Chapter 8-
ISSUES TO ADDRESS...• How do flaws in a material initiate failure?• How is fracture resistance quantified; how do different material classes compare?• How do we estimate the stress to fracture?
1
• How do loading rate, loading history, and temperature affect the failure stress?
Ship-cyclic loadingfrom waves.
Computer chip-cyclicthermal loading.
Hip implant-cyclicloading from walking.
Adapted from Fig. 8.0, Callister 6e. (Fig. 8.0 is by Neil Boenzi, The New York Times.)
Adapted from Fig. 18.11W(b), Callister 6e. (Fig. 18.11W(b) is courtesy of National Semiconductor Corporation.)
Adapted from Fig. 17.19(b), Callister 6e.
CHAPTER 8:MECHANICAL FAILURE
Chapter 8-
Mechanical Failure
• The usual causes for failure are:– Improper materials selection and processing– Inadequate design– Misuse
• Cost of failure– 1000 Billions of $ or YTL annually– Loss of human life !
Chapter 8 -
Fracture mechanisms
• Ductile fracture– Occurs with plastic deformation
• Brittle fracture– Little or no plastic deformation– Catastrophic
Chapter 8 -
Ductile vs. Brittle Failure
Adapted from Fig. 8.3, Callister 7e.
cup-and-cone fracture brittle fracture
Chapter 8-
Heverill Fire Department aerial ladder failure from: http://www.engr.sjsu.edu/WofMatE/FailureAnaly.htm
From http://plane-truth.com/comet.htm
Chapter 8-
Mechanical Failure:How do materials break ?
• Fracture: crack growth to rupture at a critical load– Ductile vs Brittle fracture
– Principles of Fracture Mechanics• Stress Concentration
– Impact Fracture Testing
• Fatigue: crack growth due to cycling loads– Cyclic stresses, the S-N curve
– Crack initiation and propagation
– Factors that effect fatigue behavior
• Creep: high temperature plastic deformation– Stress and temperature effects
– Alloys for hi-temperature usage
Chapter 8-
Very Ductile
Moderately Ductile BrittleFracture
behavior:
Large Moderate%AR or %EL: Small
2
• Ductile fracture is desirable!
• Classification:
Ductile: warning before
fracture
Brittle: No warning
Failure is catastrophic
Adapted from Fig. 8.1, Callister 6e.
DUCTILE VS BRITTLE FAILURE
Substantial plastic deformationAbsorb high amounts of energy before fractureWhat is the reduction in x-sectional area ?
Chapter 8-
Fracture, in detail
• Two steps involved in fracture:– Crack formation– Crack growth
• Two fracture modes can be defined– Ductile (preferred, most metals and some polymers)
• extensive plastic deformation in the vicinity of a crack• Extension of crack length requires an increase in the applied load,
hence crack is stable unless stress is increased. Crack propagation is therefore slow
– Brittle (undesired, ceramics, metals at low temperatures)• Takes place w/o appreciable plastic deformation• Crack is unstable, will propagate with high speed once formed
and w/o increase in applied stress
Chapter 8-
Ductile vs Brittle
Q1:What is ductility ?
Q2: What is toughness?
Chapter 8 -
• Ductile failure: --one piece --large 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: Failure of a Pipe
• Brittle failure: --many pieces --small deformation
Observe the variation in the amount of plastic deformation
Chapter 8 -
• Evolution to failure:
• Resulting fracture surfaces (steel)
50 mm
particlesserve as voidnucleationsites.
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 mmFracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.
Moderately Ductile Failure
necking
void nucleation
void growth and linkage
shearing at surface fracture
Chapter 8-
Ductile Fracture
Cup and cone fracture in Aluminum
SEM of the fracture surface:Fractographic studies
Dimples, micro-cavities that initiate crack formation, on the surface will be observed during high resolution investigation of the cup and cone type fracture surfaces.
Cup Cone
Dimple
Micro-void
Chapter 8 -
• Intergranular(between grains)
• 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.)
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.
3 mm
4 mm160 mm
1 mm(Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p. 1119.)
Brittle Fracture Surfaces
Chapter 8-5
• INTERgranular (between grains)
• TRANSgranular (within grains)
Al Oxide(ceramic)
316 S. Steel (metal)
304 S. Steel (metal)
Polypropylene(polymer)
3m
4 mm160m
1 mm
BRITTLE FRACTURE SURFACES
1. No appreciable plastic deformation2. Fast moving crack3. Propagation direction is nearly 90º to
applied stress4. Crack often propagates by cleavage,
breaking of bonds along specific crystallographic planes, aka cleavage planes
Transgranular fracture: Cracks move in and through grains. Fracture surface have faceted texture because of different orientation of cleavage planes .
Intergranular fracture: Crack propagation isalong grain boundaries (grain boundaries are weak or embrittle due to impurity segregation, etc.)
Chapter 8 -
• Stress-strain behavior (Room T):
Ideal vs Real Materials
TS << TSengineeringmaterials
perfectmaterials
E/10
E/100
0.1
perfect mat’l-no flaws
carefully produced glass fiber
typical ceramic typical strengthened metaltypical polymer
• DaVinci (500 yrs ago!) observed... -- the longer the wire, the smaller the load for failure.• Reasons: -- flaws cause premature failure. -- Larger samples contain more flaws!
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-
Flaws ; Stress concentrators
• Fracture strength of a brittle solid is related to the cohesive forces between atoms, bond strength. It can be estimated that the theoretical cohesive strength of a brittle material should be around ~ E/10. But experimental fracture strength is normally E/100 - E/10,000.
• Much lower fracture strength is explained by the effect of stress concentration at microscopic flaws. The applied stress is amplified at the tips of micro-cracks, voids, notches, surface scratches, corners, etc. that are called stress concentrators raisers.
• The magnitude of this amplification depends on micro-crack orientations, geometry and dimensions.
TABLES 6.1 and 6.2In chapter 6
Chapter 8-7
• Elliptical hole in a plate:
• Stress distrib. in front of a hole:
• Stress concentration factor:
BAD! Kt>>3
o
2a
Kt max /o
• Large Kt promotes failure:
FLAWS ARE STRESS CONCENTRATORS!
Sharper cracks amplify stress !More important for brittle materials as in ductile material Plas. Dfm takes place and stress is distributed more uniformly around a crack !
max
t
2o
a
t
NOT SO BAD
Kt=2
Chapter 8 -
Flaws are Stress Concentrators!
Results from crack propagation• Griffith Crack
where t = radius of curvature
o = applied stress
m = stress at crack tip
ot
/
tom K
a
21
2
t
Adapted from Fig. 8.8(a), Callister 7e.
Chapter 8 -
Concentration of Stress at Crack Tip
Adapted from Fig. 8.8(b), Callister 7e.
Chapter 8 -
Engineering Fracture Design
r/h
sharper fillet radius
increasing w/h
0 0.5 1.01.0
1.5
2.0
2.5
Stress Conc. Factor, K t
max
o=
• Avoid sharp corners!
Adapted from Fig. 8.2W(c), Callister 6e. (Fig. 8.2W(c) is from G.H. Neugebauer, Prod. Eng. (NY), Vol. 14, pp. 82-87 1943.)
r , fillet
radius
w
h
o
max
Chapter 8-From http://plane-truth.com/comet.htm
Anything peculiar in this image !
Chapter 8-10
• Condition for crack propagation:
• Values of K for some standard loads & geometries:
2a2a
aa
K a K 1.1 a
K ≥ KcStress Intensity Factor:Depends on applied stress, crack length & component geometry.
Fracture Toughness:Depends on the material, temperature, environment, & rate of loading.
unitsof K :
MPa m
or ksi in
Adapted from Fig. 8.8, Callister 6e.
GEOMETRY, LOAD, & MATERIAL
Chapter 8 -
When Does a Crack Propagate?
Crack propagates if above critical stress
where– E = modulus of elasticity s = specific surface energy
– a = one half length of internal crack
– Kc = c/0
For ductile => replace s by s + p
where p is plastic deformation energy
212
/
sc a
E
i.e., m > c
or Kt > Kc
Chapter 8-
• t at a cracktip is verysmall!
9
• Result: crack tip stress is very large.
• Crack propagates when: the tip stress is large enough to make: distance, x,
from crack tip
tip K2x
tip
increasing K
K ≥ Kc
WHEN DOES A CRACK PROPAGATE?
Chapter 8 -
Crack Propagation
Cracks propagate due to sharpness of crack tip • A plastic material deforms at the tip, “blunting” the
crack.
deformed region
brittle
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 energy
plastic
Chapter 8-
• Energy to break a unit volume of material• Approximate by the area under the stress-strain curve.
20
smaller toughness- unreinforced polymers
Engineering tensile strain,
Engineering tensile stress,
smaller toughness (ceramics)
larger toughness (metals, PMCs)
TOUGHNESS & RESILIENCE
RESILIENCE is energy stored in the material w/o plastic deformation ! U r = σy2 / 2 E
TOUGHNESS is total energy stored in the material upon fracture !
Chapter 8 -
Fracture Toughness
Based on data in Table B5,Callister 7e.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 crystalGlass -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
40506070
100
Al oxideSi nitride
C/C( fibers) 1
Al/Al oxide(sf) 2
Al oxid/SiC(w) 3
Al oxid/ZrO 2(p)4Si nitr/SiC(w) 5
Glass/SiC(w) 6
Y2O3/ZrO 2(p)4
Kcmetals
Kccomp
KccerKc
poly
incr
easi
ng
Fracture toughness is the resistance of a material to brittle fracture when a crack is present !
Chapter 8 -
• Crack growth condition:
• Largest, most stressed cracks grow first!
Design Against Crack Growth
K ≥ Kc = aY
--Result 1: Max. flaw size dictates design stress.
max
cdesign
aY
K
amax
no fracture
fracture
--Result 2: Design stress dictates max. flaw size.
2
1
design
cmax Y
Ka
amax
no fracture
fracture
Chapter 8 -
• 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 c• Reducing flaw size pays off!
• Material has Kc = 26 MPa-m0.5
Design Example: Aircraft Wing
• Use...max
cc
aY
K
c amax A
c amax B
9 mm112 MPa 4 mm --Result:
Chapter 8 -
Loading Rate
• Increased loading rate... -- increases y and TS -- decreases %EL
• Why? An increased rate gives less time for dislocations to move past obstacles.
y
y
TS
TS
larger
smaller
Chapter 8 -
Impact Testing
final height initial height
• Impact loading: -- severe testing case -- makes material more brittle -- decreases toughness
Adapted from Fig. 8.12(b), Callister 7e. (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 -
• Increasing temperature... --increases %EL and Kc
• Ductile-to-Brittle Transition Temperature (DBTT)...
Temperature
BCC metals (e.g., iron at T < 914°C)
Imp
act
Ene
rgy
Temperature
High strength materials (y > E/150)
polymers
More Ductile Brittle
Ductile-to-brittle transition temperature
FCC metals (e.g., Cu, Ni)
Adapted from Fig. 8.15, Callister 7e.
Chapter 8-
DBTT
1. As temperature decreases a ductile material can become behave brittle - ductile-to-brittle transition
2. FCC metals remain ductile down to very low temperatures.3. For ceramics, this type of transition occurs at much higher
temperatures than for metals.4. The ductile-to-brittle transition can be measured by impact testing:
the impact energy needed for fracture drops suddenly over a relatively narrow temperature range – temperature of the ductile-to-brittle transition.
Chapter 8 -
• Pre-WWII: The Titanic • WWII: Liberty ships
• Problem: Used a type of steel with a DBTT ~ Room temp.
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:Stay Above The DBTT!
Chapter 8-17
• Fatigue = failure under cyclic stress.
tension on bottom
compression on top
countermotor
flex coupling
bearing bearing
specimen
• Stress varies with time. --key parameters are S and
m
max
min
time
mS
• Key points: Fatigue... --can cause part failure, even though max <
critical. --causes ~ 90% of mechanical engineering failures.
Adapted from Fig. 8.16, Callister 6e. (Fig. 8.16 is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.)
FATIGUE
Load
Explain!
Chapter 8-
FATIGUE
• How ?– Under fluctuating / cyclic stresses, failure can occur at loads considerably
lower than tensile or yield strengths of material under a static load:
• Important ?– Estimated to causes 90% of all failures of metallic structures (bridges,
aircraft, machine components, etc.)
• What is the failure type ?– Fatigue failure is brittle-like (relatively little plastic deformation) - even in
normally ductile materials. Thus sudden and catastrophic!
• Applied stresses causing fatigue may be axial (tension or compression), flextural (bending) or torsional (twisting).
• Fatigue failure proceeds in three distinct stages: – Crack initiation in the areas of stress concentration (near stress raisers), – incremental crack propagation, – final catastrophic failure.
Chapter 8-
Periodic and symmetricalRotating Car axle
Periodic and asymmetrical
Random stress fluctuations
Chapter 8 -
• Fatigue limit, Sfat:
--no fatigue if S < Sfat
Adapted from Fig. 8.19(a), Callister 7e.
Fatigue Design Parameters
Sfat
case for steel (typ.)
N = Cycles to failure103 105 107 109
unsafe
safe
S = stress amplitude
• Sometimes, the fatigue limit is zero!
Adapted from Fig. 8.19(b), Callister 7e.
case for Al (typ.)
N = Cycles to failure103 105 107 109
unsafe
safe
S = stress amplitude
Chapter 8-18
• Fatigue limit, Sfat: --no fatigue if S < Sfat
• Sometimes, the fatigue limit is zero!
Adapted from Fig. 8.17(a), Callister 6e.
Adapted from Fig. 8.17(b), Callister 6e.
FATIGUE DESIGN PARAMETERS
Sfat
case for Steel % Ti
N = Cycles to failure103 105 107 109
unsafe
safe
S =
str
ess
amp
litu
de
case for Al (typ.)
N = Cycles to failure103 105 107 109
unsafe
safe
S =
str
ess
amp
litu
de
• For steels Sfat = 35%-60% of YS
• Think about design criteria factor, N in chapter 6
Low cycle fatigue: high loads, plastic and elastic deformationHigh cycle fatigue: low loads, elastic deformation (N > 105)
Endurance Limit
Chapter 8-19
• Crack grows incrementally
dadN
K mtyp. 1 to 6
~ a
increase in crack length per loading cycle
• Failed rotating shaft --crack grew even though
Kmax < Kc
--crack grows faster if • increases • crack gets longer • loading freq. increases.
crack origin
Adapted fromFig. 8.19, Callister 6e. (Fig. 8.19 is from D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.)
FATIGUE MECHANISM
Chapter 8 -
Improving Fatigue Life
1. Impose a compressive surface stress (to suppress surface cracks from growing)
N = Cycles to failure
moderate tensile mLarger tensile m
S = stress amplitude
near zero or compressive mIncreasing
m
--Method 1: shot peening
put surface
into compression
shot--Method 2: carburizing
C-rich gas
2. Remove stress concentrators. Adapted from
Fig. 8.25, Callister 7e.
bad
bad
better
better
Adapted fromFig. 8.24, Callister 7e.
Chapter 8-
1. Impose a compressive surface stress (to suppress surface cracks from growing)
20
--Method 1: shot peening
2. Remove stress concentrators.
bad
bad
better
better
--Method 2: carburizing
C-rich gasput
surface into
compression
shot
Adapted fromFig. 8.23, Callister 6e.
N = Cycles to failure
moderate tensile mlarger tensile m
S = stress amplitude
near zero or compressive m
Adapted fromFig. 8.22, Callister 6e.
IMPROVING FATIGUE LIFE
POLISH THE SURFACE !
Chapter 8-
timeelastic
primary secondary
tertiary
T < 0.4 Tm
INCREASING T
0
strain,
• Occurs at elevated temperature, T > 0.4 Tmelt
• Deformation changes with time.
21
Adapted fromFigs. 8.26 and 8.27, Callister 6e.
CREEP
0 t
Chapter 8-
• Most of component life spent here.• Strain rate is constant at a given T, --strain hardening is balanced by recovery
22
stress exponent (material parameter)
strain rateactivation energy for creep(material parameter)
applied stressmaterial const.
• Strain rate increases for larger T,
10
20
40
100
200
Steady state creep rate (%/1000hr)10-2 10-1 1
s
Stress (MPa)427C
538C
649C
Adapted fromFig. 8.29, Callister 6e.(Fig. 8.29 is from Metals Handbook: Properties and Selection: Stainless Steels, Tool Materials, and Special Purpose Metals, Vol. 3, 9th ed., D. Benjamin (Senior Ed.), American Society for Metals, 1980, p. 131.)
s K2nexp
QcRT
.
SECONDARY CREEP
Chapter 8-
• Failure: along grain boundaries.
23
time to failure (rupture)
function ofapplied stress
temperature
T(20 logtr ) L
L(103K-log hr)
Str
ess
, ks
i
100
10
112 20 24 2816
data for S-590 Iron
20appliedstress
g.b. cavities
• Time to rupture, tr
• Estimate rupture time S 590 Iron, T = 800C, = 20 ksi
T(20 logtr ) L
1073K
24x103 K-log hr
Ans: tr = 233hr
Adapted fromFig. 8.45, Callister 6e.(Fig. 8.45 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).)
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.)
CREEP FAILURE
Chapter 8-24
• 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 and T < 0.4Tm, failure stress decreases with: increased maximum flaw size, decreased T, increased rate of loading.-for cyclic : cycles to fail decreases as increases.
-for higher T (T > 0.4Tm): time to fail decreases as or T increases.
SUMMARY (I)
Chapter 8-
SUMMARY (II)
Chapter 8-
Reading: Chapter 8 and Chapter 9 at least twice !Use the CD and review Chapter 7 and 8 !
Core Problems: 8.7,8.10, 8.13, 8.17, 8.22
Self-help Problems: 8.1, 8.2, 8.3, 8.15, 8.20, 8.21
0
ANNOUNCEMENTS
Homework due January 5th , 2009