Issue 39

S. K. Kudari et alii, Frattura ed Integrità Strutturale, 39 (2017) 216-225; DOI: 10.3221/IGF-ESIS.39.21 217 Several researchers [3-13] have shown that the specimen thickness has major effect on the magnitude of stress intensity factor and T stresses. Kwon and Sun [7] have presented 3D FE analyses, to investigate the stress fields near the crack-tip and suggested a simple technique to determine 3D K I at the mid-plane by knowing 2D K I and Poisson’s ratio (  ) of the material using the Eq. (1): D D K K 3 2 2 1 1    (1) For quantifications of in-plane and out-of- plane constraint issues, magnitudes of T 11 and T 33 stresses are to be computed. But simple formulations such as Eq. (1) to estimate 3D K I , are not available to compute constraint parameters, T 11 and T 33 stresses. Usually they are obtained by complex 3D numerical methods. The aim of this investigation is to study the variation of K I , T 11 and T 33 along the crack-front considering a CT specimen geometry having varied thickness, B, crack length to width ratio (a/W) and applied stress,  , using 3D elastic FE analysis. Based on the present finite element results an effort is made to formulate approximate analytical equations to estimate the magnitudes of maximum 3D K I , T 11 and T 33 for a CT specimen. The proposed analytical formulations can be used to estimate the maximum 3D K I , T 11 and T 33 for the CT specimen, which are helpful in quantifying in-plane and out-of- plane constraint issues in fracture. By means of numerical analyses, it is shown that specimen thickness and crack length play an important role on the constraint effects. Figure 1 : The geometry of the CT specimen used in the analysis (W=20 mm). F INITE ELEMENT ANALYSIS ommercial FE software ABAQUS 6.5 [14] is used for the 3D FEA. The dimensions of CT specimen have been chosen according to ASTM standard E1820 [15] and the specimen geometry is shown in the Fig.1. One-half of the specimen geometry is modeled due to specimen symmetry. Twenty noded quadratic brick elements available in the ABAQUS are used to discretize the analysis domain. This kind of elements was used in the earlier works [8, 9] available in the literature. Initially, three-dimensional FE analyses on CT specimens were made by varying number of layers in thickness direction (each layer is of element thickness). It is observed that the variation in results of K I is insignificant for 8-14 layers. Consequently, in the present analyses 11 layers along the thickness direction were chosen as it gives ten numbers of elements along the thickness direction to extract the K I and T-stress. Due to half symmetry, the symmetrical boundary conditions have been imposed (u x2 =0) along the ligament of the model. Load is applied on approximately 1/3 rd portion nodes of the loading-hole circle perpendicular to the ligament. To keep the loading in perfectly Mode-I condition corresponding nodes are arrested except x 2 -direction. A typical mesh used in the analyses along with boundary conditions is shown in Fig.2. The magnitudes of K I and T-stresses have been extracted by using ABAQUS post processor. The details of extraction of stress 3D stress intensity factor (K I ) and T-stresses are discussed elsewhere [11,12,16,17]. The variation of K I and T-stresses along the crack-front has been studied for different specimen thickness (B/W=0.1-1.0) and crack length to width ratio (a/W=0.45-0.70). In this work the magnitude of applied stress,  , for the CT specimen is computed using the relation [18]: C

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