The relationship of the critical stress versus impulse theory of spall fracture to the stress-gradient theory

A spall fracture criterion based on critical stress versus stress gradient is briefly reviewed and discussed. An extension of a technique used by Tuler and Butcher is employed to show that the results of the stress-gradient theory can be interpreted in terms of criteria involving critical stress versus either impulse or pulse duration. The latter criteria are represented by smooth curves that depend on two parameters—the static strength limit for long-duration loads and an impulse limit for short-duration loads. Expressions for these parameters are presented in terms of the two parameters of the stress-gradient theory. Examples are presented for submicrosecond loads on 1100 aluminum and copper that show the stress-impulse interpretation differs little from the pure-impulse interpretation of Tuler and Butcher.