Approximate rotation vector expressions to consider crystal orientation changes in plastically deformed materials
Approximate rotation vector expressions to consider crystal orientation changes in plastically deformed materials
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DOI：
10.1007/s10853-019-04030-5
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发表时间：
2020-02-01
影响因子：
4.5
通讯作者：
Onaka，Susumu
中科院分区：
文献类型：
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作者：
Onaka，Susumu
在考虑塑性变形引起的材料微观结构变化时，取向变化是重要因素，因为这些变化与位错的排列和密度有关。旋转矩阵对数的三个元素称为对数角，它们组成旋转矢量，可以用作表示晶体取向的参数。这里，针对两个小角度旋转的乘积导出旋转矢量的近似表达式。讨论了一阶、二阶和三阶近似的次数。使用近似表达式以图形方式说明了两个旋转的非交换性。考虑冷轧铜双晶中取向变化的实验结果来评估近似表达式的有效性。结果表明，旋转矢量乘积的线性近似对于处理具有位错结构的塑性变形晶体中的小角度取向变化是有效的。
Orientation changes are important factors when considering microstructural changes in materials caused by plastic deformation because these are related to the arrangement and density of dislocations. The three elements of a logarithm of a rotation matrix are called log angles, which compose a rotation vector that can be used as a parameter to represent crystal orientations. Herein, approximate expressions of a rotation vector are derived for a product of two small-angle rotations. The degrees of the first-order, second-order and third-order approximations are discussed. The non-commutativity of two rotations is graphically illustrated using the approximate expressions. Experimental results of orientation changes in a cold-rolled Cu bicrystal are considered to evaluate the validity of the approximate expressions. It is shown that a linear approximation for the product of rotation vectors is valid to treat small-angle orientation changes in plastically deformed crystals with dislocation structures.