夹杂对两相材料界面裂纹的影响
Influence of inclusions on bi-materials interface crack
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摘要: 根据界面上应力和位移的连续条件，得到了单向拉伸状态下，含有椭圆夹杂的无限大双材料组合板的复势解. 进一步通过求解Hilbert问题，得到了含有夹杂和半无限界面裂纹的无限大板的应力场，并由此给出了裂尖的应力强度因子K. 计算了夹杂的形状、夹杂的位置、夹杂的材料选取以及上、下半平面材料与夹杂材料的不同组合对裂尖应力强度的影响. 计算结果表明夹杂到裂尖的距离和夹杂材料的性质对$K$影响较大，对于不同材料组合，该影响有较大差异. 夹杂距裂尖较近时，会对$K$产生明显屏蔽作用，随着夹杂远离裂尖，对$K$的影响也逐渐减小. 另外，软夹杂对$K$有屏蔽作用，硬夹杂对K有反屏蔽作用，而夹杂形状对$K$几乎没有影响Abstract: With the continuity conditions of stress and displacement on materialinterface, complex potentials solutions for a bi-material infinite platewith an elliptical inclusion under uniaxial tension are given. The stressfield of a bi-material infinite plate with an elliptical inclusion and asemi-infinite interface crack are given on the base of the complexpotentials solutions obtained above. And the corresponding stress intensityfactor $K$ is given. The influences of the position, the shape,material property, and different material combinations of inclusion on the stressintensity factor $K$ are calculated. The results indicate that the distance ofinclusion from crack tip and the property of inclusion have remarkableinfluence on the stress intensity factor $K$, and these influences vary notablywith different material combinations, whereas the shape of inclusion haslittle influence on $K$. When the inclusion is soft, the shield effect isoccurred for $K$; conversely, it is inverse shield.
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