Tensile cracks in polycrystalline ice under transient creep: Part I — Numerical modeling

Abstract

The interaction between creep deformations and a stationary or growing crack is a fundamental problem in ice mechanics. Knowledge concerning the physical mechanisms governing this interaction is necessary: (1) to establish the conditions under which linear elastic fracture mechanics can be applied in problems ranging from ice-structure interaction to fracture toughness testing; and (2) to predict the ductile-to-brittle transition in the mechanical behavior of ice and, especially, the stability and growth of cracks subjected to crack-tip blunting by creep deformations. This requires a quantitative estimate of the creep zone surrounding a crack-tip, i.e., the zone within which creep strains are greater than the elastic strains. The prediction of the creep zone in previous ice mechanics studies is based on the theory developed by Riedel and Rice (1980) for tensile cracks in creeping solids. This theory is valid for a stationary crack embedded in an isotropic material obeying an elastic, power-law creep model of deformation and for a suddenly applied uniform far-field tension load that is held constant with time. The deformation of ice at strain-rates ahead of a crack (i.e., 10−6 to 10−2 s−1) is dominated, however, by transient (not steady power-law) creep and the loading, in general, is not instantaneous and constant. A numerical model is developed in this paper to investigate the role of transient creep and related physical mechanisms in predicting the size, shape and time evolution of the creep zone surrounding the tip of a static crack in polycrystalline ice. The model is based on the fully consistent tangent formulation derived in closed form (Shyam Sunder et al., 1993) and used in the solution of the physically-based constitutive theory developed by Shyam Sunder and Wu (1989a, b) for the multiaxial behavior of ice undergoing transient creep. The boundary value problem involving incompressible deformations ahead of a stationary, traction-free mode I crack in a semi-infinite medium is modeled and solved by a finite element analysis using the boundary layer approach of Rice (1968). This model is verified by comparing its predictions with (i) the known theoretical solutions for the elastic and HRR asymptotic stress and strain fields in an elastic-plastic material of the Ramberg-Osgood type, and (ii) the creep zone size for an isotropic material obeying the elastic power-law creep model of deformation.