Monte Carlo and molecular dynamics simulations of screw dislocation locking by Cottrell atmospheres in low carbon Feâ€“C alloys

On-lattice Monte Carlo shows strong carbon segregation at a screw dislocation in bcc iron for carbon contents that vary from 20 to 500 ppm, typical in ultra low and low carbon steels. Molecular dynamics simulations are then carried out using the atomic coordinates of equilibrated Cottrell atmospheres. The stresses required to make the screw dislocation break free of the carbon cloud are very high compared to carbon in solid solution; the locking time is also much longer. All simulations are performed at 300 K. 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Static strain ageing (SSA) refers to the hardening of a material that has undergone plastic deformation and is then aged for a certain period of time. The underlying atomistic mechanism behind SSA, according to the theory proposed by Cottrell and Bilby [1], is the segregation of solute atoms to dislocations forming the so-called ‘‘Cottrell atmospheres’’, which hinders dislocation motion. Higher stresses are then required to free the dislocations. SSA is of great importance for a number of applications of metallic alloys. It is, for instance, the phenomenon behind the bake-hardenable [2–4] and quenched-and-partitioned [5] steels used in the automotive industry. Despite being an old topic in physical metallurgy, the study of the role of solute-dislocation interactions in steel plasticity has benefited from advances in experimental characterization and computational methods, as can be seen in recent works [4,6,7]. Cottrell and Bilby treated carbon atoms as hydrostatic dilatation centers and used Maxwell–Boltzmann statistics to predict both the atmosphere formation and the associated hardening. This model fails to handle site saturation (i.e., for high carbon contents, it predicts many carbon atoms at the same octahedral site). To overcome this limitation, other authors rather used Fermi–Dirac statistics [8–11]. However, since Fermi–Dirac statistics assumes non-interacting particles, it also results in unrealistically high carbon concentrations in the dislocation core, where carbon–carbon interactions play an important role. More recently, Veiga et al. [12] combined Louat formulation with an estimate of the saturation concentration in the dislocation core to improve the description of carbon occupancies near dislocations. All these models are very crude approximations and none of them considered properly the wide range of elastic/chemical interactions within the atmosphere. Carbon interaction with the tensile stress field of edge dislocations is stronger than with the pure shear stress field of screw dislocations [12,13]. Molecular dynamics simulations were used to model the effect of a single carbon atom [14] and many carbon atoms in solid solution [7] on the glide of an edge dislocation. Given the prominent role of screw dislocations in the plasticity of iron, it is also worth studying the effect of carbon in their mobility. The binding energy of a single carbon atom to a screw dislocation reaches 0.41 eV [13,15], thus it may behave as an important carbon sink. In this work, Monte Carlo (MC) is employed to build Cottrell atmospheres around a 2 111 1⁄2 11 2 screw dislocation in bcc iron. Based on an appropriate interatomic potential, this approach circumvents most of the weaknesses of the simplest models mentioned above. The dislocation unpinning from the resulting carbon cloud, in turn, is simulated by molecular dynamics (MD). We used in all simulations a simulation box built according to the following procedure. The carbon-free simulation box consists of about 250,000 iron atoms arranged on a bcc lattice with