Engineering 45
Material
Failure (1)
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Learning Goals.1 – Failure
 How Flaws In A Material Initiate Failure
 How Fracture Resistance is Quantified
• How Different Material Classes Compare
 How to Estimate The Stress at Fracture
 Factors that Change the Failure Stress
• Loading Rate
• Loading History
• Temperature
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Learning Goals.2 – Failure
 FATIGUE Failure
• Fatigue Limit
• Fatigue Strength
• Fatigue Life
 CREEP at Elevated Temperatures
• Incremental Yielding at <σy Over a Long
Time Period at Elevated Temperature
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Ductile vs Brittle Fracture
• Classification:Fracture
behavior:
• Ductility:
%Ra or %EL : Large
• Ductile
fracture is
desirable!
Engineering-45: Materials of Engineering
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Very
Ductile
Moderately
Ductile
Brittle
Moderate
Small
Ductile:
warning before
fracture
Brittle:
No
warning
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Example: Pipe Failure
 Ductile Failure
• One Piece
• Large Deformation
• LEAK before BURST
 Brittle Failure
• Many Pieces
• Small Deformation
• EXPLOSIVE Burst
– NOT Good
Engineering-45: Materials of Engineering
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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.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Fracture Formation

Fracture Formation
Steps
1. Crack Initiation
2. Crack Propagation
 DUCTILE Fracture
• Significant PLASTIC
Deform. at Crack Tip
• Crack(s) Grow
Relatively Slowly
 BRITTLE Fracture
Engineering-45: Materials of Engineering
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• Once Brittle-Crack
Starts Propagation
can NOT be stopped
– Can Proceed at
Speeds up to
MACH-1Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Moderately Ductile Fracture
 Stages to Fracture upon Loading
necking
s
void
nucleation
void growth
and linkage
shearing
at surface
fracture
s
50
50mm
mm
 Resulting
From V.J. Colangelo and F.A. Heiser,
of Metallurgical Failures
fracture Analysis
(2nd ed.), Fig. 11.28, p. 294, John
and Sons, Inc., 1987. (Orig.
surfaces Wiley
source: P. Thornton, J. Mater. Sci.,
(steel) Vol. 6, 1971, pp. 347-56.)
Engineering-45: Materials of Engineering
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Fracture surface of tire cord wire
loaded in tension. Courtesy of F.
Roehrig, CC Technologies,
Dublin,100
OH. Used
mm with
permission.
Particles serve as void
nucleation sites
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Ductile vs. Brittle Tensile Failure
 Ductile Failure
 Brittle Failure
 “Cup-and-Cone”
Fracture Surface
 “Matted” Fracture
Surface
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Brittle-Fracture Surfaces
• Intragranular
• Intergranular
(between grains)
4 mm
304 S. Steel
(metal)
Reprinted w/permission
(metal)
from "Metals
Reprinted w/ permission
Handbook", 9th ed, Fig.
from "Metals
633, p. 650. Copyright Handbook", 9th ed, Fig.
1985, ASM
650, p. 357. Copyright
International, Materials
1985, ASM
Park, OH. (Micrograph International, Materials
by J.R. Keiser and A.R.
Park, OH. (Micrograph
Olsen, Oak Ridge
by D.R. Diercks,
National Lab.)
Argonne National Lab.)
Polypropylene
(polymer)
1 mm
160mm
Al Oxide
(ceramic)
Reprinted w/
Reprinted w/ permission
permission from R.W.
from "Failure Analysis
Hertzberg,
of Brittle Materials", p.
"Deformation and
78. Copyright 1990, The
Fracture Mechanics
American Ceramic
of Engineering
Society, Westerville,
Materials", (4th ed.)
OH. (Micrograph by
Fig. 7.35(d), p. 303,
R.M. Gruver and H.
John Wiley and Sons,
Kirchner.)
Inc., 1996.
Engineering-45: Materials of Engineering
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(within/across
grains)
316 S.
Steel
3mm
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Brittle-Fracture
 Characteristics of Brittle
Fracture
• No Significant Deformation
• Proceeds by Rapid Crack
Propagation
• Crack Direction Almost  to
Applied Load
• Relatively Flat Fracture
Surface
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Ideal vs Real materials
 Rm-Temp Stress-Strain Behavior
s
E/10
perfect mat’l-no flaws
carefully produced glass fiber
E/100 typical ceramic
TS Engineering  TS Perfect
Materials
typical strengthened metal
typical polymer
0.1
e
• DaVinci (500 yrs ago!) Observed
– The LONGER the Wire, the
SMALLER to Load Needed to Cause
Failure
• Reasons
– Matl Flaws Cause Premature Failure
– Larger samples have more flaws
Engineering-45: Materials of Engineering
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Materials
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.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
6
Stress Concentration
 Elliptical hole in a plate:
so
s
2a
 σ distrib. in front of hole:
ρt  Local Hole,
or CrackTip,
Radius
 Define Stress
Concentration Factor:
 Large Kt Promotes
Facture-Failure
NOT
SO
BAD
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Kt=3
BAD!
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Kt>>3
Engineering Fracture Design
• Avoid sharp corners!
s
so
Stress Conc. Factor, Kt= max
s
o
w
smax
h
r
= Fillet
Radius
2.5
2.0
increasing w/h
1.5
1.0
Engineering-45: Materials of Engineering
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0
0.5
1.0
sharper fillet radius
r/h
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
8
Griffith Theory of Brittle Fracture
 A. A. Griffith (1920s)
proposed that very small,
MICROSCOPIC cracks
weaken brittle materials
• This is why the theoretical
Tensile strength of a brittle
elastic solid (~E/10) is not
achieved
 Griffith proposed that all
brittle materials contain a
POPULATION of small
cracks and flaws that have a
VARIETY of sizes, shapes,
and orientations
Engineering-45: Materials of Engineering
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 Fracture occurs when the
THEORETICAL cohesive
strength of the material is
exceeded at the TIP of one
of these flaws
• This was shown with glass,
where very fine and superstrong WHISKERS were
shown to have strengths
CLOSE to the
THEORETICAL
• However, larger samples
very quickly form surface
flaws, and the strength
drops!
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Glass Rod Bending Fracture
 Cantilever-Load on
Glass Rod
 Load to Failure by
Brittle Fracture
 The Fracture
Surface
Engineering-45: Materials of Engineering
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 The Facture Surface
displays 3, more or
less, Distinct
Regions
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Glass Rod Bending Fracture
 Mirror Zone  A smooth region surrounding the fracture origin
 Mist Zone  A small band of rougher surface surrounding the
mirror region.
 Hackle Zone  Area composed of large irregularly oriented facets.
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Crack Propagation
 Cracks propagate due to SHARPNESS
of the crack tip
 A PLASTIC material DEFORMS at the tip,
“blunting” the crack
Deformed
Region
Brittle
plastic
 Perform Energy balance on the crack
• Elastic 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
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Griffith Brittle-Fracture Theory
 When a Crack
Propagates
• There is a RELEASE
of Elastic Strain
Energy
• There is Energy
CONSUMED To
Extend The Crack By
Creating NEW
Fracture Surfaces
 Griffith’s Proposal for
Crack Propagation
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• Propagation Requires
– [release of elastic strain
energy] > [energy
required to form new
crack surfaces]
sc 
2 E s
a
– sc  Critical Stress for
Crack Propagation (Pa)
– E  Elastic Modulus (Pa)
– s  Surface Energy (J/m)
– a  Crack Length
(m)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Example – Brittle Fracture
 Given Glass Sheet
with
• Tensile Stress,
s = 40 Mpa
• E = 69 GPa
•  = 0.3 J/m
 Find Maximum
Length of a
Surface Flaw
 Plan
Engineering-45: Materials of Engineering
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• Set sc = 40Mpa
• Solve Griffith Eqn for
Edge-Crack Length
a
2 E s
2
sapplied
 Solving
a


2 69  109 N/m 2 0.3 N/m 
 40 10 N/m
6
a  8.2  10 6 m  8.2 µm
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt

2 2
When Does a Crack Propagate?
 The Crack Tip
Radius, ρt, can
be Quite Small
 Thus σCrk-Tip can be
Very Large
 Crack propagates when
the tip stress is large
enough to make:
K ≥ Kc
• Kc  Fracture Toughness
(MPa•m)
stip
stip 
K
2 a
increasing K
distance, x,
from crack tip
– Cool units
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
K, Kc: Geometry, Load, Matl
 Recall Condition for Crack Propagation
K ≥ Kc
Stress Intensity Factor:
--Depends on load &
geometry.
Fracture Toughness:
--Depends on the material,
temperature, environment,
&
rate of loading.
• Values of K for Some Standard Loads & Geometries
s
s
units of K :
K  s a
2a
2a
MPa m
a
K  1.1s a
or ksi in
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Crack Extension Modes
 Cracks can Extend in 3 Modes: I, II, III
• Mode-I:
• Mode-II: Shearing
Opening Mode
or Sliding Mode
• Mode-III: Tearing or
AntiPlane Mode
 Combination of Modes Can Occur; Particularly
Modes I+III (think Drive Shaft)
 Mode-I is By Far the Most Common
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
KIc for Several Metals
Engineering-45: Materials of Engineering
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 Higher Values
of KIc are
Desired
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
increasing
Fracture Toughness
Based on data in Table B5,
Callister 6e.
Composite reinforcement geometry
is: f = fibers; sf = short fibers; w =
whiskers; p = particles. Addition
data as noted (vol. fraction of
reinforcement):
Engineering-45: Materials of Engineering
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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.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
11
Design Against Crack Growth
• Crack growth condition: K ≥ Kc
(Y  Unitless Geometry Factor)
Ys a
• Largest, most stressed cracks grow first
--Result 1: Max flaw size
--Result 2: Design stress
dictates design stress.
dictates max. flaw size.
2


1  K c

a max  
 Ysdesign 

sdesign 
Kc
Y a max
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
12
The Y-Parameter
 Y for Some Geometries and Loading
• B  Material Base-depth (into Screen/Page)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Design Ex: Aircraft Wing
• Material has KIc = 26 MPa-m0.5
• Two designs to consider...
Design B
Design A
--largest physical flaw is 9 mm
--failure stress = 112 MPa
K Ic
• Use... s c 
Y amax
--use same material
--largest physical flaw is 4
mm
--failure stress = ?
• Key point: Y and KIc are the same in both designs.
--Result:
112 MPa 9 mm
sc
a max
A  sc
• Reducing flaw size pays off!
Engineering-45: Materials of Engineering
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4 mm
a max
B
Answer:
sc B  168MPa
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
13
Loading Rate
 Increased
Loading Rate
s
sy
• INcreases σy and TS
• DEcreases %EL
sy
 Reason
• An increased rate
gives less time for
dislocations to move
past obstacles
Engineering-45: Materials of Engineering
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TS
Larger de/dt
TS
Smaller de/dt
e
 Thus Material
Deformation Can Be
Different based on
the DYNAMICS of
the Load Application
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Temperature Effects
 Increasing Temperature Increases %EL & Kc
Impact Energy
• As Discussed Previously, Some Materials Exhibit a
Ductile-to-Brittle Transition-Temperature (DBTT)
BCC metals (e.g., iron at T < 914C)
polymers
Brittle
More Ductile
High strength materialsσy>E/150)
Temperature
Ductile-to-brittle
transition temperature
Engineering-45: Materials of Engineering
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Charpy V-Notch
(CVN) Impact Test
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
Design Criteria: Stay Above 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 Sons, Inc., 1996. (Orig.
source: Dr. Robert D. Ballard, The Discovery of
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.)
 Problem: DBTT ~ Room Temperature
• Fabricate-OK; CRACK in Cold Water
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt
WhiteBoard Work
 None Today
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-19_Failure-1.ppt