The mechanisms of dislocation/precipitate interactions were analyzed in an Al-Cu alloy containing a homogeneous dispersion of $θ'$ precipitates by means of discrete dislocation dynamics simulations. The simulations were carried out within the framework of the discrete-continuous method and the precipitates were assumed to be impenetrable by dislocations. The main parameters that determine the dislocation/precipitate interactions (elastic mismatch, stress-free transformation strains, dislocation mobility and cross-slip rate) were obtained from atomistic simulations, while the size, shape, spatial distribution and volume fraction of the precipitates were obtained from transmission electron microscopy. The predictions of the critical resolved shear stress (including the contribution of solid solution) were in agreement with the experimental results obtained by means of compression tests in micropillars of the Al-Cu alloy oriented for single slip. The simulations revealed that the most important contribution to the precipitation hardening of the alloy was provided by the stress-free transformation strains followed by the solution hardening and the Orowan mechanism due to the bow-out of the dislocations around the precipitates.
Atomistic simulations were carried out to analyze the interaction between $< a>$ basal dislocations and precipitates in Mg-Al alloys and the associated strengthening mechanisms.
This paper develops the small strain continuum dislocation theory accounting for statistically stored dislocations and Taylor hardening for single crystals. As illustration, the problem of anti-plane constrained shear of single crystal deforming in single slip is solved within the proposed theory. The distribution of geometrically necessary dislocations in the final state of equilibrium as well as the stress-strain curve exhibiting the Bauschinger translational work hardening and the size effect are found. Comparison with the stress-strain curve obtained from the continuum dislocation theory w…
The current work extends the well established approach of Kocks and Mecking by a more realistic description of strain-hardening using an original dislocation density law with a revisited physical understanding of dynamic recovery, without new material parameters and keeping only one internal variable.
When metals are plastically deformed, the total density of dislocations increases with strain as the microstructure is continuously refined, leading to the strain hardening behavior. Here we report the fundamental role played by the junction formation process in the connection between dislocation microstructure evolution and the strain hardening rate in face-centered cubic (FCC) Cu, as revealed by discrete dislocation dynamics (DDD) simulations. The dislocation network formed during [001] loading consists of line segments whose lengths closely follow an exponential distribution. This exponenti…
The influence of initial heat treatment on anomalous Cr precipitation within high temperature solubility region in Fe-9Cr alloy has been investigated using positron lifetime studies. Air-quenched samples with pre-existing dislocations exhibited a distinct annealing stage in positron lifetime between 800 and 1100 K corresponding to Cr-precipitation. During this stage, Transmission Electron Microscopy showed fine precipitates of average size 4 nm, dispersed throughout the sample and from EDS analysis they are found to be Cr-enriched. The existence of dislocations is found to be responsible for C…
This work proposes a dislocation density-based strain gradient $J_2$ plasticity framework that models the strength contribution due to Geometrically Necessary Dislocations (GNDs) using a lower order, Taylor hardening backstress model. An anisotropy factor is introduced to phenomenologically represent the differential hardening between grains in this $J_2$ plasticity framework. An implicit numerical algorithm is implemented for the time integration of the finite deformation plasticity model. The framework is first used to predict directional hardening due to the GND-induced backstress during cy…
We propose an explanation of anomalies observed in the behavior of deformation hardening of Invars. An extremely strong volume magnetostriction, typical of Invars, results in an enhancement of the exchange contribution to the energy of the dislocation system by about three orders of magnitude with respect to its value in conventional ferromagnetics. Both the self energy of individual dislocations and the interaction between them, determined usually only by the elastic deformation, in Invars is strongly diminished by the contribution of the exchange energy. This fact explains a strong suppressi…
The interaction of crystalline defects leads to strain hardening in bulk metals. Metals with high stacking fault energy (SFE), such as aluminum, tend to have low strain hardening rates due to an inability to form stacking faults and deformation twins. Here, we use in situ SEM mechanical compressions to find that colloidally synthesized defect-free 114 nm Al nanocubes combine a high linear strain hardening rate of 4.1 GPa with a high strength of 1.1 GPa. These nanocubes have a 3 nm self-passivating oxide layer that has a large influence on mechanical behavior and the accumulation of dislocation…
The combined strengthening effects of grain refinement and high precipitated volume fraction (~6at.%) on the mechanical properties of FeSiTi alloy subjected to SPD processing prior to aging treatment were investigated by atom probe tomography and scanning transmission electron microscopy. It was shown that the refinement of the microstructure affects the precipitation kinetics and the spatial distribution of the secondary hardening intermetallic phase, which was observed to nucleate heterogeneously on dislocations and sub-grain boundaries. It was revealed that alloys successively subjected to …
An exactly solvable phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations resulting from a piecewise quadratic Peierls potential; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles and lattice friction, resulting in hardening, path depende…
Interactions among dislocations and solute atoms are the basis of several important processes in metals plasticity. In body-centered cubic (bcc) metals and alloys, low-temperature plastic flow is controlled by screw dislocation glide, which is known to take place by the nucleation and sideward relaxation of kink pairs across two consecutive \emph{Peierls} valleys. In alloys, dislocations and solutes affect each other's kinetics via long-range stress field coupling and short-range inelastic interactions. It is known that in certain substitutional bcc alloys a transition from solute softening to…
A relative contribution to irradiation hardening caused by dislocation loops and solute-rich precipitates is established for RPV steels of WWER-440 and WWER-1000 reactors, based on TEM measurements and mechanical testing at reactor operating temperature of 563 K. The pinning strength factors evaluated for loops and precipitates are shown to be much lower than those obtained for model alloys based on the room temperature testing as well as those evaluated by means of atomistic simulations in the temperature range of 300 to 600 K. This discrepancy is explained in the framework of a model of ther…
Combined effect of Carbon and Nitrogen levels and isothermal holding temperature on the microstructure, precipitation and the tensile properties of Vanadium microalloyed steels with 0.05 weight percent Vanadium were studied. Two different Vanadium steels, one having higher Carbon and lower Nitrogen content, HCLN steel, and the other having lower Carbon and higher Nitrogen content, LCHN steel, were prepared and subjected to isothermal holding treatment over a temperature range of 500 to 750 degree Celsius, after hot-deformation. Maximum precipitation strengthening from fine Vanadium carbonitrid…
A multidisciplinary approach is presented to analyse the precipitation process in a model Al-Cu alloy. Although this topic has been extensively studied in the past, most of the investigations are focussed either on transmission electron microscopy or on thermal analysis of the processes. The information obtained from these techniques cannot, however, provide a coherent picture of all the complex transformations that take place during decomposition of supersaturated solid solution. Thermal analysis, high resolution dilatometry, (high resolution) transmission electron microscopy and density func…
Dislocation slip is a general deformation mode and governs the strength of metals. Via discrete dislocation dynamics and molecular dynamics simulations, we investigate the strain rate and dislocation density dependence of the strength of bulk copper single crystals using 192 simulations spanning over 10 orders of magnitude in strain rate and 9 orders of magnitude in dislocation density. Based on these large set of simulations and theoretical analysis, a new analytical relationship between material strength, dislocation density, strain rate and dislocation mobility is proposed, which is in exce…
A recently developed reduced activation ferritic/martensitic steel MNHS was irradiated with 200keV He ions to a fluence of 1E21ions/m^2 at 450 celsius degree and 1E20ions/m^2 at 300 celsius degree and 450 celsius degree, respectively. The irradiation hardening of the steel was investigated by nanoindentation measurements combined with transmission electron microscopy (TEM) analysis. Dispersed barrier-hardening (DBH) model was applied to predict the hardness increments based on TEM analysis. The predicted hardness increments are consistent with the values obtained by nanoindentation tests. It i…
In this paper, we investigate plasticity in irradiated FeCrAl nanopillars using discrete dislocation dynamics simulations (DDD), with comparisons to transmission electron microscopic (TEM) in situ tensile tests of ion and neutron irradiated commercial FeCrAl alloy C35M. The effects of irradiation-induced defects, such as a/2 111 and a 100 type loops and composition fluctuations representative of phase separation in irradiated FeCrAl alloys, are investigated separately as well as superposed together in simulations. We explore the effects of defects on the stress-strain behavior, specifically yi…
Nanostructures have the immense potential to supplant the traditional metallic structure as they show enhanced mechanical properties through strain hardening. In this paper, the effect of grain size on the hardening mechanism of Al-Cu nanostructure is elucidated by molecular dynamics simulation. Al-Cu (50-54% Cu by weight) nanostructure having an average grain size of 4.57 to 7.26 nm are investigated for tensile simulation at different strain rate using embedded atom method (EAM) potential at a temperature of 50~500K. It is found that the failure mechanism of the nanostructure is governed by t…
Through millennia humans exploited the natural property of metals to get stronger or hardened when mechanically deformed. Ultimately rooted in the motion of dislocations, mechanisms of metal hardening remained in the crosshairs of physical metallurgists for over a century. Here, we performed atomistic simulations at the limits of supercomputing, which are sufficiently large to be statistically representative of macroscopic crystal plasticity yet fully resolved to examine the origins of metal hardening at its most fundamental level of atomic motion. We demonstrate that the notorious staged (inf…
An increase of the critical resolved shear stress of Invar alloys (Invar hardening) with a lowering temperature is explained. The effect is caused by a growth of the exchange interaction between dangling $d$-electron states of dislocation cores and paramagnetic obstacles (e.g., Ni atoms in FeNi alloys) which occurs below the Curie temperature. The spins of the two electrons align along the magnetization due to the exchange interaction with the surrounding atoms of the ferromagnetic. The exchange interaction between the dislocations and obstacles is enhanced in Invars due to a strong growth of …
We conduct dislocation dynamics (DD) simulations of Fe periodic single crystals under tensile load at several high strain rates and temperatures. The simulations are enabled by the recent development of temperature-dependent dislocation mobility relations obtained from atomistic calculations. The plastic evolution in the simulations is governed by rapid initial dislocation multiplication, followed by a saturation of the flow stress when the subpopulation of slow plastic carriers becomes stabilized by dislocation annihilation. Above 500 K, edge dislocations coexist with screw dislocations and c…
Both continuous and discontinuous precipitation is known to occur in CuAg alloys. The precipitation of Ag-rich phase has been experimentally investigated by atom probe tomography and transmission electron microscopy after ageing treatment of Cu-5%wtAg at 440$^\circ$C during 30'. Both continuously and discontinuously formed precipitates have been observed. The precipitates located inside the grains exhibit two different faceted shapes: tetrahedral and platelet-shaped precipitates. Dislocations accommodating the high misfit at the interface between the two phases have also been evidenced. Based …
The gradient crystal plasticity framework of Wulfinghoff et al. [53] incorporating an equivalent plastic strain and grain boundary yielding, is extended with additional grain boundary hardening. By comparison to averaged results from many discrete dislocation dynamics (DDD) simulations of an aluminum type tricrystal under tensile loading, the new hardening parameter in the continuum model is calibrated. It is shown that although the grain boundaries (GBs) in the discrete simulations are impenetrable, an infinite GB yield strength corresponding to microhard GB conditions, is not applicable in t…
Cellular patterns formed by self-organization of dislocations are a most conspicuous feature of dislocation microstructure evolution during plastic deformation. To elucidate the physical mechanisms underlying dislocation cell structure formation, we use a minimal model for the evolution of dislocation densities under load. By considering only two slip systems in a plane strain setting, we arrive at a model which is easily amenable to analytical stability analysis and numerical simulation. We use this model to establish analytical stability criteria for cell structures to emerge, to investigate…
A phase field model is presented to investigate dislocation formation (coherency loss) and workhardening in two-phase binary alloys. In our model the elastic energy density is a periodic function of the shear and tetragonal strains, which allows multiple formation of slips (dislocation dipoles). By numerically integrating the dynamic equations in two dimensions, we find that dislocations appear in pairs in the interface region and grow into slips. One end of each slip glides preferentially into the softer region, while the other end remains trapped at the interface. Under uniaxial stretching a…
Interpretation of thermal hardening phenomenon at high strain rate has recently become a critical problem in shock wave physics. In this letter, this problem is addressed from a viewpoint of dislocation generation, and a novel conclusion is gained that forest hardening induced by homogeneous nucleation (HN) results in thermal hardening behavior in a BCC metal significantly, apart from phonon drag mechanism. Through numerical simulations with a dislocation based crystal plasticity model, we have reproduced the experimental results quantitatively and predicted a thermal hardening behavior in oth…
A recently presented model is adapted to predict the effects of strain path change on the strain aging (bake hardening) behaviour of an ultra low carbon (ULC) steel. Samples pre-deformed by rolling were aged and then tested in uniaxial tension at 0, 45 and 90$^\circ$ degrees to the prior rolling direction. The results show that aging changes not only the yield strength of the material but also the work hardening rate. The increase in yield strength is interpreted to be dominated by a reduction in mobile dislocation density, this reflecting the classic ideas of Hahn and others. The change in wo…
We present a dislocation density-based strain hardening model for single crystal copper through a systematic coarse-graining analysis of more than 200 discrete dislocation dynamics (DDD) simulations of plastic deformation under uniaxial tension. The proposed constitutive model has two components: a generalized Taylor relation connecting resolved shear stresses to dislocation densities on individual slip systems, and a generalized Kocks-Mecking model for dislocation multiplication. The DDD data strongly suggests a logarithmic dependence of flow stress on the plastic shear strain rate on each sl…
The present paper is concerned with the development of a micromechanical model of the hardening, rate-sensitivity and thermal softening of bcc crystals. In formulating the model we specifically consider the following unit processes: double-kink formation and thermally activated motion of kinks; the close-range interactions between primary and forest dislocations, leading to the formation of jogs; the percolation motion of dislocations through a random array of forest dislocations introducing short-range obstacles of different strengths; dislocation multiplication due to breeding by double cros…
The precipitation microstructure of the γ' (AlAg2) intermetallic phase has been examined in aluminium-silver-copper alloys. The microstructure developed in an Al-0.90at.%Ag-0.90at.%Cu alloy was significantly different from that reported for binary Al-Ag alloys. The orientation relationship between the matrix and precipitate was unchanged; however, the γ' phase formed as aggregates with a two-dimensional open assemblies. Each such assembly contained two variants of the γ' phase alternately arranged to form a faceted elliptical unit. The θ' (Al2Cu) phase formed on these assemblies after further …
We reformulate the theory of polycrystalline plasticity, in externally driven, nonequilibrium situations, by writing equations of motion for the flow of energy and entropy associated with dislocations. Within this general framework, and using a minimal model of thermally assisted depinning with essentially only one adjustable parameter, we find that our theory fits the strain-hardening data for Cu over a wide range of temperatures and six decades of strain rate. We predict the transition between stage II and stage III hardening, including the observation that this transition occurs at smaller …
Atomistic simulations are used to study linear complexion formation at dislocations in a body-centered cubic Fe-Ni alloy. Driven by Ni segregation, precipitation of the metastable B2-FeNi and stable L10-FeNi phases occurs along the compression side of edge dislocations. If the Ni segregation is not intense enough to ensure precipitate growth and coalescence along the dislocation lines, linear complexions in the form of stable nanoscale precipitate arrays are observed. Critical conditions such as global composition and temperature are defined for both linear complexion formation and dislocation…
Mg represents a group of technically important hexagonal-close packed (hcp) metals whose mechanical behaviors are very different from body-centered cubic (bcc) and face-centered cubic (fcc) metals and the underlying mechanisms remain poorly-understood. It has been long known that Mg has high hardening and low ductility, and this was conventionally attributed to the scarce of active pyramidal slip. Recently immobilization of pyramidal dislocations was proposed to be the origins. Here we present a different scenario that has hitherto never been reported for Mg: mobile screw pyramidal dislocation…
The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pile-up against, absorption by, and transfer through the grain boundary, is developed for nonuniform plastic deformations in polycrystals. The case study is carried out on the boundary conditions affecting work hardening of a bicrystal subjected to plane constrained shear for three types of grain boundaries: (i) impermeable hard grain boundary, (ii) grain boundary that allows dislocation transfer without absorption, (iii) grain boundary that absorbs dislocations and allows them to pass later.
The present work deals with the microstructure and texture evolutions of a TWIP high entropy alloy at various temperatures. Toward this end, the tensile tests were conducted at temperatures ranging from 298 to 873 K under the strain rate of 0.001s-1. The experimented material exhibited an extraordinary room temperature work hardening behavior, in respect of both the instantaneous strain hardening exponent and the work hardening rate values. This resulted in an acceptable ultimate tensile strength /ductility balance and was justified considering the high activity of twinning and planar slip. Su…
The mechanical properties of Mg-Al alloys are greatly influenced by the complex intermetallic phase Mg$_{17}$Al$_{12}$, which is the most dominant precipitate found in this alloy system. The interaction of basal edge and 30$^\text{o}$ dislocations with Mg$_{17}$Al$_{12}$ precipitates is studied by molecular dynamics and statics simulations, varying the inter-precipitate spacing ($L$), and size ($D$), shape and orientation of the precipitates. The critical resolved shear stress $τ_c$ to pass an array of precipitates follows the usual $\ln((1/D + 1/L)^{-1})$ proportionality. In all cases but the…
The spontaneous emergence of heterogeneous dislocation patterns is a conspicuous feature of plastic deformation and strain hardening of crystalline solids. Despite long-standing efforts in the materials science and physics of defect communities, there is no general consensus regarding the physical mechanism which leads to the formation of dislocation patterns. In order to establish the fundamental mechanism, we formulate an extremely simplified, minimal model to investigate the formation of patterns based on the continuum theory of fluxes of curved dislocations. We demonstrate that strain hard…
The interaction between edge dislocations and carbon nanotubes (CNTs) embedded into an Al matrix is investigated. Both pristine and Ni-coated CNTs are considered. It is demonstrated that the embedded CNTs lead to a flow stress contribution equivalent to that of an array of non-shearable inclusions that are by-passed via the Orowan mechanism. The strain hardening mechanism associated with multiple dislocation passes shows, however, characteristic differences from the Orowan picture that indicate that the embedded CNTs behave analogous to embedded voids.
Discovering relationships between materials' microstructures and mechanical properties is a key goal of materials science. Here, we outline a strategy exploiting Bayesian optimization to efficiently search the multidimensional space of microstructures, defined here by the size distribution of precipitates (fixed impurities or inclusions acting as obstacles for dislocation motion) within a simple two-dimensional discrete dislocation dynamics model. The aim is to design a microstructure optimizing a given mechanical property, e.g., maximizing the expected value of shear stress for a given strain…
On the basis of the classical dislocation theory, the Solid Solution Hardening (SSH) is commonly ascribed to the pinning of the edge dislocations. At the atomic level, the theoretical study of the dislocation cores contrasts with such a prediction. Using the static molecular simulations with some interatomic effective potentials, we demonstrate numerically that the critical resolved shear stress associated to a screw dislocation in a random Ni(Al) single crystal has same order as the edge one. Such a result is imposed by the details of the dislocation stacking fault and the core dissociation i…
The strength of the lithosphere is typically modelled based on constitutive equations for steady-state flow. However, models of lithospheric flexure reveal differences in lithospheric strength that are difficult to reconcile based on such flow laws. Recent rheological data from low-temperature deformation experiments on olivine suggest that this discrepancy may be largely explained by strain hardening. Details of the mechanical data, specifically the effects of temperature-independent back stresses stored in the samples, indicate that strain hardening in olivine occurs primarily due to long-ra…
The quasicontinuum method is used to simulate three-dimensional Lomer-Cottrell junctions both in the absence and in the presence of an applied stress. The simulations show that this type of junction is destroyed by an unzipping mechanism in which the dislocations that form the junction are gradually pulled apart along the junction segment. The calculated critical stress needed for breaking the junction is comparable to that predicted by line tension models. The simulations also demonstrate a strong influence of the initial dislocation line directions on the breaking mechanism, an effect that i…
The effects of dislocation climb on plastic deformation during loading and unloading are studied using a two-dimensional discrete dislocation dynamics model. Simulations are performed for polycrystalline thin films passivated on both surfaces. Dislocation climb lowers the overall level of the stress inside thin films and reduces the work hardening rate. Climb decreases the density of dislocations in pile-ups and reduces back stresses. These factors result in a smaller Bauschinger effect on unloading compared to simulations without climb. As dislocations continue to climb at the onset of unload…
Discrete Dislocation Dynamics Modeling of Nanotwinned Materials: Orientation Effects in a Multilayer Twinned Structure of Copper
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Aeronautics（四川省力学与结构安全重点实验室，力学与航空学院）；Department of Materials Science and Engineering, Institute of Materials Simulation WW8, Friedrich-Alexander University of Erlangen-Nuremberg（埃尔朗根-纽伦堡大学材料工程系，材料模拟研究所WW8）；Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所）
We use three-dimensional discrete dislocation dynamics simulations (DDD) to study the evolution of interfacial dislocation network (IDN) in particle-strengthened alloy systems subjected to constant stress at high temperatures. We have modified the dislocation mobility laws to incorporate the recovery of the dislocation network by the climb. The microstructure consists of uniformly distributed cuboidal inclusions embedded in the simulation box. Based on the systematic simulations of IDN formation as a function of applied stress for prescribed inter-particle spacing and glide-to-climb mobility r…
