A stress analytical solution for Mode III crack within modified gradient elasticity |
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Institution: | 1. Mechanical Engineering Department, University of Kansas, 1530 W 15th Street, Learned Hall, Lawrence, KS 66047-7609, United States;2. Civil, Environmental and Architectural Engineering Department, University of Kansas, 1530 W 15th Street, Learned Hall, Lawrence, KS 66045-7609, United States |
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Abstract: | The strain gradient exists near a crack tip may significantly influence the near-tip stress field. In this paper, the strain gradient and the internal length scales are introduced into the basic equations of mode III crack by the modified gradient elasticity (MGE). By using a complex function approach, the analytical solution of stress fields for mode III crack problem is derived within MGE. When the internal length scales vanish, the stress fields can be simplified to the stress fields of classical linear elastic fracture mechanics. The results show that the singularity of the shear stress is made up of two parts, r?1/2 part and r?3/2 part, and the sign of the stress σyz changes. With the increase of lx, the peak value of σyz decrease and its location moves farther from the fracture vertex. The influence of strain gradient for mode III crack problem cannot be ignored. |
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Keywords: | Modified gradient elasticity (MGE) Mode III crack Strain gradient Internal length scale Singularities |
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