Micromechanical modelling of hydrogen-assisted crack initiation in metals under monotonic and fatigue loading

Abstract

Hydrogen embrittlement (HE) in metals and alloys is an age old problem, the solution of which is still not in sight. It leads to the loss of a significant percentage of gross domestic product values of industrialised nations, leading to continuous ongoing researches to unravel the various multifaceted mechanisms of HE. Researchers have come up with a plethora of possible HE mechanisms encompassing all length scales based on multi-scale experiments and simulations. However, it is realised that no individual mechanism functions alone towards HE. The state-of-the-art is about the understanding of a synergistic interplay among various HE mechanisms. The interaction of hydrogen with metal lattice as well as various defects such as dislocations, vacancies, grain boundaries (GB) etc. significantly affect the material deformation behaviour and generally leads to the reduction in their ductility and strength bearing capacity. The micromechanical modelling using crystal plasticity at meso-scale provides an unique possibility to understand the role of metallic microstructure on hydrogen distribution as well as identify its effect on degradation of material properties at engineering scale. With a focus on indentifying the role of hydrogen on crack initiation in metallic microstructures, a coupled framework consisting of non-local, dislocation density based crystal plasticity, and dislocation assisted hydrogen flux within the slip-rate based hydrogen transport model is developed in this work. The non-local, dislocation density based crystal plasticity model incorporates the additional hardening due to evolution of geometrically necessary dislocations (GNDs) and the backstress due to the pileup of GNDs in the metallic microstructure. The dislocation assisted hydrogen flux within the slip-rate based hydrogen transport model is able to incorporate the hydrogen flux associated with mobile dislocations as well as accounts for enhanced trap density and role of hydrostatic stress on hydrogen distribution in the microstructure with deformation. The coupled framework is shown to predict hydrogen-assisted crack initiation in polycrystalline nickel under both monotonic and fatigue loading using set of simulations on both virtual as well as realistic metallic microstructure. These simulations are performed using representative volume elements (RVEs) containing different number of grains, at different loading rates and loading types (i.e. monotonic, shear and cyclic loading) to understand hydrogen distribution in a metallic microstructure with deformation towards their role on crack initiation. In the first simulation study, various microstructural factors such as grain size and GB type, and external factors such as loading direction and strain rate affecting the distribution of hydrogen in metallic microstructures is studied using a three-grain virtual nickel polycrystal. Deformation simulation were performed on three-grain virtual polycrystals (having two special GBs) with different grain sizes along three mutually perpendicular directions with respect to GB plane. Two types of special GBs (one with hydrogen binding energy higher than that of dislocations i.e. 3[1 10](111) and others with lower binding energy than dislocations such as 5[210](001)) are considered in these simulations at various strain-rates. Results from these simulations suggest that hydrostatic stress and binding energies of various types of GBs are the prime factors that affect hydrogen distribution in the nickel microstructures. In the second simulation study, motivated by the recent experimental findings in our research group, the role of hydrogen on low-cycle fatigue (LCF) crack initiation in polycrystal nickel is investigated. For this work, in-situ LCF testing of hydrogen charged (electrochemically) shallow-notch specimens using tensile/fatigue stage under scanning electron microscope is taken as reference. Experiments reveal the inter-granular fatigue crack initiation (FCI) at those GBs and triple junctions (TJs) that are surrounded by grains with severe plastic deformation. Also, most of the participating GBs are found to be normal to the loading direction. Through detalined examination of the TJs, it was found that major fraction of TJs involved in the crack initiation process are those with one 3 and two random GBs. These experiments reveals the prominent role of plasticity, GB normal stress, critical hydrogen concentration and specific character of TJs on intergranular FCI. The role of these factors on FCI of hydrogen-charged nickel polycrystals is simulated using a partially two-way coupled framework of dislocation density based non-local crystal plasticity model with the slip-based hydrogen transport model. The cumulative effect of these factors on intergranular FCI is shown through a scalar fracture indicator parameter (FIP) which is able to identify GBs and TJs as potential FCI sites. Similar to experiments, simulations reveal that the TJs between 3 and two random GBs are most favourable FCI sites mainly due to high hydrostatic stresses and lower hydrogen diffusivity through 3 GB that holds the hydrogen for longer time at these sites. The proposed FIP shows the possibility to model both the individual role of various HE mechanisms such as hydrogen enhanced localized plasticity (HELP), hydrogen enhanced decohesion (HEDE) and their synergistic role such as HELP+HEDE and HELP mediated HEDE etc on hydrogen assisted FCI in metals. One of the salient features of HE is that it causes ductile to brittle transition in metals at the crack front. This is caused by several competing processes such as hydrogen segregation, dislocations emission and cleavage failure at the crack front. For a hydrogen free metal, using single crystal fracture studies, the competition between ductile and brittle fracture is shown to be a function of crystal orientations. For metallic specimens with hydrogen, such information can be vital for mitigating HE by designing the microstructures with certain crystal orientations that can prevent the ductile to brittle transition due to hydrogen. In the next simulation study, the role of factors such as source of hydrogen (internal or external), defect binding energy, deformation rate coupled with the effect of crystal orientation on the dominance of a particular HE mechanisms at the crack front is investigated. A chemical potential based boundary condition, more appropriate to simulate the case where hydrogen ingress into metals through external source, is specified at the crack surface. To correctly simulate the hydrogen evolution at the crack front under Mode-I loading, the previously developed coupled framework of dislocation density based non-local crystal plasticity model with the slip-based hydrogen transport model is updated to consider hydrogen transport through mobile dislocations in relation to the their velocity. Total hydrogen concentration, accumulated plastic strain and stress triaxiality are then considered as prime factors controlling hydrogen based damage, the combined effect of which is implemented through a novel FIP developed for such scenarios. The proposed FIP highlights the competition between the individual HE mechanisms (HEDE or HELP) and their synergistic action (HELP+HEDE) towards brittle failure as a strong function of crystal orientation. In the last simulation study, hydrogen-assisted crack initiation in a realistic metallic microstructure is simulated under monotonic loading. This work is motivated by the recently reported experimental framework that correlates the stress maps of the metallic microstructure with hydrogen-assisted crack initiation under monotonic loading. A coupled computational framework of hydrogen transport model and dislocation based crystal plasticity model developed in our previous work is used for performing these simulations. At first, the maximum Schmid factor and elastic modulus maps are plotted with respect to the loading direction for the undeformed simulation model with similar microstructure as used for experimental studies. Further, normal strain, hydrostatic stress, stress triaxiality are plotted in-line with the experimental framework at low strain levels. Finally, the FIP (defined previously as a function of factors like total hydrogen concentration, accumulated plastic slip and stress triaxiality) maps obtained at low strains is shown to predict the crack initiation sites observed in experiment at high strain values for hydrogen charged metallic specimens. The scaling factors corresponding to each HE mechanisms is fitted to match the experimental crack initiation behavior thus providing the exact role of individual (HEDE or HELP) as well as synergistic action (HEDE+HELP) of HE mechanisms on crack initiation.