8 Chapter - Failure
Lectures begin Mar. 27 or Apr. 1, 08
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Chapter 8: Failure
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? How do loading rate, loading history, and temperature affect the failure stress?
Welded ship fracture stress at low temperature
Computer chip-cyclic thermal loading.
Hip implant-cyclic loading from walking.
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Fracture mechanisms
Fracture
Ductile fracture
Requires much plastic flow and energy dissipation
Brittle fracture
Little or no plastic flow and often catastrophic failure
Fracture under repetitive loading Fatigue
Can be ductile and brittle, or just brittle
Fracture under constant loading at high temperatures (>~0.6TM) Creep
At high temperature, thermal activation allows timedependent plastic flow even at constant stress ductile failure modes
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Ductile vs Brittle Failure
Classification:
Fracture behavior: Very Ductile Moderately Ductile Brittle
%AR or %EL
Ductile fracture is usually desirable!
Large
Ductile: warning before fracture
Moderate
Small
Brittle: No warning
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Examples: Ductile and Brittle Failure of a Pipe
Ductile failure:
--one piece --large deformation
Brittle failure:
--many pieces --small deformations
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Moderately Ductile Failure
Evolution to failure:
necking
void nucleation
void growth and linkage
shearing at surface
fracture
Resulting fracture surfaces
(steel)
particles serve as void nucleation sites.
50 mm 50 mm
100 mm
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Ductile fracture summary
ductile
Macroscopic neck appears
Stress increases in necked region and thus stress changes from homogenous to inhomogeneous
Intense local flow tears around precipitates and inclusions to produce microvoids that elongate to produce macrovoids Load carrying cross-section continually decreases so load must be carried by strong work-hardening Finally work-hardening cannot support the load and rapid fracture occurs A cup and cone is characteristic of the slow (cup) and fast (cone) fracture
brittle
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Brittle Failure
Arrows indicate point where failure originates
Dark area is a rough, energy-absorbing area it is where the crack started, bright means little energy dissipation easy propagation part
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Brittle Fracture Surfaces
Intergranular
(between grains)
304 Stainless Steel (SS) (metal)
Intragranular
(within grains)
316 SS (metal)
4 mm
160 mm
Polypropylene (polymer)
Al oxide (ceramic)
3 mm 1 mm
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Little work is done in brittle fracture = very little energy is dissipated as crack passes through material
Fracture path is straight and can be either transgranular (cleavage) or intergranular schematic below shows transgranular (within grain) fracture grains crack path Ductile cast iron showing mainly Fe and occasional graphite grains
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A view of intergranular fracture
grains crack path
Notice how smooth the fracture is and thus how little energy is expended Intergranular fracture is generally very bad! Can be produced by bad heat treatments that segregate noxious elements to GBs 11 e.g. P and S to steel grain boundaries (GB) by heat treatments at 300-500C
Real materials contain flaws and the flaws matter
Stress-strain behavior (Room Temperature):
E/10
perfect mat'l-no flaws
carefully produced glass fiber typical ceramic 0.1
TSengineering << TS perfect
materials materials
E/100
typical strengthened metal typical 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!
Key point fracture does not occur at E/10 but at much, much less
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Fracture mechanics
Fracture mechanics is a quantitative approach to predicting and thus avoiding failure It quantifies the relations between
Material properties Stress level Presence of flaws Crack propagation mechanisms
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Engineering Fracture Design
Avoid sharp corners o max Stress Conc. Factor, K t =
w
max
2.5 2.0 1.5 1.0 0 0.5 1.0 sharper fillet radius increasing w/h
o
r, fillet radius
h
r/h
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Flaws are Stress Concentrators
Results from crack propagation Griffith Crack criterion
a m = ( max ) = 2 o t
t where
1/ 2
= K t o
t = radius of curvature o = applied stress m = max =stress at crack tip Kt = stress concentration factor (unitless)
a K t = 2 t
1 2
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Crack Propagation
Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip, "blunting" the crack. deformed region
brittle
plastic
Energy balance on the crack Elastic strain energy-
Crack tip radius ~ a0 ~ 1nm versus very blunted tip of radius 1-100 m
energy stored in material as it is elastically deformed (E2/unit vol) this energy is released when the crack propagates creation of new surfaces requires energy (2s J/m2)
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When Does a Crack Propagate?
Crack propagates when the max stress (m) at the crack is greater than a critical stress c 1/ 2 i.e., m > c 2E s c = a or Kt > Ktc = critical stress conc.
where
E = modulus of elasticity (MPa = N/m2) s = specific surface energy (J/m2 = N/m) a = half length of crack (m) Ktc = c/0 (unitless)
For ductile fracture, replace s by s + p
where p is plastic deformation energy and 102-104 times s
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Fracture Toughness Kc and KIc
K c = Y c a
1 2
where Y 1 and Y is unitless
2 E s 0.5 0.5 Kc = Y (a ) = Y (2 E s ) a valid for brittle materials - but much too small for ductile materials
1 2
K c has units of MPa m
K Ic = K c when deformation is tensile plane strain
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Fracture modes
3 crack displacement modes: Mode I is the most critical plane strain tensile Kc is then written as KIc and is the plane strain fracture toughness Mode I tensile plane strain
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Fracture Toughness
Metals/ Alloys 100 70 60 50 40
Steels Ti alloys Al alloys Mg alloys 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
Graphite/ Ceramics/ Semicond
Polymers
Composites/ fibers
C-C(|| fibers) 1
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.
K Ic (MPa m 0.5 )
30 20 10 7 6 5 4 3 2
Diamond Si carbide Al oxide Si nitride PET PP PVC PC
KIC ~ 1 MPa.m1/2 means brittle plastic zone is very small
Glass 6
1 0.7 0.6 0.5
Si crystal <111> Glass -soda Concrete
<100>
PS Polyester
100 MPa.m1/2 significant means plasticity and 20 a tough material
Design Against Crack Growth
Y a Largest, most stressed cracks grow first! For design to prevent crack growth, can vary 2 out of 3 of the quantities KIc, , and a
Ex.1. Set KIc (choose
material) and amax
Crack growth condition:
> c =
K Ic
Y~1
Ex. 2. Set KIc (choose material) and design
design
K Ic < Y amax
amax
1 K Ic < Y design
2
fracture no fracture
amax
fracture
amax
no fracture
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Design Example: Aircraft Wing
Material has KIc = 26 MPa-m0.5 Two designs to consider... Design B Design A
--largest flaw is 9 mm --failure stress = 112 MPa --use same material --largest flaw is 4 mm --failure stress = ?
Use...
K Ic c = Y amax
112 MPa
Key point: Y and KIc are the same in both designs.
--Result:
(
9 mm
c
amax
) = (
A
4 mm
c
amax
)
B
Answer: ( c )B = 168 MPa Reducing flaw size pays off! Good fracture mechanics design 22 builds the minimum detectable flaw size into the design
Loading Rate
-- increases y and TS -- decreases %EL
Increase loading (strain) rate
Why? Increasing the
deformation rate gives less time for dislocations to move past obstacles.
What are the units for ?
y
TS
larger TS smaller
y
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Charpy Impact Testing
Impact loading:
-- severe testing case -- makes material more brittle -- decreases toughness
(Charpy)
final height
initial height 24
Ductile-Brittle Transition Temperature
Increasing temperature...
--increases %EL and KIc
Ductile-to-Brittle Transition Temperature (DBTT)...
FCC metals (e.g., Cu, Ni)
Impact Energy
BCC metals (e.g., iron at T < 914C) polymers Brittle More Ductile High strength materials ( y > E/150)
Temperature
Ductile-to-brittle transition temperature
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Stay Above The DBTT plain C steel is around RT!
Pre-WWII: The Titanic WWII: Liberty ships
Problem: Used a type of steel with a DBTT ~ Room temp. so
the steel became brittle in cold water.
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Fatigue 90% of all failures?
Fracture under dynamic or fluctuating stress at much less than TS or even y
Often occurs without warning and may be catastrophic Often brittle-like failure (little or no plastic deformation or very localized), even in normally ductile materials
Taking precautions against fatigue fracture is vital
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Fatigue testing
Rotating bend test is common
specimen compression on top
bearing bearing motor counter
flex coupling tension on bottom
max m min
a
time
Stress varies with time. -- key parameters are a (stress
amplitude), m, stress ratio, R = 28 min/max) and frequency
Fatigue curves - 1
Fatigue limit, Sfat:
--no fatigue if S < Sfat
Typical of steels
Sfat
3
S = stress amplitude Unsafe = fatigue failure Safe = no fatigue failure 10 10 5 10 7 10 9 N = Cycles to failure
Sometimes, the fatigue limit is zero! Typical of non-ferrous metals
S = stress amplitude unsafe safe 10 3 10 5 10 7 10 9 N = Cycles to failure
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Fatigue curves - 2
In fact, fatigue is statistical because it depends on so many factors
Looks well defined but............
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Fatigue Mechanism
Crack grows in response to the fluctuating stress thus incrementally typ. 1 to 6 da m = (K ) dN
~ ( ) a
increase in crack length per loading cycle crack origin
Failed rotating shaft
--crack grew even though Kmax < Kc --crack grows faster as
increases crack gets longer loading frequency increases.
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Macroscopic and microscopic
At left we see the whole sample and macroscopic marks that show the extent of crack propagation in each major cycle, while at right by TEM we see the striations 32 produced by the advance of the crack during one load cycle
Improving Fatigue Life
1. Impose a compressive surface stress
(to suppress surface cracks from growing)
m
S = stress amplitude Increasing near zero or compressive m moderate tensile m Larger tensile m N = Cycles to failure
--Method 1: shot peening
shot put surface into compression
--Method 2: carburizing
C-rich gas
2. Remove stress concentrators.
bad bad
better
.
better
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Environmental factors
Stress-corrosion cracking is particularly bad
E.g. salt Cl- ion is very bad for many steels, even stainless steel Avoid (not easy) or protect (e.g. Cr plate) Be aware of the potential for such cracking
E.g. use stainless steel rebar for pre-tensioning concrete roadways in key areas
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Creep
Time dependent deformation at high temperatures when thermal activation allows slip in response to the applied stress
Will start at about 0.4-0.6 TM, depending on material and level of strain that is important
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Creep Curve and testing
Deformation at constant stress () vs. time ,
0
t
Primary Creep: slope (creep rate) decreases with time. Secondary Creep: steady-state i.e., constant slope. Tertiary Creep: slope (creep rate) increases with time, i.e. rate accelerates
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Creep
Primary or transient creep initial dislocation movement followed by work-hardening Secondary or steady state creep hardening due to dislocation motion is in balance with softening due to annealing of defects Tertiary creep or the rupture phase necking occurs and stress cannot be supported, leading to failure
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Creep curves
Plots are logarithmic
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Secondary Creep defines the window where the material can be used (,T)
Strain rate is constant at a given T and
-- strain hardening is balanced by recovery
stress exponent (material parameter)
strain rate material const.
Qc & s = K 2 exp - RT
n
activation energy for creep (material parameter)
What are units for K2 when n = 4? 427C 538 C
applied stress
200 100 40 20 10 10 -2 10 -1 Steady state creep rate
Strain rate increases for higher T and
n ~4 very often
Stress (MPa)
649 C 1 s (%/1000hr)
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Mechanisms of Creep
Dislocations control plastic flow at lower T and stress, changing to grain boundary sliding at higher T and stress
Use stable precipitates to block dislocation motion (like low-temperature strengthening) Use single crystal, not polycrystalline material (unlike low-temperature strengthening)
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Creep Failure Larson-Miller (L) prediction
Failure:
along grain boundaries.
g.b. cavities applied stress
data for S-590 Iron 1 12 16 20 24 28 L(10 3 K-log hr)
Estimate rupture time
S-590 Iron, T = 800C, = 20 ksi
100 20 10 Stress, ksi
Time to rupture, tr
temperature
24x103 K-log hr
T ( 20 + logt r ) = L
T ( 20 + logt r ) = L
1073K
function of applied stress time to failure (rupture)
Ans: tr = 233 hr
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Alloys for high temperature use
Turbine blades are the summit of HT creepresistant design
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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 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.
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