Crack tip fields of transiently propagating cracks along functionally gradient direction in anisotropic materials with having variations in elasticity and density are developed. The Laplace-transformed dynamic equilibrium equations with dilatation and distortion wave potentials are obtained using the complex variable method, and the higher order crack tip fields near the crack tip are obtained and the validity of the crack tip fields is confirmed. Next, the isochromatics (contours of maximum shear stress) and isopachics (contours of first stress invariant) for the transiently propagating cracks in anisotropic functionally gradient materials are created, and their transient characteristics are discussed.

中文翻译：

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在各向异性函数梯度材料中瞬时传播裂纹尖端场


在各向异性材料中，裂纹沿功能梯度方向瞬时扩展，具有弹性和密度变化。采用复变量法得到具有膨胀波势和畸变波电位的拉普拉斯变换动态平衡方程，得到裂纹尖端附近的高阶裂纹尖端场，并证实了裂纹尖端场的有效性。接下来，创建了各向异性功能梯度材料中瞬态扩展裂纹的等色（最大剪切应力的等值线）和等长（第一应力不变的等值线），并讨论了它们的瞬态特性。