Thermal and thermo-mechanical influence on crack propagation using an extended mesh free method Lyazid Bouhala ⇑ , Ahmed Makradi, Salim Belouettar Centre de Recherche Public Henri Tudor, 29, Avenue John F. Kennedy, L-1855 Luxembourg, G.D. of Luxembourg, Luxembourg article info Article history: Received 13 July 2011 Received in revised form 17 February 2012 Accepted 1 April 2012 Keywords: Crack growth Thermo-mechanical loading Meshfree method Stress intensity factor J-integral abstract In this paper, the eXtended Element Free Galerkin method (XEFG) is used to model the crack growth in elastic materials. The effect of thermo-mechanical loading on the crack growth is investigated. The partition of unity principle is introduced to enhance the accu- racy and to better simulate the crack growth. In order to get the direction of the crack growth, first the Stress Intensity Factors (SIF) are calculated using the interaction energy integral, then the crack is assumed to propagate in the direction of the maximum principal stress. The different steps of the mesh free method implementation from the governing equations to the discretized system of linear equations are recalled. The method is vali- dated by calculating the stress intensity factors for static cracks and to comparing them those found in the literature. Further, the capability of the mesh free method for predicting crack growth under thermo-mechanical loading is demonstrated by comparing the obtained paths with others results from the literature. The implemented method presents a good efficiency and accuracy with relatively sparse node distributions. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction In thermo-mechanical applications, simulations are helpful for examining various numerical parameters such as defor- mations, stresses, temperatures, heat generation and crack effects [1]. However, only few existing models take into account the thermo-mechanical failures, which are critical to many applications such as fuel cells, aircraft engines, nuclear plants, etc. In fact, under combined mechanical and thermal loadings, the presence of cracks induces a strong variation in fields, which can affect the crack growth direction. To predict crack growth under thermal and/or mechanical loadings, different modeling and simulation methods are developed and the different complexities are highlighted. For instance, the study in [2] showed that the effect of thermal loading can alter the computation of stress intensity factors (SIF) of sub-interfacial cracks. In [3], the finite element method is used to study the catastrophic failure in coatings under thermal loading. The dy- namic propagation of cracks in functionally graded materials (FGM) under thermo-mechanical loading using an asymptotic analysis of temperature is studied in [4]. Analytical studies based on the SIF have been made in [5–7] to investigate the influ- ence of cyclic thermal loading on crack propagation. The challenge of such methods is the accuracy and the smoothness of the obtained fields, which are necessary in the process [8] and the post-process stages [9]. For example, the evaluation of the thermal stress intensity factors near the crack tip needs accurate displacement, stress and temperature fields. To reach this goal, displacement and temperature should be approximated taking into account the singularities in stresses and thermal flux at the crack tip, respectively. These asymptotic approximations of fields are taken into account successfully in the extended finite element method (XFEM) to model thermo-mechanical failures [9]. Combining the advantages of the mesh free method with those of the XFEM, we introduce in this work the eXtended Element Free Galerkin method (XEFG) to model 0013-7944/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engfracmech.2012.04.001 ⇑ Corresponding author. Tel.: +352 54 55 80 574; fax: +352 42 59 91 555. E-mail address: lyazid.bouhala@tudor.lu (L. Bouhala). Engineering Fracture Mechanics 88 (2012) 35–48 Contents lists available at SciVerse ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech