Yield Criteria for Anisotropic Materials

A very simple yield criterion for anisotropic materials is the critical resolved shear stress of Schmid [14]. This is concerned with crystal slip. The law states that yield occurs when the resolved shear stress in the slip direction in the slip plane reaches a critical value. Although this law is extensively used in metal plasticity, it is of restricted application in polymers. 

Hill [15] has developed a generalisation of the von Mises criterion for anisotropic materials. Anisotropy is defined with respect to specific axes fixed within the material which, in the case of orthotropic materials, are mutually perpendicular. Then, a 1-2-3 axes set can be chosen to align with the directions of orthotropy and the yield criterion defined with respect to the stresses in this axis set. This precludes the use of principal stresses as the principal directions do not in general coincide with the directions of orthotropy. Therefore, Hill s criterion is a generalisation of Equation (12.9) 

Here F, G, FI, L, M and N are material parameters that define the anisotropy. When they are all equal to unity, the criterion reduces to that of von Mises. Clearly the observed tensile yield stress will depend on the direction of stress according to this criterion. This criterion has recently been applied to particle-filled polymers by Van Dommelen and Meijer [16], who made use of the direction-dependent yield stress to fit their model. 

Brown et al. showed that this modified version gave a better fit to the yield in simple shear of oriented polycarbonate than Equation (12.11). For experiments in which the direction of 

I Experimental points -- Prediction of Simple Hill Theory a = (G+F+4H)sin 20+2Ncos 20 2 

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