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首页> 外文期刊>Acta Geophysica Polonica >TENSOR ANALYSIS OF DISLOCATION-STRESS RELATIONSHIP BASED ON THE EXTENDED DEFORMATION GRADIENT
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TENSOR ANALYSIS OF DISLOCATION-STRESS RELATIONSHIP BASED ON THE EXTENDED DEFORMATION GRADIENT

机译：基于扩展形变梯度的位移应力关系张量分析

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The dislocation density used to estimate the magnitude of paleostress in rocks has been expressed in terms of a scalar quantity. Dislocations are classified into two types: edge dislocations and screw dislocations. However, the scalar expression of dislocations does not contain information on the type of dislocations. Therefore, we cannot see the effect of stress on the type of dislocations. In other words, we can extract the information related to the magnitude but not the orientation from previous dislocation-stress relationship. Then, we attempted to derive the tensor equation for dislocation-stress field. For this analysis, we introduced the extended deformation gradient tensor, that is, a differential geometrical expression of the ordinary deformation gradient tensor. We assumed that: (1) the higher order terms and spatial derivatives of dislocation density can be ignored; (2) the material is isotropic. We found that our tensor equation for dislocation-stress field is the square root expression of the equation derived from the experimental data of aluminum under static tension. Moreover, we found that the type of dislocation affects the stress field through the difference in the value of coefficients of the dislocation-stress relationship.
机译：用于估计岩石中古应力大小的位错密度已用标量表示。位错分为两种类型：边缘位错和螺钉位错。但是，位错的标量表达式不包含有关位错类型的信息。因此，我们看不到应力对位错类型的影响。换句话说，我们可以从以前的位错-应力关系中提取与强度有关的信息，而不是与方向有关的信息。然后，我们尝试导出位错应力场的张量方程。为了进行此分析，我们引入了扩展的变形梯度张量，即普通变形梯度张量的微分几何表达式。我们假设：（1）位错密度的高阶项和空间导数可以忽略； （2）材料是各向同性的。我们发现，位错应力场的张量方程是从铝在静态张力下的实验数据得出的方程的平方根表达式。此外，我们发现，位错的类型通过位错-应力关系的系数值的差异影响应力场。

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