jiangyu li, university of washington yielding and failure criteria plasticity fracture fatigue...
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Jiangyu Li, University of Washington
Yielding and Failure CriteriaPlasticityFractureFatigue
Jiangyu LiUniversity of Washington
Mechanics of Materials Lab
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Jiangyu Li, University of Washington
Failure Criteria
• Materials Assumed to be perfect:– Brittle Materials
• Max Normal Stress
– Ductile Materials• Max Shear Stress• Octahedral Shear
Stress
• Materials have flaw or crack in them:– Linear Elastic Fracture
Mechanics (LEFM)• Stress intensity factor (K)
describes the severity of the existing crack condition
• If K exceeds the Critical stress intensity (Kc), then failure will occur
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Jiangyu Li, University of Washington
Maximum Normal Stress Fracture Criterion
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Jiangyu Li, University of Washington
Octahedral Shear Stress Criterion
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Jiangyu Li, University of Washington
Safety Factor and Load Factor
• 7. 32 A circular bar must support a axial loading of 200 kN and a torque of 1.5 kN.m. Its yield strength is 260 MPa.– What diameter is needed if load factors YP=1.6 and YT=2.5
are required.
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Jiangyu Li, University of Washington
Stress Strain Curve
Bauschinger Effect
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Jiangyu Li, University of Washington
Elastic-Perfect Plastic and Linear Hardening
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Jiangyu Li, University of Washington
Power Hardening and Ramberg-Osgood Relation
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Jiangyu Li, University of Washington
Secant Modulus
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Jiangyu Li, University of Washington
Stress-Strain Curve
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Jiangyu Li, University of Washington
Displacement Mode
Opening mode Sliding mode Tearing mode
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Jiangyu Li, University of Washington
Stress Concentration
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Jiangyu Li, University of Washington
Stress Intensity Factor: Tension
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Jiangyu Li, University of Washington
Stress Intensity Factor: Bending
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Jiangyu Li, University of Washington
Stress Intensity Factor: Circumferential Crack
-
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Jiangyu Li, University of Washington
Stress Intensity Factor
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Jiangyu Li, University of Washington
Superposition
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Jiangyu Li, University of Washington
Brittle vs. Ductile Behavior
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Jiangyu Li, University of Washington
Plastic Zone
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Jiangyu Li, University of Washington
Limitation of LEFM
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Jiangyu Li, University of Washington
Effect of Thickness
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Jiangyu Li, University of Washington
Correlation with Strength
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Jiangyu Li, University of Washington
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Jiangyu Li, University of Washington
Energy Release Rate
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Jiangyu Li, University of Washington
Strain Energy
Modulus of toughness & modulus of resilience
Increasing the strain rate increase strength, but
decrease ductility
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Jiangyu Li, University of Washington
Impact Test
• Charpy V-notch & Izod tests most common
• Energy calculated by pendulum height difference
• Charpy – metals, Izod - plastics
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Jiangyu Li, University of Washington
Trend in Impact Behavior
• Toughness is generally proportional to ductility• Also dependent on strength, but not so strongly• Brittle Fractures
– Lower energy– Generally smooth in appearance
• Ductile Fracture– Higher energy– Rougher appearance on interior with 45° shear lips
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Jiangyu Li, University of Washington
Effect of Temperature
Decrease temperature increase strength, but decrease ductility
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Jiangyu Li, University of Washington
Ductile-Brittle Transition
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Jiangyu Li, University of Washington
Static Failure
• Load is applied gradually• Stress is applied only once• Visible warning before failure
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Jiangyu Li, University of Washington
Cyclic Load and Fatigue Failure
• Stress varies or fluctuates, and is repeated many times
• Structure members fail under the repeated stresses
• Actual maximum stress is well below the ultimate strength of material, often even below yield strength
• Fatigue failure gives no visible warning, unlike static failure. It is sudden and catastrophic!
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Jiangyu Li, University of Washington
Characteristics
• Primary design criterion in rotating parts.• Fatigue as a name for the phenomenon based
on the notion of a material becoming “tired”, i.e. failing at less than its nominal strength.
• Cyclical strain (stress) leads to fatigue failure.• Occurs in metals and polymers but rarely in
ceramics.• Also an issue for “static” parts, e.g. bridges.• Cyclic loading stress limit<static stress
capability.
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Jiangyu Li, University of Washington
Characteristics
• Most applications of structural materials involve cyclic loading; any net tensile stress leads to fatigue.
• Fatigue failure surfaces have three characteristic features:– A (near-)surface defect as the origin of the crack– Striations corresponding to slow, intermittent crack
growth– Dull, fibrous brittle fracture surface (rapid growth).
• Life of structural components generally limited by cyclic loading, not static strength.
• Most environmental factors shorten life.
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Jiangyu Li, University of Washington
Fatigue Failure Feature
• Flat facture surface, normal to stress axis, no necking
• Stage one: initiation of microcracks
• Stage two: progress from microcracks to macrocracks, forming parallel plateau-like facture feature (beach marks) separated by longitudinal ridge
• Stage three: final cycle, sudden, fast fracture.
Bolt, unidirectional bending
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Jiangyu Li, University of Washington
Fatigue-Life Method
• Stress-life method
• Facture mechanics method
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Jiangyu Li, University of Washington
Alternating Stress
a = (max-min)/2
m = (max+min)/2
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Jiangyu Li, University of Washington
S-N Diagram
Note the presence of afatigue limit in manysteels and its absencein aluminum alloys.
log Nf
a
mean 1
mean 2
mean 3
mean 3 > mean 2 > mean 1 The greater the number ofcycles in the loading history,the smaller the stress thatthe material can withstandwithout failure.
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Jiangyu Li, University of Washington
S-N Diagram
Endurance limit
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Jiangyu Li, University of Washington
Safety Factor
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Jiangyu Li, University of Washington
Facture Mechanics Method of Fatigue
aFK
aFK
I
I
minmax
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Jiangyu Li, University of Washington
Crack Growth
> >
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Jiangyu Li, University of Washington
Fatigue Life
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Jiangyu Li, University of Washington
Crack Growth Rate
f
i
f a
am
N
f
mI
aF
daC
dNN
KCdNda
)(
1
)(
0
2
max)(
1 F
Ka Ic
f
aFK I
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Jiangyu Li, University of Washington
Fatigue Failure Criteria
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Jiangyu Li, University of Washington
Effect of Mean Stress
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Jiangyu Li, University of Washington
Fatigue Failure Criteria
1yt
m
yt
a
SS
SS
1yt
m
e
a
SS
SS
m
ar1)( 2
ut
m
e
a
SS
SS
1ut
m
e
a
SS
SS
1)()( 22 yt
m
e
a
SS
SS
Multiply the stressBy safety factor n
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Jiangyu Li, University of Washington
Example: Gerber Line
AISI 1050 cold-drawn bar, withstand a fluctuating axial load varying from 0 to16 kip. Kf=1.85; Find Sa and Sm and the safety factor using Gerber relation
Sut=100kpsi; Sy=84kpsi; Se’=0.504Sut kpsi
1
1)( 2
r
SS
SS
ut
m
e
a
kpsiK
kpsid
F
aofma
moa
ao
38.8
,53.44
3
Changeover
Table 7-10
1
2
3
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Jiangyu Li, University of Washington
Safety Factor with Mean Stress