PSI - Issue 21

2

Sahin H./ Structural Integrity Procedia 00 (2019) 000 – 000

Hakan Şahin et al. / Procedia Structural Integrity 21 (2019) 38–45 Peer-review under responsibility of the 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials organizers

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Keywords: Finite element method; three-dimensional; stress intensity factor

1. Introduction

Nomenclature K

stress intensity factor stress intensity factor crack aspect ratio normalized crack depth crack inclination angle

SIF a/c

a/t



One of the problems encountered in engineering structures is the damage or breakage of the materials because of the manufacturing processes or operational conditions. These defects, eventually may lead to sharp cracks in the structure. Because of the singularity at the crack tip, classical mechanics solutions cannot provide adequate assessment and fracture mechanics is used for calculating stress intensity factors (SIF) for linear elastic fracture mechanics (LEFM) conditions. Three different modes (opening, slighting, tearing) are defined depending of relative deformation directions of crack surfaces and the related SIFs are solved. The literature about the calculation of the three-dimensional SIF for surface cracks in the last years is quite extensive. Solutions for surface cracks in three-dimensional structures are presented using different numerical techniques. Shah and Kobayashi (1973), Liao and Atluri (1989) calculated SIFs for an infinite plate. Guozhong and Kangda (1996) developed a hybrid boundary method and calculated SIFs for a finite plate, which is subjected to the tensile load. It is seen that they provide a large solution library, which is similar to this study. Frangi et al. (2002) used the boundary element method to calculate SIFs in the linear elastic region and results are given for some examples. Livieri and Segala (2016) calculated SIFs for embedded elliptical cracks in a spherical and cylindrical pressure vessels by using weight function. Finite element method (FEM) is one of the most widely used method in the literature. Studies by Raju and Newman (1979) provided significant contribution to three-dimensional mode-I fracture solutions. There are some studies solved by using enriched finite elements for surface cracks in plates. For a three-dimensional plate subjected to remote mode I tension stress, SIFs are calculated by finite element method, Wang and Lambert (1995). Ayhan and Nied (2002) calculated SIFs in surface cracks by using enriched finite elements. Further, Ayhan (2004, 2007) solved deflected and inclined semi-circular surface and corner cracks under remote tensile load. In the last five years, Okada et al. (2016) performed parametric analyses with high aspect ratios for a semi elliptical surface cracks in three dimensional plate under tensile loading. Kurt and Ayhan (2019) investigated inner/outer surface cracks with different inclination angles for a spherical pressure vessels by using the enriched finite element method. Plates are commonly used in engineering applications. In addition, some fracture problems contained in other type of structures can be reduced to a crack in a plate, if the focus is on the crack locally and the related local geometric conditions are appropriate. Thus, in this paper, by considering realistic intervals of the main parameters which affect SIFs for a surface crack under mixed-mode loading in a plate, parametric fracture analyses are performed and a large class of solutions are obtained. Representative results are provided in this paper in terms of normalized mixed mode SIFs along crack fronts of semi-elliptical surface cracks. 2. Method FEM models are created in ANSYS APDL. The information of nodes, elements, loads and boundary conditions are transferred to FRAC3D, then fracture analyses are performed to calculate mixed mode SIFs along crack front using enriched finite elements. The enriched finite element method is an attractive way for three-dimensional SIF