In this paper, the analytical solution of two dissimilar orthotropic functionally graded half-layers with interface Volterra-type screw dislocation under anti-plane transient loading is studied using linear elasticity theory. The energy loss is displayed by viscous damping, and the rate of gradual alteration of elastic stiffness, damping constant and mass density of two dissimilar non-homogeneous half-layers are modeled with exponential law. In the first stage, a single dislocation, Laplace and Fourier transform are applied to obtain the stress components with simple Cauchy kernel in the interface of the layers. Then, by means of the image method, the stress fields are derived in the interface of two half-layers. The dynamic stress intensity factors (DSIFs) are calculated in time domain by using numerical Laplace inversion and the distributed dislocation technique. Eventually, various examples are reported to demonstrate the effects of the crack length, cracks location, geometrical parameters, material specifications, viscous damping and the interaction of cracks on the DSIFs.

中文翻译：

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两个非均匀半层中多界面裂纹的瞬态行为

本文利用线弹性理论研究了反平面瞬态载荷作用下具有界面Volterra型螺位错的两个不同的正交各向异性功能梯度半层的解析解。能量损失由粘性阻尼显示，两个不同的非均匀半层的弹性刚度、阻尼常数和质量密度的逐渐变化率用指数定律建模。在第一阶段，应用单位错、拉普拉斯和傅立叶变换来获得层界面中具有简单柯西核的应力分量。然后，通过图像方法，推导出两个半层界面的应力场。通过使用数值拉普拉斯反演和分布式位错技术在时域中计算动态应力强度因子 (DSIF)。最后，报告了各种示例以证明裂纹长度、裂纹位置、几何参数、材料规格、粘性阻尼和裂纹对 DSIF 的相互作用的影响。