Abstract We extend Inglis’s two dimensional elliptic tensile crack solution in elastic material after visiting his original work in 1913. Solving static elastic equation of motion, we find a general elliptic crack solution in elliptic coordinate. We transform the solution from elliptic to that in rectangular coordinate system and derive a general singular stress and displacement field in the slit crack model. We then derive extended Irwin’s energy release rate and acceleration associated with the crack just before crack propagation. Pointing out that tensile fracture becomes dominant when the crack velocity approaches zero, we show that splitting is one of the fundamental mode of tensile fracture in confined and compressive stresses in qualitative agreement with experiment.

中文翻译：

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英格利斯椭圆裂纹解法的扩展

摘要 我们在查阅了英格利斯 1913 年的原著后，扩展了他在弹性材料中的二维椭圆拉伸裂纹解。求解静弹性运动方程，我们找到了椭圆坐标下的一般椭圆裂纹解。我们将解从椭圆坐标系转换为直角坐标系，并推导出狭缝裂纹模型中的一般奇异应力和位移场。然后我们推导出扩展 Irwin 的能量释放速率和裂纹扩展前与裂纹相关的加速度。指出当裂纹速度接近零时，拉伸断裂变得占主导地位，我们表明分裂是在有限和压缩应力下与实验定性一致的拉伸断裂的基本模式之一。