Plastic Flow Instabilities at Crack Tips

Abstract

Instabilities of plastic flow can occur near crack tips for several reasons. In some cases they can be due to inherent features of the macroscopic phenomenological plasticity behavior and the unstable region spreads over distances large compared to the microstructure. For example, localization of flow in shear bands can occur in large scale yielding. In other cases, microscopic activity can set up geometric or material features which induce the instability on an initally small scale. An example of the latter circumstance is the nucleation of large voids from hard particles in the alloy near a blunt tip leaving an unstable highly strained ligament. These examples are but two of many possibilities that can operate at different size scales. In addition, the presence of an embrittling agent may play an important role in the nature of plasticity and so complicate the picture of crack tip instability. In this chapter, the continuum viewpoint of small scale failure processes involving plasticity near a monotonically loaded crack tip will be outlined. To be able to do this, we must first review recent developments in crack tip plasticity solutions. This will lead naturally to the work that has been done on modelling the ductile failure processes at crack tips. Most of these models involve a plastic instability of one kind or another.