三维界面力学理论及应用

A special finite element method has been developed for analyzing the singular order of the stress field near a three dimensional interface edge, based on the minimum potential principle. By the discretion of the integral equation in angular direction only , which is obtained by assuming the singular stress field and applying the minimum potential principle, this method is highly accurate and strict. Moreover, a database of the singular order vs. geometry and mechanical properties has been constituted Users can find the singular order simply without any computation. This study also has deduced theoretically the singular stress field and the electric displacement field around the three dimensional axisymmetric interface edge between bonded dissimilar piezoelectric materials, and given out the eigenequation to determine its stress singularity. Two effective experimental method to detect the singular behavior near the interface edge have been proposed too. It is found that the electric charges really concentrated to the interface edge of bonded piezomaterials. By introducing an initial crack near or from the interface edge, an effective strength evaluation method for an interface edge has been proposed. The stress intensity factors of the cracks can be easily calculated by the formula deduced by this study, if the singular order and singular stress coefficient of the stress field near the interface edge has been determined. Considering that the fracture of a three dimensional interface edge usually occurs under mixed modes I/II/II, fracture tests for such a mixed mode condition has been carried out, and a fracture criterion has been proposed, based on the viewpoint of facture energy and the experimental results. This criterion continues to the existed criteria of mixed modes I/II and I/III, and also contains the criteria for single mode fracture. The results obtained by this study have been used into the strength and life evaluations of coating materials and fretting fatigue. It is found the interface mechanics is an effective tool to evaluate such an engineering problem. A numerical method for determing the elastic-plastic singularity at an interface edge has also been proposed.

近年来发展起来的界面力学理论是建立在平面近似基础上。由于三维效应，结合材料界面端的应力奇异实际上与平面近似的结果有所不同。本研究首先按三维弹性理论求解，考虑三维效应的界面端应力奇异性及奇异应力场，考察其与平面近似结果的异同；其次按三维奇异性和应力场建立强度评价方法；最终通过实验验证其正确性，并分析二维理论的近似性。