Tresca yield theory

Tresca and R. von Mises criteria are for isotropic materials. In 1948, Rodney Hill provided a quadratic yield criterion for anisotropic materials. A special case of this criterion is von Mises criterion. In 1979, Hill proposed a non-quadratic yield criterion. Later on several other criteria were proposed including Hill s 1993 criterion. Rodney HiU (1921-2011) was bom in Yorkshire, England and has tremendous contribution in the theory of plasticity. 

Compare this to the prediction of ay/2 from the Tresca criterion. The yield criteria for both the Tresca and Von Mises theories are shown graphically in Figure 6. For simplicity, the plots are shown for conditions of plane stress (ie 03 = 0). We can see that the Von Mises criterion describes an ellipse in stress space, with the Tresca criterion consisting of a series of straight lines bounded by the Von Mises limits. 

Maximum shear stress theory (Tresca) Failure occurs when the maximum shear stress at-an arbitrary point in a stressed body is equal to the maximum shear stress at failure (rupture or yield) in a uniaxial tensile test. 

The standard criteria for yielding developed in elasticity theory for metals, namely the Tresca, von Mises or Mohr-Coulomb, do not apply quantitatively to polymeric materials because these criteria ignore the effect of the hydrostatic component of the stress tensor. This is important in determining the yield behaviour of polymers, not neces-... 

Consider for example, the maximum shear stress (or Tresca) theory of failure with respect to yielding, which can be stated as follows A material subjected to any combination of loads will yield whenever the maximum shear stress at any point in the material exceeds the value of the maximum shear stress in a simple tensile test at yield. ... 

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