Plastic instability in uni-axially anisotropic (r value) materials

Abstract

In the framework of mechanics of plasticity plastic instability has been taken up as the onset of ductile fracture. Hill established a sufficient criterion for uniqueness of boundary-value problem set by given velocities on a part of surface of a body and given nominal traction-rates on the remainder without any restriction placed on changes on geometry. Hill also obtained eigenstates intrinsic to the material and holding true at the collapse stages of uniqueness. The eigenstates demand work done in second order to vanish. We adopted the eigenstates as the concept of instability, and discussed here the onset of plastic instability occurred under simple and bi-axial tensions in uni-axially anisotropic (r value) plastic materials which are deduced from Hill's formulation. The anisotropy results in high formability with increasing of r value in many cases except for roughly negative strain rate ratio ε₂ / ε₁ < 0 . Superimposed pressure also gives high formability. We also showed the second order work done with respect to coordinate components at plastic instability.