M. Verdier

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.

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.

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.

Dislocation densities and stored energy after cold rolling of Al-Mg alloys: Investigations by resistivity and differential scanning calorimetry

The authors have shown that the heat released during heating samples of Al-2.5%Mg cold rolled at different strains stems from two contributions: one corresponds to the annihilation of defects during recrystallization and the other to desegregation of solute atoms from the core of dislocations. A low temperature endotherm peak is also observed and can be attributed to dissolution of Mg clusters formed in dislocation walls. The authors have shown that the hardness of the material can be described by a single internal variable which is the density of dislocations. In contrast to this, the energy stored during cold rolling can not be described by a single variable theory. As a consequence, the yield stress alone can not be sufficient to depict stored energy and thus recrystallization kinetics.

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.

Microstructural evolution during recovery in Al–2.5%Mg alloys

Abstract Microstructural evolution in Al–2.5%Mg alloys with various Fe content deformed by cold rolling [ ϵ =0.1–3] and recovered during static annealing (160 and 220°C) was studied experimentally using the transmission electron microscopy techniques. Detailed investigations of the dislocation structures at small prestrains reveal a channel-like planar arrangement which does not show significant subgrain growth during annealing, whereas subgrain structures formed at higher prestrains lead to the onset of recrystallization when annealed. The microstructural evolution is discussed in relationship with the mechanical properties (yield stress) of the alloys.

Elasto-plastic behaviour of thin metal films

By extracting the variation of the plastic strain rate from measurements of the stress–strain curves of thin films of varying thickness, the large extent of the microdeformation stage was determined for tensile deformation of free-standing thin films, as well as for films on substrates deformed by cyclic heating. The stress varies dramatically with strain during this stage. It is demonstrated that this behaviour is common to most fine-grained polycrystals, and that the extent of the microdeformation stage is much larger than the conventional 0.2% proof strain, and depends both on the material as well as on the measurement technique. Therefore a careful analysis of this stage is essential in measuring the mechanical behaviour of these materials.

Inversion Domain Boundaries in GaN Wires Revealed by Coherent Bragg Imaging

Interfaces between polarity domains in nitride semiconductors, the so-called Inversion Domain Boundaries (IDB), have been widely described, both theoretically and experimentally, as perfect interfaces (without dislocations and vacancies). Although ideal planar IDBs are well documented, the understanding of their configurations and interactions inside crystals relies on perfect-interface assumptions. Here, we report on the microscopic configuration of IDBs inside n-doped gallium nitride wires revealed by coherent X-ray Bragg imaging. Complex IDB configurations are evidenced with 6 nm resolution and the absolute polarity of each domain is unambiguously identified. Picoscale displacements along and across the wire are directly extracted from several Bragg reflections using phase retrieval algorithms, revealing rigid relative displacements of the domains and the absence of microscopic strain away from the IDBs. More generally, this method offers an accurate inner view of the displacements and strain of interacting defects inside small crystals that may alter optoelectronic properties of semiconductor devices.

Scanning force microscope for in situ nanofocused X-ray diffraction studies

An atomic force microscope has been developed for combination with sub-micrometer focused X-ray diffraction at synchrotron beamlines and in situ mechanical tests on single nanostructures.

Signature of dislocations and stacking faults of face-centred cubic nanocrystals in coherent X-ray diffraction patterns: a numerical study.

Crystal defects can be identified by their fingerprint in coherent X-ray diffraction patterns. Realistic defects in face-centred cubic nanocrystals are studied numerically, revealing various signatures in diffraction patterns depending on the Miller indices and providing an identification method.