Failure Criteria and Plasticity

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Mechanics of Materials Lab

• Lecture 21
• Failure Criteria and Plasticity
• Mechanical Behavior of Materials Sec. 7.1-7.6,
  12.1-12.3
• Jiangyu Li
• University of Washington

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Failure Mode

• Ductile yielding
• Brittle Fracture

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Multi-axial Load
Tension or compression
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Maximum Normal Stress Fracture Criterion
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Maximum Shear Stress Yielding Criterion
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Three-dimensional Stress State
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Octahedral Shear Stress
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Octahedral Shear Stress Criterion
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Three-dimensional Stress State
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Comparison
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Example

• For a stress state of sx120, sy-50, sz200,
  txy60 Mpa, and a safety factor of 2.0 again
  yielding, what is the minimum yield strength by
  (1) maximum shear stress criterion and (2)
  octahedral shear stress criterion

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Comparison
Note the difference when stress have opposite sign
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Load Factor Design

• 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 YP1.6
  and YT2.5 are required.

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Stress Strain Curve
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Cyclic Loading
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Elastic-Perfect Plastic and Linear Hardening
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Power Hardening and Ramberg-Osgood Relation
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Rheological Modeling of Nonlinear Hardening
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Assignment

• Mechanical Behavior of Materials
• 7.2, 7.6, 7.33, 12.4