Plastic Deformation of Metals

Abstract

The classical theory of plasticity is based on the concept of a yield criterion f(б _ij )= k , where б _ij is the stress tensor and k is a material constant, which is in general a function of the previous strain history. For an isotropic material, the function f may be expressed in terms of the three invariants I₁, I₂, I₃, of the stress tensor. Experimentally, it is found that the hydrostatic component of stress does not affect plastic flow, so that the stress may be replaced by the stress deviation

$$$$

(1.1.1)

where б = б_kk and δ _ij is the Kronecker delta. The yield criterion thus reduces to f(J₂, J₃) = k , where J₂ , J₃ are the second and third invariants of s _ij (J₁ being identically zero). In the von Mises criterion this is further simplified to J ^1/2₂ = k where k is now identified with the yield stress in simple shear.