非局部断裂与尺寸效应

RESEARCH RHEOLOGICL FRACTURE OF CRACK PROPAGATION

根据流变断裂学的理论和方法,结合非局部场理论和不可逆热力学,对裂纹扩展过程中的变形、热力平衡、热流变响应以及断裂的尺寸效应进行了探讨.由于变形的非协调性.以及裂纹扩展过程中新表面的产生,导致体积与表面物理量的相互转换,而使局部化假设失效,文中导出了一组更为广泛的描述裂纹扩展过程的局部热力平衡方程以及相应的边界条件,本文将断裂作为变形的极限行为,首次将它引入本构方程,把裂纹扩展表面能作为本构变量,给出了裂纹扩展对热流变响应的影响的一般形式,进一步揭示了Griffith表面能的本质和断裂的不可逆性,从而把流变与断裂在不可逆热力学基础上更紧密地结合起来了。最后,从一般的角度研究了断裂的尺寸效应,并指出非均质是产生尺寸效应的重要原因之一。

According to the theory and methods of rheological fracture,through the experiment and research on the phenomena of rheology anddissipation in the process of crack propagation,and consistence of inte-gral deformation,inconsistence of local deformation,and the formationof new surface during crack propagation, and the mutual conversion ofphysical quantities between volume and surface,a set of thermodynoamicequilibrium equations describing crack propagation have been derived inthis paper,which enable the matual action inside the body to expresswithin the equilibrium equation,but without the need for leading-in addi-tional physical quantities and any additional evolution equations to thesequantities, and which give out the boundary condition suitable to this set of thermodynamic equilibrium equations.This exactly expounds whyclassical theory can't explain the phenomena relevant to the geometricshape of sample and means of loading. This article proves that during crack propagation,the mutual inver-sion of physical quantities between volume and area because of produ-cing new crack surfaces makes the partial mass, momentum, angularmomentum and energy unable to be close,and should produce localiza-tion remainder, and makes the transport theorem and the hypothesis forlocalization in classic continuum mechanics failure.This paper regardsfracture as limitation action of deformation, for the first time introdu-ces the surface energy in crack propagation into constitutive equations,sets up the generalized dissipation inequqlity for crack propagation,anduses operator decomposition theorem and Onsagex reciprooity principleto change the generalized dissipation inequality into certain functionaldifferentiable inequality,from which the complete solution for constitu-tive relation can be obtained,thus, we can convert the research oncrack propagation into the research on rheology of materials and organi-cally combine rheology with fracture on the base of thermodynamics.