Non-conservation of grain volume during diffusion creep

In theories of the diffusion creep of polycrystals it has traditionally been assumed that individual grain volumes are conserved as they change shape. However a recent application of the theory to the creep of beams under small bending moments has shown that this need not be the case (Burton, to be published). In the present paper the theory is further extended to include cases where grain volume is not conserved during creep under tension. An analysis is presented for the grain boundary diffusion creep of a uniform array of orthorhombic grains of dimensions X, Y and Z, aligned with continuous boundaries in the XZ planes and a tensile stress normal to these planes. The analysis is simplified by assuming Z>>X and Y, so that diffusion occurs along boundaries in the x and y directions only. In specimens of finite size, the non-conservation of grain volume is shown to occur as an inevitable consequence of diffusion creep. Surface grains lose volume by diffusion to grains in the interior, which gain in volume. The effect diminishes with the distance of the grain from the surface. The effects are largest for grains highly elongated along the stress axis (Y/X>> 1), when diffusion along boundaries in the y direction is relatively low. For smaller Y/X ratios, diffusion in the y direction makes increasing contributions but grain volume is again not conserved. When the number of grains in the cross-section is large, creep rates are predicted to converge with those for an infinite array.