Lecture 13 (Chapter 8)
Failure
Chapter 8 -
Chapter 8: Mechanical Failure
ISSUES TO ADDRESS...
• How do cracks that lead to failure form?
• How is fracture resistance quantified? How do the fracture
resistances of the different material classes compare?
• How do we estimate the stress to fracture?
• How do loading rate, loading history, and temperature
affect the failure behavior of materials?
Ship-cyclic loading
from waves
waves.
Adapted from chapter-opening photograph,
Chapter 8, Callister & Rethwisch 8e. (by
Neil Boenzi, The New York Times.)
Computer chip-cyclic
loading
thermal loading.
Adapted from Fig. 22.30(b), Callister 7e.
(Fig. 22.30(b) is courtesy of National
Semiconductor Corporation.)
Hip implant-cyclic
loading from walking
walking.
Adapted from Fig. 22.26(b),
Callister 7e.
Chapter 8 - 2
The lighter side of Fracture
Mechanics
Fracture mechanics works to your advantage here (seldom the
case in engineering applications…We don’t like fracture and want
to prevent it! Guess why….
Chapter 8 - 3
Fracture mechanisms
• Ductile fracture
– Accompanied by significant plastic
deformation
• Brittle fracture
– Little or no plastic deformation
– Catastrophic
Chapter 8 - 4
Ductile vs Brittle Failure
• Classification:
Fracture
behavior:
Very
Ductile
Moderately
Ductile
Brittle
Large
Moderate
Small
Adapted from Fig. 8.1,
Callister & Rethwisch 8e.
%AR or %EL
• Ductile fracture is
usually more desirable
than brittle fracture!
Ductile:
Warning before
fracture
Brittle:
No
warning
Chapter 8 - 5
Closer look at Ductile Failure
Chapter 8 - 6
Example: Pipe Failures
• Ductile failure:
-- one piece
-- large deformation
• Brittle failure:
-- many pieces
-- small deformations
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.
Chapter 8 - 7
Moderately Ductile Failure
• Failure Stages:
necking

• Resulting
fracture
surfaces
void
nucleation
shearing
void growth
and coalescence at surface
50
50mm
mm
(steel)
particles
serve as void
nucleation
sites.
fracture
100 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.)
Fracture surface of tire cord wire
loaded in tension.
tension Courtesy of F
F.
Roehrig, CC Technologies, Dublin,
OH. Used with permission.
Chapter 8 - 8
Moderately Ductile vs. Brittle Failure
cup-and-cone fracture
brittle fracture
Chapter 8 - 9
Brittle Failure
Arrows indicate point at which failure originated
Adapted from Fig. 8.5(a), Callister & Rethwisch 8e.
Chapter 8 - 10
Chapter 8 - 11
Brittle Fracture Surfaces
• Transgranular
• Intergranular
Intergran lar
(between grains)
4 mm
304 S. Steel
(metal)
(through grains)
316 S. Steel
(metal)
Reprinted
p
w/permission
p
from "Metals Handbook",
Reprinted w/ permission
9th ed, Fig. 633, p. 650.
from "Metals Handbook",
Copyright 1985, ASM
9th ed, Fig. 650, p. 357.
International, Materials
Copyright 1985, ASM
Park, OH. (Micrograph by
International, Materials
J.R. Keiser and A.R.
Park, OH. (Micrograph by
Olsen, Oak Ridge
D.R. Diercks, Argonne
National Lab.)
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.
160 mm
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
1 mm
(Orig. source: K. Friedrick, Fracture 1977, Vol.
3, ICF4, Waterloo, CA, 1977, p. 1119.)
Chapter 8 -
12
Transgranular Brittle Fracture in
Brittle
Materials
B ittl M
t i l
Chapter 8 - 13
Intergranular Brittle Fracture in
Brittle
Materials
B ittl M
t i l
Brittle phase at grain boundaries such as Fe3C in
C > 0.77 wt% steels!
Chapter 8 - 14
Ideal vs Real Materials
• Stress-strain behavior (Room T):
E/10
 perfect mat’l-no flaws
TSengineering << TS perfect
carefully produced glass fiber
E/100
typical ceramic
0.1
materials
materials
typical strengthened metal
typical polymer

• DaVinci (500 yrs ago!) observed...
-- the longer the wire, the
smaller the load for failure
failure.
• Reasons:
-- flaws cause premature failure.
-- larger
l
samples
l contain
t i llonger flflaws!!
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 - 15
Geometric Definitions
Chapter 8 - 16
Flaws are Stress Concentrators!
• Griffith Crack
1/ 2
a
m  2o  
 t 
t
 K t o
where
t = radius of curvature
o = applied stress
m = stress at crack tip
Chapter 8 - 17
Concentration of Stress at Crack Tip
Chapter 8 - 18
The 3 Modes of Crack Surface
Displacement
Chapter 8 - 19
Engineering Fracture Design
• Avoid sharp corners!

w
max
r,
fillet
radius
Stress Conc
Conc. Factor
Factor, K t =
max
0
2.5
2.0
increasing w/h
h
1.5
1.0
0
0.5
1.0
sharper
h
fill
fillett radius
di
r/h
Chapter 8 - 20
Crack Propagation
Cracks 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
ductile
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
q
energy
gy
Chapter 8 - 21
Something to Remember
(forever)
Compressive stress
Tensile stress
brittle
ductile
brittle
ductile
Tensile stresses acting on the crack induce crack propogation……very bad!
Compressive stresses acting on the crack cause crack closure…..good.
Chapter 8 - 22
Criterion for Crack Propagation
Crack propagates if crack-tip stress (m)
exceeds a critical stress ((c)
i.e., m > c
1/ 2
 2E s 
c  

 a 
where
– E = modulus of elasticity
– s = specific surface energy
– a = one half length of internal crack
For ductile materials => replace s with s + p
where p is p
plastic deformation energy
gy
Chapter 8 - 23
Plane Strain Fracture Toughness
KIc
For thin specimens, the value of Kc depends on the thickness.
However, when the speciment thickness is much greater than the
crack dimensions,, Kc becomes independent
p
of thickness under
which circumstances a plane strain condition exists leading to
plane strain fracture toughness KIc.
Mode 1
K Ic = Y   a
KIc is a material pproperty
p y like yyield strength!
g
24
Chapter 8 -
Things to Known and Understand
About KIc
1) Brittle materials have low KIc as there is no plasticity at the
front of the crack tip.
2)) Ductile materials have high
g KIc as the pplastic zone in front
of the crack tip makes crack propagation difficult. It may even
stop it.
3) KIc depends on temperature
temperature, strain rate and microstructure
(including grain size). KIc  as T , KIc  as strain rate ,
smaller the grain size the larger the KIc
K IcI = Y   a
25
Chapter 8 -
Fracture Toughness Ranges
Metals/
Alloys
100
K Ic (MPa
a · m0.55 )
70
60
50
40
30
p
Graphite/
Ceramics/
Semicond
Polymers
C-C(|| fibers) 1
Steels
Ti alloys
Al alloys
Mg alloys
Based on data in Table B.5,
C lli t & R
Callister
Rethwisch
th i h 8
8e.
20
Al/Al oxide(sf) 2
Y2 O 3 /ZrO 2 (p) 4
C/C( fibers) 1
Al oxid/SiC(w) 3
Si nitr/SiC(w) 5
Al oxid/ZrO 2 (p) 4
Glass/SiC(w) 6
10
7
6
5
4
Di
Diamond
d
Si carbide
Al oxide
Si nitride
3
0.7
0.6
0.5
PET
PP
PVC
2
1
Composites/
fibers
PC
<100>
100
Si crystal
<111>
Glass -soda
Concrete
PS
Glass 6
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
1
Handbook, Vol.
Vol 21
21, ASM Int
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.
Proc.,
Vol 7 (1986) pp
pp. 978
978-82.
82
Polyester
Chapter 8 - 26
27
Chapter 8 -
Design Against Crack Growth
• Crack growth condition:
K ≥ Kc = Y a
• Largest, most highly stressed cracks grow first!
--Scenario
Scenario 1: Max.
Max flaw
size dictates design stress.
design
d i
Kc

Y amax

fracture
no
fracture
--Scenario
Scenario 2: Design stress
dictates max. flaw size.
amax
amax
1  K c

  Ydesign




2
fracture
amax
no
fracture

Chapter 8 - 28
Design Example: Aircraft Wing
• Material has KIc = 26 MPa-m0.5
• Two designs to consider...
Design A
--use same material
--largest flaw is 4 mm
--failure
f il
stress
t
=?
--largest flaw is 9 mm
--failure stress = 112 MPa
c 
• Use...
Design B
K Ic
Y amax
• Key point: Y and KIc are the same for both designs.
KIc
=  a = constant
Y 
--Result:
112 MPa

c
9 mm
amax
  
A
4 mm
c
amax
Answer: (c )B  168 MPa

B
Chapter 8 - 29
How is it Measured…K
Measured KIc
30
Chapter 8 -
Impact Testing
• Impact loading:
(Charpy)
-- severe testing case
-- makes
k material
t i l more b
brittle
ittl
-- decreases toughness
Adapted from Fig
Fig. 8
8.12(b),
12(b)
Callister & Rethwisch 8e. (Fig.
8.12(b) is adapted from H.W.
Hayden, W.G. Moffatt, and J.
Wulff, The Structure and
Properties
p
of Materials,, Vol. III,,
Mechanical Behavior, John Wiley
and Sons, Inc. (1965) p. 13.)
fi l height
final
h i ht
i iti l h
initial
height
i ht
Chapter 8 - 31
Influence of Temperature on
Impact Energ
Energy
• Ductile-to-Brittle Transition Temperature (DBTT)...
(
)
Impac
ct Energy
FCC metals (e.g., Cu, Ni)
BCC metals (e.g., iron at T < 914ºC)
polymers
Brittle
tt e
o e Ductile
uct e
More
High strength materials (  y > E/150)
Temperature
Adapted from Fig. 8.15,
Callister & Rethwisch 8e.
Ductile-to-brittle
p
transition temperature
Chapter 8 - 32
Effect of Carbon Concentration on
Ductile to Brittle Transition in Plain C
Steels
Chapter 8 - 33
Design Strategy:
Stay
The
St Above
Ab
Th DBTT!
• Pre-WWII: The Titanic
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
Materials
Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard,
The Discovery of the Titanic.)
• WWII: Liberty
y 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
Materials
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.)
• Problem: Steels were used having DBTT’s just below
room temperature.
Chapter 8 - 34
Summary of Important Equations
You should Understand
35
Chapter 8 -
ANNOUNCEMENTS
Reading: Chapter 8 (Full chapter). Start studying
This chapter early. Don’t leave it to the last few
Da s leading to the Celebration of Learning 03
Days
HW Problems: TBA
36
Chapter 8 -