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Stress components on a 2D rotating element. Click to see animation. Example of how stress components vary on the faces (edges) of a rectangular element as the angle of its orientation is varied. Principal stresses occur when the shear stresses simultaneously disappear from all faces. The orientation at which this occurs gives the principal ...
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
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.
Visualisation of a Cauchy stress tensor σ in the Haight-Westergaard stress space. In continuum mechanics, Haigh–Westergaard stress space, or simply stress space is a 3-dimensional space in which the three spatial axes represent the three principal stresses of a body subject to stress.
axial stress, a normal stress parallel to the axis of cylindrical symmetry. radial stress, a normal stress in directions coplanar with but perpendicular to the symmetry axis. These three principal stresses- hoop, longitudinal, and radial can be calculated analytically using a mutually perpendicular tri-axial stress system. [1]
Figure 1: View of Mohr–Coulomb failure surface in 3D space of principal stresses for =, =. The Mohr–Coulomb [7] failure criterion represents the linear envelope that is obtained from a plot of the shear strength of a material versus the applied normal stress.
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.
This plot demonstrates that an intuitive approximation for the Lode angle is the relative position of the middle principal stress with respect to the low and high principal stresses. The Lode angle can be considered, rather loosely, a measure of loading type.