Effect of yield surface vertex on failure of ductile materials

This paper is concerned with the lengthening of a solid rod or tubular specimen along the principal axis about which it is being twisted, this aspect of the elastic-plastic deformation of a material being referred to as the Poynting-Swift effect. The Swift effect is the counterpart in the plastic range of deformation to the Poynting effect in the elastic range of deformation. Central to any study of the Swift effect is the problem of identifying an appropriate yield criterion. A generalised isotropic yield criterion is formulated in such a way that it can be applied to materials which satisfy the von Mises yield criterion, or some modified, but continuously difierentiable form of it, and to materials which satisfy a piece-wise continuous yield condition such as the Tresca yield criterion. The choice of the constitutive equation describing the purely elastic deformation behaviour determines the initial yield function. In this context, the constitutive equation of a simple elastic material is only compatible with von Mises yield criterion, a conclusion which applies also to classical infinitesimal theory. An attempt is made to generalise the constitutive equation of a simple elastic material to give a constitutive equation which is compatible with the proposed generalised isotropic yield criterion. This approach introduces an additional term into the constitutive equation which is quadratic in the stress. The two loading coefficients associated with the stress loading function are assumed to be deriveable from the generalised isotropic yield criterion which is now assumed to hold over the entire range of deformation, and in this context is referred to as the stress intensity function. It is a matter of observation that the proposed constitutive equation describes the total, post-yield, elastic-plastic response to simple loading. Consideration is given to the application of the Poynting-Swift effect to the failure of ductile materials using the proposed constitutive equation.