TENSILE CRACKS IN POLYCRYSTALLINE ICE UNDER TRANSIENT CREEP .1. NUMERICAL MODELING

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 mechan ics can be applied in problems ranging from ice-structure interaction to fracture toughness testing; and (2) to predict the ductile-to-britt le transition in the mechanical behavior of ice and, especially, the s tability 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 ar e greater than the elastic strains. The prediction of the creep zone i n previous ice mechanics studies is based on the theory developed by R iedel and Rice (1980) for tensile cracks in creeping solids. This theo ry is valid for a stationary crack embedded in an isotropic material o beying an elastic, power-law creep model of deformation and for a sudd enly 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 stead y power-law) creep and the loading, in general, is not instantaneous a nd constant. A numerical model is developed in this paper to investiga te the role of transient creep and related physical mechanisms in pred icting the size, shape and time evolution of the creep zone surroundin g the tip of a static crack in polycrystalline ice. The model is based on the fully consistent tangent formulation derived in closed form (S hyam Sunder et al., 1993) and used in the solution of the physically-b ased constitutive theory developed by Shyam Sunder and Wu (1989a, b) f or the multiaxial behavior of ice undergoing transient creep. The boun dary value problem involving incompressible deformations ahead of a st ationary, traction-free mode I crack in a semi-infinite medium is mode led and solved by a finite element analysis using the boundary layer a pproach of Rice (1968). This model is verified by comparing its predic tions 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 isotropi c material obeying the elastic power-law creep model of deformation.