论三维非线性断裂动力学中的路径无关积分
On Path-Independent Integrals in 3-Dimentional Nonlinear Fracture Dynamics
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摘要: 本文讨论三维非线性断裂动力学中的路径无关积分,它是文[4]关于二维情况结果的拓充.在研究三维非线性固体中埋藏裂纹或表面裂纹的动力传播问题中,这种拓充是必要的.固体介质是非线性弹性的或弹塑性的的情况均被加以考虑,并作出了相应的向量型路径无关积分.解释了这种路径无关积分的力学意义,它被证明联系于动力裂纹扩展力,因而,它们可用于构作非线性断裂动力学中的断裂准则.Abstract: This paper deals with the path-independent integrals in nonlinear three-dimensional fracture dynamics. Both the nonlinear elastic case and the elastic-plastic case are considered, and some path-independent integrals have been worked out.For explaining the physical meaning of these integrals, a specimen with plane notch is considered, and the relation between the integral and dynamical crack extension force is established. Thus, such integrals may serve as a fracture criterion in nonlinear fracture dynamics.
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[1] Rice,J.R.,J.A.M.,Vol.35,No.2,(1968). [2] Ouyanq,C.,Int.J.Eng.Sci.,Vol.18,No.2,(1980). [3] Ouyang,C.,TICOM Report,UT Austin,U.S.A.(1981). [4] 欧阳曾,非线性断裂动力学中的路经无关积分和断裂准则,应用数学和力学,3.3(1982).297-305. -
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