Marc Fivel

Mesoscopic scale simulation of dislocation dynamics in fcc metals: Principles and applications

This paper reviews the methods and techniques developed to simulate dislocation dynamics on a mesoscopic scale. Attention is given to techniques of acceleration and to the implementation of special boundary conditions. Typical results concerning the deformation of a bulk crystal, the effect of image forces and the combination with a finite-element code to simulate the indentation test are presented. The limits and future development of each application are discussed.

Three-dimensional modeling of indent-induced plastic zone at a mesoscale

Abstract In order to better understand how an indent-induced plastic zone forms, the experimental conditions associated with nanoindentation testing on f.c.c. crystals are modeled, using a combination of three- dimensional discrete dislocation simulation and the finite element method (FEM). At each stage of the loading, the FEM elastic solution enforcing the boundary conditions is superimposed to the infinite medium elastic solution of the discrete dislocations. The plastic character of the indented material is accounted for by relaxing the elastic loading stresses through both the introduction of new nucleated discrete dislocations (loops) and their motion within the sample. Transmission Electron Microscopy observations of the indent-induced plastic volume and analysis of the experimental loading curve help in defining a complete set of nucleation rules. A validation of the model is performed through direct comparisons between a simulation of a nanoindentation test on a [001] copper single crystal and the same experimental indentation.

Introducing dislocation climb by bulk diffusion in discrete dislocation dynamics

We report a method to incorporate dislocation climb controlled by bulk diffusion in a three-dimensional discrete dislocation dynamics (DDD) simulation for fcc metals. In this model we couple the vacancy diffusion theory to the DDD in order to obtain the climb rate of the dislocation segments. The capability of the model to reproduce the motion of climbing dislocations is examined by calculating several test-cases of pure climb-related phenomena and comparing the results with existing analytical predictions and experimental observations. As test-cases, the DDD is used to study the activation of Bardeen–Herring sources upon the application of an external stress or under vacancy supersaturation. Loop shrinkage and expansion due to vacancy emission or absorption is shown to be well described by our model. In particular, the model naturally describes the coarsening of a population of loops having different sizes.

Low-strain fatigue in AISI 316L steel surface grains: a three-dimensional discrete dislocation dynamics modelling of the early cycles I. Dislocation microstructures and mechanical behaviour

The early stages of the formation of dislocation microstructures in low-strain fatigue are analysed, using three-dimensional discrete dislocation dynamics modelling. Simulations under various conditions of loading amplitude and grain size have been performed. Both the dislocation microstructures and the associated mechanical behaviour are accurately reproduced in single-slip as well as in double-slip loading conditions. The microstructures thus obtained are analysed quantitatively, in terms of number of slip bands per grain, band thickness and band spacing. The simulations show the crucial role of cross-slip both for the initial spreading of strain inside the grain and for the subsequent strain localization in the form of slip bands. A complete and detailed scheme for the persistent slip band formation is proposed, from the observation of the numerical dislocation arrangements.

Dislocation–impenetrable precipitate interaction: a three-dimensional discrete dislocation dynamics analysis

In an attempt to better understand the effect of the difference between the shear moduli of the particle and matrix on the flow stress and the work hardening, a numerical approach based on discrete dislocation simulations is developed in which the image stress caused by a second phase impenetrable particle on dislocations is implemented. Glide of a dislocation line of initially screw type through a channel between two spherical particles of shear modulus G p is simulated. Shear stress is applied incrementally on the slip plane and the equilibrium position of the dislocation line is calculated for the given applied stress. It is found that the flow stress at which the dislocation bypasses the obstacles by bowing between a pair of particles varies as , where G m is the shear modulus of the matrix and ΔG is the difference between shear moduli. α is found to be less than 1 and the effect of ΔG is amplified as the radius of the spherical particles increases. The stress increment required to force a dislocation to glide between the particles which have remaining Orowan loops from previous slip becomes higher as the particle gets harder. A relationship giving the hardening stress as a function of the number of loops is proposed. Finally, it is found that dislocations can bypass particles by cross-slip as soon as a certain number of Orowan loops surrounding the particles is reached. The image stress field around the particle induced by a difference between the shear moduli seems to enhance the cross-slip probability.

Low-strain fatigue in 316L steel surface grains: a three dimension discrete dislocation dynamics modelling of the early cycles. Part 2: Persistent slip markings and micro-crack nucleation

The early stages of the formation of persistent slip markings in fatigue are analysed using three-dimensional discrete dislocation dynamics modelling. Surface displacements due to slip are computed using a specific post-processing method. Fatigue simulations under various strain ranges and grain sizes have been performed. The resulting surface slip markings and their evolutions are analyzed quantitatively in terms of marking height and thickness. A detailed scheme for persistent slip marking formation and morphology is proposed in relation to the persistent slip-band dislocation arrangements present within the grain. The simulations show the crucial role of these arrangements for the extrusion–intrusion growth and localisation of slip at the band edges. Local stress concentrations inside the crystal and their relationship to damage initiation are also analysed. The results provide insights for an original micro-crack initiation scheme, combining different initiation mechanisms as described in the literature.

Developing rigorous boundary conditions to simulations of discrete dislocation dynamics

Mesoscale simulations have recently been developed in order to better understand the collective behaviour of dislocations and their effects on the mechanical response. Those simulations deal with dislocations discretized into segments which are allowed to move in a three-dimensional (3D) discrete network. This network is a sublattice of the original crystalline lattice network. The minimum distance between two points is defined by the annihilation distance for two edge dislocations, i.e. the minimum distance for which two edge dislocations can coexist without instantaneous collapse. The elastic theory can still be applied in the simulated volume, since the minimum distance is large compared to the dislocation core radius within which nonlinear expressions should be taken into account in the dislocation-dislocation interaction. This property allows us to use the superposition principle to enforce boundary conditions on the simulation box. This paper details the rigorous boundary conditions applied when the simulation box is supposed to be either a bulk crystal, a free standing film or a finite crystal submitted to a complex loading.

A study of dislocation junctions in FCC metals by an orientation dependent line tension model

Abstract The formation and strength of dislocation junctions in FCC crystals have been calculated using an orientation-dependent line tension model. The structure of the different types of junctions existing in FCC metals in the absence of an applied stress is examined with particular emphasis on the Lomer–Cottrell lock, the Hirth lock and the glissile junction. We have determined the ‘yield surface’ in stress space corresponding to the dissolution of junctions. Although this model represents a huge simplification of the physics of dislocations, the comparison with more sophisticated models shows that it is able to satisfactorily reproduce both the structure of junctions as well as their response to an applied stress. Moreover, it is in qualitative agreement with available experimental data. It is claimed that this simple model can provide useful parameters related to junction strength in higher level models of single crystal plasticity.

3D simulation of a nanoindentation test at a mesoscopic scale

A 3D simulation of the dynamics and interactions of dislocations in FCC metals has been developed in the last few years. This simulation is based on discretization of both time and space at a mesoscopic scale. The model has been validated on results coming from the dislocation theory in the case of the bulk crystal behaviour. In order to compare the simulation to experimental results, we choose to apply full complex boundary conditions to the simulated volume. Following that goal, the 3D dislocation simulation has been linked to a finite element code CASTEM2000. The heterogenous stress field is computed on every segment through a finite element resolution. Through this method, we present first results of a nano-indentation simulation.

Dislocation substructure in 316L stainless steel under thermal fatigue up to 650 K

In an attempt to investigate damage accumulation mechanisms in thermal fatigue, dislocation substructures forming in 316L steel during one specific test were examined and simulated. Hence, thin foils taken out of massive, tested specimens were first observed in transmission electron microscopy (TEM). These observations helped in determining one initial dislocation configuration to be implemented in a numerical model, combining 3D discrete dislocation dynamics simulation (DDD) and finite element method computations (FEM). It was found that the simulated mechanical behaviour of the DDD microstructure is compatible with FEM and experimental data. The numerically generated dislocation microstructure is similar to ladder-like dislocation arrangements as found in many fatigued f.c.c. materials. Distinct mechanical behaviour for the two active slip systems was shown and deformation mechanisms were proposed. Up to T= 650 K, no evidence for direct effect of temperature on climb and cross slip phenomena was found.