Investigation of precipitation hardening by dislocation dynamics simulations

Dislocation dynamics (DD) simulations are used to investigate precipitation-induced strengthening in a Zr–1% Nb alloy. A method is proposed to carry out simulations under dynamical conditions in connection with the microstructure of the investigated alloy. First, a sensitivity study of simulation parameters, suspected of altering simulation results, is presented. It allows setting up simulation conditions ensuring statistical representativeness. The effect of the strain rate is then investigated and analyzed in connection with the random distribution adopted to describe precipitation distribution. The strengthening induced by two different families of Nb precipitates is estimated from simulations whose simulation box is reduced to the volume of a single grain. It is shown that the obtained strengthening values are smaller than those predicted by most published models. Determination of total strengthening shows that usual superposition rules do not apply. A mixture law, fitting DD results well, is proposed in this paper.     

Characterization of precipitation hardening mechanisms by investigating dislocation dynamics in the HVEM

MgO single crystals and an Al-Zn-Mg alloy were deformed inside the HVEM. The static dislocation configurations and the dynamical character of the dislocation motion yield information on the applied effective stress and on the stress to surmount the array of dispersed obstacles in the athermal mode.     

From dislocation junctions to forest hardening

The mechanisms of dislocation intersection and strain hardening in fcc crystals are examined with emphasis on the process of junction formation and destruction. Large-scale 3D simulations of dislocation dynamics were performed yielding access for the first time to statistically averaged quantities. These simulations provide a parameter-free estimate of the dislocation microstructure strength and of its scaling law. It is shown that forest hardening is dominated by short-range elastic processes and is insensitive to the detail of the dislocation core structure.     

Discrete dislocation dynamics study of strained-layer relaxation

Numerical simulations are performed to follow the evolution of an initial density of dislocation loops in an infinite strained layer to the point where the dislocations have stopped moving. Several unexpected results are obtained. First, many of the threading arms are either annihilated or prematurely immobilized by hardening interactions such as jogging and junction formation. Second, the remaining dislocation arms are eventually trapped by stress fluctuations that arise more from local overrelaxation than from the blocking mechanisms usually considered. Third, the degree of relaxation that can be attained depends strongly on the initial density of threading arms.     

Understanding acoustoplasticity through dislocation dynamics simulations

The acoustoplastic effect in metals is routinely utilised in industrial processes involving forming, machining and joining, but the underlying mechanism is still not well understood. There have been earlier suggestions that dislocation mobility is enhanced intrinsically by the applied ultrasound excitation, but in subsequent deliberations it is routinely assumed that the ultrasound merely adds extra stresses to the material without altering its dislocation density or intrinsic resistance to deformation. In this study, a dislocation dynamics simulation was carried out to investigate the interactions of dislocations under the combined influence of quasi-static and oscillatory stresses. Under such combined stress states, dislocation annihilation is found to be enhanced leading to larger strains at the same load history. The simulated strain evolution under different stress schemes also closely resembles certain previously obtained experimental observations. The discovery here goes far beyond the simple picture that the ultrasound effect is merely an added-stress one, since here, the intrinsic strain-hardening potency of the material is found to be reduced by the ultrasound, through its effect on enhancing dislocation annihilation.     

Discrete dislocation dynamics: an important recent break-through in the modelling of dislocation collective behaviour

Recent results obtained by 3D discrete Dislocation Dynamics (DD) simulations are reviewed. Firstly, in the case of fatigued AISI 316L stainless steel, it is shown how DD simulations can both explain the formation of persistent slip bands and give a criterion for crack initiation. The same study is performed in the case of precipitate hardened metals where the precipitate size plays a crucial role. Secondly, we show how molecular dynamics (MD) simulations can feed the DD simulations for two applications. The first concerns the modelling of BCC Fe for which the dislocation mobility is derived from MD simulations. The second considers the modelling of irradiated stainless steels (FCC), where MD is used to define the local rules of interactions between dislocations and Frank loops. To cite this article: M.C. Fivel, C. R. Physique 9 (2008).     

Inhomogeneity of misfit stresses in nickel-base superalloys: Effect on propagation of matrix dislocation loops

It is shown experimentally that, during annealing and creep under low applied stresses, matrix dislocation loops frequently cross-glide. The periodic length of the zigzag dislocations deposited in the interfaces is equal to that of the γ/γ′-microstructure. Initially, the zigzag dislocations move in the (001) interface by a combination of glide and climb but then they stop near the γ′-edges and align along ?100?. Reactions of such dislocations lead to the formation of square interfacial networks consisting of ?100? oriented edge dislocations. The complex dislocation movement is explained by the inhomogeneity of the misfit stresses between γ- and γ′-lattices. The tensile components of the stress tensor drive the dislocations through the channel, whereas the shear components near the γ′-edges cause the zigzag movement and the ?100? alignment. The total effect is the most efficient relaxation of the misfit stresses. The results are relevant, especially for single-crystal superalloys of the newest generations, which have an increased γ/γ′-misfit due to the high level of refractory elements.     

Multiscale dislocation dynamics simulations of shock-induced plasticity in small volumes

Multiscale dislocation dynamics plasticity (MDDP) was used to investigate shock-induced deformation in monocrystalline copper. In order to enhance the numerical simulations, a periodic boundary condition was implemented in the continuum finite element (FE) scale so that the uniaxial compression of shocks could be attained. Additionally, lattice rotation was accounted for by modifying the dislocation dynamics (DD) code to update the dislocations’ slip systems. The dislocation microstructures were examined in detail and a mechanism of microband formation is proposed for single- and multiple-slip deformation. The simulation results show that lattice rotation enhances microband formation in single slip by locally reorienting the slip plane. It is also illustrated that both confined and periodic boundary conditions can be used to achieve uniaxial compression; however, a periodic boundary condition yields a disturbed wave profile due to edge effects. Moreover, the boundary conditions and the loading rise time show no significant effects on shock–dislocations interaction and the resulting microstructures. MDDP results of high strain rate calculations are also compared with the predictions of the Armstrong–Zerilli model of dislocation generation and movement. This work confirms that the effect of resident dislocations on the strain rate can be neglected when a homogeneous nucleation mechanism is included.     

The effect of size on dislocation cell formation and strain hardening in aluminium

The formation of dislocation cells has a significant impact on the strain hardening behaviour of metals. Dislocation cells can form in metals with a characteristic size defined by three-dimensional tangles of dislocations that serve as “walls” and less dense internal regions. It has been proposed that inhibiting the formation of dislocation cells could improve the strain hardening behaviour of metals such as Al. Here we employ in situ scanning electron microscope compression testing of pure Al single crystal pillars with physical dimensions larger, close to and smaller than the reported cell size in Al, respectively, to investigate the possible size effect on the formation of dislocation cell and the consequent change of mechanical properties. We observed that the formation of dislocation cells is inhibited as the pillar size decreases to a critical value and simultaneously both the strength and the strain hardening behaviour become strongly enhanced. This phenomenon is discussed in terms of the effect of dimensional restriction on the formation of dislocation cells. The reported mechanism could be applied in polycrystalline Al where the tunable physical dimension could be grain size instead of sample size, providing insight into Al alloy design.     

Simulation of screw dislocation motion in iron by molecular dynamics simulations

Molecular dynamics (MD) simulations are used to investigate the response of a/2<111> screw dislocation in iron submitted to pure shear strain. The dislocation glides and remains in a (110) plane; the motion occurs exclusively through the nucleation and propagation of double kinks. The critical stress is calculated as a function of the temperature. A new method is developed and used to determine the activation energy of the double kink mechanism from MD simulations. It is shown that the differences between experimental and simulation conditions lead to a significant difference in activation energy. These differences are explained, and the method developed provides the link between MD and mesoscopic simulations.     

Two hardening mechanisms in single crystal thin films studied by discrete dislocation plasticity

Two-dimensional discrete dislocation plasticity simulations of the evolution of thermal stress in single crystal thin films on a rigid substrate are used to study size effects. The relation between the residual stress and the dislocation structure in the films after cooling is analyzed using dislocation dynamics. A boundary layer characterized by a high stress gradient and a high dislocation density is found close to the impenetrable film-substrate interface. There is a material-dependent threshold film thickness above which the dislocation density together with the boundary layer thickness and stress state are independent of film thickness. In such films the stress outside the boundary layer is on average very low, so that the film-thickness-independent boundary layer is responsible for the size effect. A larger size effect is found for films thinner than the threshold thickness. The origin of this size effect stems from nucleation activity being hindered by the geometrical constraint of the small film thickness, so that by decreasing film thickness, the dislocation density decreases while the stress in the film increases. The size dependence is only described by a Hall–Petch type relation for films thicker than the threshold value.     

Discrete dislocation simulation of nanoindentation: the influence of obstacles and a limited number of dislocation sources

Nanoindentation is simulated on the computer by means of a 2D discrete dislocation model under the conditions of a constrained geometry. First, an indentation test near a grain boundary is investigated by the arrangement of only one boundary and second, an indentation test into the center of the surface of a small grain (lamella) is mimicked by the arrangement of two boundaries. The effect of a limited number of dislocation sources is studied by the simulations of an indentation test in a plastically deformable film on an ideal elastic substrate and by such tests on an ideal elastic film on a plastically deformable substrate. The discrete nature of plasticity is shown to have a significant influence on the mechanical material behavior in all our investigations.     

Effect of dislocation hardening on monotonic and cyclic strength of severely deformed copper

The present study aims at clarifying the role of dislocation strengthening in fatigue of materials manufactured by severe plastic deformation (SPD) techniques. Employment of single crystals hardened via equal channel angular pressing (ECAP) helps to minimise or completely eliminate the effect of high angle boundaries on strengthening and fatigue behaviour. Both monotonic strength and high cycle fatigue (HCF) resistance were improved significantly after the first ECAP pressing, when low-angle dislocation configurations dominate in the microstructure. The essential role of dislocation accumulation during severe plastic deformation is highlighted for both tensile and fatigue strength (SPD). Dilute alloying of copper by silver stabilises the deformation microstructure and further improves the fatigue properties considerably.     

Irradiation hardening of reactor pressure vessel steels due to the dislocation loop evolution

The irradiation hardening of reactor pressure vessel steels due to the formation of dislocation loops is analyzed. The analysis is based on the original model for the nucleation and subsequent evolution of dislocation loops in irradiated materials. The loop formation in displacement cascades is taken into account, along with the homogeneous clustering of point defects. The loop evolution is shown to contribute mainly to the athermal component of the yield stress, which is determined by interaction of gliding dislocations with strong barriers. Irradiation-induced hardening is evaluated as a function of irradiation dose and temperature, dose rate, material parameters and initial microstructure. The model results are compared with experimental data for neutron irradiated pressure vessel steels of various grades and with empirical low power expressions of the yield stress increase with increasing irradiation dose.     

Initial dislocation density effect on strain hardening in FCC aluminium alloy under laser shock peening

Abstract

The effect of initial dislocation density on subsequent dislocation evolution and strain hardening in FCC aluminium alloy under laser shock peening (LSP) was investigated by using three-dimension discrete dislocation dynamics (DD) simulation. Initial dislocations were randomly generated and distributed on slip planes for three different dislocation densities of 4.21 × 10¹², 8.12 × 10¹² and 1.26 × 10¹³ m^?2. Besides, variable densities of prismatic loops were introduced into the DD cells as nanoprecipitates to study the dislocation pinning effect. The flow stresses as a function of strain rate obtained by DD simulation are compared with relevant experimental data. The results show a significant dislocation density accumulation in the form of dislocation band-like structures under LSP. The overall yield strength in FCC aluminium alloy decreases with increasing initial dislocation density and forest dislocation strengthening becomes negligible under laser induced ultra-high strain rate deformation. In addition, yield strength is enhanced by increasing the nanoprecipitate density due to dislocation pinning effect.     

Molecular dynamics study on the evolution of interfacial dislocation network and mechanical properties of Ni-based single crystal superalloys

The evolution of misfit dislocation network at $\gamma /{\gamma }^{\prime }$ phase interface and tensile mechanical properties of Ni-based single crystal superalloys at various temperatures and strain rates are studied by using molecular dynamics (MD) simulations. From the simulations, it is found that with the increase of loading, the dislocation network effectively inhibits dislocations emitted in the γ matrix cutting into the ${\gamma }^{\prime }$ phase and absorbs the matrix dislocations to strengthen itself which increases the stability of structure. Under the influence of the temperature, the initial mosaic structure of dislocation network gradually becomes irregular, and the initial misfit stress and the elastic modulus slowly decline as temperature increasing. On the other hand, with the increase of the strain rate, it almost has no effect on the elastic modulus and the way of evolution of dislocation network, but contributes to the increases of the yield stress and tensile strength. Moreover, tension–compression asymmetry of Ni-based single crystal superalloys is also presented based on MD simulations.     

A study of the system Fe-V-C-N with a view to the precipitation hardening process

The paper deals with the analysis of the precipitate composition and the precipitation mechanism in the system Fe-V-C-N. The aim of this paper is also to discuss the way of vanadium carbide hardening in commercial type CrMoV steel. Further, the paper quotes data on hexagonal vanadium nitride V₂N which becomes an important element in the development of high-strength steels.     

On the role of solute atom — dislocation elastic interaction in solid solution hardening of Cu single crystals

Elastic interaction of solute atoms with dislocations has been reconsidered in Labusch's theory of solid solution hardening. New interaction parametersε are suggested and tested on dΤ/dc ^2/3 dependence onε ^4/3 for Cu base solid solutions.