Expansion Of Dislocation Loops Research Articles

Robust crystal structure identification at extreme conditions using a density-independent spectral descriptor and supervised learning

The increased time- and length-scale of classical molecular dynamics simulations have led to raw data flows surpassing storage capacities, necessitating on-the-fly integration of structural analysis algorithms. As a result, algorithms must be computationally efficient, accurate, and stable at finite temperature to reliably extract the relevant features of the data at simulation time. In this work, we leverage spectral descriptors to encode local atomic environments and build crystal structure classification models. In addition to the classical way spectral descriptors are computed, i.e. over a fixed radius neighborhood sphere around a central atom, we propose an extension to make them independent from the material’s density. Models are trained on defect-free crystal structures with moderate thermal noise and elastic deformation, using the linear discriminant analysis (LDA) method for dimensionality reduction and logistic regression (LR) for subsequent classification. The proposed classification model is intentionally designed to be simple, incorporating only a limited number of parameters. This deliberate simplicity enables the model to be trained effectively even when working with small databases. Despite the limited training data, the model still demonstrates inherent transferability, making it applicable to a broader range of scenarios and datasets. The accuracy of our models in extreme conditions (high temperature, high density, large deformation) is compared to traditional algorithms from the literature, namely adaptive common neighbor analysis (a-CNA), polyhedral template matching (PTM) and diamond structure identification (IDS). Finally, we showcase two applications of our method: tracking a solid–solid BCC-to-HCP phase transformation in Zirconium at high pressure up to high temperature, and visualizing stress-induced dislocation loop expansion in single crystal FCC Aluminum containing a Frank–Read source, at high temperature.

Effect of orientation and loading rate on the incipient behavior of Ti60(AlCrVNb)40 medium entropy alloy

The influence of orientation and loading rate on the pop-in behavior of Ti60(AlCrVNb)40 medium entropy alloy (MEA) under nanoindentation was investigated. The crystal structure of Ti60(AlCrVNb)40 is a single body centered cubic phase, confirmed by both X-ray diffractometer and transmission electron microscopy. Nanoindentation experiments were carried out on the (100), (110) and (111) orientations and over loading rates of 10–500 μN/s. The incipient plasticity showed a clear orientation and loading rate dependences. Specifically, the (110) data exhibit the lowest pop-in load and pop-in displacement, and the associated loads of all orientations increase with increasing loading rate. In addition, the spread of the load at pop-in for (110) is narrower compared to those for (100) and (111), which is caused by the lower influence from defects on (110). The activation volume was estimated to be ~0.7 b3, which falls between those of conventional metals (~0.3 b3) and high entropy alloys (HEAs) (~1.7 b3), suggesting that dislocation activities in MEAs is more difficult than that in traditional metals but easier than that in HEAs. Such a medium activation volume implies that the onset of yielding is associated with a mixture of two mechanisms: heterogeneous nucleation of dislocation through atomic-sized precursors and/or expansion of dislocation loop by pre-existing dislocation multiplication. The crystalline orientation effects can be rationalized by the different densities and dislocation configurations resulted from the different numbers of activated slip systems and Schmid factors for different loading planes.

Mobility of dislocations in aluminum: The role of non-Schmid stress state

The extent that non-Schmid stresses influence the mobility of dislocations in Al is studied using molecular dynamics (MD) simulations. Specifically, mobility laws for straight screw, 30°, 60° and edge dislocations are atomistically derived for different combinations of Escaig stress, τe, and stress normal to the (111) slip plane, σn. MD simulations show that the mobility of each dislocation is distinctly influenced by non-Schmid stresses. Furthermore, MD simulations of dislocation shear loop expansion show that mobility laws derived from straight dislocations are applicable to describe the more complex behavior of stress-state dependent expansion of a dislocation loop. Data describing the dislocation mobility laws are incorporated into discrete dislocation dynamics (DDD) simulations using a hierarchical multiscale approach. DDD simulations of isolated dislocation loop expansion show strong agreement with MD simulation results, validating the nonlinear multiscale implementation. DDD simulations of dislocation network evolution show that the use of stress state dependent dislocation mobility laws provides quantifiable changes to the plastic deformation path, which leads to different final microstructures. The results presented here demonstrate the key role that local stresses, experienced by the dislocation core, play on the evolution of a dislocation network during plastic deformation.

Numerical simulation of model problems in plasticity based on field dislocation mechanics

The aim of this paper is to investigate the numerical implementation of the field dislocation mechanics (FDM) theory for the simulation of dislocation-mediated plasticity. First, the mesoscale FDM theory of Acharya and Roy (2006 J. Mech. Phys. Solids 54 1687–710) is recalled which permits to express the set of equations under the form of a static problem, corresponding to the determination of the local stress field for a given dislocation density distribution, complemented by an evolution problem, corresponding to the transport of the dislocation density. The static problem is solved using FFT-based techniques (Brenner et al 2014 Phil. Mag. 94 1764–87). The main contribution of the present study is an efficient numerical scheme based on high resolution Godunov-type solvers to solve the evolution problem. Model problems of dislocation-mediated plasticity are finally considered in a simplified layer case. First, uncoupled problems with uniform velocity are considered, which permits to reproduce annihilation of dislocations and expansion of dislocation loops. Then, the FDM theory is applied to several problems of dislocation microstructures subjected to a mechanical loading.

A 3D phase field dislocation dynamics model for body-centered cubic crystals

In this work, we present a 3D Phase Field Dislocation Dynamics (PFDD) model for body-centered cubic (BCC) metals. The model formulation is extended to account for the dependence of the Peierls barrier on the line-character of the dislocation. Simulations of the expansion of a dislocation loop belonging to the 110111 slip system are presented with direct comparison to Molecular Statics (MS) simulations. The extended PFDD model is able to capture the salient features of dislocation loop expansion predicted by MS simulations. The model is also applied to simulate the motion of a straight screw dislocation through kink-pair motion.

Mobility of dislocations in Aluminum: Faceting and asymmetry during nanoscale dislocation shear loop expansion

Dislocation loop expansion in Al is studied with a hierarchical multiscale approach via atomistic and discrete dislocation dynamics (DDD) simulations. First, mobility laws for straight screw, 30°, 60°, and edge dislocations are calculated using molecular dynamics (MD) simulations. Each atomistic mobility law is described by an empirical piecewise function with a character angle dependent power law exponent to capture the nonlinear damping regime. For the dislocation velocity range considered in this work, the mobilities of screw and 60° dislocations are lower than edge and 30° dislocations. The mobilities of mixed dislocations, such as 30° and 60°, are found to depend on the character of the leading Shockley partial. Second, MD simulations of dislocation loop expansion under a constant external Schmid stress are performed. The expanded dislocation loop is found to facet in the 60° and screw segments due to low mobilities. The dislocation loop is also found to have reflection asymmetry about the edge axis due to mixed dislocation mobility asymmetry. Finally, the nonlinear atomistic mobility laws are implemented into DDD simulations to illustrate that atomistic mobility laws for straight dislocations can describe faceting and asymmetric behaviors observed during dislocation loop expansion in higher length scale simulations.

Thermally activated twin thickening and solute softening in magnesium alloys - a molecular simulation study

Thickening of the tension twin {10 − 12}⟨10 − 11⟩ in Mg-Al and Mg-Y alloys varies systematically with temperature, strain rate and solute concentration. The twin boundary propagates through the nucleation and expansion of twin dislocation loops, a thermally activated process. Solute softening is observed in both alloys. The softening saturates with increasing solute concentration due to solute hardening of twin dislocation loop expansion. With the present interatomic potential, Al solutes are more effective in both softening and hardening than Y solutes. Twin thickening exhibits weak strain rate sensitivity for pure Mg but the strain rate sensitivity increases with solute concentration.

Combined Effects of Texture and Grain Size Distribution on the Tensile Behavior of α-Titanium.

This work analyzes the role of both the grain size distribution and the crystallographic texture on the tensile behavior of commercially pure titanium. Specimens with different microstructures, especially with several mean grain sizes, were specifically prepared for that purpose. It is observed that the yield stress depends on the grain size following a Hall–Petch relationship, that the stress–strain curves have a tendency to form a plateau that becomes more and more pronounced with decreasing mean grain size and that the hardening capacity increases with the grain size. All these observations are well reproduced by an elasto-visco-plastic self-consistent model that incorporates grain size effects within a crystal plasticity framework where dislocations’ densities are the state variables. First, the critical resolved shear stresses are made dependent on the individual grain size through the addition of a Hall–Petch type term. Then, the main originality of the model comes from the fact that the multiplication of mobile dislocation densities is also made grain size dependent. The underlying assumption is that grain boundaries act mainly as barriers or sinks for dislocations. Hence, the smaller the grain size, the smaller the expansion of dislocation loops and thus the smaller the increase rate of mobile dislocation density is. As a consequence of this hypothesis, both mobile and forest dislocation densities increase with the grain size and provide an explanation for the grain size dependence of the transient low work hardening rate and hardening capacity.

Dislocation-density dynamics for modeling the cores and Peierls stress of curved dislocations

Although continuum dislocation models can describe dislocation cores, they are generally incapable of describing the Peierls stress, due to the invariance of the misfit energy and a lack of means to trigger configurational changes in the dislocation core as the dislocation moves. In this work, a dislocation-density dynamics framework for modeling dislocations at an “intensive” resolution scale finer than the dislocation core is established. In this approach, the inter-dislocation elastic interaction is accounted for via Mura's formula after singularity removal, and the interaction within the dislocation core is modeled by introducing a phenomenological formalism of the lattice misfit stress to balance the elastic interaction between dislocation contents, leading to not only a stable width of the dislocation as it travels, but also the expected Peierls stress. This framework is implemented numerically by using a divergence-preserving finite-volume method for curved dislocations gliding on 2D slip planes in general. Simulation examples of various dislocation mechanisms, including shrinkage and expansion of dislocation loops, the Frank-Read source, and Orowan looping, are given. The simulated results exhibit excellent preservation of continuity of dislocation densities during their evolution, while the detailed core structures and Peierls stress are clearly elucidated.

Molecular dynamics simulation of AlN thin films under nanoindentation

A large-scale molecular dynamics (MD) simulation of nanoindentation was performed to study the structural deformation on wurtzite aluminum nitride (B4-AlN). The nanoindentation induced B4-B1 phase-transition, amorphization and dislocation glide in AlN (0001) thin films were found. It shows that the B4-B1 phase-transition path includes two processes: an anti-parallel vertical movement of N and Al atoms along the [0001] axis, followed by horizontal rearrangements of the two types of atoms. Indentation force-depth (P-h) curve shows minor and major pop-in events. Detailed analysis of the results shows that the first three minor load drops in the P-h curve are related to the nucleation of amorphous structure, whereas the subsequent major load drop is related to the dislocation nucleation and expansion. The dislocations in AlN thin film involve perfect dislocations and Shockley partial dislocations, the latter is associated with the formation of intrinsic stacking faults (SFs) type I2 during the expansion of dislocation loops.

Estimation of the shear zone size in FCC – single crystals based on the model of dislocation interactions

The main objective of the mathematical modeling of a shear plastic strain is estimation of the shear zone size. The paper is devoted to refinement of estimations of the shear zone size based on the model of dislocation interactions proposed by the authors. It is assumed that shear-forming dislocation loops, emitted by the dislocation source, are stopped by strong dislocation barriers that arise from the interaction of segments of expanding dislocation loops with reacting dislocations of non-coplanar slip systems. The formed barriers hinder further expansion of dislocation loops and, as a result, form the boundary of the shear zone. A refined estimation of the shear zone size has been obtained.

Prediction of Transient Hardening after Strain Path Change by a Multi-scale Crystal Plasticity Model with Anisotropic Grain Substructure

Multi-scale modelling offers physical insights in the relationship between microstructure and properties of a material. The macroscopic anisotropic plastic flow may be accounted for by consideration of (a) the polycrystalline nature and (b) the anisotropic grain substructure. The latter contribution to anisotropy manifests itself most clearly in the event of a change in the strain path, as occurs frequently in multi-step forming processes. Under monotonic loading, both the crystallographic texture and the loading-dependent strength contribution from substructure influence the macroscopically observed strength.The presented multi-scale plasticity model for BCC polycrystals combines a crystal plasticity model featuring grain interaction with a substructure model for anisotropic hardening of the individual slip systems. Special attention is given to how plastic deformation is accommodated: either by slip of edge dislocation segments, or alternatively by dislocation loop expansion. Resultsof this multi-scale modelling approach are shown for a batch-annealed IF steel. Whereas both model variants are seen to capture the transient hardening after different types of strain path changes, the dislocation loop model offers more realistic predictions under a variety of monotonic loading conditions.

Atomistic simulation of the deformation mechanism during nanoindentation of gamma titanium aluminide

In this paper we present a large-scale molecular dynamics simulation that describes the deformation mechanism of an ordered intermetallic compound (TiAl) during a nanoindentation procedure. Using a totally rigid spherical indenter we were able to address the question on which mechanism underlies its plastic deformation, namely homogeneous defect nucleation followed by the expansion of dislocation loops. By means of the calculated local pressure, local shear stress and spatial rearrangements of atoms beneath the indenter, it was possible to quantify the indentation damage on the crystalline structure. Our results show that both emission and interaction of dislocations are mediated by expansion of glide loops on the {111} planes resulting in the formation of prismatic loops. Moreover, through the load-penetration depth response we estimated the elastic modulus and hardness values of the system, which are in good agreement with experimental results.

Indentation Crystal Plasticity: Experiments and Multiscale Simulations

AbstractThis work aims at a quantitative simulation of instrumented indentation test based on physics of crystal plasticity. Indentation loading is associated with a complex 3D deformation path: it can be viewed as an ideal benchmark to test various crystal plasticity assumptions. For large scale indentation (micron size), a 3D numerical simulation using finite element crystal plasticity (FEM) is setup and quantitatively compared to experimental results using critical constraints: the load/stiffness-displacement curves and the surface displacements. Various set of parameters obtained from Dislocation Dynamics (DD) are used. A comparison with experiments shows the dominant effect of initial dislocation density and slip system interactions. For smaller depth (maximum 100 nm), Dislocation Dynamics coupled simulations to FEM are setup. Since this approach does not provide defect nucleation rules, several strategies are implemented and tested: fitting to Molecular Dynamics (MD) load-depth curve for spherical tip, or automatic generation of deformation accommodating dislocation (GND) for conical tip geometry for example. In this framework, size effects show up in the modification of the dislocation structures with depth through critical expansion of dislocation loops and junction formation.

The stress–strain response of nanocrystalline metals: A quantized crystal plasticity approach

This paper develops a finite element-based model with quantized crystal plasticity (QCP) to study distinctive features of nanocrystalline (nc) metal behavior, including an enhanced flow stress, extended plastic transition strain and propensity for strain localization. The QCP feature is motivated by molecular dynamics simulations of dislocation loop propagation across nc grains, showing that the grain-averaged plastic strain jumps by discrete amounts. Further, a simple geometric analysis suggests that the magnitude of the jumps is ∼1/ grain size, thereby incorporating a grain size effect. QCP simulations of 1000-grain polycrystals can reproduce the unique experimental stress–strain features of nc metals, but only if the probability density distribution for a slip event increases abruptly at a threshold stress ∼1/ grain size. Possible explanations for such a unique signature are discussed in terms of dislocation loop expansion conditions that become important in the nc limit.

Multimillion-atom nanoindentation simulation of crystalline silicon carbide: Orientation dependence and anisotropic pileup

We have performed multimillion-atom molecular dynamics simulations of nanoindentation on cubic silicon carbide (3C-SiC) surfaces corresponding to three different crystallographic directions, (110), (001), and (111), using pyramidal-shaped Vickers indenter with 90° edge angle. Load-displacement (P-h) curves show major and minor pop-in events during loading. Detailed analysis of the (110) indentation shows that the first minor discontinuity in the P-h curve is related to the nucleation of dislocations, whereas the subsequent major load drops are related to the dissipation of accumulated energy by expansion of dislocation loops and changes of slip planes. Motion of dislocation lines in the indented films involves a kink mechanism as well as mutually repelling glide-set Shockley partial dislocations with associated extension of stacking faults during the expansion of dislocation loops. Our simulations provide a quantitative insight into the stress distribution on slip planes and stress concentration at kinks and dislocation cores. The estimated Peierls stress is 7.5GPa≈3.9×10−2G, where G is the shear modulus. We find that similar deformation mechanisms operate during nanoindentation of the three surfaces but the calculated hardness values are different, the highest being 27.5GPa for the (111) plane. Anisotropic pileup patterns are observed after the indenter is unloaded and they all reside on (111) and (1¯1¯1) slip planes. These patterns are closely related to dislocation activities on the two slip planes. The anisotropy is a consequence of the asymmetry of the 3C-SiC crystal in which only (111) and (1¯1¯1) slip planes are active out of the {111} family.

Minimum size of 180 degree domains in ferroelectric thin films covered by electrodes

Ferroelectric domain switching under low voltage or short pulses is of interest for the development of high-density random access memory (FRAM) devices. Being necessarily very small in size, instability and back switching often occur when the external voltage is removed, which creates serious problems. In this investigation, a general approach to determine the minimum size of ferroelectric domain to avoid back switching was developed, and as an example, a 180° domain in a ferroelectric thin film covered by the upper and lower electrodes was considered in detail. We note that our approach is generally applicable to many other fields, including phase transformation, nucleation and expansion of dislocation loops in thin films, etc.

Strain relaxation of GeSi/Si(001) heterostructures grown by low-temperature molecular-beam epitaxy

Plastic relaxation in GexSi1−x∕Si(001) heterostructures with x=0.18–0.62, grown at temperatures of 300–600 °C with the use of a low-temperature (350 °C) Si buffer layer, is considered. It is shown that the use of low-temperature Si and low temperature of growth of GeSi films decreases the density of threading dislocations to the value of 105–106cm−2 in heterostructures with a germanium content x<¯0.3, whereas the density of the threading dislocations in heterostructures with a higher content of Ge remains at the level of ∼108cm−2 and higher. By means of transmission electron microscopy, it is shown that the origination of dislocation half-loops from the surface in the case of a high content of germanium in the film is the main reason for the high density of threading dislocations. Growing of GeSi films with a two-step change in composition is considered. The fact that the density of the threading dislocations in the first step of the film is significantly higher than that in the substrate is noted. Because of their presence, the real thickness of insertion of misfit dislocations into the second step of the film is in ten times less than for the first layer. With an allowance for this effect, almost complete plastic relaxation of the second and further heterostructure steps can be reached at low temperatures and at a smaller thickness of GeSi films. It is concluded that the main factors of low-temperature epitaxy of GeSi, which reduce the density of the threading dislocations in heterostructures are (i) a decrease in the initial threading dislocation density and (ii) an increase in the rate of expansion of dislocation loops, which facilitates plastic relaxation with a smaller number of threading dislocations.

Stability of 180° domain in ferroelectric thin films

Ferroelectric random access memory (FRAM) has attracted much attention in the last two decades due to its ideal properties such as nonvolatility, high speed, and low power consumption. There is a strong incentive to develop high-density FRAMs, in which the switched domains, developed under low voltage or short pulses, are necessarily very small, and are therefore usually unstable and suffer from significant backswitching upon removal of the external voltage. In this investigation, a general form of energy expression for a ferroelectric material containing 180° domains is derived, from which evolution equations of the domain are established. By choosing the change in internal energy as the Liapunov function, a general formulation is developed to determine the stability conditions of the switched domain. This is applied to the case of an ellipsoidal 180° domain and yields a criterion for the stability of switched domains. We note that our approach is generally applicable to many other fields, including phase transformation, nucleation, expansion of dislocation loops in thin films, etc.

Constrained and unstable expansion of dislocation loops using an invariant formulation of the free energy

The expression of the free energy related with the Eshelby-Kröner's inelastic inclusion problem is simplified using the theory of irreductible representations. This formulation simplifies significantly problems requiring energy derivatives and particularly moving boundary problems. As a first application, the stability of a dislocation loop under applied stress is studied and a new interpretation of the critical shear stress in single crystal is obtained. The second application deals with the problem of grain size effect in polycrystalline plasticity: The yield stress σ y follows a relation like σ y ≈ d − n where n = 1 2 holds for low grain size (equivalent to the classical Hall Petch relation) while for large grain size n is equal to unity.