【摘要】 本文用二维弹塑性有限元素法分析了交变载荷作用下Ⅰ型裂纹准静态稳定扩展时裂尖前方应力场、应变场的变化和裂纹面的开闭现象;得到了裂纹扩展过程中的闭合应力和张开应力;裂尖塑性区和裂尖反向塑性区与裂纹长度的关系。在文献[1]的基础上,本文分析了扩展裂纹的开闭行为,进而揭示其与静止裂纹的差异。这种差异是由裂纹扩展时残留在裂纹面上的拉伸变形所致。本文详细地讨论了模拟裂纹扩展时,裂尖节点力释放技巧的重要性及其力学意义;并且利用共线双裂纹模型的概念对裂纹闭合现象作了进一步的分析。文中所得到的裂纹扩展时裂尖张开角的结论与文献[2]的实验结果基本一致。更多还原

【Abstract】 Since Elber’s discovery of the crack closure in 1971 [3], many papers[1, 4-9]have been published on this phenomenon. Theoretically, the closurephenomenon is a complex dynamic elastic-plastic contact problem. Starting fromthe Dugdale-Barenblatt model, Budiansky [5] et al. made a theoretical analysisof the closure phenomenon in the stable Mode I crack growth subjected to aconstant amplitude cyclic loading. References [1, 6-9] investigated the closurephenomenon and its influence on the crack growth rate using Finite ElementMethod (FEM). Although much work has been done, none of them, to theauthors’ best knowledge, has studied the influence of the crack-tip-node forcerelaxation technique on the simulation of a growing crack. Two dimensional elastic-plastic FEM has been employed to simulate thequasi-static stable Mode I crack growth under an alternating loading. Theimportance and physical meaning of the crack-tip-node force relaxation techni-que were carefully examined. In this paper, the following model is proposedto describe the closing and opening of a growing crack. Under compresiveload, the crack closes first at the crack-tips, then at the midpoint of the cracksurface, forming two collinear cracks. As the compresive load further increases,the contact at the midpoint spreads. Under the tensile load, the two collinearcracks become wider and wider until at a certain load the two collinear cracksjoin to form a single crack. The two major findings are as follows: (1) When the ralaxation technique is applied, the number of steps (atleast 10 in this paper) and step length should be carefully chosen in order tosimulate the crack growth correctly. Otherwise, it will cause incorrect shiftfrom old crack-tip to new crack-tip of stress, strain, plastic zone and cracksurface. (2) The proposed model explains two opposite phenomena: (a) a crackcloses fast at first, then slower and slower; (b) A crack opens slowly at thebeginning, then faster and faster. The magnitude of the maximum stress and theshifting of the point of stress concentration are also consistent with the model.更多还原