Tensile cracks in polycrystalline ice under transient creep: Part II — Numerical simulations

Abstract

Abstract This paper discusses predictions of a numerical model presented in the companion paper (Nanthikesan and Shyam Sunder, 1995) to analyze tensile cracks in polycrystalline ice undergoing transient creep. The numerical model is based on the internal state variable constitutive theory of transient creep in ice developed by Shyam Sunder and Wu (1989a,b, 1990). The finite element model uses the boundary layer approach of Rice (1968), in conjunction with a mid-point crack-tip element and reduced integration, to simulate the asymptotic stress and deformation fields in the vicinity of the crack tip, including incompressible creep deformations. The problem of a stationary, traction-free, tensile (mode I) crack is analyzed to predict the size, shape and time evolution of the creep-dominated fracture process zone surrounding the crack-tip. The numerical simulations quantify the effects of transient creep, material strain hardening, fabric anisotropy, loading rate, temperature, and finite fracture test-specimen boundary on the development of the creep zone. A range of stress-intensity rates from 1 to 100 kPa m 1 2 s−1 and temperatures from −5° to −25°C is considered in the simulations. The results from a comprehensive numerical simulation study show that: (i) transient creep increases the creep zone size by more than an order of magnitude over that for a power-law creeping material, i.e., about 40 times for the isotropic, equiaxed granular ice tested by Jacka (1984); (ii) material strain hardening significantly affects the creep zone size, i.e., the creep zone for the transversely-isotropic columnar-grained ice tested by Sinha (1978), with the crack loaded in the plane of isotropy, is about 4 times smaller than that for the granular isotropic ice; (iii) fabric anisotropy increases the size of the creep zone by a factor of at least two for cracks in the transversely-isotropic, columnar-grained ice loaded in the plane of isotropy; (iv) the Riedel and Rice (1980) equation, which was derived for an isotropic power-law creeping material subjected to a suddenly applied constant stress-intensity, overestimates the creep zone size by a factor of 4.2 for a constant stress-intensity rate loading; and (v) as the crack size increases, linear elastic fracture mechanics becomes increasingly applicable at lower loading rates and higher temperatures.