H. Dündar et alii, Frattura ed Integrità Strutturale, 35 (2016) 360-367; DOI: 10.3221/IGF-ESIS.35.41 361 used boundary element method (BEM) and compared their results to experimental data. Jonesa et.al . [2] analyzed interacting multiple cracks using finite element method (FEM) and a hybrid formulation which represents stiffness changes. Yan analyzed interacting multiple cracks and complex crack configurations in linear elastic media using an effective numerical method which is an extended form of Bueckners’ princible [3]. Leonel et.al used two-dimensional BEM method for multiple crack propagation analyses [4]. They used maximum circumferential stress theory for evaluating stress intensity factors (SIF) and propagation angle, and Paris’ law to predict structural life. Another 2D linear elastic fracture mechanics (LEFM) problem is analyzed by Yan [5] using BEM method for propagating multiple cracks. Yan also used maximum circumferential stress theory and Paris’ law. A Java-based boundary element program front end was developed by Hsieh et.al . for fracture analysis of multiple curvilinear cracks in general anisotropic materials [6]. Citarella et.al. compared DBEM and FEM methods by 3D fatigue crack growth of two anti-symmetric cracks [7]. Price and Trevelyan analyzed two eccentric crack that propagate nonplanarly in a thin geometry [8]. Bouchard and Chastel used maximum circumferential stress criterion, strain energy density fracture criterion and maximum strain energy release rate criterion for single and multiple nonplanar crack growth analyses [9]. The objective of this study is to apply, demonstrate and validate usage of FCPAS for multiple cracks propagating in a non-planar manner under fatigue loading. In the study, finite element method with enriched elements is used to obtain stress intensity factors (SIF) [10]. SIF values are calculated during nodal displacement calculation which is a step of finite element (FE) solution. By using enriched element method, SIFs are calculated accurately and no special re-processing or meshing techniques and post-processing of results are needed. It is shown that FCPAS results for multiple non-planar cracks agree well with those from the literature. M ETHOD or nonplanar crack propagation analyses, FCPAS finite element software is used. Also ANSYS™ [11] commercial FE software is used for generating FE model of the cracked geometry. All calculations for SIFs and propagation process are performed by FRAC3D solver of FCPAS software. Crack propagation process with FCPAS software consists of FE modeling of cracked geometry, solution step, propagation of the cracks and best ellipse fit for the propagated cracks. These steps are repeated until failure or some other geometric limit. Work flow scheme of FCPAS analysis is shown in Fig. 1. FCPAS solver, FRAC3D, uses enriched element method for calculating SIFs [12]. A general form of displacements for enriched elements is given in Eqs. 1-3. 0 1 1 1 0 1 1 0 1 ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( ) ( , , ) ( , , ) ( , , ) ( ) ( , , ) ( , , ) ( , , ) ntip m m i j j u j uj i I j j i ntip m i u j uj i II j i m u j uj j u N u Z f N f N K Z g N g N K Z h N h N 1 ( ) ntip i i III i K (1) 0 1 1 1 0 1 1 0 1 ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( ) ( , , ) ( , , ) ( , , ) ( ) ( , , ) ( , , ) ( , , ) ntip m m i j j v j vj i I j j i ntip m i v j vj i II j i m v j vj j v N v Z f N f N K Z g N g N K Z h N h N 1 ( ) ntip i i III i K (2) F

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