Abstract The effect of strain-induced grain shape anisotropy on diffusional creep viscosity is analysed in two dimensions via a model representing grains by cylinders with elliptical cross section. Both cases of dominance of grain boundary diffusion and lattice diffusion are considered. Anisotropic creep viscosity is described by two coefficients calculated by considering different loading configurations with respect to the ellipse axes. Upper and lower bounds on these coefficients are obtained using kinematic and statical variational principles and assuming affine velocity, or uniform stress trial boundary fields, respectively. The analysis emphasises the dependence of the viscosity coefficients on aspect ratio and grain boundary viscosity. The difference between the bounds increases with grain elongation. A method is proposed for deriving estimates for the effective viscosity coefficients by coupling the two bounds. The strain hardening effect is analysed. Lattice diffusion contributes less to viscosity anisotropy than diffusion and sliding at grain boundaries.

中文翻译：

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Nabarro-Herring-Coble蠕变中晶粒形状各向异性对剪切粘度影响的变分分析

摘要 应变诱导晶粒形状各向异性对扩散蠕变黏​​度的影响通过一个用椭圆截面圆柱体表示晶粒的模型进行二维分析。考虑了晶界扩散和晶格扩散占优势的两种情况。各向异性蠕变粘度由通过考虑相对于椭圆轴的不同载荷配置计算的两个系数来描述。这些系数的上限和下限分别使用运动学和静态变分原理并假设仿射速度或均匀应力试验边界场来获得。分析强调了粘度系数对纵横比和晶界粘度的依赖性。边界之间的差异随着晶粒伸长而增加。提出了一种通过耦合两个边界来推导有效粘度系数估计值的方法。分析了应变硬化效应。与晶界处的扩散和滑动相比，晶格扩散对粘度各向异性的贡献较小。