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The von Mises yield surfaces in principal stress coordinates circumscribes a cylinder with radius around the hydrostatic axis. Also shown is Tresca 's hexagonal yield surface. Mathematically the von Mises yield criterion is expressed as:
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.
Functions of the principal stresses, such as the yield function, can be represented by surfaces in 'stress space. In particular, the surface represented by von Mises yield function is a right circular cylinder, equiaxial to each of the three stress axes.
Figure 3 shows the von Mises yield surface in the three-dimensional space of principal stresses. It is a circular cylinder of infinite length with its axis inclined at equal angles to the three principal stresses. Figure 4 shows the von Mises yield surface in two-dimensional space compared with Tresca–Guest criterion.
Principal stresses are often expressed in the following equation for evaluating stresses in the x and y directions or axial and bending stresses on a part. [14]: p.58–59 The principal normal stresses can then be used to calculate the von Mises stress and ultimately the safety factor and margin of safety.
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. Using the double angle approach we measure the angles ∠BOC and ∠BOE in the Mohr Circle (Figure 8) to find double the angle the major principal stress and the ...
Von Mises found that, even though none of the principal stresses exceeds the yield stress of the material, it is possible for yielding to result from the combination of stresses. The Von Mises criteria is a formula for combining these 3 stresses into an equivalent stress, which is then compared to the yield stress of the material.
In continuum mechanics, stress triaxiality is the relative degree of hydrostatic stress in a given stress state. [1] It is often used as a triaxiality factor, T.F, which is the ratio of the hydrostatic stress, , to the Von Mises equivalent stress, . [2] [3] [4].