Comparison of Tresca and Von Mises Yield Theories

Study Notes

Failure prediction in materials depends on reaching specific stress levels, such as yield strength for ductile materials and ultimate strength for brittle materials.
Failure theories help predict material failure by comparing stress states with material properties like yield strength.
Maximum Principal Stress theory (Rankine theory) predicts failure based on the maximum or minimum principal stresses reaching yield or ultimate strengths, but it is not ideal for ductile materials.
For ductile materials, Tresca and von Mises failure criteria are commonly used. Tresca theory looks at maximum shear stress, while von Mises theory considers distortion energy.
Tresca theory states yielding occurs when the maximum shear stress equals the shear stress at yielding in a tensile test, independent of hydrostatic stresses.
Von Mises theory predicts yielding when the equivalent von Mises stress exceeds the yield strength of the material, also independent of hydrostatic stress.
Yield surfaces represent failure theories in principal stress space, with different shapes based on the theory.- The text discusses the comparison between the Tresca and von Mises yield theories for ductile materials, with von Mises showing slightly better agreement with experimental data.
Tresca is considered more conservative than von Mises as its yield surface lies entirely inside the von Mises surface.
The maximum difference between the two theories is calculated to be 15.5%, with von Mises generally preferred due to better agreement with experimental data.
Different failure theories exist for brittle materials, such as the Coulomb-Mohr theory, which considers the sensitivity to hydrostatic stresses and the difference between tensile and compressive strengths.
Coulomb-Mohr theory is visualized using Mohr's circle and a failure envelope, with Modified Mohr theory being a variation that fits experimental data better for brittle materials.

Description

Explore the differences between Tresca and Von Mises yield theories for ductile materials, and understand how each theory predicts material failure based on shear stress and distortion energy. Learn about the advantages of Von Mises theory over Tresca theory, and the importance of yield surfaces in predicting material failure.