On the constitutive modeling of transient creep in polycrystalline ice

Abstract

The theoretical generality of constitutive models for the transient creep of polycrystalline ice and the ability of such models to represent knowledge derived from experimentation in a physically consistent manner are examined in this paper. The focus is on physically based but phenomenological models that employ evolving internal state variables to characterize the deformation resistance offered by the material. These include the models of Le Gac and Duval (1980) and Shyam Sunder and Wu (1989a, b). The widely used model of Sinha (1978), though not based on the theory of internal state variables, is also discussed briefly. A set of nine criteria are identified that should be used in evaluating transient-creep models for polycrystalline ice. These include the well-known correspondence between the creep and constant strain-rate responses observed experimentally by Mellor and Cole (1982, 1983) and the ability to reduce creep and constant strain-rate responses into non-dimensional forms that are independent of the loading parameters, viz., temperature and stress or strain rate, as proposed by Ashby and Duval (1985). The kinematic consistency between the response variables during transient creep, i.e., strain, strain rate and time, also emerges as an important consideration in constitutive modeling and the subsequent use of such models in a finite element framework. To satisfy this requirement, the model must accurately predict the experimentally observed relationship between all three pairs of kinematic variables (strain versus time, strain rate versus time, and strain rate versus strain) keeping the material parameters fixed. This paper finds that the formulations of Le Gac and Duval (1980) and Sinha (1978) are unable to satisfy the requirement of kinematic consistency. On the basis of the nine evaluation criteria, the formulation proposed by Shyam Sunder and Wu (1989a) emerges as the more complete creep model for polycrystalline ice. In conclusion, the paper identifies difficult problems that will benefit from future research.