A numerical study of intergranular cavity growth in creep

Abstract

In a previous paper, a general model of geometrically unconstrained intergranular cavity growth in creep was developed together with a numerical method, method I, based on application of the polar (R, θ) coordinate system and the finite difference technique, enabling cavity shape evolution during its growth to be studied. Extensive results of cavity growth modelling using method I were presented. In the present paper, another numerical method, method II, again based on the finite difference technique, was applied. In the method, the cylindrical (r, z) coordinate system is used and a procedure is involved which allows the addition of new nodes when there are an insufficient number and the removal of other nodes when they become abundant during cavity growth because of cavity shape changes. Both methods are critically compared. It is shown that they provide almost the same results when the ratio Δ = D S δS / D B δB of the surface diffusion conductance to the grain boundary diffusion conductance is about 10 −1 or more; however, method I is several times faster than method II. At smaller Δ values, method II must be used to obtain accurate results, particularly the time to fracture and its stress dependence. Extensive results of modelling cavity growth in a broad region of variables are presented and shown to be in full agreement with the predictions of current cavity growth models as well as with some results of the numerical study of cavity growth published by Martinez and Nix.