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
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
Jiangyu Li, University of Washington
Maximum Normal Stress Fracture Criterion
Jiangyu Li, University of Washington
Octahedral Shear Stress Criterion
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.
Jiangyu Li, University of Washington
Stress Strain Curve
Bauschinger Effect
Jiangyu Li, University of Washington
Elastic-Perfect Plastic and Linear Hardening
Jiangyu Li, University of Washington
Power Hardening and Ramberg-Osgood Relation
Jiangyu Li, University of Washington
Secant Modulus
Jiangyu Li, University of Washington
Stress-Strain Curve
Jiangyu Li, University of Washington
Displacement Mode
Opening mode Sliding mode Tearing mode
Jiangyu Li, University of Washington
Stress Concentration
Jiangyu Li, University of Washington
Stress Intensity Factor: Tension
Jiangyu Li, University of Washington
Stress Intensity Factor: Bending
Jiangyu Li, University of Washington
Stress Intensity Factor: Circumferential Crack
-
Jiangyu Li, University of Washington
Stress Intensity Factor
Jiangyu Li, University of Washington
Superposition
Jiangyu Li, University of Washington
Brittle vs. Ductile Behavior
Jiangyu Li, University of Washington
Plastic Zone
Jiangyu Li, University of Washington
Limitation of LEFM
Jiangyu Li, University of Washington
Effect of Thickness
Jiangyu Li, University of Washington
Correlation with Strength
Jiangyu Li, University of Washington
Jiangyu Li, University of Washington
Energy Release Rate
Jiangyu Li, University of Washington
Strain Energy
Modulus of toughness & modulus of resilience
Increasing the strain rate increase strength, but
decrease ductility
Jiangyu Li, University of Washington
Impact Test
• Charpy V-notch & Izod tests most common
• Energy calculated by pendulum height difference
• Charpy – metals, Izod - plastics
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
Jiangyu Li, University of Washington
Effect of Temperature
Decrease temperature increase strength, but decrease ductility
Jiangyu Li, University of Washington
Ductile-Brittle Transition
Jiangyu Li, University of Washington
Static Failure
• Load is applied gradually• Stress is applied only once• Visible warning before failure
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!
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.
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.
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
Jiangyu Li, University of Washington
Fatigue-Life Method
• Stress-life method
• Facture mechanics method
Jiangyu Li, University of Washington
Alternating Stress
a = (max-min)/2
m = (max+min)/2
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.
Jiangyu Li, University of Washington
S-N Diagram
Endurance limit
Jiangyu Li, University of Washington
Safety Factor
Jiangyu Li, University of Washington
Facture Mechanics Method of Fatigue
aFK
aFK
I
I
minmax
Jiangyu Li, University of Washington
Crack Growth
> >
Jiangyu Li, University of Washington
Fatigue Life
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
Jiangyu Li, University of Washington
Fatigue Failure Criteria
Jiangyu Li, University of Washington
Effect of Mean Stress
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
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
Jiangyu Li, University of Washington
Safety Factor with Mean Stress
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