MSE 3300-Lecture Note 13-Chapter 08 Failure

MSE 3300 / 5300 UTA Spring 2015 Lecture 13 -

Lecture 13. Failure

Learning ObjectivesAfter this lecture, you should be able to do the following:

1. Describe the mechanism of crack propagation for both ductile and brittle modes of fracture.2. Define fatigue and determine (a) fatigue lifetime and (b) fatigue strength in a fatigue plot.3. Define creep and determine (a) the steady-state creep rate and (b) the rupture lifetime in a creep plot.

Reading• Chapter 8: Failure

Multimedia• Virtual Materials Science & Engineering (VMSE):

http://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/

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1. Fracture

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• Simple fracture is the separation of a body into two or more pieces in response to an imposed stress that is static (i.e., constant or slowly changing with time) and at temperatures that are low relative to the melting temperature of materials.

• Two fracture modes: (1) ductile and (2) brittle.• Fracture process (two steps): (1) crack formation and (2) propagation in

response to an imposed stress.

Ship-cyclic loading from waves. Computer chip-cyclic thermal loading

MSE 3300 / 5300 UTA Spring 2015 Lecture 13 - 3

Fracture Mechanisms: Two Fracture Modes

1. Ductile fracture– Accompanied by significant plastic

deformation

2. Brittle fracture– Little or no plastic deformation– Catastrophic


Review: Ductility

4

Stre

ss

Strain

• Ductility: Measure of the degree of plastic deformation that has been sustained at fracture

• Brittle: little or not plastic deformation (approximately, a fracture strain < 5%)

• Ductility usually increases with temperature.

• Percent elongation

• Percent reduction in area

1. It indicates the degree to which a structure will deform plastically before fracture2. It specifies the degree of allowable deformation during fabrication operations


Ductile vs Brittle FractureVery

DuctileModerately

Ductile BrittleFracturebehavior:

Large Moderate%AR or %EL Small

• Classification:

Ductile fracture is usually more desirable than brittle fracture!

Ductile:Warning before

fracture

Brittle:No

warning

Necks down to a point fracture

Moderate necking


• 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: Pipe Failures

• Brittle failure:-- many pieces-- small deformations


Ductile Fracture

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Fracture Stages(a) Initial necking(b) Formation of small cavities (microvoids)(c) Crack formation: Coalescence of cavities to form a crack(d) Crack propagation(e) Final shear fracture at a 45 angle relative to the tensile direction (The

shear stress is a maximum at the angle.)

Cup-and-cone fracture


• 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• Failure Stages:

neckingσ

void nucleation

void growthand coalescence

shearing at surface fracture


Brittle Fracture

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• Brittle fracture takes place without any appreciable deformation and by rapid crack propagation.

• The direction of crack motion is very nearly perpendicular to the direction of the applied tensile stress.

• It yields a relatively flat fracture surface.

Brittle fracture without any plastic

deformation


Brittle Fracture

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Transgranular fracture: cracks propagate through grains.

Intergranular fracture: cracks propagate along grain boundaries.


Moderately Ductile vs. Brittle Failure

Fig. 8.3, Callister & Rethwisch 9e.

cup-and-cone fracture brittle fracture


Stress Concentration: Brittle Fracture of ductile materials

• The measured fracture strengths are significantly lower than those predicted by theoretical calculations based on atomic bonding energies, which is explained by microscopic flaws or cracks (stress raisers).

• Griffith Crack (elliptical hole)

where t = radius of curvatureσo = applied stressσm = stress at crack tip

t


Concentration of Stress at Crack Tip

Stress concentration factor:

A measure of the degree to which an external stress is amplified at

the tip of a crack (Stress amplification)


Crack PropagationCracks having sharp tips propagate easier than cracks

having blunt tips• A plastic material deforms at a crack tip, which

“blunts” 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

ductile


Criterion for Crack Propagation

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Crack propagates if crack-tip stress (σm) exceeds a critical stress (σc)

where– E = modulus of elasticity– s = specific surface energy– a = one half length of internal crack

For ductile materials => replace γs with γs + γpwhere γp is plastic deformation energy

i.e., σm > σc


• Fracture toughness (Kc): a property of the material that is a measure of a material’s resistance to brittle fracture when a crack is present [MPa m-1/2].

c: critical stress for crack propagationa: crack lengthY: Dimensionless parameter or function that depends on both crack

and specimen sizes and geometries and the manner of load application

• Plane strain fracture toughness: When specimen thickness is much greater than the crack dimensions, Kc becomes independent of thickness; under these conditions a condition of plane strain exists.

Fracture Toughness

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• Fracture toughness (Kc): a material property that is a measure of a material’s resistance to brittle fracture when a crack is present [MPa m-1/2].

Fracture Toughness

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Y = 1.0 Y = 1.1.


• Plane strain fracture toughness (KIc): a fundamental material property (Mode I) that depends on many factors, the most influential of which are temperature, strain rate, and microstructuredepnds on [MPa m-1/2].

Fracture Toughness

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Table 8.1: Yield Strength and Plane Strain Fracture Toughness

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Fracture Toughness Ranges

Based on data in Table B.5,Callister & Rethwisch 9e.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/ fibersPolymers

5

KIc

(MP

a · m

0.5)

1

Mg alloysAl alloys

Ti alloys

Steels

Si crystalGlass -sodaConcrete

Si carbide

PC

Glass 6

0.5

0.7

2

43

10

20

30

<100><111>

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)3

Al oxid/ZrO2(p)4Si nitr/SiC(w) 5

Glass/SiC(w)6

Y2O3/ZrO 2(p)4


• Crack growth condition:

• Largest, most highly stressed cracks grow first!

Design Against Crack Growth

K ≥ Kc =

--Scenario 1: Max. flaw size dictates design stress.

σ

amaxno fracture

fracture

--Scenario 2: Design stressdictates max. flaw size.

amax

σno fracture

fracture


Design Example: Aircraft Wing

Answer:

• 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 KIc are the same for both designs.

• Material has KIc = 26 MPa-m0.5

• Use...

9 mm112 MPa 4 mm--Result:

constant


2. Fatigue• Fatigue: failure under applied cyclic stress, dynamic and fluctuating

stresses (e.g., bridges, aircraft, and machine components).• Failure can occur at a stress level considerably lower than the tensile or

yield strength for a static load.• The term “fatigue” is used because this type of failure normally occurs

after a lengthy period of repeated stress or strain cycling.• It is the single largest cause of failure in metals (~90%).• Fatigue failure is brittle-like in nature even in normally ductile metals in

that here is very little gross plastic deformation associated with failure.

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

cycling frequency

σmax

σmin

σ

time

σmS

• Key points: Fatigue--can cause part failure, even though σmax < σy.--responsible for ~90% of mechanical engineering failures.


Cyclic Stress with Time

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(a) Reversed stress cycle

(b) Repeated stress cycle

(c) Random stress cycle


S–N Curve

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Stress amplitude (S) versus logarithm of the number of cycles to fatigue failure (N) for (a) a material that displays a fatigue limit, and (b) a material that does not display a fatigue limit.

• Fatigue limit: a limiting stress level (or endurance limit), below which fatigue failure will not occur.

• For many steels, fatigue limits range between 35% and 60% of the tensile strength.

• Fatigue strength: the stress level at which failure will occur for some specified number of cycles (e.g., 107cycles).

• Fatigue life: the number of cycles to cause failure at a specified stress level, as taken from the S–N plot (e.g., S1)


Adapted from Fig. 8.19(a), Callister & Rethwisch 9e.

S–N Curve: Types of Fatigue Behavior

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

Sfat

case for steel (typ.)

N = Cycles to failure103 105 107 109

unsafe

safe

S=

stre

ss a

mpl

itude

• For some materials, there is no fatigue limit!

Adapted from Fig. 8.19(b), Callister & Rethwisch 9e.

case for Al (typ.)

N = Cycles to failure103 105 107 109

unsafe

safe

S=

stre

ss a

mpl

itude


S–N Curve

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3. Creep

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• Creep: time-dependent and permanent deformation of materials when subjected to a constant load or stress.

• Materials are often placed in service at elevated temperatures and exposed to static mechanical stresses (e.g., turbine rotors in jet engines and steam generators that experience centrifugal stresses, and high-pressure steam lines).

• Important when T > 0.4Tm

Rupture time

Steady-state Creep Rate


Creep• Sample deformation at a constant stress (σ) vs time at a

constant temperature

Primary Creep: slope (creep rate) decreases with time.Secondary Creep: steady-statei.e., constant slope ∆ /∆t)Tertiary Creep: slope (creep rate) increases with time (acceleration of rate) and rupture.

σσe

0 t

Increase in creep resistance or strain hardening

Steady-state creep

Steady-state creep rate = ∆ /∆t

Steady-state creep rate

Rupture time


Stress and Temperature Effects


Secondary Creep• Strain rate is constant at a given T,

-- strain hardening is balanced by recoverystress exponent (material parameter)

strain rateactivation energy for creep(material parameter)

applied stressmaterial const.

• Strain rateincreaseswith increasingT, σ

102040

100200

10-2 10-1 1Steady state creep rate (%/1000hr)e s

Stre

ss (M

Pa) 427°C

538°C

649°C


Stress versus Rupture Time

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Carbon–nickel alloy


Stress versus Steady-State Creep Rate

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Carbon–nickel alloy


Summary1. Fracture: Mechanism of crack propagation for both

ductile and brittle modes of fracture2. Fatigue: (a) fatigue lifetime and (b) fatigue strength

in a fatigue plot.3. Creep: (a) the steady-state creep rate and (b) the

rupture lifetime in a creep plot

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Homework 6• 7.7, 7.12, 7.14, 7.24, 7.30• 8.7, 8.18, 8.22, 8.31, 8.34

Figure 7.6b: Lecture note 11-14 and 15.Figure 8.20: Lecture note 13-27Figure 8.32: Lecture note 13-33

* Problems from Callister, 9th Edition

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MSE 3300-Lecture Note 13-Chapter 08 Failure

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