Mixed-mode stress intensity factor evaluation by interaction integral method for quadratic tetrahedral finite element with correction terms Ryutaro Daimon, Hiroshi Okada ⇑ Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science, 2641 Noda, Chiba 278-8510, Japan article info Article history: Received 9 May 2013 Received in revised form 31 August 2013 Accepted 6 November 2013 Available online 20 November 2013 Keywords: Interaction integral method Domain integral method Stress intensity factors Finite element method Fracture mechanics abstract In this paper, a simple and accurate formulation of the interaction integral method for the quadratic tetrahedral finite element is presented. It was found in the course of present investigation that the auxiliary solutions set by the asymptotic solutions of the crack did not satisfy the equilibrium in terms of the finite element model consisting of the quadratic tetrahedral element. Thus, the results of the interaction integral computations contained a large magnitude of numerical error. To overcome this problem, the authors propose to add correction terms to the asymptotic solutions and to form new auxiliary solutions. The cor- rection terms are determined so that the auxiliary solutions satisfy the equilibrium of the finite element model by performing finite element computations. Some numerical demon- strations are presented and they show that proposed methodology can give more accurate stress intensity factor solutions than the case without the correction terms. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Stress intensity factor evaluation is the key process in a structural integrity analysis for a damaged structure with cracks due to fatigue or stress corrosion cracking (SCC) (see, for example, Atluri et al. [1] and Nakamura et al. [2]). Engineering struc- tures are generally very complex in their configurations and the cracks often initiate at the locations of stress concentration as shown in the recent publication of Qian et al. [3] as an example. The stress analyses for such structures are generally car- ried out by the three-dimensional finite element method (FEM). When performing the FEM analysis in present computer hardware and software environment, we often use a three-dimensional solid modeler to define the model geometry. Then, we generate the FEM model using automatic meshing software and perform the three-dimensional FEM computation. How- ever, the automatic model generation software is not able to generate an analysis model with cracks, in general. Therefore, when we perform the fracture analysis, the FEM model generation relies on our manual operations and takes a lot of man hours. In last two decades, a series of works by many researchers have been presented to reduce the manual labor in the model generation processes. The meshless methods which are represented by the element-free Galerkin method (EFGM) (see, for example, [4–6]) totally eliminated the needs for meshing. Moving least square Petrov–Galerkin method (MLPG) was also proposed by Atluri and Zhu [7,8]. The EFGM and MLPG can perform analyses based only on nodal points. The extended finite element method (X-FEM) was proposed and applied to crack problems by Belytschko and Black [9] and Sukumar et al. [10]. 0013-7944/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engfracmech.2013.11.009 ⇑ Corresponding author. Tel.: +81 4 7122 1808. E-mail address: hokada@rs.noda.tus.ac.jp (H. Okada). Engineering Fracture Mechanics 115 (2014) 22–42 Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech