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Published 1993 | public
Book Section - Chapter

Nucleation, kinetics and admissibility criteria for propagating phase boundaries

Abstract

This paper reviews our recent studies on the nucleation and kinetics of propagating phase boundaries in an elastic bar and relates them to various admissibility criteria. First, we discuss how the field equations and jump conditions of the quasi-static theory of such a bar must be supplemented with additional constitutive information pertaining to the initiation and evolution of phase boundaries. The kinetic relation relates the driving traction f at a phase boundary to the phase boundary velocity ṡ; thus f = φ (ṡ), where φ is a materially-determined function. The nucleation criterion specifies a critical value of f at an incipient phase boundary. We then incorporate inertial effects, and we find in the context of the Riemann problem that, as long as phase boundary velocities are subsonic, the theory again needs — and has room for — a nucleation criterion and a kinetic relation. Finally, we describe the sense in which each of three widely studied admissibility criteria for phase boundaries is equivalent to a specific kinetic relation of the form f = φ (ṡ) for a particular choice of φ A kinetic relation based on thermal activation theory is also discussed.

Additional Information

© 1993 Springer. The authors have benefited from conversations with William Blackshaw, Richard James, James Rice and Phoebus Rosakis, to whom we express our thanks. We also thank Robert Pego and Michael Shearer for informative discussions concerning the "chord criterion", and Edward Zukoski for his helpful comments on deflagrations and detonations. The support of the work summarized hero by the Solid Mechanics Program of the Office of Naval Research through Contract N00014-87-K-0117 and Grant N00014-90-J-1871 is gratefully acknowledged. The support and hospitality of the Institute for Mathematics and its Applications at the University of Minnesota during the Workshop on Shock-Induced Transitions and Phase Structures in General Media, October 15-19, 1990, and the associated funding from the National Science Foundation, are also acknowledged with thanks.

Additional details

Created:
August 20, 2023
Modified:
January 13, 2024