ABSTRACT

Solid polycrystalline materials undergoing diffusion creep are usually described by Cauchy continuum models with a Newtonian viscous rheology dependent on the grain size. Such a continuum lacks the rotational degrees of freedom needed to describe grain rotation. Here we provide a more general continuum description of diffusion creep that includes grain rotation, and identifies the deformation of the material with that of a micropolar (Cosserat) fluid. We derive expressions for the micropolar constitutive tensors by a homogenisation of the physics describing a discrete collection of rigid grains, demanding an equivalent dissipation between the discrete and continuum descriptions. General constitutive laws are derived for both Coble (grain-boundary diffusion) and Nabarro-Herring (volume diffusion) creep. Detailed calculations are performed for a two-dimensional tiling of irregular hexagonal grains, which illustrates a potential coupling between the rotational and translational degrees of freedom. If only the plating out or removal of material at grain boundaries is considered, the constitutive laws are degenerate: modes of deformation that involve pure tangential motion at the grain boundaries are not resisted. This degeneracy can be removed by including the resistance to grain-boundary sliding, or by imposing additional constraints on the deformation.

摘要

经历扩散蠕变的固体多晶材料通常由柯西连续介质模型描述，该模型具有依赖于晶粒尺寸的牛顿粘性流变学。这种连续体缺乏描述颗粒旋转所需的旋转自由度。在这里，我们提供了一个更一般的扩散蠕变连续描述，包括晶粒旋转，并用微极 (Cosserat) 流体的变形来识别材料的变形。我们通过描述离散的刚性颗粒集合的物理均匀化推导出微极本构张量的表达式，要求离散和连续描述之间的等效耗散。为 Coble（晶界扩散）和 Nabarro-Herring（体积扩散）蠕变推导出一般本构定律。对不规则六边形晶粒的二维平铺进行了详细计算，这说明了旋转自由度和平移自由度之间的潜在耦合。如果仅考虑在晶界处镀出或去除材料，则本构法则是退化的：不抵抗涉及晶界处纯切向运动的变形模式。这种退化可以通过包括对晶界滑动的阻力来消除，或者通过对变形施加额外的约束。不抵抗在晶界处涉及纯切向运动的变形模式。这种退化可以通过包括对晶界滑动的阻力来消除，或者通过对变形施加额外的约束。不抵抗在晶界处涉及纯切向运动的变形模式。这种退化可以通过包括对晶界滑动的阻力来消除，或者通过对变形施加额外的约束。