PSI - Issue 42

V. Shlyannikov et al. / Procedia Structural Integrity 42 (2022) 714–721 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction The main feature of fatigue crack growth under conditions of initial mode II is that the direction of crack propagation almost never coincides with the plane of its initial orientation. In the literature, there are some well known theories so far for evaluating the direction of crack initiation and to predict the crack kinking angle for mixed Mode I/II crack problems, such as the minimum strain energy density (SED) criterion, maximum tangential stress criterion and maximum energy release rate criterion. To improve theoretical predictions on the fracture behaviours of quasi-brittle materials, Ayatollahi et.al. (1998, 2017) suggested the use of some modified forms of the above criterion based on T-stress. However, all of the above criteria are based only on the elastic constants of the material (E, ν). The crack deviation criterion proposed by Shlyannikov V.N. (1999 ), which is based on singular solutions and elastic – plastic properties of the material. The size of the plasticity zone at the crack tip can be considerably larger under conditions of mode II compared to mode I. Aoki S et.al. (1987) conducted a numerical study on the mixed-mode crack tip fields and found that there exists both the blunting and sharpening effect around a mode II crack tip for elastic – plastic materials. Also, Nayeb Hashemi (1987) и Matsunaga (2014) have associated crack growth rate accelerati on or retardation caused by the occasional mode II loading with crack closure mechanisms caused by a large stretch of materials near the crack tip. Shlyannikov V.N. (1996, 2021), Richard et.al. (2017) represents new theoretical, experimental, and numerical approaches for mixed-mode crack growth investigation based on the fracture process, cohesive zones, and 3D-full field analysis. One of the most widespread full-field displacements techniques is the method of displacement field measurement using DIC. Today, DIC methods make it possible to restore the fields of displacement vectors on the surface of the studied specimens or structural elements; to study the patterns of development of inhomogeneous deformation fields in the areas of stress concentrators, to investigate deformation processes, damage accumulation, crack development and destruction of materials. The method is used to analyze the stress-strain state on the surface of specimens of various geometries. This procedure is based on the comparison of images acquired at different stages of a mechanical test and quantitative descriptions of local responses, which allow the evaluation of the impact of material heterogeneity on the strain distribution. Since the works of Peters and Ranson (1982) and Sutton et al. (1983), the powerful technique of 2D-DIC has been extensively applied in the research field of mechanics of solids (Sutton et al. (2009)), and to various classes of materials such as metals and alloys. For many years, the optical method of digital image correlation has been thoroughly researched and improved to achieve high measurement accuracy Sutton et al. (2009), Pan et al. (2009, 2010). Its main characteristic is the ability to measure the entire displacement field of the specimen surface in a wide range of displacement values. In the literature are reported for many different applications of the DIC method for assessing crack growth in metals. In Vanlanduit et al. (2009) the DIC method is used to track the process of crack growth on an aluminum U-shaped profile during fatigue test, where the specified offset accuracy is several hundredths of a pixel. The effects of gradient plasticity are manifested on small scales with respect to the structure of the material, leading to a sufficient increase in true local stresses. The problem is that classical theories of plasticity of continuum mechanics are unable to evaluate these micro-scale effects, since their constitutional models do not contain an internal parameter of the characteristic length of the material. The first theories of gradient plasticity were proposed by Fleck and Hutchinson (1993, 1997) and Fleck et al. (1994) correspond to the mathematical structure of elasticity theories taking into account high-order terms with deformation gradients. Out of the need to correlate the dimensions of deformations and deformation gradients, a new scale parameter of intrinsic material length was introduced, which is introduced into the plasticity of the deformation gradient and is associated with the density of dislocations. The theory of Nix and Gao (1998) partially elucidated the property embodied by the characteristic material length, and indicated the need to further refine the gradient theory of plasticity by an experimental law based on an analysis of the dominant deformation mechanisms. The analysis of Nix and Gao (1998) is based on the dislocation model of Taylor (1938), which interacts between the shear strength and dislocation density of a material. Later, Gao et al. (1999) supplemented the formulation with a more detailed analysis, which is referred to as the Mechanism based theory of Strain Gradient plasticity (MSG).