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The maximum stress criterion assumes that a material fails when the maximum principal stress in a material element exceeds the uniaxial tensile strength of the material. Alternatively, the material will fail if the minimum principal stress σ 3 {\displaystyle \sigma _{3}} is less than the uniaxial compressive strength of the material.
The Hoek–Brown criterion has the form [2] = + + where is the effective maximum principal stress, is the effective minimum principal stress, and , are materials constants. In terms of the mean normal stress and maximum shear stress ()
This means that, at the onset of yielding, the magnitude of the shear stress in pure shear is times lower than the yield stress in the case of simple tension. The von Mises yield criterion for pure shear stress, expressed in principal stresses, is
and the normal stresses acting on the same planes where the minimum and maximum shear stresses act are equal to . We can choose to either use the double angle approach (Figure 8) or the Pole approach (Figure 9) to find the orientation of the principal normal stresses and principal shear stresses.
Mohr–Coulomb theory is a mathematical model (see yield surface) describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as normal stress. Most of the classical engineering materials follow this rule in at least a portion of their shear failure envelope.
Within the branch of materials science known as material failure theory, the Goodman relation (also called a Goodman diagram, a Goodman-Haigh diagram, a Haigh diagram or a Haigh-Soderberg diagram) is an equation used to quantify the interaction of mean and alternating stresses on the fatigue life of a material. [1]
The chief advantage of critical plane analysis over earlier approaches like Sines rule, or like correlation against maximum principal stress or strain energy density, is the ability to account for damage on specific material planes.
The magnitude of the maximum compressive stress should be less than ultimate compressive stress divided by factor of safety. Maximum strain energy theory postulates that failure will occur when the strain energy per unit volume due to the applied stresses in a part equals the strain energy per unit volume at the yield point in uniaxial testing ...