1. Chapter 9 Failure of Materials

2. Failure of Materials Why study materials failure?
- design of structure needs
the engineer to minimize (prevent) failure.
- important to understand the concept of
3 failure modes;
1. Fracture.
2. Fatigue.
3. Creep.
Topics covered in this chapter…
Fundamental concept
- crack (defects).
- modes of failure.
- characteristic & mechanisms.
- fracture mechanics.
Testing techniques
Failure of materials…
- failure of engineering materials is undesirable.
- several cause of failure:
-- improper materials selection, processing
& design.
-- defects (i.e: internal/external flaws/cracks).
-- economic losses.
-- interference with availability of products &
services.
need an appropriate preventive measurement
to against failure.
- produce & prevent failure.
• Ductile fracture:
-- one piece
-- large deformation
Failure of Materials
mode
mechanism
testing technique
Fracture
Ductile fracture
Impact test
Brittle fracture
Fatigue
Initial crack
Fatigue test
Crack grow
Creep test
• Brittle fracture:
-- many pieces
-- small deformations
Creep
Other examples of failure
Computer chip-
cyclic thermal loading.
Hip implant-
cyclic loading from walking.
Ship-cyclic loading from waves.
Adapted from Fig (b), Callister 7e. (Fig (b) is courtesy of National Semiconductor Corporation.)
Adapted from chapter-opening photograph, Chapter 9, Callister & Rethwisch 3e. (by Neil Boenzi, The New York Times.)
Adapted from Fig (b), Callister 7e.

3. Failure of Materials mode of failure: Fracture
Fracture of materials results in separation of stressed solid into two or more parts.
ductile fracture
ductile fracture
brittle fracture
accompanied by significant plastic
deformation & slow crack propagation.
- common at low strain rate & high temp.
- three steps :
1. Specimen forms neck & cavities
within neck.
2. Cavities form crack & crack
propagates towards surface,
perpendicular to stress.
3. Direction of crack changes to 45o
resulting in cup-cone fracture.
no significant plastic deformation
before fracture & high crack propagation.
- Catastrophic (rapid crack propagation).
- common at high strain rates & low temp.
- three stages:
1. Plastic deformation concentrates
dislocation along slip planes.
2. Microcracks nucleate due to shear
stress where dislocations are blocked.
3. Crack propagates to fracture.
characteristic of fracture
SEM micrograph
At low operating temp., ductile to brittle transition (DBT) takes place
Fracture behavior
Very ductile
Moderately ductile
Brittle
brittle fracture
Schematic diagram
SEM micrograph
%AR or %EL
Large
Moderate
Small
Ductile fracture is
usually more desirable
than brittle fracture!
Ductile:
Warning before fracture
Brittle:
No warning

4. mode of failure: Fracture
Failure of Materials
mode of failure: Fracture
Moderately ductile fracture
ductile fracture
necking s
void nucleation
shearing
at surface
fracture
void growth
& linkage
100 mm
Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.
SEM micrograph
evolution to failure
brittle fracture surfaces
Intergranular (between grains)
Intragranular (within grains)
304 S. Steel (metal)
Reprinted w/permission from "Metals Handbook", 9th ed, Fig. 633, p Copyright 1985, ASM International, Materials Park, OH. (Micrograph by J.R. Keiser and A.R. Olsen, Oak Ridge National Lab.)
V-shaped “chevron”
316 S. Steel (metal)
Reprinted w/ permission from "Metals Handbook", 9th ed, Fig. 650, p Copyright 1985, ASM International, Materials Park, OH. (Micrograph by D.R. Diercks, Argonne National Lab.)
160 mm
brittle fracture
4 mm
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.
Al Oxide
(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.)
3 mm
SEM micrograph
origin of crack
1 mm

5. mode of failure: Fracture
Failure of Materials
mode of failure: Fracture
brittle fracture (in ceramics)
ductile fracture
- characteristic of fracture behavior:
-- origin point.
-- initial region (mirror) is flat & smooth.
-- after reaches critical velocity crack branches
(mist & hackle).
SEM micrograph
ductile fracture (in thermoplastic polymer)
characteristic of fracture behavior:
-- craze formation prior to cracking.
-- during crazing, plastic deformation of spherulites and formation of micro voids and fibrillar bridges.
brittle fracture
aligned chains
SEM micrograph
fibrillar bridges
microvoids
crack

6. mode of failure: Fracture
Failure of Materials
mode of failure: Fracture
concept of fracture mechanics
- engineering materials don't reach theoretical strength.
- flaws produce stress concentrations that cause
premature failure.
Flaws are stress concentrators
Stress concentration at crack tip
Engineering Fracture Design
- avoid sharp corners. t
, r
fillet
radius w h o s
max
smax
Stress Conc. Factor, K t = s0
2.5
2.0
increasing
w/h
Results from crack propagation.
Griffith Crack
Crack Propagation
- cracks propagate due to sharpness of crack tip.
1.5
where t = radius of curvature
so = applied stress
sm = stress at crack tip
brittle
1.0
r/h
deformed region
0.5
1.0
ductile
sharper fillet radius

7. mode of failure: Fracture
Failure of Materials
mode of failure: Fracture
concept of fracture mechanics
- engineering materials don't reach theoretical strength.
- flaws produce stress concentrations that cause
premature failure.
Crack Propagation
TS << TS
engineering
materials
perfect s e
E/10
E/100
0.1
perfect mat’l-no flaws
carefully produced glass fiber
typical ceramic
typical strengthened metal
typical polymer
Stress-strain curves (Room T) perfect & engineering materials
- crack propagates if above critical stress.
i.e., sm > sc
or Kt > Kc
where
E = modulus of elasticity
s = specific surface energy
a = one half length of internal crack
Kc = c/so
Design Against Crack Growth
- crack growth condition:
K ≥ Kc =
- largest, most stressed cracks grow first!
-- Result 1: Max. flaw size
dictates design stress.
-- Result 2: Design stress
dictates max. flaw size. s
amax no
fracture
amax s no
fracture

8. Design Example: Aircraft Wing
Failure of Materials
mode of failure: Fracture
concept of fracture mechanics
- engineering materials don't reach theoretical strength.
- flaws produce stress concentrations that cause
premature failure.
Design Example: Aircraft Wing
Fracture Toughness, KIC for selected materials
• Material has Kc = 26 MPa-m0.5
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers 5 K Ic
(MPa·m
0.5 ) 1
Mg alloys
Al alloys
Ti alloys
Steels
Si crystal
Glass -
soda
Concrete
Si carbide PC 6
0.7 2 4 3 10
<100>
<111>
Diamond
PVC PP
Polyester PS
PET
C-C
(|| fibers)
0.6 7
100
Al oxide
Si nitride
C/C
( fibers)
Al/Al oxide(sf)
Al oxid/SiC(w)
Al oxid/ZrO
(p)
Si nitr/SiC(w)
Glass/SiC(w) Y O
/ZrO
• 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 = ?
• Use...
• Key point: Y and Kc are the same in both designs.
9 mm
112 MPa
4 mm
-- Result:
Answer:
• Reducing flaw size pays off! 8

9. mode of failure: Fracture
Failure of Materials
mode of failure: Fracture
testing technique: Impact test
aim: to investigate the energy absorbed &
fracture of materials during impact loading
at various temperature.
Important information from impact test…
1. Fracture ductile).
2. Brittleness (impact % shear).
3. Ductility (impact % shear).
4. Toughness (energy absorbed).
5. Ductile-to-Brittle Transition (DBT)
temperature.
Pre-WWII: The Titanic
- classify into 3:
1. Charpy impact test.
2. Izod impact test.
3. Drop weight impact test.
fracture behavior can be shown in impact
energy vs temperature curves.
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., (Orig. source: Dr. Robert D. Ballard, The Discovery of the Titanic.)
BCC metals (e.g., iron at T < 914°C)
Impact Energy
Temperature
High strength materials (s y
> E/150)
& polymers
DBT temperature
FCC metals (e.g., Cu, Ni)
more brittle
more ductile
final height
initial height
(Charpy)
WWII: Liberty ships
Design Strategy: Stay above the DBT!
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., (Orig. source: Earl R. Parker, "Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 1957.)
Adapted from Fig. 9.18(b), Callister & Rethwisch 3e. (Fig. 9.18(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.)
Sinking of Titanic: Titanic was made up of steel which has DBT temperature 32oC. On the day of sinking, sea temperature was –2oC which made the the structure highly brittle and susceptible to more damage.

10. mode of failure: Fatigue
Failure of Materials
mode of failure: Fatigue
Key points: Fatigue...
- failure under cyclic loading.
can cause part failure, even though
smax < sc.
causes ~ 90% of mechanical
engineering failures.
metals often fail at much lower stress at cyclic
loading compared to static loading.
crack nucleates at region of stress
concentration & propagates due to cyclic
loading.
failure occurs when cross sectional area of
the metal too small to withstand applied load.
Fatigue fractured surface of keyed shaft
- stress varies with time.
-- key parameters are:
1. stress amplitude, S a).
2. mean stress, sm.
3. frequency, f (will convert to no. of cycle, N).
Fracture started here
Stress amplitude, S = stress to cause failure
Number of cycle, N = 1/f
Final rupture
- fatigue behavior can be shown in SN curves.
Important point from fatigue test…
1. Fatigue limit.
2. Fatigue strength.
3. Fatigue life.
testing technique: Fatigue test s
max
min
time m S
Mean stress
Stress amplitude
tension on bottom
compression on top
counter
motor
flex coupling
specimen
bearing
Stress range
Stress range

11. mode of failure: Fatigue
Failure of Materials
mode of failure: Fatigue
Fatigue Design Parameters
Sometimes, the fatigue limit is zero!
-- fatigue occurs at any time.
Improving Fatigue Life
- Fatigue limit, Sfat:
-- no fatigue if S < Sfat
1. Impose a compressive
surface stress (to suppress
surface cracks from growing)
example: SN curves for typical steel
Adapted from Fig. 9.25(a), Callister & Rethwisch 3e.
Sfat
N = Cycles to failure 10 3 5 7 9
unsafe
safe
S = stress amplitude
S = stress amplitude
--Method 1: shot peening
shot
unsafe
safe 10 3 10 5 10 7 10 9
put surface into compression
N = Cycles to failure
Adapted from Fig. 9.25(b), Callister & Rethwisch 3e.
--Method 2: carburizing
C-rich gas
example: SN curves for typical polymers
• Fatigue limit:
- PMMA, PP, PE
2. Remove stress concentrators.
• No fatigue limit:
- PET, Nylon (dry)
bad
better
Adapted from Fig. 9.32, Callister & Rethwisch 3e.

12. Failure of Materials T(20 + log tr) = L mode of failure: Creep
Creep is progressive deformation under
constant stress.
- Occurs at elevated temperature, T > 0.4 Tm
-- important in high temperature applications.
Creep failure
along grain boundaries.
applied
stress
g.b. cavities
creep calculation…
Time to rupture, tr
Adapted from Figs. 9.36, Callister & Rethwisch 3e.
Data from creep test…
1. creep strain, 
2. temperature, T
3. time, t
s,e t s
T = temperature
tr = time to failure (rupture)
L = function of applied stress
example:
elastic
primary
secondary
tertiary
Estimate rupture time for S-590 Iron, T = 800°C & s = 20 ksi
testing technique: Creep test
Creep test determines the effect of
temperature & stress on creep rate.
Metals are tested at constant stress at
different temperature & constant
temperature with different stress.
100 20
Stress, ksi 10
data for
- creep behavior can be shown in -t curves.
S-590 Iron
Important information from -t curve… 1 12 20 24 28 16
Primary creep:
creep rate (slope) decreases with time
due to strain hardening.
Secondary creep:
creep rate is constant due to simultaneous
strain hardening and recovery process.
-- steady-state.
Tertiary creep:
creep rate (slope) increases with time
leading to necking & fracture.
L(10 3
K-log hr)
24x103
T(20 + log tr) = L
1073K
Ans: tr = 233 hr
Adapted from Fig. 9.35, Callister & Rethwisch 3e.

13. SUMMARY • Engineering materials don't reach theoretical strength.
• Flaws produce stress concentrations that cause
premature failure.
• Sharp corners produce large stress concentrations
and 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. 13