Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials |
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Authors: | Zhongrong Niu Dali Ge Changzheng Cheng Jianqiao Ye Naman Recho |
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Affiliation: | 1. School of Civil Engineering, Hefei University of Technology, Hefei 230009, PR China;2. School of Civil Engineering, The University of Leeds, Leeds LS2 9JT, UK;3. Institute JLRA – CNRS UMR 7190, University P. and M. Curie-Paris VI, 75005 Paris, France |
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Abstract: | According to the linear theory of elasticity, there exists a combination of different orders of stress singularity at a V-notch tip of bonded dissimilar materials. The singularity reflects a strong stress concentration near the sharp V-notches. In this paper, a new way is proposed in order to determine the orders of singularity for two-dimensional V-notch problems. Firstly, on the basis of an asymptotic stress field in terms of radial coordinates at the V-notch tip, the governing equations of the elastic theory are transformed into an eigenvalue problem of ordinary differential equations (ODEs) with respect to the circumferential coordinate θ around the notch tip. Then the interpolating matrix method established by the first author is further developed to solve the general eigenvalue problem. Hence, the singularity orders of the V-notch problem are determined through solving the corresponding ODEs by means of the interpolating matrix method. Meanwhile, the associated eigenvectors of the displacement and stress fields near the V-notches are also obtained. These functions are essential in calculating the amplitude of the stress field described as generalized stress intensity factors of the V-notches. The present method is also available to deal with the plane V-notch problems in bonded orthotropic multi-material. Finally, numerical examples are presented to illustrate the accuracy and the effectiveness of the method. |
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Keywords: | Stress singularity orders Ordinary differential equations (ODEs) The interpolating matrix method V-notch Bonded dissimilar materials Orthotropic material |
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