L.P. Kubin

Dislocation Mean Free Paths and Strain Hardening of Crystals

Predicting the strain hardening properties of crystals constitutes a long-standing challenge for dislocation theory. The main difficulty resides in the integration of dislocation processes through a wide range of time and length scales, up to macroscopic dimensions. In the present multiscale approach, dislocation dynamics simulations are used to establish a dislocation-based continuum model incorporating discrete and intermittent aspects of plastic flow. This is performed through the modeling of a key quantity, the mean free path of dislocations. The model is then integrated at the scale of bulk crystals, which allows for the detailed reproduction of the complex deformation curves of face-centered cubic crystals. Because of its predictive ability, the proposed framework has a large potential for further applications.

Connecting atomistic and mesoscale simulations of crystal plasticity

A quantitative description of plastic deformation in crystalline solids requires a knowledge of how an assembly of dislocations — the defects responsible for crystal plasticity — evolves under stress. In this context, molecular-dynamics simulations have been used to elucidate interatomic processes on microscopic (∼10−10 m) scales, whereas ‘dislocation-dynamics’ simulations have explored the long-range elastic interactions between dislocations on mesoscopic (∼10−6 m) scales. But a quantitative connection between interatomic processes and behaviour on mesoscopic scales has hitherto been lacking. Here we show how such a connection can be made using large-scale (100 million atoms) molecular-dynamics simulations to establish the local rules for mesoscopic simulations of interacting dislocations. In our molecular-dynamics simulations, we observe directly the formation and subsequent destruction of a junction (a Lomer–Cottrell lock) between two dislocations in the plastic zone near a crack tip: the formation of such junctions is an essential process in plastic deformation, as they act as an obstacle to dislocation motion. The force required to destroy this junction is then used to formulate the critical condition for junction destruction in a dislocation-dynamics simulation, the results of which compare well with previous deformation experiments.

Dislocation mobility and the mechanical response of b.c.c. single crystals: A mesoscopic approach

A mesoscopic simulation of dislocations and plasticity in b.c.c. crystals at low temperatures is developed and applied to the case of Ta. The thermally activated nucleation of double kinks is taken as controlling the mobility of screw dislocations. The resulting temperature and strain rate dependence of the yield stress are investigated and a detailed thermal activation analysis is performed on the output of the simulations. It is shown that within the simplifications made to the input parameters and slip geometry, one is able to simulate realistic dislocation structures and mechanical response. By checking the conformity between the input and output, it is shown that the essential dislocation property (activation energy for screw dislocation motion) can effectively be deduced from the mechanical tests. The mesoscopic simulation provides a potential tool to link atomistic studies at the microscopic scale to the macroscopic modeling of mechanical properties of b.c.c. metals at low temperatures.

Mesoscopic simulations of plastic deformation

Abstract This review is focused on recent progress achieved by mesoscopic simulations of plastic deformation. The methods presently available for discretizing the dislocation lines are critically discussed with emphasis on a new lattice-based model. Progress in large-scale simulations is represented by a study on the influence of long range elastic stresses on the formation of dislocation patterns in fcc crystals. A hybrid discrete-continuum method that provides an exact treatment of the boundary conditions is described and illustrated by an investigation of the critical conditions for dislocation motion in the channels of γ / γ ′ superalloys.

Mesoscopic simulations of dislocations and plasticity

This paper reviews the three-dimensional simulations of dislocation dynamics and interactions at the mesoscopic scale. The simulation technique is briefly sketched and examples of applications are shown. A distinction is made between situations where uniform dislocation structures result from core properties (Ni3Al) and situations where dislocation interactions leads to pattern formation (f.c.c. crystals). Limitations and potentialities of the method are discussed.

Spatio-temporal dynamics of the Portevin–Le Chatelier effect: experiment and modelling

Abstract The temporal and spatial features of the Portevin–Le Chatelier plastic instabilities in single and polycrystals of Al–Mg alloys were investigated systematically, with special emphasis being put on the character of the statistical distributions of the stress drops. The effect of strain rate, temperature and the microstructural state of the alloy was studied experimentally. It was shown that an experimentally accessible quantity, the flow stress, governs to a large extent the observed correlation between the variation of the type of serrations and of the stress drop distributions. Computer simulations of the Portevin–Le Chatelier effect were carried out using a simple spatial coupling model. It was demonstrated that the salient features of the complex spatio-temporal behaviour observed experimentally for different microstructural states are adequately reproduced by the model. A comparison between the experimental data and the simulation results suggests that the spatial coupling stems from plastic strain incompatibilities.

Spatial coupling in jerky flow using polycrystal plasticity

A multiscale approach including a finite element framework for polycrystal plasticity is used to model jerky flow, also known as the Portevin-Le Chatelier effect. The local constitutive behavior comprises the standard description of the negative strain rate sensitivity of the flow stress in the domain of instability. Due to stress gradients inherent to the polycrystal formulation, the spatial coupling involved in the spatio-temporal dynamics of jerky flow is naturally accounted for in the model, without using any ad hoc gradient constitutive formulation. For the first time, the static, hopping and propagating band types are recovered in constant strain-rate tests, as well as the temporal properties of the stress serrations. The associated dynamic regimes are characterized and found consistent with recent experimental evidence of both chaos and self-organized criticality in Al-Mg polycrystals.

Simulation of dislocation patterns in multislip

Dislocation dynamics simulations of multiple slip in f.c.c. crystals lead to the formation of patterned microstructures. The mechanisms participating to dislocation storage and dynamic recovery are investigated and discussed. Cross-slip and short-range interactions are found to govern the bifurcation from uniform to ordered microstructures.

Statistical behaviour and strain localization patterns in the Portevin-Le Chatelier effect

Abstract Statistics of the stress drops associated with the Portevin-Le Châtelier effect in an AlMg alloy were studied both experimentally and theoretically. It was shown that the character of the statistics changes from a peaked distribution of the stress drop magnitudes to a monotonically decreasing one as the imposed strain rate or the temperature are increased. A discrete model based on a micromechanically founded local constitutive equation combined with spatial coupling between the elements of the system was shown to reproduce the observed statistical behaviour. The mechanism of spatial coupling is connected with elastic stresses due to local plastic incompatibilities. The model was further applied to simulate spatial deformation patterns including propagative deformation bands. The systematics of the bands reported in the literature as well as the observed dependence of the band velocity on the imposed deformation rate were recovered. It was concluded that the model proposed provides an adequate description of both the statistics of stress discontinuities and the spatial features of the Portevin-Le Châtelier effect.

Homogenization method for a discrete-continuum simulation of dislocation dynamics

Abstract The question of the description of the elastic fields of dislocations and of the plastic strains generated by their motion is central to the connection between dislocation-based and continuum approaches of plasticity. In the present work, the homogenization of the elementary shears produced by dislocations is discussed within the frame of a discrete-continuum numerical model. In the latter, a dislocation dynamics simulation is substituted for the constitutive form traditionally used in finite element calculations. As an illustrative example of the discrete-continuum model, the stress field of single dislocations is obtained as a solution of the boundary value problem. The hybrid code is also shown to account for size effects originating from line tension effects and from stress concentrations at the tip of dislocation pile-ups.