PSI - Issue 14

Rakesh Kumar et al. / Procedia Structural Integrity 14 (2019) 668–675 Author name / Structural Integrity Procedia 00 (2018) 000–000

673

6

The proposed FIP facilitates the study of the combined effect of hydrogen on plastic deformation and dislocation motion (HELP) and grain boundary strength (HEDE). In the third term of (13), the normalized hydrogen concentration is multiplied with to enhance the role of localized plasticity in presence of hydrogen, hence depicts the pure HELP mechanism. Similarly, the last term in FIP equation considers the effect of grain boundary normal stress and hydrogen concentration to elucidate their combined role on grain boundary opening i.e. crack nucleation based on decohesion of grain boundary planes which signifies the HEDE mechanism. Whereas the fourth term considers both HELP and HEDE effects together by considering accumulated plastic strain, grain boundary normal stress and hydrogen concentration simultaneously. The present framework of nonlocal dislocation density based crystal plasticity model coupled with upgraded hydrogen transport model which is able to consider isotropic and kinematic hardening, leads to better prediction of grain boundary normal stress and hydrogen concentration, which further gives rise to better evolution of FIP. Hence the present computational framework provides a new and unique possibility for better understanding the fatigue crack nucleation process. In this study, 16 grains RVE (Fig. 2(a)) with grain size of about 25 microns and random crystallographic orientations is simulated under constant strain fatigue loading with strain range from 0.05% to 0.5% with frequency 0.28 Hz using UMATHT and UMAT subroutines in ABAQUS. A quadratic brick element C3D20T is used to calculate the various gradients required in this study using a quasi-three-dimensional RVE. 4. Results and discussion The proposed model is first calibrated based on experimental deformation behavior of hydrogen-charged and uncharged nickel single crystal samples. Yagodzinskyy et al. (2008) results of nickel single crystal tensile deformation along direction [-1 6 7] are simulated in Fig.1(a). The proposed model shows a good match with the experimental results by reproducing the stage 1 hardening caused by hydrogen. For a polycrystal specimen, the crack nucleation under hydrogen environment depends on factors like elastic and plastic anisotropy, grain boundary normal stress and local hydrogen concentration etc. as discussed earlier. The stress evolution in RVE due to fatigue loading shows the isotropic and kinematic hardening due to evolution of geometrically necessary dislocations in the regions where plastic strain gradient is present. The stress-strain behavior of a hydrogen charged and uncharged polycrystal nickel is shown in Fig. 2(b). Simulated fatigue behavior also shows a good match with the experimental result as shown in Fig. 1(b). Grain boundary normal stress is calculated for the grain boundary elements by mapping the Cauchy stress tensor along the grain boundary normal vector as . . n GB     n σ n , where � is grain boundary normal vector and as Cauchy stress. A python script is used to implement this calculation during deformation simulations. The values of various parameters used in simulations are listed in Table 1. Due to the difficulty in experimental detection of hydrogen in materials, clear information about the critical hydrogen concentration is missing. Novak et al. (2010) performed study with different hydrogen concentrations and observed the change in nominal stress required to failure of the material. Their study provided an idea about the critical hydrogen concentration, where about 0.4 ppm hydrogen concentration led to 50% decrease in nominal stress. Though their study is for steel under bending load, the critical values are taken from their work as a good approximation. Similarly the grain boundary normal stress is normalized with the initial critical resolved shear stress of the material and critical accumulated plastic strain value is taken as 400 which is in accordance with Manonukul and Dunne (2004). After establishing the critical values of hydrogen concentration, grain boundary normal stress and accumulated plastic strains, a critical value for the FIP can be evaluated. This value of FIP is microstructure dependent and a careful experimentation is underway to establish it. In the present study, the simulations were performed to identify the potential fatigue crack initiation sites by locating the high FIP value regions. The modeling of fatigue crack initiation present in this work is based upon the evolution of the underlying parameters to their critical values. Manonukul and Dunne (2004) has used accumulated plastic strain as FIP and suggested that about 2 cycles are sufficient for accumulated plastic slip to reach to the saturation regime after initial hardening. Thereafter the accumulated plastic strain increases with the increasing number of cycles and crack nucleates when the considered FIP reaches a critical value. Following the same approach, fatigue simulations are performed on shown RVE and high FIP value sites are identified (Fig. 3) after four fatigue cycles. It is mediated that