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An interaction integral method forevaluating T-stress for two-dimensional crack problems using the extended radial point interpolation method

In this paper, an interaction integral method for calculating the T-stress for two-dimensional crack problems using the extended radial point interpolation method (XRPIM) is presented. Typical advantages of RPIM shape function are the satisfactions of the Kronecker’s delta property and the high-order continuity. | SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 18, No.K4- 2015 An interaction integral method for evaluating T-stress for two-dimensional crack problems using the extended radial point interpolation method Nguyen Thanh Nha Nguyen Thai Hien Nguyen Ngoc Minh Truong Tich Thien Ho Chi Minh city University of Technology, VNU-HCM (Manuscript Received on August 01st, 2015, Manuscript Revised August 27th, 2015) ABSTRACT: The so-called T-stress, or second term of the William (1957) series expansion for linear elastic crack-tip fields, has found many uses in fracture mechanics applications. In this paper, an interaction integral method for calculating the T-stress for two-dimensional crack problems using the extended radial point interpolation method (XRPIM) is presented. Typical advantages of RPIM shape function are the satisfactions of the Kronecker’s delta property and the high-order continuity. The T-stress can be calculated directly from a path independent interaction integral entirely based on the J-integral by simply the auxiliary field. Several benchmark examples in 2D crack problem are performed and compared with other existing solutions to illustrate the correction of the presented approach. Key words: T-stress, stress intensity factors, meshless, RPIM 1. INTRO DUCTIO N The fracture behavior of cracked structures is dominated mainly by the near-tip stress field. In linear-elastic fracture mechanics interest is focused mostly on stress intensity factors (SIFs) which describe the singular stress field ahead of a crack tip and govern fracture of a specimen when a critical stress intensity factor is reached. The usefulness of crack tip parameters representing the singular stress field was shown very early by numerous investigations. Nevertheless, there is experimental evidence that also the stress contributions acting over a longer distance from the crack tip may affect fracture mechanics Page 106 properties [1, 2]. The constant stress contribution (first .