关于裂纹尖端应力应变奇异性的讨论(英文)

DISCUSSION ON SINGUL一 ARITY OF STRESS-STRAIN AT THE CRACK TIP

经典的弹性和弹塑性断裂力学解都认为裂纹尖端应力应变存在奇异性,而这在物理上是不真实。怎样来解释断裂力学解和物理事实的不一致?本文利用从能量原理导出的与积分路径无关的积分公式进行了讨论,提出了笔者的观点。文中认为应该辩证地考虑这个问题。如果我们用连续介质模型来描述裂纹尖端应力应变场,存在奇异性是可以理解的,但我们必须记住。这在物理上是不真实的,它是由于我们不适当地采用连续介质模型来描述裂纹尖端情况而引起的。事实上,断裂问题涉及到材料的分离,它与微观过程有关,连续介质模型在这里失去了理论前提。文中探讨了裂纹新表面的形成过程及表面能的物理含义。

There should be singularity of stress-strain at the crack tip for the classical elasticsolution and elastoplastic solution about fracture problems.But this is not ture in physics.How to explain the disagreement between the solution of fracture mechanics and physic-al facts? This paper tries to discuss them from the integation formula irrelevant to thepath derived from the conservative principle of energy, puts forward the openion of theauthor. In our openion, it should be considered dialectically. If we should use continuummodel to discribe the condition at the crack tip, the appearance of singularity could beunderstood, but we must remember that this does not exist trully in physics, it has beencaused because of adopting unsuitable continuum mechanics model to discribe the condi-tion at crack tip. In fact, the froblem about fracture cracks would be refered to the se-paration of materials, and the separation spot should be related to microprocess while thecontinuum model has lost its theoretical premise. In this paper, the formation process ofnew surface of crack and implication of surface energy are discussed, too.