Analytical solution for macro/micro dual scale moving crack model under the in-plane tension

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (3) : 100-108.

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Analytical solution for macro/micro dual scale moving crack model under the in-plane tension

Tang Xue-Song

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Abstract

Interaction between the macroscopic and microscopic factors and blunting effect of the crack tip during the crack dynamic propagation are investigated. A macroscopic crack moves with a constant speed under the in-plane tension. A microscopic V-notch tip is attached to the main crack by using a mesoscopic restraining stress transition zone so that a macro/micro dual scale moving crack model is thus developed. The problem is analytically solved in the framework of elastic dynamics and complex function theory and analytical solution is obtained. Two solutions under the macroscopic and microscopic scales are coupled by application of the continuity condition of crack opening displacement from macro to micro and the consistence condition of stress fields under two different scales. Two explicit equations to determine the mesoscopic and microscopic damage zone sizes are obtained. It is shown that the macroscopic stress field of a moving crack has a normal r1/2 singularity while comparatively, the microscopic stress field exhibits the weaker singularity due to the microscopic blunting effect of the crack tip. The crack moving speed can reach to the shear wave speed in the dual scale moving crack model. Therefore, the limitation that the crack moving speed can not exceed the Rayleigh wave speed in the classical moving crack theory can be removed. The numerical results show that the mesoscopic damage zone size, microscopic crack tip zone size and crack opening displacement depend on the crack moving speed, material property, restraining stress ratio and blunting angle of the crack tip etc.

Key words

moving crack / elastic dynamics / mesoscopic fracture mechanics / restraining stress zone / dual scale crack model

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Tang Xue-Song. Analytical solution for macro/micro dual scale moving crack model under the in-plane tension[J]. Journal of Vibration and Shock, 2011, 30(3): 100-108