Energy release rate in a cracked elastic-plastic solid
McMahon, James Joseph
Angel, Y. C.
Doctor of Philosophy
To predict the growth of a crack in a body, Griffith introduced, for linear elastic materials, the concept of the energy release rate. According to this concept, crack growth occurs when the work done on a body by the applied surface tractions minus the increase in the strain energy of the body is equal to the energy required to break the material bonds in front of the crack. This approach has been widely accepted as a criterion for crack growth. For elastic-plastic materials, the concept of the energy release rate is not as well established. In this thesis, a general criterion for crack growth in elastic-plastic materials is proposed. A general constitutive theory is used, and a new work postulate, which imposes a finite limit on the amount of work that can be recovered from an elastic-plastic body, is proposed. For a certain class of elastic-plastic materials, this finite limit is directly related to a potential function. Next, an elastic-plastic body containing an edge crack is considered, and an energy balance at the crack tip is derived. This energy balance states that quantities defined at the crack tip are equal to the sum of the rate of work of the applied surface tractions, the rate of recoverable work defined inside the body, and a term that is a measure of the rate of work dissipated by plastic deformations. Finally, an interpretation of each term in the energy balance is given, and the proposed criterion for crack growth is discussed. This new criterion takes into account the dissipative nature of plastic deformations.
Mechanical engineering; Engineering; Materials science; Applied mechanics