The mechanics and thermodynamics of edge fracture: the critical energy release rate, the compatibility constraint, and the bond potential

Abstract

Following Gurtin and many others, the critical energy release rate is commonly identified as an ill-defined surface energy. The primary objectives of this paper are to clarify the definition of this surface energy and the role of the entropy inequality in the discussion of critical conditions. In view of an increasing emphasis on ab initio computations, a secondary objective is to show how the critical energy release rate and the compatibility constraint 1 can be used to solve a problem for which we have experimental data, using only ab initio estimates of surface tension and bond potential, both of which are increasingly available.

Keywords:

• critical energy release rate
• compatibility constraint
• edge fracture
• critical load

Acknowledgements

This research was support by the Air Force Office of Scientific Research under grant #FA9550-06-1-0242. The authors are grateful for the many conversations that they have had with J.R. Walton and T. Sendova.

Notes

Notes

1. Since the composition is uniform, it can be written for a single-component material.

2. Recognizing that the body is isothermal and neglecting inertial effects in the current configuration, we can derive this using two forms of the energy balance, one in terms of Û and one in terms of 13, p. 279].