Shielding Effect and Emission Criterion of a Screw Dislocation Near an Interfacial Crisscross Crack

Shielding effect and emission criterion of a screw dislocation near an interracial crisscross crack are dealt within this paper. Utilizing the conformal mapping technique, the closed-form solutions are derived for complex potentialsand stress fields due to a screw dislocation located near the interracial crisscross crack. The stress intensity factor onthe crack tips and the critical stress intensity factor for dislocation emission are also calculated. The influence of theorientation of the dislocation and the morphology of the crisscross crack as well as the material elastic dissimilarity onthe shielding effect and the emission criterion is discussed in detail. The results show that positive screw dislocations canreduce the stress intensity factor of the interracial crisscross crack tip (shielding effect). The shielding effect increases withthe increase of the shear modulus of the lower half-plane, but it decreases with the increase of the dislocation azimuthangle and the distance between the dislocation and the crack tip. The critical loads at infinity for dislocation emissionincreases with the increase of emission angle and the vertical length of the crisscross crack, and the most probable anglefor screw dislocation emission is zero. The present solutions contain previous results as special cases.

Basic solution of two parallel non-symmetric permeable cracks in piezoelectric materials

The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading was studied by the Schmidt method for the permeable crack electric boundary conditions. Through the Fourier transform, the present problem can be solved with two pairs of dual integral equations in which the unknown variables are the jumps of displacements across crack surfaces. To Solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials. Finally, the relations between electric displacement intensity factors and stress intensity factors at crack tips can be obtained. Numerical examples are provided to show the effect of the distance between two cracks upon stress and electric displacement intensity factors at crack tips. Contrary to the impermeable crack surface condition solution, it is found that electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. At the same time, it can be found that the crack shielding effect is also present in the piezoelectric materials.

压电材料中非对称十字裂纹反平面问题

研究含非对称十字裂纹无限大压电弹性体在无穷远纵向剪切下任意位置作用广义集中载荷的电弹干涉效应。运用弹性复势方法,获得问题的封闭形式解答,导出非对称十字裂纹尖端的Ⅲ型广义强度因子、能量释放率和应变能密度因子表达式,并由此获得T型裂纹的相应新解答。讨论支裂纹对主裂纹尖端广义强度因子、能量释放率和应变能密度因子的影响。算例结果表明,广义集中载荷作用下非对称十字裂纹上、下半平面竖向支裂纹对横向主裂纹的干涉效应明显不同,与广义集中载荷同一半平面的支裂纹促进主裂纹扩展,而另一支裂纹抑制主裂纹扩展,且支裂纹越长,影响越大。其得到的退化结果与已有文献若干结果完全吻合。