Process region changes for rapidly propagating cracks

Abstract

A finite element model of a plate, which contains an initial crack subjected to a rapid loading at its faces, is investigated. A cell model of the prospective process region is adopted. The cell size is assumed to represent some characteristic intrinsic material length. The size of the process region is not predetermined but depends at every time on the number of cells that have reached a state characteristic for the process region i.e. essentially instability if load control would prevail. Outside the process region the material is assumed to be linearly elastic.

For low loading magnitudes the simulations show a rather long period of crack acceleration, but at higher loads this period is short or even not detectable, and a constant terminal velocity, significantly lower than the Rayleigh wave velocity, is reached. At lower loads both the energy release rate and the extension of the process region stay rather constant, but at higher loads they increase considerably with time, even though the crack tip velocity stays constant. Thus it appears that a tendency towards increased energy flow to the process region is met by increased size of this region, and thereby increased energy dissipation per unit of crack growth, rather than by increased crack edge velocity. The process region may finally occupy several cell rows, and the control of the process region by the characteristic length is thus lost. This can explain the apparent loss of the unique relation between stress intensity factor and crack edge velocity at high crack velocities.

In some simulations branching was obtained. The results from the simulations showed qualitative agreement with some recent experimental results e.g. those by Ravi-Chandar.