摘要
根据裂纹扩展过程中的流变与耗散现象,建立了裂纹扩展过程中裂纹体的热力学平衡方程。从而我们把裂纹扩展问题转化为一个含质量流源的扩散运动问题,并应用内部体力场论研究了裂纹扩展力。引入外部热汇后,我们将能量耗散问题转化为一个热传导问题。在此基础上,提出变质量断裂模型理论,并实验验证了裂尖塑性流变区存在有质量流及相应的非均匀温度场。令Clausius非补偿热为非负值,建立了裂纹扩展过程的广义熵不等式。应用算子分解定理引入耗散势函数,再依据广义Onsager互易原理,我们将广义熵不等式化为某一泛函的可积微分不等式,从而得到它的完全解。最后,给出流变性材料的严格非局部本构关系,并借助Lyapounov型的流变记忆泛函来描述裂纹扩展的全过程。据此,我们将裂纹扩展全过程分成三个阶段,即孕育期、稳定扩展期和失稳扩展期。再根据非平衡态热力学稳定性建立起起裂判据、裂纹扩展的稳定和失稳判据,并指明了裂纹扩展的方向。结果表明,仅当对称性破坏时,才能出现失稳扩展。因此,本文为流变断裂学提供了一个理论基础。
In accordance with the Theological and dissipative phenomena in the process of crack propagation, the thermodynamical balance equations of cracked body in the course of crack propagation are established. Then we transform the problem of crack propagation into a problem of diffusion motion which contains the source of mass flow, and investigate the crack extension force by the use of internal body-force field. We transform the problem of energy dissipation into a problem of heat conduction by the introduction of external heat sink. On this basis, the theory of variable-mass fracture model is proposed, and the existence of mass flow and the corresponding inhomogeneous temperature field of plastic-rheological zone at the crack-tip is experimentally demonstrated. Let Clausius non-compensatory heat to be a non-negative value, the generalized entropy inequality in the process of crack propagation is established. The dissipative potential function is introduced by the use of operator theorem of decomposition, and with the condition of generalized Onsager reciprocal principle, the generalized entropy inequality is transformed into an integrable differential inequality of a certain functional so as to obtain its complete solution. Finally, the concrete nonlocal constitutive relations for rheological materials are given and the rheological memory functional of Lyapounov function model is adopted to describe the whole process of crack propagation, In accordance with this, the whole course of crack propagation is divided into three stages, that is, the incubation period, the stable propagation period and the unstable propagation period. Then the incipient cracking criterion, the stable and unstable criteria of crack propagation are established in accordance with the non-equilibrium thermodynamical stability, and the direction of crack propagation is indicated. It shows that only when the symmetry is lost, the unstable propagation start. Therefore, in this paper, a theoretical foundation for rheological fracture is laid.
出处
《力学进展》
EI
CSCD
北大核心
1989年第1期20-35,共16页
Advances in Mechanics
基金
中国国家自然科学基金
美国国家科学基金
关键词
流变断裂学
裂纹扩展
流变
耗散
rheological fracture
rheological memory functional
dissipative potential function
localized residual
super-entropy fluX
variable-mass fracture model
temperature field of crack-tip
