论裂纹扩展过程中的流变与耗散现象(Ⅱ)(英文)

ON THE RHEOLOGICAL AND DISSIPATIVE PHENOMENA IN THE PROCESS OF CRACK PROPAGATION (Ⅰ)

本文根据非局部场理论,从对裂纹扩展过程中流变与耗散现象的大量观察和研究,建立了裂纹体在裂纹扩展过程中的热力平衡方程。在引入质量、线动量和能量等的贡献之后,证明了裂纹体的局部动量和局部能量在裂纹扩展过程中均不守恒,而且诸热力学量对裂纹扩展所造成的新表面的贡献可用其局部化剩余来表示。从流变理论和耗散理论出发,建立非局部热力平衡基本方程后,论证了前文提出的关于裂纹扩展过程的五个基本观点。从耗散势函数出发建立了热流变性材料的非局部本构关系。如果这种本构关系对于每个独立体元和时间增量均能导出它的局部化形式,则可提出表面-体积能量密度理论。在体积随表面变化的意义上,给出耗散与不可逆性的定义。从而正确认识涉及体积和表面变化的热能与机械能交换的本质。本文与前文证明了裂纹扩展的全过程本质上是一个非线性非平衡态不可逆热力学过程,进一步完善了流变断裂学的理论基础。

In accordance with the rheological and dissipative phenomena in the process ofcrack propagation, the thermodynamical balance equations of cracked body in the courseof crack propagation are again discussioned in view of the preceding paper. The concretenonlocal constitutive relations for rheological materials are given. Then the mutuallyinteracting thermal/mechanical effects are accounted for by retaining the rate ofchange of volume with surface, in the surface/volume energy density theory, therebythe theoretical foundation for the temperature field at crack-tip are established. Look far and wide the parts (Ⅰ) and (Ⅱ) of this work, a theoretical basis forrheological fracture is laid. which in contrast to the classical approach, the wholeprocess of crack propagation is inspected.