Solid Mechanics

15.

Failure Theories and Design

15.1.

Failure Criteria for Ductile Materials

15.1.1.

Maximum Shear Stress Theory

15.1.1.1.

Tresca Criterion

15.1.1.2.

15.1.2.

Maximum Distortion Energy Theory

15.1.2.1.

von Mises Criterion

15.1.2.2.

Equivalent Stress

15.1.3.

Comparison of Theories

15.2.

Failure Criteria for Brittle Materials

15.2.1.

Maximum Normal Stress Theory

15.2.1.1.

Rankine Criterion

15.2.1.2.

Applications and Limitations

15.2.2.

Maximum Strain Theory

15.2.2.1.

Saint-Venant Criterion

15.2.3.

15.2.3.1.

Mohr-Coulomb Criterion

15.2.3.2.

Internal Friction Angle

15.3.

Fatigue Failure

15.3.1.

High-Cycle Fatigue

15.3.2.

Low-Cycle Fatigue

15.3.3.

15.3.4.

Endurance Limit

15.3.5.

Mean Stress Effects

15.3.6.

Cumulative Damage

15.4.

Fracture Mechanics

15.4.1.

Linear Elastic Fracture Mechanics

15.4.2.

Stress Intensity Factor

15.4.3.

15.4.4.

Fatigue Crack Propagation

15.5.

Design Applications

15.5.1.

Factor of Safety Selection

15.5.2.

Reliability-Based Design

15.5.3.

Probabilistic Methods

15.5.4.

Design Optimization

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14. Energy Methods in Mechanics

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1. Introduction to Solid Mechanics