Measurement of glass transition temperature, Tg

Measure thermal strain, , or the change in length, , of a specimen of original length which is subjected to a temperature change in an environmental chamber

T LoL

T

0

T LCTE

T L T

Measured coefficient of thermal expansion is

ASTM 696-08 test for measurement of coefficient of thermal expansion, CTE

(10.37)

Variation of measured longitudinal and transverse thermal strains for unidirectional Kevlar 49/epoxy and S-glass/epoxy with temperature. (From Adams, D.F., Carlsson, L.A., and Pipes, R.B., 2003. Experimental Characterization of Advanced Composite Materials. CRC Press, Boca Raton, FL. With permission.)

1 11

01

1T L

T L T

2 22

02

1T L

T L T

Measured longitudinal CTE

Measured CTEs for undirectional orthotropic lamina

Measured transverse CTE

ASTM D5229 test for measurement of moisture absorption properties

22

2 1

2 14z

m

M MhD

M t t

Through-thickness Diffusivity

Saturation moisture content, Mm

Wei

ght %

abs

orbe

d m

oist

ure,

M

M1

M2

(10.40)

Split disk loading fixtures Composite ring specimen

Load

ASTM D2290 Split Disk Test for tensile strengthof filamentwound composite rings

Example of test done to determine quality or acceptability of specific components during manufacturing

Exploded view of test fixture for ASTM D2290Split Disk Test for Rings