IntermediateTopic 64 of 106Engineering Mechanics
Failure theories
Tresca and von Mises criteria predict yielding under multiaxial stress.
In depth
Predict yield under combined stress. Tresca: maximum shear stress equals that at yield (σ₁-σ₃=σy). von Mises: equivalent stress σ_vm=√(σ₁²-σ₁σ₂+σ₂²) ≤ σy for ductile metals. Brittle materials use Rankine or Mohr-Coulomb.
Key points
- von Mises is more accurate for metals
- Tresca is conservative
- Use ductile or brittle criterion by material
ExampleA shaft with σ=100 and τ=50 MPa has σ_vm=√(100²+3·50²)=132 MPa.
What is Failure theories?
Tresca and von Mises criteria predict yielding under multiaxial stress.
Why is it important to understand failure theories?
Failure theories predict when a material yields under combined stress, which is needed when the simple tensile test does not apply directly.
What is the difference between Tresca and von Mises?
Tresca uses the maximum shear stress and is more conservative. Von Mises uses the distortion energy and fits ductile metals more closely.
Which theory should I use for brittle materials?
Brittle materials are often assessed with maximum normal stress or Mohr-Coulomb, because they fail by fracture rather than yielding.
How is Failure theories used in practice?
Typical applications include checking a shaft under combined torsion and bending for yield, choosing a yield criterion for a ductile steel component and assessing the strength of a pressure vessel under combined stresses.
What should I learn before Failure theories?
Study "Thin-walled pressure vessels" first (topic 63 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
What are the key points of Failure theories?
von Mises is more accurate for metals. Tresca is conservative. Use ductile or brittle criterion by material.
Can you give an example of Failure theories?
A shaft with σ=100 and τ=50 MPa has σ_vm=√(100²+3·50²)=132 MPa.
What comes after Failure theories?
The next topic is "Buckling of columns", which builds directly on this one.
How difficult is Failure theories?
It is classed as Intermediate in Engineering Mechanics (topic 64 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.