An analysis on three-dimensional effects near the tip of a crack in an elastic plate |
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Authors: | Zhi-He Jin and Keh-Chih Hwang |
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Institution: | (1) Northern Jiaotong University, Beijing, China;(2) Tsinghua University, Beijing, China |
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Abstract: | An infinite plate containing a finite through crack under tensile loading is analysed by Fourier transform based on the Kane-Mindlin kinematic assumptions for the quasi-three-dimensional deformation of plates in extension. The asymptotic expressions of stress and displacement fields near the crack tip, the variation of the stress intensity factor with the plate-thickness and the three-dimensional deformation zone near the crack tip are investigated. The results of the analysis show that, (a) the crack-tip stress and displacement fields accounting for the plate-thickness effects are different from the plane stress solutions and this is true even for extremely small parameter (=1–vh/6 a). In a very small region near the crack tip, plane strain solutions prevail; (b) the ratio of the stress intensity factor KI to the corresponding plane stress one KI, KI/K
I
o
, approaches 1/(1–v2) as tends to zero; (c) plane stress solutions can give satisfactory results for points a distance from the crack tip greater than about three-fourths of the plate-thickness; (d) the linear elastic result for the zone of three-dimensional effects is approximately valid for an elasto-plastic material with linear strain-hardening when the plastic tangential mudulus Et is not very small.The Project Supported by National Natural Science Foundation of China. |
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Keywords: | crack-tip field three-dimensional effect plate thickness Kane-Mindlin assumptions |
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