chapter 8: mechanical failure - advanced ceramics group · chapter 8 - 13 fracture toughness:...

Chapter 8 - 1

ISSUES TO ADDRESS...

• How do micro-cracks lead to failure?

• How do the fracture resistances of the different materials

compare?

• How do loading rate, loading history, and temperature

affect the failure behavior of materials?

Ship-cyclic loading

from waves.

Computer chip-cyclic

thermal loading.

Hip implant-cyclic

loading from walking.Adapted from Fig. 22.30(b), Callister 7e.

(Fig. 22.30(b) is courtesy of National

Semiconductor Corporation.)

Adapted from Fig. 22.26(b),

Callister 7e.

Chapter 8: Mechanical Failure

Adapted from chapter-opening photograph,

Chapter 8, Callister & Rethwisch 8e. (by

Neil Boenzi, The New York Times.)

• What are the common modes of mechanical failures?

Chapter 8 - 2

The First (#1) Type of Mechanical

Failure - Fracture

• Ductile fracture

– Accompanied by significant plastic deformation

– More predictable

• Brittle fracture

– Little or no plastic deformation

– Often sudden & catastrophic

Chapter 8 - 3

Ductile vs Brittle Fracture

Very

Ductile

Moderately

DuctileBrittle

Fracture

behavior:

Large Moderate%AR or %EL Small

• Ductile fracture is

usually more desirable

than brittle fracture!

Adapted from Fig. 8.1,

Callister & Rethwisch 8e.

• Morphology difference:

Ductile:

Warning before

fracture

Brittle:

No

warning

Chapter 8 - 4

• Ductile fracture:-- large plastic

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 Fractures

• Brittle fracture:-- many pieces

-- almost no plastic

deformations

Chapter 8 - 5

• 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.

Ductile Fracture• Failure process:

necking

s

void nucleation

void growthand coalescence

shearing at surface

fracture

Chapter 8 - 6

Ductile vs. Brittle Fracture

Adapted from Fig. 8.3, Callister & Rethwisch 8e.

cup-and-cone for

ductile fracture

flat cross-section for

brittle fracture

Chapter 8 - 7

• Intergranular(between grains) 304 S. Steel

(metal)Reprinted w/permission

from "Metals Handbook",

9th ed, Fig. 633, p. 650.

Copyright 1985, ASM

International, Materials

Park, OH. (Micrograph by

J.R. Keiser and A.R.

Olsen, Oak Ridge

National Lab.)

Polypropylene

(polymer)Reprinted w/ permission

from R.W. Hertzberg,

"Defor-mation and

Fracture Mechanics of

Engineering Materials",

(4th ed.) Fig. 7.35(d), p.

303, John Wiley and

Sons, Inc., 1996.

4 mm

• Transgranular(through grains)

Al2O3

(ceramic)Reprinted w/ permission

from "Failure Analysis of

Brittle Materials", p. 78.

Copyright 1990, The

American Ceramic

Society, Westerville, OH.

(Micrograph by R.M.

Gruver and H. Kirchner.)

316 S. Steel

(metal)Reprinted w/ permission

from "Metals Handbook",

9th ed, Fig. 650, p. 357.

Copyright 1985, ASM

International, Materials

Park, OH. (Micrograph by

D.R. Diercks, Argonne

National Lab.)

3 mm

160 mm

1 mm(Orig. source: K. Friedrick, Fracture 1977, Vol.

3, ICF4, Waterloo, CA, 1977, p. 1119.)

Fracture Surfaces

Chapter 8 - 8

• Stress-strain behavior (Room T):

Fracture (Tensile) Strength of

Ideal (Perfect) Material vs Real Materials

TS << TSengineering

materials

perfect

materials

s

e

E/10

E/100

0.1

Perfect/ideal materials (i.e., no flaws)

carefully produced glass fiber

typical ceramic typical strengthened metaltypical polymer

• Material (3D) defects degrades strength-- Example: the longer the wire, the

smaller the load for failure.

• Reasons:

-- flaws cause premature failure.

-- larger samples contain more & larger

flaws/defects (especially micro-cracks)!

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.

Chapter 8 - 9

Flaws are Stress Concentrators!

• Micro-cracks are examples of

common flaws or 3D defects

• Stress concentration at tip of a

micro-crack

where

t = radius of curvature at the

crack tip

so = (average) applied stress

sm = stress at crack tip

a = crack width

t

Adapted from Fig. 8.8(a), Callister & Rethwisch 8e.

ott

om K s

ss

2/1

2a

Stress at the tip of a micro-crack

is many times higher than the

average applied stress σ0

Chapter 8 - 10

Concentration of Stress at Crack Tip



Chapter 8 - 11

Crack Propagation• Cracks having sharp tips propagate easier than

cracks having blunt tips

• A material with better toughness plastically deforms before cracks grows at its tip, which need more energy for the crack to grow (or propagate) compared with brittle material.

deformed region

brittle ductile

Chapter 8 - 12

Criterion for Crack Propagation

Crack propagates when crack-tip “concentrated” stress (sm) exceeds the critical stress (sc), which can be theoretically estimated

where– E = modulus of elasticity

– s = specific surface energy

– a = one half length of internal crack

2/12

s

as

cE

i.e., sm > sc

Chapter 8 - 13

Fracture Toughness: Measure of Materials

Property as Resistance to Brittle Fracture

Based on data in Table B.5,

Callister & Rethwisch 8e.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

Chapter 8 - 14

Impact Testing for Evaluating Fracture

Toughness

final height initial height

• Impact loading:-- severe testing case


Callister & Rethwisch 8e. (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.)

(Charpy)

Chapter 8 - 15

Influence of Temperature on

Materials’ Fracture Toughness



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

certain metals and polymers, they are ductile above

DBTT, but suddenly become brittle below DBTT

BCC metals (e.g., iron) & some polymers

Imp

act E

ne

rgy

Temperature

High strength materials (s y > E/150), no obvious DBTT

Ductile-to-brittle

transition temperature

(DBTT)

FCC metals (e.g., Cu, Ni), no obvious DBTT

Chapter 8 - 16

• Pre-WWII: The Titanic • WWII: Liberty ships

• Problem: Steels used had DBTT’s just below room

temperature in those cases

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:

Use Materials with DBTT Much

Lower than Lowest Usage Temperature

Chapter 8 - 17

A Second (#2) Type of Mechanical

Failure - Fatigue



(Fig. 8.18 is from Materials

Science in Engineering, 4/E

by Carl. A. Keyser, Pearson

Education, Inc., Upper

Saddle River, NJ.)

• Fatigue = failure under repeated applied or cyclic stress.

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

cycling frequency

smax

smin

s

time

smS

• Fatigue--can cause part failure, even though smax < sy.

--responsible for ~ 90% of mechanical engineering failures.

tension on bottom

compression on top

countermotor

flex coupling

specimen

bearing bearing

Chapter 8 - 18

Adapted from Fig.

8.19(a), Callister &

Rethwisch 8e.

Types of Fatigue Behavior

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

i.e., material can be used

indefinitely as long as

applied stress stays below

the fatigue limit value

Sfat

Example:steel

N = Cycles to failure10

310

510

710

9

unsafe

safe

S=

str

ess a

mplit

ude

• For some materials,

there is no apparent

fatigue limit!

i.e., to use it for

longer/more cycles, the

maximum stress applied

has to be reduced further

Adapted from Fig.

8.19(b), Callister &

Rethwisch 8e.

Example:Al

N = Cycles to failure10

310

510

710

9

unsafe

safe

S=

str

ess a

mplit

ude

Chapter 8 - 19

• Failed rotating shaft-- Crack grew with relatively

low stress level

-- Crack grows faster as• Ds or S increases

• crack gets longer

• loading freq. increases.

crack origin

Adapted from

Fig. 8.21, Callister &

Rethwisch 8e. (Fig.

8.21 is from D.J.

Wulpi, Understanding

How Components Fail,

American Society for

Metals, Materials Park,

OH, 1985.)

Fatigue Crack Growth

Chapter 8 - 20

Improving Fatigue Life

2. Remove stress

concentrators. Adapted from


Rethwisch 8e.

bad

bad

better

better

Adapted from


Rethwisch 8e.

1. Impose compressive

surface stresses(to suppress surface

cracks from growing)

N = Cycles to failure

moderate tensile smLarger tensile sm

S =

str

ess a

mp

litu

de

near zero or compressive sm

Increasing mean

(tensile) stress sm

leads to shorter

cycle life

--Method 1: shot peening

put surface

into compression

shot--Method 2: carburizing

C-rich gas

Chapter 8 - 21

A Third (#3) Type of Mechanical

Failure - CreepSample deforms more and more at a constant stress (s)

over time - Creep

Adapted from


Rethwisch 8e.

Primary Creep: slope (creep rate)

decreases with time.

Secondary Creep: steady-state

i.e., constant slope (De/Dt).

Tertiary Creep: slope (creep rate)

increases with time, i.e. acceleration of rate.

ss,e

0 t

Chapter 8 - 22

• Occurs at elevated or higher temperature: T > 0.4 Tm (in K)• Higher temperature faster creep!



Creep - Temperature Dependence

elastic

primarysecondary

tertiary

Chapter 8 -

Creep Failure

• Failure: often along grain boundaries.

applied

stress

g.b. cavities

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

Metallurgical Failures (2nd ed.), Fig. 4.32, p. 87, John

Wiley and Sons, Inc., 1987. (Orig. source: Pergamon

Press, Inc.)

23

Chapter 8 -

Creep for Al2O3 Ceramics• Al2O3: Melting point: Tm = 2025oC

24

http://www.mtixtl.com/AluminaCeramicTube-EQ-TA-40D-700.aspx

As received Al2O3 tube

After running at >1400oC for hours without proper mechanical support

Curved Al2O3 tube after creep

Chapter 8 - 25

• Sharp corners produce large stress concentrations

and premature failure.

SUMMARY• Engineering materials not as strong as predicted by theory

• Flaws/microcracks act as stress concentrators that cause

failure, fracture in particular, at stress level much lower than

theoretical values.

• Failure type depends on T and s :-For simple fracture (noncyclic s and T < 0.4Tm), failure stress

decreases with:

- increased maximum flaw size

- For fatigue (cyclic s):

- cycles to fail decreases as Ds or sm increases or increase T.

- For creep (T > 0.4Tm):

- time to rupture decreases as s or T increases.

Chapter 8 -

Homework

• Read chapter 8 and give a statement confirm reading

• Explain in your own words the following concepts:

– Brittle fracture

– Ductile fracture

– Ductile to brittle transition temperature (DBTT)

– Fatigue

– Creep

26

chapter 8: mechanical failure - advanced ceramics group · chapter 8 - 13 fracture toughness:...

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