1Fracture and fatigueKey point:

Preexisting surface flaws and preexisting internal cracks play a central role in the failure of materials.

How do flaws in a material initiate failure? How is fracture resistance quantified; how do different

material classes compare? How do we estimate the stress to fracture? How do loading rate, loading history, and temperature

affect the failure stress?

ISSUES TO ADDRESS...

Fracture mechanisms

Ductile fracture Occurs with plastic deformation and with high energy

absorption before fracture

Brittle fracture Little or no plastic deformation with low energy

absorption Catastrophic

2An oil tanker that fractured in a brittle manner by crack propagation around its girth

Ductile vs Brittle Failure

Very Ductile Moderately Ductile BrittleFracture behavior

Large Moderate%AR or %EL Small

Classification:

Ductile fracture is usually desirable! Ductile: warning before fracture Brittle: no warning

3 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

Evolution to failure:

Resultingfracturesurfaces(steel)

50 mm

particlesserve as voidnucleationsites.

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 mmFracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.

Moderately Ductile Failure

neckings

void nucleation

void growth and linkage

shearing at surface fracture

4Ductile vs. Brittle Failure

Adapted from Fig. 8.3, Callister 7e.

cup-and-cone fracture brittle fracture

Fractured aluminium alloy I, with a dimpled texture Fractured aluminium alloy II, with a typical cleavage texture

Fractured tensile test bars

Cup and cone

5Scanning electron micrographs (a) spherical dimples characteristic of ductile fracture, (b) parabolic-shaped dimples characteristic of ductile fracture.

Brittle Failure

Arrows indicate origin of crack

6Transgranular fracture Intergranular fracture

Brittle Failure

Flaws are Stress Concentrators or stress raisers

Results from crack propagation Griffith Crack

where rt = radius of curvature of the crack tipso = applied stresssm = stress at crack tip

Kt : stress concentration factor

ot

/

tom K

as=

r

s=s

21

2

rt

Principles of fracture mechanics

7Concentration of Stress at Crack Tip

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

Engineering Fracture Design

r/hsharper fillet radius

increasing w/h

0 0.5 1.01.0

1.5

2.0

2.5

Stress Conc. Factor, K ts

maxs

o=

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

ot

/

tom K

as=

r

s=s

21

2

8Crack Propagation

Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip, blunting the crack.

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

plasticbittle

Deformed region

When Does a Crack Propagate?

Critical stress for crack propagates in a brittle material

where E = modulus of elasticity gs = specific surface energy a = one half length of internal crack Kc = sc/s0

For ductile => replace gs by gs + gpwhere gp is plastic deformation energy

212 /sc a

E

pg

=si.e., sm > sc

or Kt > Kc

Example problem 8.1, p217

9Fracture toughness

KC: fracture toughnessthe critical (c) value of the stress intensity factor at a crack tip necessary to produce failure

KC = Ysc ( a)1/2

1. Y: geometry factor, on the order of 12. sc the overall applied stress at failure3. a: the length of a surface crack (one-half the

length of an internal crack)4. Unit of KIC: MPa m1/2

p

a

a

Critical stress for crack propagation (sc) and crack length (a)

The three modes of crack surface displacement

(a) mode I, opening or tensile modeplane strain fracture toughness

(b) mode II, sliding mode(c) mode III, tearing mode

KIC = Ysc ( a)1/2p

10

Room-temperature mechanical properties for selected engineering materials

Fracture ToughnessGraphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

5

KIc

(MPa

m

0.5 )

1

Mg alloysAl alloys

Ti alloysSteels

Si crystalGlass -sodaConcrete

Si carbide

PC

Glass 6

0.5

0.7

2

43

10

20

30

Diamond

PVCPP

Polyester

PS

PET

C-C(|| fibers) 1

0.6

67

40506070

100

Al oxideSi nitride

C/C( fibers) 1

Al/Al oxide(sf) 2

Al oxid/SiC(w) 3Al oxid/ZrO 2(p)4Si nitr/SiC(w) 5

Glass/SiC(w) 6

Y2O3/ZrO 2(p)4

11

Crack growth condition:

Largest, most stressed cracks grow first!

Design Against Crack Growth

K Kc = aY ps

--Result 1: Max. flaw sizedictates design stress.

max

cdesign

aYKp

12

Loading Rate Increased loading rate...

-- increases sy and TS-- decreases %EL

Why? An increased rategives less time for dislocations to move past obstacles.

s

e

sy

sy

TS

TS

largere

smallere

Charpy test of impact energy

1. A notched specimen stress concentrating

2. Loading applied rapidly3. impact energy - the energy

necessary to fracture the test specimen

The swinging pendulumThe intial height hThe final height h

Impact fracture testing

Izod test

Charpy test

13

1040 carbon steel: Fe-0.4C-0.75 MnJ: joule. 1J = 1N m

Cu: fcc, ductileMg alloy: hcp, relatively brittle

Toughness = , the area under the s - ecurve esd

Fracture

Unit of toughness: N/m2Or (N/m2) (mm / mm) = N m / (mm)3

Toughness: the energy necessary to fracture per unit volume of material

Toughness obtained in a tensile test

14

Temperature dependence of the Charpy V-notch inpact energy and shear fracture for an A283 steel.

Schematic curves for the three general types of impact energy-versus-temperature behavior

More DuctileBrittle

15

Ductile-to-Brittle Transtion Temperature (DBTT)

1. in bcc alloys2. an abrupt drop in ductility and toughness as the temperature is lowered

Plain-carbon steels with various carbon levels

Fe-Mn-0.05C alloys with various manganese levels

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.)

Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Earl R. Parker, "Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 1957.)

Design Strategy: Stay Above The DBTT!

16

Fatique

Fatique = failure under cyclic stress failure after N cycles load < T.S

Fatique-testing apparatusfor making rotating-bending tests

17

Stress varies with time.-- key parameters are S, sm, and frequency

smax

smin

s

time

smS

Key points: Fatigue...--can cause part failure, even though smax < sc.--causes ~ 90% of mechanical engineering failures.

Random stress cycle.

S = stress amplitude, sm= mean stress,sm = (smax + smin)/2S = (smax smin)/2Load ratio R = smin/smax

Typical fatique curve (S-N curve)

or fatigue strength

18

Fatigue limit, Sfat:--no fatigue if S < Sfat

Fatigue Design Parameters

Sfat

case for steel (typ.)

N = Cycles to failure103 105 107 109

unsafe

safe

S = stress amplitude

Sometimes, thefatigue limit is zero! (a

material does not display a fatique limit)

Adapted from Fig. 8.19(b), Callister 7e.

case for Al (typ.)

N = Cycles to failure103 105 107 109

unsafe

safe

S = stress amplitude

Fatique S-N probability of failure curves for a 7075-T6 Al alloy

19

Crack grows incrementallytyp. 1 to 6

( ) a~ sDincrease in crack length per loading cycle

Failed rotating shaft--crack grew even though

Kmax < Kc--crack grows faster as

Ds increases crack gets longer loading freq. increases.

crack origin

Fatigue Mechanism

( )mKdNda

D=

Texture of the fatigue fracture surface clamshell or beachmark texture

Intrusions and extrusions. SEM.

20

Transmission electron fractograph showing fatique striations in aluminumEach striationis thougth to represent the advance distance of a crack front during a single load cycle, striation width deponds on and incearses with increasing stress range.

Improving Fatigue Life

2. Impose a compressive surface stress (to suppress surface cracks from growing)

--Method 1: shot peening

put surface

into compression

shot--Method 2: carburizing

C-rich gas

3. Remove stress concentrators.bad

bad

better

better

1. Decrease the mean stress level

21

Engineering materials don't reach theoretical strength. Flaws produce stress concentrations that cause

premature failure.

Sharp corners produce large stress concentrationsand premature failure.

Failure type depends on T and stress:- for noncyclic s and T < 0.4Tm, failure stress decreases with:

- increased maximum flaw size,- decreased T,- increased rate of loading.

- for cyclic s:- cycles to fail decreases as Ds increases.

- for higher T (T > 0.4Tm):- time to fail decreases as s or T increases.

SUMMARY

Homework 8.6 and 8.12, p246