Failure of material

1. Chapter 9
Failure of Materials

2. Failure of
Materials
Why study materials failure?
- design of component @ structure needs
the engineer to minimize (prevent) failure.
- important to understand the concept of
3 failure modes;
1. Fracture.
2. Fatigue.
3. Creep.
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.
Adapted from chapter-opening photograph, Chapter 9, Callister
& Rethwisch 3e. (by Neil Boenzi, The New York Times.)
Other examples of failure
• Brittle fracture:
-- many pieces
-- small deformations
• Ductile fracture:
-- one piece
-- large deformation
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.
Fundamental concept
- flaws @ crack (defects).
- characteristic & mechanisms.
Testing techniques
- modes of failure.
- produce & prevent failure.
mode
Fracture
Fatigue
Creep
Ductile fracture
Brittle fracture
mechanism testing technique
Impact test
Initial crack
Crack grow
Topics covered in this chapter…
Fatigue test
Creep test
Failure of Materials
- fracture mechanics.

3. Failure of
Materials
brittle fracture
mode of failure: Fracture
ductile fracture brittle fracture
Very ductile Moderately ductile Brittle
Fracture behavior
Large Moderate
%AR or %EL Small
Ductile fracture is
usually more desirable
than brittle fracture!
Ductile:
Warning before
fracture
Brittle:
No warning
- 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.
- little @ 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
SEM micrograph
ductile fracture
At low operating temp., ductile to
brittle transition (DBT) takes place
Schematic diagram
Fracture of materials results in separation of stressed solid into two or more parts.

4. Failure of
Materials
brittle fracture
mode of failure: Fracture
Moderately ductile fracture
brittle fracture surfaces
SEM micrograph
SEM micrograph
ductile fracture
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
Intragranular (within grains)
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.)
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
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.
evolution to failure
V-shaped
“chevron”
origin of
crack

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

6. Failure of
Materials
- engineering materials don't reach theoretical strength.
- flaws produce stress concentrations that cause
premature failure.
t
Results from crack propagation.
Griffith Crack
sm  2so
a
t






1/2
 Ktso
where
t = radius of curvature
so = applied stress
sm = stress at crack tip
Stress concentration at crack tip
Flaws are stress concentrators Engineering Fracture Design
- avoid sharp corners.
, r
fillet
radius
w
h
so
smax
r/h
sharper fillet radius
increasing w/h
0 0.5 1.0
1.0
1.5
2.0
2.5
Stress Conc. Factor, Kt =
smax
s0
Crack Propagation
- cracks propagate due to
sharpness of crack tip.
ductile
brittle deformed
region
mode of failure: Fracture
concept of
fracture
mechanics

7. Failure of
Materials
Crack Propagation
- crack propagates if above critical stress.
2
1
2
/
s
c
a
E









s
i.e., sm > sc
or Kt > Kc
where
E = modulus of elasticity
s = specific surface energy
a = one half length of
internal crack
Kc = sc/so
Design Against Crack Growth
mode of failure: Fracture
- crack growth condition:
K ≥ Kc = a
Y 
s
- engineering materials don't reach theoretical strength.
- flaws produce stress concentrations that cause
premature failure.
concept of
fracture
mechanics
- largest, most stressed cracks grow first!
-- Result 1: Max. flaw size
dictates design stress.
m
ax
c
design
a
Y
K


s
s
amax
no
fracture
fracture
-- Result 2: Design stress
dictates max. flaw size.
2
1








s


design
c
max
Y
K
a
amax
s
no
fracture
fracture
sTS << sTS
engineering
materials
perfect
materials
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

8. Design Example: Aircraft Wing
• 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
• Use...
max
c
c
a
Y
K


s
   B
max
A
max a
a c
c s

s
9 mm
112 MPa 4 mm
-- Result:
Failure of
Materials
mode of failure: Fracture
- engineering materials don't reach theoretical strength.
- flaws produce stress concentrations that cause
premature failure.
concept of
fracture
mechanics
Fracture Toughness, KIC for selected materials
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
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
6
7
40
50
60
70
100
Al oxide
Si 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

9. Failure of
Materials
mode of failure: Fracture
testing technique: Impact test
final height initial height
(Charpy)
- classify into 3:
1. Charpy impact test.
2. Izod impact test.
3. Drop weight impact test.
Important information from impact test…
1. Fracture (brittle @ ductile).
2. Brittleness (impact energy @ % shear).
3. Ductility (impact energy @ % shear).
4. Toughness (energy absorbed).
5. Ductile-to-Brittle Transition (DBT)
temperature.
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.)
Pre-WWII: The Titanic
WWII: Liberty ships
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 DBT!
BCC metals
(e.g., iron at
T < 914°C)
Impact
Energy
Temperature
High strength materials
(sy > E/150)
& polymers
DBT temperature
FCC metals (e.g., Cu, Ni)
more brittle more ductile
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.)
- aim: to investigate the energy absorbed &
fracture of materials during impact loading
at various temperature.
- fracture behavior can be shown in impact
energy vs temperature curves.
•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. Failure of
Materials
mode of failure: Fatigue
- 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
Fracture started here
Final rupture
Key points: Fatigue...
- failure under cyclic loading.
- can cause part failure, even though
smax < sc.
- causes ~ 90% of mechanical
engineering failures.
- stress varies with time.
-- key parameters are:
1. stress amplitude, S (@ sa).
2. mean stress, sm.
3. frequency, f (will convert to no. of cycle, N).
smax
smin
s
time
sm
S
2
min
max s
s
s


m
Mean stress
2
min
max s
s
s


a
Stress amplitude
min
max s
s
s 

r
Stress range
max
min
s
s

R
Stress range
Stress amplitude, S = stress to cause failure
Number of cycle, N = 1/f
- fatigue behavior can be shown in SN curves.
testing technique: Fatigue test
Important point from fatigue test…
1. Fatigue limit.
2. Fatigue strength.
3. Fatigue life.
tension on bottom
compression on top
counter
motor
flex coupling
specimen
bearing bearing

11. Failure of Materials
mode of failure: Fatigue
Fatigue Design Parameters
- Fatigue limit, Sfat:
-- no fatigue if S < Sfat
Adapted from Fig. 9.25(a),
Callister & Rethwisch 3e.
Sfat
N = Cycles to failure
103 105 107 109
unsafe
safe
S = stress amplitude
example: SN curves for typical steel
- Sometimes, the fatigue limit is zero!
-- fatigue occurs at any time.
Adapted from Fig. 9.25(b),
Callister & Rethwisch 3e.
N = Cycles to failure
103 105 107 109
unsafe
safe
S = stress amplitude
• Fatigue limit:
- PMMA, PP, PE
• No fatigue limit:
- PET, Nylon (dry)
example: SN curves for typical polymers
Improving Fatigue Life
1. Impose a compressive
surface stress (to suppress
surface cracks from growing)
--Method 1: shot peening
shot
--Method 2: carburizing
C-rich gas
put surface into
compression
2. Remove stress concentrators.
bad
bad
better
better
Adapted from Fig. 9.32,
Callister & Rethwisch 3e.

12. Failure of
Materials
mode of failure: Creep
- Creep is progressive deformation under
constant stress.
- Occurs at elevated temperature, T > 0.4 Tm
-- important in high temperature applications.
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.
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.
s,e
0 t
s
Important information from e-t curve…
Adapted from Fig. 9.35, Callister & Rethwisch 3e.
Adapted
from
Figs.
9.36,
Callister
&
Rethwisch
3e.
elastic
primary secondary
tertiary
Data from creep test…
1. creep strain, e
2. temperature, T
3. time, t
- creep behavior can be shown in e-t curves.
tr = time to failure (rupture)
L = function of applied stress
T = temperature
L
)
t
(
T r 
log
20
Time to rupture, tr
Creep failure
along grain boundaries.
applied
stress
g.b. cavities
creep calculation…
Estimate rupture time for
S-590 Iron, T = 800°C &
s = 20 ksi
example:
24x103
1073K
Ans: tr = 233 hr
L(103K-log hr)
Stress,
ksi
100
10
1
12 20 24 28
16
data for
S-590 Iron
20
T(20 + log tr) = L

13. • 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.
SUMMARY