Self-maintaining regimes for deformation and fracture of solids

Abstract

Deformation and fracture often take place in a nonuniform manner such as being localized in a narrow zone of the strained body despite the fact that external conditions do not suggest other than the development of a uniform process. The development of cracks in fracture and the propagation of “necks” during the stretching of a polymer specimen are examples of such a process in deformation. In spite of large external differences, these processes exhibit some specific common features which constitute the subject matter of this paper. In all these processes the material passes from its initial state into a new equilibrium state that corresponds to the stress applied to the body. This new state is energetically more advantageous than the initial state, however a considerable energy barrier has to be overcome before this state can be attained. The process therefore takes place very slowly under intermediate level stresses. One specific feature is very characteristic for all processes of the class under consideration, namely, the transition into a new state developed at some spot in the body promotes an activating action in the near neighbourhood, thus stimulating the spreading of transition all over the body. The spreading rate depends on the rate at which the activating action is transmitted and (or) the rate of relaxation process in the material.