扩散蠕变的微极连续模型
A micropolar continuum model of diffusion creep
摘要：
固体多晶材料的扩散蠕变过程通常采用柯西连续介质模型描述，其粘性流变特性是依赖于晶粒尺寸的牛顿流体。这种连续体缺乏描述晶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连续描述的扩散蠕变，包括晶粒旋转，并确定与微极（Cosserat）流体的材料的变形。我们推导出的微极本构张量的物理描述的离散收集刚性颗粒，要求离散和连续描述之间的等效耗散的均匀化的表达式。一般的本构关系推导出Coble（晶界扩散）和Nabarro-Herring（体积扩散）蠕变。详细的计算进行了二维平铺的不规则的六边形晶粒，这说明了一个潜在的耦合之间的旋转和平移的自由度。如果只考虑晶界处的材料的镀出或去除，则本构律是退化的：涉及晶界处的纯切向运动的变形模式不被抵抗。这种简并可以通过包括晶界滑动的阻力，或通过对变形施加额外的约束来消除。
英文摘要：
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.
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