PSI - Issue 14

Sanjeev M Kavale et al. / Procedia Structural Integrity 14 (2019) 584–596 Sanjeev M. Kavale, Krishnaraja G Kodancha, Nagaraj Ekbote / Structural Integrity Procedia 00 (2018) 000–000

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Keywords: Finite Element Methods; Stress Intensity Factor; Constraint Issue; Poisson’s Ratio; T-Stress;

1. Introduction Constraint at the crack tip/front is the resistance against plastic deformation and is created because of many factors like specimen geometry and loading conditions (Kim et al. (2001)). Stress Intensity factor (Irwin (1958)), T stresses (Williams (1957)), Q stress (O'Dowd & Shih, 1992), etc. are the well-known parameters which explain the characteristics of a crack. Large scale deformations at crack-tips necessitate modification of the single parameter description of the stress field to multi parameter description and such cases are usually referred to the domain of constraint issues. Good amount of literature is available on 2D crack characterization, however very limited to 3D cracks (Kim et al. (2001)). Out of plane stress levels become inevitable for measuring fracture parameters for real time situations since cracks in reality are 3D in nature than 2D. Thus according to Nakamura (1988), Guo (1999) and Petti et al. (2004), 3D triaxial stress field near the crack front has an important role in a fracture mechanics framework. According to Gonzalez et al. (2011) the existing triaxial constraint effects are due to the in-plane and out-of-plane condition and both are related to the geometry and loading configuration of the cracked structure. Gonzalez et al. (2011) have mentioned that the T ij stress terms ( T 11 and T 33 ) affect the triaxiality in the near crack-front stress-fields and are directly related to the in-plane and out-of plane constraint. According to Meshii and Tanaka (2010), Giner et al. (2010) and Kodancha and Kudari (2009), the T ij stress terms, together with the stress intensity factor ( K I ), can provide a set of practical parameters for the characterization of near crack-front fields, nominally K-T ij . Gonzalez et al. (2011) have mentioned that the T ij stress terms ( T 11 and T 33 ) affect the triaxiality in the near crack-front stress-fields and are directly related to the in-plane and out-of-plane constraint. From the Irwin’s formulation (1958) for estimating SIF for any material, it is evident that the SIF is not dependent on Young’s Modulus of the material. The same is observed in the work of Williams (1957) for both SIF and T Stress. However the effect of Poisson’s ratio on SIF and T -stresses are very limited. In specimens with short height to width ratio, a reduction in the SIF is observed for varying Poisson’s ratio in the FE analyses done by Perl and Ore (1986). A change in the magnitudes of K I , T 11 and T 33 are observed across the thickness of the specimen in the FE work done by Pavel et al. (2010). Pavel et al. (2010) also indicated that only for zero Poisson’s ratio ( ߥ ൌ Ͳ ) the single parameter fracture analysis becomes feasible. For higher values of Poisson’s ratio, the single parameter fracture analysis is not sufficient enough because of the existence of T -stress, thus, indicating the effect of Poisson’s ratio on constraint parameters. Similar conclusions are made by Aliha and Saghafi (2013). The simplest formulation for estimating K I for a 3D specimen is suggested by Kwon and Sun (2000) and is mentioned in Eq. 1. However, the formulation doesn’t take into consideration the effect of thickness of the specimen. (1) Thus a systematic 3D FE analysis and comparative examination of variation of K I and T ij stresses along the crack front with respect to various crack configurations, specimen geometries, specimen thicknesses and Poisson’s ratio are required. In this investigation, effort has been put to understand the variation of K I and T ij stresses along the crack-front for SENB and CT specimens of various thicknesses and a/W =0.50 with different Poisson’s ratio. 2 2 3 1 1    D D K K

Nomenclature SIF

Stress Intensity Factor

Stress Intensity Factor under mode I loading conditions

K I

Crack length

a

Width of the specimen Thickness of the specimen

W

B

Poisson’s ratio

ν

T-Stress

T ij