PSI - Issue 14

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

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inflated hysteresis loop for a hydrogen-charged polycrystalline nickel specimen, as shown in Fig. 1(b). In addition, multiple cracks nucleated simultaneously along the grain boundaries for hydrogen-charges specimen, as shown in Fig. 1(c). These experimental results are taken as benchmark for the newly developed computational model to be reproduced at least qualitatively, if not quantitatively. This paper consists of four sections. Following a brief introduction, section 2 describes the simulation framework that uses dislocation densities as an internal variable for the non-local crystal plasticity model and hydrogen transport model. The effect of local plastic strain, grain boundary normal stress and high hydrogen concentration on the crack initiation is incorporated through a fatigue indicator parameter (FIP) formulated in section 3. Section 4 presents the fatigue loading imposed on Represented Volume Element (RVE) and the critical crack nucleation sites identified by high FIP values at grain boundaries, followed by conclusion and outlook.

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Fig. 1. (a) Comparison of experimental results of hydrogen-charged and uncharged nickel single crystals with tensile axis oriented along [-1 6 7] (Yagodzinskyy et.al. 2008). Correspondingly, the simulation results are also shown for hydrogen-charged and uncharged nickel single crystals, which will be discussed later in the text, (b) Experimental cyclic stress-strain behavior of hydrogen-charged and uncharged polycrystalline nickel shallow-notched specimens, and (c) Multiple fatigue crack nucleation sites observed by in-situ fatigue tests performed on a fatigue stage under SEM. The loading direction is indicated by arrows (Arora et al. 2018). 2. Modeling framework Using physics-based model to investigate the role of microstructure on fatigue crack initiation provide an opportunity to understand various effects of hydrogen in material e.g. rise in elastic stresses due to insertion of hydrogen as a solute, dislocation pinning by hydrogen leading to rise in stage 1 hardening, increase in dislocation velocity due to hydrogen leading to delay in stage II hardening emergence etc. The proposed model can capture such interactions associated with hydrogen-metal systems. 2.1. Nonlocal crystal plasticity model A rate-dependent dislocation density-based crystal plasticity model coupled with hydrogen transport model is developed by considering nonlocal effects caused by deformation inhomogeneities. The deformation gradient F is multiplicatively decomposed into elastic , plastic and elastic dilatation part due to hydrogen as  e h p F F F F . (1) The plastic deformation gradient rate is calculated using flow rule as   p p p F L F (2) where is plastic velocity gradient given as   n α 1 γ      α α m n  p L . (3)