FRACTURE - gtu.edu.tr

A T-2 tanker was lying quietly at pier when,

without warning, she suddenly broke in two

with a report that was heard for at least a

mile.

FRACTURE

Types of fracture in metals• The concept of material strength and fracture has long beenstudied to overcome failures.

• The introduction of malleable irons during the revolution ofmaterial construction led to the perception of brittle and ductile fractures as well as fatigue failure in metals.

Failure in metallic materials can be divided into twomain categories:

Ductile failure : Ductile fracture involves a large amount of plastic deformation and can be detected beforehand.

Brittle failure:Brittle fracture is more catastrophic and has been intensively studied.

Ductile vs Brittle FailureVery

Ductile

Moderately

DuctileBrittle

Fracture

behavior:

Large Moderate%AR or %EL Small

• Ductile

fracture is usually

desirable!

Adapted from Fig. 8.1,

Callister 7e.

• Classification:

Ductile:

warning before

fracture

Brittle:

No

warning

• Ductile failure:--one piece

--large deformation

Figures from V.J. Colangelo and F.A.

Heiser, Analysis of Metallurgical Failures

(2nd ed.), Fig. 4.1(a) and (b), p. 66 John

Wiley and Sons, Inc., 1987. Used with

permission.

Example: Failure of a Pipe

• Brittle failure:--many pieces

--small deformation

Factors affecting modes of fracture

Strain rate

Metallurgical aspect

Temperature

State of stresses

(notch effect)

Loading condition

Ductile vs. Brittle Failure

cup-and-cone fracture brittle fracture

Failure modes

High energy is absorbed bymicrovoid coalescence during ductile failure (high energy fracture mode)

Low energy is absorbed duringtransgranular cleavage fracture(low energy fracture mode)

Less catastrophic More catastrophic

• Evolution to failure:

• Resulting

fracture

surfaces

(steel)

50 mm

particles

serve as void

nucleation

sites.

50 mm

From V.J. Colangelo and F.A. Heiser,

Analysis of Metallurgical Failures (2nd

ed.), Fig. 11.28, p. 294, John Wiley and

Sons, Inc., 1987. (Orig. source: P.

Thornton, J. Mater. Sci., Vol. 6, 1971, pp.

347-56.)

100 mm

Fracture surface of tire cord wire

loaded in tension. Courtesy of F.

Roehrig, CC Technologies, Dublin,

OH. Used with permission.

Moderately Ductile Failurenecking

s

void nucleation

void growth and linkage

shearing at surface

fracture

Microvoid shapeMicrovoid shape is strongly influenced by the type of loading.

Uniaxial tensile loading

Equiaxed dimples.

Shear loading

Elongated and parabolic dimples

pointing in the opposite directions

on matching fracture surfaces.

Tensile tearing

Elongated dimples pointing in the

same direction on matching fracture

surface.

Theoretical cohesive strength of metals• In the most basic term, strength is due to the cohesive forces between atoms.• The attractive and repulsive force acting on the two atoms lead to cohesive force between two atoms which varies in relation to the separation between these atoms.

The theoretical cohesive strengthσmax can be obtained in relation tothe sine curve and become.

wheregs is the surface energy (J/m2)ao is the unstrained interatomic spacing

Note: Convenient estimates of σmax ~ E/10.

Cohesive force as a function ofthe separation between atoms.

o

s

ltheoreticaa

Egs

Example: Determine the cohesive strength of a silica fibre,if E = 95 GPa, gs = 1 J.m-2, and ao = 0.16 nm.

• This theoretical cohesive strength is exceptionally higher thanthe fracture strength of engineering materials.• This difference between cohesive and fracture strength is due to inherent flaws or defects in the materials which lower the fracture strength in engineering materials.• Griffith explained the discrepancy between the fracture strength and theoretical cohesive strength using the concept of energy balance.

Fractographic observationin brittle fracture

The process of cleavage fractureconsists of three steps:

1) Plastic deformation to producedislocation pile-ups.2) Crack initiation.3) Crack propagation to failure.

Distinct characteristics of brittlefracture surfaces:

1) The absence of gross plasticdeformation.2) Grainy or Faceted texture.3) River marking or stress lines(chevron nothces).

Brittle fracture indicating the origin of thecrack and crack propagation path

Brittle FailureArrows indicate points at which failure originated

• Stress-strain behavior (Room T):

Ideal vs Real Materials

TS << TSengineering

materials

perfect

materials

s

e

E/10

E/100

0.1

perfect mat’l-no flaws

carefully produced glass fiber

typical ceramic typical strengthened metaltypical polymer

• DaVinci (500 yrs ago!) observed...-- the longer the wire, the

smaller the load for failure.

• Reasons:

-- flaws cause premature failure.

-- Larger samples contain more flaws!

Reprinted w/

permission from R.W.

Hertzberg,

"Deformation and

Fracture Mechanics

of Engineering

Materials", (4th ed.)

Fig. 7.4. John Wiley

and Sons, Inc., 1996.

Stress Concentration for A Circular Hole

s

s

y

aq

x

r

sy=0

sx=-s

sy=3s

sx=0

• Tensile stresses reach 3 times of the applied stress at stress concentration points.

Flaws are Stress Concentrators!

where t = radius of curvature

so = applied stress

sm = stress at crack tip

Kt = stress concentration factor

ot

/

t

om Ka

s

ss

21

2

t

Adapted from Fig. 8.8(a), Callister 7e.

Concentration of Stress at Crack Tip

Adapted from Fig. 8.8(b), Callister 7e.

Engineering Fracture Design

r/h

sharper fillet radius

increasing w/h

0 0.5 1.01.0

1.5

2.0

2.5

Stress Conc. Factor, K t

smax

so

=

• Avoid sharp corners!s

Adapted from Fig.

8.2W(c), Callister 6e.

(Fig. 8.2W(c) is from G.H.

Neugebauer, Prod. Eng.

(NY), Vol. 14, pp. 82-87

1943.)

r , fillet

radius

w

h

o

smax

Stress concentrations for different geometrical shapes

Stress Concentration at A Discontinuity

Crack PropagationCracks propagate due to sharpness of crack tip

• A plastic material deforms at the tip, “blunting” the crack.

deformed region

brittle

Energy balance on the crack

• Elastic strain energy-• energy stored in material as it is elastically deformed

• this energy is released when the crack propagates

• creation of new surfaces requires energy

plastic

Theories of brittle fracture

Griffith theory of brittle fracture

The first analysis on cleavage fracture was initiated by Griffith using the concept of energy balance in order to explain discrepancy between the theoretical cohesive strength and observed fracture strength of ideally brittle material (glass).

Irwin and Orowan modified the Griffith theory to include plastic deformation at the crack tip.

2a

t

s

s

Elastic energy released by crack formation:

E

ta22s

Energy to create new surfaces

ss atat gg 422

satE

taUUU g

s4

22

0 Potansiyel Enerji (U)

Çatlak boyu

(a)

4atgs

U

acr

E

ta 22s

02

42

E

att

a

Us

sg

a

E scr

gs

2

Griffith’s Fracture Theory

When Does a Crack Propagate?

Crack propagates if the applied stress isabove critical stress

where– E = modulus of elasticity

– gs = specific surface energy

– a = one half length of internal crack

For ductile => replace gs by gs + gp

where gp is plastic deformation energy

212

/

sc

a

E

gs

i.e., sm > sc

Griffith’s theory of brittle fracture

Observed fracture strength isalways lower than theoreticalcohesive strength

Griffith explained that the discrepancy is due to the inherent defects in brittlematerials leading to stress concentration lower the fracture strength

Consider a through thickness crack of length 2a,subjected to a uniform tensile stress σ, at infinity.

Crack propagation occurs when the releasedelastic strain energy is at least equal to theenergy required to generate new crack surface.

The stress required to create the new crack surface is

In plane strain condition, it is given by:

Modified Griffith equation• The Griffith equation is strongly dependent on the crack size a,and satisfies only ideally brittle materials like glass.

• Irwin and Orowan suggested Griffith’s equation can beapplied to brittle materials undergone plastic deformationbefore fracture by including the plastic work, gp, into the totalelastic surface energy required to extend the crack wall, givingthe modified Griffith’s equation as follows

s

Criterion of Failure

gs and gp are material properties.

Gc is called critical energy release rate, and it is a material property.

a

EGccr

s For a given crack length, a, Failure occurs if s >

Also, if the s is given we can find the critical crack length for failure.

Failure occurs if G > Gc

Gc = 2(gs + gp ) (J / m2)

Applied energy release rate is G=s2a/E

In many cases we would like to know the design stress.

Linear Elastic Fracture Mechanics

It can be shown that the stress field, s, at the tip of a crack is a

function of the stress intensity factor, K.

Notice: s infinity as r 0

r

q

K is a function of the applied stress, the crack length, and the geometry.

K = aY s

K= f(s,a)

Usually

Critical K that a material can stand: Kc the fracture toughness.

)( mMPa

Failure occurs if K > Kc

1

Y

aYK s

12.1

Y

aYK s P

P

atPK /

(c)

GEK

E

KG

c

c

2

G or K, which approach is correct

From Griffith, a

GE

s

From LEFM, aK s /

If we write in terms of material properties

Fracture Toughness

Based on data in Table B5,

Callister 7e.Composite reinforcement geometry is: f

= fibers; sf = short fibers; w = whiskers;

p = particles. Addition data as noted

(vol. fraction of reinforcement):1. (55vol%) ASM Handbook, Vol. 21, ASM Int.,

Materials Park, OH (2001) p. 606.

2. (55 vol%) Courtesy J. Cornie, MMC, Inc.,

Waltham, MA.

3. (30 vol%) P.F. Becher et al., Fracture

Mechanics of Ceramics, Vol. 7, Plenum Press

(1986). pp. 61-73.

4. Courtesy CoorsTek, Golden, CO.

5. (30 vol%) S.T. Buljan et al., "Development of

Ceramic Matrix Composites for Application in

Technology for Advanced Engines Program",

ORNL/Sub/85-22011/2, ORNL, 1992.

6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci.

Proc., Vol. 7 (1986) pp. 978-82.

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibers

Polymers

5

KIc

(MP

a ·

m0

.5)

1

Mg alloys

Al alloys

Ti alloys

Steels

Si crystal

Glass -soda

Concrete

Si carbide

PC

Glass 6

0.5

0.7

2

4

3

10

20

30

<100>

<111>

Diamond

PVC

PP

Polyester

PS

PET

C-C(|| fibers) 1

0.6

67

40

506070

100

Al oxideSi nitride

C/C( fibers) 1

Al/Al oxide(sf) 2

Al oxid/SiC(w) 3

Al oxid/ZrO 2(p)4

Si nitr/SiC(w) 5

Glass/SiC(w) 6

Y2O3/ZrO 2(p)4

Toughness versus Strength

• Crack growth condition:

• Largest, most stressed cracks grow first!

Design Against Crack Growth

K ≥ Kc = aY s

--Result 1: Max. flaw size

dictates design stress.

max

cdesign

aY

K

s

s

amax

no fracture

fracture

--Result 2: Design stress

dictates max. flaw size.2

1

s

design

cmax

Y

Ka

amax

sno fracture

fracture

• Two designs to consider...

Design A--largest flaw is 9 mm

--failure stress = 112 MPa

Design B--use same material

--largest flaw is 4 mm

--failure stress = ?

• Key point: Y and Kc are the same in both designs.

Answer: MPa 168)( B sc• Reducing flaw size pays off!

• Material has Kc = 26 MPa-m0.5

Design Example: Aircraft Wing

• Use...max

cc

aY

K

s

sc amax A

sc amax B

9 mm112 MPa 4 mm--Result:

ac decreases dramatically with

decreasing toughness, espically if

the design stress is to be increased.

Design against fracture

Loading Rate

• Increased loading rate...-- increases sy and TS

-- decreases %EL

• Why?

s

e

sy

sy

TS

TS

largere

smallere

An increased rate gives less time for

dislocations to move past obstacles.

Impact Testing

• Impact loading:-- severe testing case

-- makes material more brittle

-- decreases toughness

(Charpy)

Impact Testing

final height initial height

Adapted from Fig. 8.12(b),

Callister 7e. (Fig. 8.12(b) is

adapted from H.W. Hayden,

W.G. Moffatt, and J. Wulff, The

Structure and Properties of

Materials, Vol. III, Mechanical

Behavior, John Wiley and Sons,

Inc. (1965) p. 13.)

• Increasing temperature...--increases %EL and Kc

• Ductile-to-Brittle Transition Temperature (DBTT)...

Temperature

BCC metals (e.g., iron at T < 914°C)

Imp

act E

ne

rgy

Temperature

High strength materials (s y > E/150)

polymers

More DuctileBrittle

Ductile-to-brittle transition temperature

FCC metals (e.g., Cu, Ni)

Adapted from Fig. 8.15,

Callister 7e.

Temperature vs. Charpy

• Pre-WWII: The Titanic

• WWII: Liberty ships

• Problem: Used a type of steel with a DBTT ~ Room temp.

Reprinted w/ permission from R.W. Hertzberg,

"Deformation and Fracture Mechanics of Engineering

Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and

Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard,

The Discovery of the Titanic.)

Design Strategy:Stay Above The DBTT!

• An oil tanker that fractured in a

brittle manner by crack propagation

around its girth.