Plot Mohr's circle on chart. Mohr's Circle is used to visualize relationships between normal and shear stresses.
The maximum shear stress criterion, also known as Tresca's or Guest's criterion, is often used to predict the yielding of ductile materials. Yield in ductile materials is usually caused by the slippage of crystal planes along the maximum shear stress surface. Therefore, a given point in the body is considered safe as long as the maximum shear stress at that point is under the yield shear stress obtained from a uniaxial tensile test.
The von Mises Criterion, also known as the maximum distortion energy criterion, octahedral shear stress theory, or Maxwell-Huber-Hencky-von Mises theory, is often used to estimate the yield of ductile materials.
The maximum stress criterion, also known as the normal stress, Coulomb, or Rankine criterion, is often used to predict the failure of brittle materials.
The maximum stress criterion states that failure occurs when the maximum (normal) principal stress reaches either the uniaxial tension strength, or the uniaxial compression strength.
The Mohr Theory of Failure, also known as the Coulomb-Mohr criterion or internal-friction theory, is based on the application of Mohr's Circle. Mohr's theory is often used in predicting the failure of brittle materials. Mohr's theory asserts that failure occurs when Mohr's Circle at a point in the body exceeds the envelope created by the two Mohr's circles for uniaxial tensile strength and uniaxial compression strength.
Christensen published a series of papers between 1997 and 2007 developing a three dimensional failure criterion suitable for isotropic materials, bridging the gap between failure criteria for ductile and brittle materials. The results are summarized in www.FailureCriteria.com.
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