Crystal plasticity model for BCC iron atomistically informed by kinetics of correlated kinkpair nucleation on screw dislocation

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Abstract

The mobility of dislocation in body-centered cubic (BCC) metals is controlled by the thermally activated nucleation of kinks along the dislocation core. By employing a recent interatomic potential and the Nudged Elastic Band method, we predict the atomistic saddle-point state of 1/2111 screw dislocation motion in BCC iron that involves the nucleation of correlated kinkpairs and the resulting double superkinks. This unique process leads to a single-humped minimum energy path that governs the one-step activation of a screw dislocation to move into the adjacent {110} Peierls valley, which contrasts with the double-humped energy path and the two-step transition predicted by other interatomic potentials. Based on transition state theory, we use the atomistically computed, stress-dependent kinkpair activation parameters to inform a coarse-grained crystal plasticity flow rule. Our atomistically-informed crystal plasticity model quantitatively predicts the orientation dependent stress–strain behavior of BCC iron single crystals in a manner that is consistent with experimental results. The predicted temperature and strain-rate dependencies of the yield stress agree with experimental results in the 200–350 K temperature regime, and are rationalized by the small activation volumes associated with the kinkpair-mediated motion of screw dislocations.

Introduction

Plastic flow in body-centered cubic (BCC) metals is controlled by the motion of screw dislocations due to their high intrinsic lattice resistance (Argon, 2008, Vitek, 2008, Weinberger et al., 2013a). The resolved shear stress required to move a screw dislocation at 0 K (i.e., Peierls stress) is much higher than that for the edge dislocation, owing to the three-fold compact core of the former. However, this inherent difficulty to move a screw dislocation at finite temperatures can be mitigated by the thermal activation of kinks, which are essentially local perturbations on the straight dislocation line arising from the thermal fluctuation of atoms at the dislocation core. Hence, at finite temperatures (and low stresses) thermal activation of kinks is the rate-limiting step for the motion of screw dislocations in BCC metals (Seeger, 1956).

Thermally activated dislocation motion and its influence on the macroscopic plasticity of BCC crystals comprise a multiscale problem due to the extremely fine length and time scales of atomic vibration and the coarse scales of dislocation motion and interaction during plastic flow. Regarding the atomistic aspect of this problem, molecular statics studies have considered the Peierls stress for dislocation motion based on two-dimensional (2D) simulations (Chaussidon et al., 2006, Chen et al., 2013, Groger et al., 2008a, Groger et al., 2008b, Koester et al., 2012). They also evaluated the material parameters quantifying the so-called non-Schmid effects on the Peierls Stress, i.e., the effect of (non-glide) stresses other than the maximum resolved shear stress (Bassani et al., 2001). However, these studies were limited to the 2D mode of dislocation motion at 0 K and could not account for the three-dimensional (3D) nature of the kinetics of dislocation motion via kink formation in the finite temperature regime.

Molecular dynamics (MD) studies have also been performed in the past with the aim of understanding the motion of screw dislocations for example in BCC Fe at finite temperatures (Chaussidon et al., 2006, Domain and Monnet, 2005, Gilbert et al., 2011). However, direct MD is limited in simulation of the kinetic dislocation motion owing to the rare event nature of thermally activated kink nucleation. Also, the stress levels predicted using MD are elevated due to the high strain rates, and it is implausible to use MD to predict the stress–strain behavior of typical laboratory experiments at low strain rates. These limitations of MD underscore the need for a coarse-grained approach that can predict mechanical behavior at longer time scales without sacrificing the richness of atomistic information to inform the rate-controlling mechanisms of dislocation motion.

One coarse-grained modeling approach involves computing activation parameters of unit processes of thermally activated dislocation motion and then using them to inform a crystal plasticity model by invoking transition state theory (Vineyard, 1957). In this scheme, the Nudged Elastic Band (NEB) method (Jonsson et al., 1998, Zhu and Li, 2010, Zhu et al., 2013) has been used to compute the activation parameters of kink nucleation along a screw dislocation in BCC metals (Gordon et al., 2010, Groger and Vitek, 2008, Ngan and Wen, 2002, Proville et al., 2012). For example, Groger and Vitek (2008) employed a periodically varying analytical Peierls potential for NEB studies of BCC Mo. Ngan and Wen (2002) used the NEB method and Embedded Atom Method (EAM) potential to study kink nucleation along the core of a screw dislocation in BCC Fe. They predicted a degenerate dislocation core that is inconsistent with the non-degenerate core predicted by newer EAM potentials (Gordon et al., 2011, Mendelev et al., 2003), Bond Order potential (Groger et al., 2008a) and Density Functional Theory (DFT) (Ventelon and Willaime, 2007). The EAM potential for Fe used in Gordon et al. (2010) yielded the metastable dislocation core and associated double-humped minimum energy path which are likely artifacts of the potential, based on comparison with more accurate DFT studies (Ventelon and Willaime, 2007, Weinberger et al., 2013b). Recently, Proville et al. developed an EAM potential (hereafter referred to as Proville-EAM) (Proville et al., 2012) that predicted a single-humped 2D energy barrier, which agrees with the DFT results.

In this work, we employ the Proville-EAM potential and NEB method to compute the stress-dependent activation parameters for the 3D mode of thermally activated screw dislocation motion. We find a single-humped reaction pathway (i.e., minimum energy path) that is physically manifested as a correlated process of nucleation of leading and trailing kinkpairs, each of which consists of two atomically discrete kinks. Such a composite kink structure arises from the discrete 3D nature of the saddle-point state of screw motion, in contrast to the conventional line tension model of kink nucleation (Seeger, 1956). The corresponding atomistic material parameters are used to inform a plastic flow rule by invoking transition state theory. This atomistically informed crystal plasticity model predicted the deformation behavior of BCC Fe single crystals, specifically for the experimentally relevant low stress and finite temperature regime, where kink activation is the rate-limiting step in the kinetics of screw dislocation motion. This departs from other atomistically informed crystal plasticity models for BCC crystals (Koester et al., 2012, Weinberger et al., 2012, Yalcinkaya et al., 2008) and other coarse-grained models (Patra and McDowell, 2012, Tang et al., 1998) that adopt an empirical relation (Kocks et al., 1975) for describing the energetics of kink nucleation as a function of stress. The predictions of the orientation dependent tensile stress–strain relation from our model are in good agreement with experimental results for a BCC Fe single crystal (Keh, 1965, Yalcinkaya et al., 2008), thus providing some measure of validation. Our model also predicts the temperature dependence of the yield stress, in quantitative agreement with the experimental results for BCC Fe (Kuramoto et al., 1979). The details of our atomistic methods and the crystal plasticity model are described in Section 2. The results and their implications are discussed in 3 Results, 4 Discussion, respectively. Concluding remarks are given in Section 5.

Section snippets

Computational methods

The atomistic Nudged Elastic Band method and the atomistically informed crystal plasticity model are described in detail in the following two subsections, respectively.

Molecular statics and 2D NEB

We performed several benchmark calculations to verify that the Proville-EAM predicts the correct features of BCC Fe apart from the basic crystalline properties verified in Proville et al. (2012). Fig. 2 shows the differential displacement plot of a screw dislocation core (Vitek, 2004) as predicted by Proville-EAM based on a conjugate gradient energy minimization calculation. The core spreads onto the three {110} planes of the [111] zone and is non-degenerate, as it does not exhibit dyadic

Discussion

In this section we discuss the implications of our atomistic results regarding kinkpair nucleation, as well as the assumptions made in our atomistic and crystal plasticity models, and their linkage. First, we emphasize that the mechanism of correlated kinkpair nucleation revealed in our atomistic simulations is a direct outcome of the single hump of the energy barrier predicted by Proville-EAM. We observed that the correlated kinkpair nucleation occurred at all levels of applied shear stress

Conclusions

The major results and conclusions from this work are summarized below.

  • We have developed an atomistically informed crystal plasticity framework for BCC Fe single crystal that is in full fidelity with the atomic mechanism of thermally activated dislocation motion via kink nucleation. The nudged elastic band method was used to capture the activation pathway and evaluate the stress dependent activation parameters of kink nucleation.

  • Our atomistic results demonstrated a novel correlated kinkpair

Acknowledgments

The funding from the DOE Office of Nuclear Energy׳s Nuclear Energy University Programs (NEUP) is greatly acknowledged.

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