The condition of transition to unstable state (necking) of a compressible elastic-plastic medium


On the stress-strain curves obtained in simple tensile experiments for the metallic specimens a region of instability due to the formation of a neck is observed. In the theory of plasticity the conditions of transition to the unstable state and the appearance of the maximum point on the of stress-strain curve are defined. When this condition is derivate, the assumption of incompressibility of the material is accepted. However, this assumption cannot be justified, because in the neck region the numerous damages appear, i.e. the material becomes compressible. In the article, the condition of transition to unstable state for a compressible plastic medium is formulated.