# Analysis of Elastic-Plastic J Integrals for 3-Dimensional Cracks Using Finite Element Alternating Method

• 박재학 (충북대학교 공과대학 안전공학과)
• 발행 : 2009.02.01
• 93 5

#### 초록

SGBEM(Symmetric Galerkin Boundary Element Method)-FEM alternating method has been proposed by Nikishkov, Park and Atluri. In the proposed method, arbitrarily shaped three-dimensional crack problems can be solved by alternating between the crack solution in an infinite body and the finite element solution without a crack. In the previous study, the SGBEM-FEM alternating method was extended further in order to solve elastic-plastic crack problems and to obtain elastic-plastic stress fields. For the elastic-plastic analysis the algorithm developed by Nikishkov et al. is used after modification. In the algorithm, the initial stress method is used to obtain elastic-plastic stress and strain fields. In this paper, elastic-plastic J integrals for three-dimensional cracks are obtained using the method. For that purpose, accurate values of displacement gradients and stresses are necessary on an integration path. In order to improve the accuracy of stress near crack surfaces, coordinate transformation and partitioning of integration domain are used. The coordinate transformation produces a transformation Jacobian, which cancels the singularity of the integrand. Using the developed program, simple three-dimensional crack problems are solved and elastic and elastic-plastic J integrals are obtained. The obtained J integrals are compared with the values obtained using a handbook solution. It is noted that J integrals obtained from the alternating method are close to the values from the handbook.

#### 키워드

유한요소 교호법;삼차원균열;탄소성해석;J 적분;대칭 Galerkin 경계요소법

#### 참고문헌

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#### 피인용 문헌

1. Examination and Improvement of Accuracy of Three-Dimensional Elastic Crack Solutions Obtained Using Finite Element Alternating Method vol.34, pp.5, 2010, https://doi.org/10.3795/KSME-A.2010.34.5.629