Finite element calculation of elastodynamic stress field around a notch tip via contour integrals |
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Affiliation: | 1. CEA, DAM, DIF, Bruyères-le-Châtel, F-91297 Arpajon, France;2. Université Paris-Sud 11, Département de Physique, 91405 Orsay Cedex, France;1. School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, PR China;2. Anhui Economic and Management Institute, Hefei 230059, PR China;3. ERMESS, EPF-Ecole d’Ingénieurs, Sceaux 92330, France;4. Blaise Pascal Institute, Blaise Pascal University, Clermont Ferrand 63000, France;1. School of Engineering, Liverpool John Moores University, James Parsons Building, Byrom Street, Liverpool L3 3AF, UK;2. Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 3BX, UK;1. School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China;2. ERMESS, EPF-Ecole d’Ingénieurs, Sceaux 92330, France;3. Blaise Pascal Institute, Blaise Pascal University, Clermont Ferrand 63000, France |
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Abstract: | Direct computation of the mixed-mode dynamic asymptotic stress field around a notch tip is difficult because the mode I and mode II stresses are in general governed by different orders of singularity. In this paper, we propose a pair of elastodynamic contour integrals JkR(t). The integrals are shown to be path-independent in a modified sense and so they can be accurately evaluated with finite element solutions. Also, by defining a pair of generalized stress intensity factors (SIFs) KI,β(t) and KII,β(t), the relationship between JkR(t) and the SIF’s is derived and expressed as functions of the notch angle β. Once the JkR(t)-integrals are accurately computed, the generalized SIF’s and, consequently, the asymptotic mixed-mode stress field can then be properly determined. No particular singular elements are required in the calculation. The proposed numerical scheme can be used to investigate the dynamic amplifying effect in the near-tip stress field. |
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