Micropillar compression using discrete dislocation dynamics and machine learning

Discrete dislocation dynamics(DDD)simulations reveal the evolution of dislocation structures and the interaction of dislocations.This study investigated the compression behavior of single-crystal copper micropillars using fewshot machine learning with data provided by DDD simulations.Two types of features are considered:external features comprising specimen size and loading orientation and internal features involving dislocation source length,Schmid factor,the orientation of the most easily activated dislocations and their distance from the free boundary.The yielding stress and stress-strain curves of single-crystal copper micropillar are predicted well by incorporating both external and internal features of the sample as separate or combined inputs.It is found that the machine learning accuracy predictions for single-crystal micropillar compression can be improved by incorporating easily activated dislocation features with external features.However,the effect of easily activated dislocation on yielding is less important compared to the effects of specimen size and Schmid factor which includes information of orientation but becomes more evident in small-sized micropillars.Overall,incorporating internal features,especially the information of most easily activated dislocations,improves predictive capabilities across diverse sample sizes and orientations.

CYCLIC HARDENING BEHAVIOR OF POLYCRYSTALS WITH PENETRABLE GRAIN BOUNDARIES:TWO-DIMENSIONAL DISCRETE DISLOCATION DYNAMICS SIMULATION

A two-dimensional discrete dislocation dynamics （DDD） technology by Giessen and Needleman （1995）, which has been extended by integrating a dislocation-grain boundary interaction model, is used to computationally analyze the micro-cyclic plastic response of polycrystals containing micron-sized grains, with special attentions to significant influence of dislocationpenetrable grain boundaries （GBs） on the micro-plastic cyclic responses of polycrystals and underlying dislocation mechanism. Toward this end, a typical polycrystalline rectangular specimen under simple tension-compression loading is considered. Results show that, with the increase of cycle accumulative strain, continual dislocation accumulation and enhanced dislocation-dislocation interactions induce the cyclic hardening behavior; however, when a dynamic balance among dislocation nucleation, penetration through GB and dislocation annihilation is approximately established, cyclic stress gradually tends to saturate. In addition, other factors, including the grain size, cyclic strain amplitude and its history, also have considerable influences on the cyclic hardening and saturation.

MECHANICAL BEHAVIOR OF FCC CRYSTAL SIMULATED BY 3-D DISCRETE DISLOCATION DYNAMICS

To simulate the mechanical behavior of the FCC crystal with the lower Peierls stress, the stiff property and physical meaning of the differential equation group consisting of dislocation evolution and mechanical state was investigated based on the 3-D discrete dislocation dynamics; the results indicate that the differential equation group is serious stiff, namely the external stress changes more quickly than dislocation evolution. Using the established numerical algorithm, the mechanical behavior of FCC crystal was simulated with the dislocations located in the parallel slip planes, and the effect of strain rate on the dislocation configuration and mechanical behavior, and the sat- uration process of mobile dislocation were discussed. The simulation results indicate that the numerical algorithm can efficiently simulate the dislocation dipole and the low strain rate loading.

Multiple time step molecular dynamics simulation for interaction between dislocations and grain boundaries

A multiple time step algorithm, called reversible reference system propagator algorithm, is introduced for the long time molecular dynamics simulation. In contrast to the conventional algorithms, the multiple time method has better convergence, stability and efficiency. The method is validated by simulating free relaxation and the hypervelocity impact of nano-clusters. The time efficiency of the multiple time step method enables us to investigate the long time interaction between lattice dislocations and low-angle grain boundaries.

A CONSTITUTIVE MODEL FOR CREEP-PLASTICITY INTERACTION BASED ON DISLOCATION DYNAMICS

A glide-plus-climb micromechanism of dislocation evolution with the formation of subgrains is pro- posed for modelling of the creep-plasticity interaction (CPI). The long-range internal stress can be divided into the resistance for dislocation climb in subgrain boundaries and that for dislocation glide within grains or subgrains. Their evolution equations are then derived based on dislocation dynamics. Furthermore, a unified constitutive model for CPI is developed from Orowan's formula. Theoretical calculations on the basis of this model show a very good agreement between the model prediction and experimental results of benchmark tests for 2 1/4 Cr -1 Mo steel at 600℃.

A multi-scale algorithm for dislocation creep at elevated temperatures

Dislocation creep at elevated temperatures plays an important role for plastic deformation in crystalline metals.When using traditional discrete dislocation dynamics(DDD)to capture this process,we often need to update the forces on N dislocations involving~N 2 interactions.In this letter,we introduce a multi-scale algorithm to speed up the calculations by dividing a sample of interest into sub-domain grids:dislocations within a characteristic area interact following the conventional way,but their interaction with dislocations in other grids are simplified by lumping all dislocations in another grid as a super one.Such a multi-scale algorithm lowers the computational load to~N 1.5.We employed this algorithm to model dislocation creep in Al-Mg alloy.The simulation leads to a power-law creep rate in consistent with experimental observations.The stress exponent of the power-law creep is a resultant of dislocations climb for~5 and viscous dislocations glide for~3.

Geometrically-Compatible Dislocation Pattern and Modeling of Crystal Plasticity in Body-Centered Cubic(BCC)Crystal at Micron Scale Dedicated to Professor Karl Stark Pister for his 95th birthday

The microstructure of crystal defects,e.g.,dislocation patterns,are not arbitrary,and it is possible that some of them may be related to the microstructure of crystals itself,i.e.,the lattice structure.We call those dislocation patterns or substructures that are related to the corresponding crystal microstructure as the Geometrically Compatible Dislocation Patterns(GCDP).Based on this notion,we have developed a Multiscale Crystal Defect Dynamics(MCDD)to model crystal plasticity without or with minimum empiricism.In this work,we employ the multiscale dislocation pattern dynamics,i.e.,MCDD,to simulate crystal plasticity in body-centered cubic(BCC)single crystals,mainlyα-phase Tantalum(α-Ta)single crystals.The main novelties of the work are:(1)We have successfully simulated crystal plasticity at micron scale without any empirical parameter inputs;(2)We have successfully employed MCDD to perform direct numerical simulation of inelastic hysteresis of the BCC crystal;(3)We have used MCDD crystal plasticity model to demonstrate the size-effect of crystal plasticity and(4)We have captured cross-slip which may lead to size-effect.

Discrete dislocation plasticity analysis of dispersion strengthening in oxide dispersion strengthened(ODS) steels

A discrete dislocation plasticity analysis of dispersion strengthening in oxide dispersion strengthened(ODS) steels was described. Parametric dislocation dynamics(PDD) simulation of the interaction between an edge dislocation and randomly distributed spherical dispersoids(Y2O3) in bcc iron was performed for measuring the influence of the dispersoid distribution on the critical resolved shear stress(CRSS). The dispersoid distribution was made using a method mimicking the Ostwald growth mechanism. Then, an edge dislocation was introduced, and was moved under a constant shear stress condition. The CRSS was extracted from the result of dislocation velocity under constant shear stress using the mobility(linear) relationship between the shear stress and the dislocation velocity. The results suggest that the dispersoid distribution gives a significant influence to the CRSS, and the influence of dislocation dipole, which forms just before finishing up the Orowan looping mechanism, is substantial in determining the CRSS, especially for the interaction with small dispersoids. Therefore, the well-known Orowan equation for determining the CRSS cannot give an accurate estimation, because the influence of the dislocation dipole in the process of the Orowan looping mechanism is not accounted for in the equation.

Small amplitude approximation and stabilities for dislocation motion in a superlattice

Starting from the traveling wave solution, in small amplitude approximation, the Sine–Gordon equation can be re- duced to a generalized Duffing equation to describe the dislocation motion in a superlattice, and the phase plane properties of the system phase plane are described in the absence of an applied field. The stabilities are also discussed in the presence of an applied field. It is pointed out that the separatrix orbit describing the dislocation motion as the kink wave may transfer the energy along the dislocation line, keep its form unchanged, and reveal the soliton wave properties of the dislocation motion. It is stressed that the dislocation motion process is the energy transfer and release process, and the system is stable when its energy is minimum.

A Mesh-Independent Brute-Force Approach for Traction-Free Corrections in Dislocation Problems

Simulation of dislocation dynamics opens the opportunity for researchers and scientists to observe in-depth many plastic deformation phenomena. In 2D or 3D media, modeling of physical boundary conditions accurately is one of the keys to the success of dislocation dynamics (DD) simulations. The scope of analytical solutions is restricted and applies to specific configurations only. But in dynamics simulations, the dislocations’ shape and orientation change over time thus limiting the use of analytical solutions. The authors of this article present a mesh-based generalized numerical approach based on the collocation point method. The method is applicable to any number of dislocations of any shape/orientation and to different computational domain shapes. Several verifications of the method are provided and successful implementation of the method in 3D DD simulations have been incorporated. Also, the effect of free surfaces on the Peach-Koehler force has been computed. Lastly, the effect of free surfaces on the flow stress of the material has been studied. The results clearly showed a higher force with increased closeness to the free surface and with increased dislocation segment length. The simulations’ results also show a softening effect on the flow stress results due to the effect of the free surfaces.

A hierarchical dislocation-grain boundary interaction model based on 3D discrete dislocation dynamics and molecular dynamics

We develop a new hierarchical dislocation-grain boundary （GB） interaction model to predict the mechanical behavior of poly- crystalline metals at micro and submicro scales by coupling 3D Discrete Dislocation Dynamics （DDD） simulation with the Molecular Dynamics （MD） simulation. At the microscales, the DDD simulations are responsible for capturing the evolution of dislocation structures; at the nanoscales, the MD simulations are responsible for obtaining the GB energy and ISF energy which are then transferred hierarchically to the DDD level. In the present model, four kinds of dislocafion-GB interactions, i.e. transmission, absorption, re-emission and reflection, are all considered. By this methodology, the compression of a Cu mi- cro-sized bi-crystal pillar is studied. We investigate the characteristic mechanical behavior of the bi-crystal compared with that of the single-crystal. Moreover, the comparison between the present penetrable model of GB and the conventional impenetrable model also shows the accuracy and efficiency of the present model.

Effect of Hydrogen on Dislocation Nucleation and Motion:Nanoindentation Experiment and Discrete Dislocation Dynamics Simulation

The hydrogen effect on the nucleation and motion of dislocations in single-crystal bcc Fe with(110)surface was investigated by both nanoindentation experiments and discrete dislocation dynamics(DDD)simulation.The results of nanoindentation experiments showed that the pop-in load decreased evidently for the electrochemical hydrogen charging specimen,indicating that the dislocation nucleation strength might be reduced by hydrogen.In addition,the decrease of hardness due to hydrogen charging was also captured,implying that the dislocation motion might be promoted by hydrogen.By incorporating the effect of hydrogen on dislocation core energy,a DDD model was specifically proposed to investigate the influence of hydrogen on dislocation nucleation and motion.The results of DDD simulation revealed that under the effect of hydrogen,the dislocation nucleation strength is decreased and the motion of dislocation is promoted.

Strain Hardening Associated with Dislocation,Deformation Twinning,and Dynamic Strain Aging in Fe–20Mn–1.3C–(3Cu) TWIP Steels

The effects of Cu on stacking fault energy,dislocation slip,mechanical twinning,and strain hardening in Fe–20Mn–1.3C twinning-induced plasticity（TWIP） steels were systematically investigated.The stacking fault energy was raised with an average slope of 2 mJ/m2 per 1 wt% Cu.The Fe–20Mn–1.3C–3Cu steel exhibited superior tensile properties,with the ultimate tensile strength reached at 2.27 GPa and elongation up to 96.9% owing to the high strain hardening that occurred.To examine the mechanism of this high strain hardening,dislocation density determination by XRD was calculated.The dislocation density increased with the increasing strain,and the addition of Cu resulted in a decrease in the dislocation density.A comparison of the strain-hardening behavior of Fe–20Mn–1.3C and Fe–20Mn–1.3C–3Cu TWIP steels was made in terms of modified Crussard–Jaoul（C–J） analysis and microstructural observations.Especially at low strains,the contributions of all the relevant deformation mechanisms—slip,twinning,and dynamic strain aging—were quantitatively evaluated.The analysis revealed that the dislocation storage was the leading factor to the increase of the strain hardening,while dynamic strain aging was a minor contributor to strain hardening.Twinning,which interacted with the matrix,acted as an effective barrier to dislocation motion.

Effect of template shape on metal nanoimprinting:a dislocation dynamics study

Dislocation dynamics simulations are performed to investigate the effect of template shape on the nanoimprinting of metal layers. To this end, metal thin films are imprinted by a rigid template made of an array of equispaced indenters of various shapes, i.e., rectangular, wedge, and circular. The geometry of the indenters is chosen such that the contact area is approximately the same at the final imprinting depth. Results show that, for all template shapes, the final patterns strongly depend on the dislocation activity, and that each imprint differs from the neighboring ones. Large material pile ups appear between the imprints, such that polishing of the metal layer is suggested for application of the patterns in electronics. Rectangular indenters require the lowest imprinting force and achieve the deepest retained imprints.

Modeling Dislocations at Different Scales

In this article,we give an introduction to the basic theory of dislocations and some dislocation models at different length scales.Dislocations are line defects in crystals.The continuum theory of dislocations works well at the length scale of several lattice constants away from the dislocations.In the region surrounding the dislocations(core region),the crystal lattice is heavily distorted,and atomistic models are used to describe the atomic arrangement and related properties.The Peierls-Nabarro models of dislocations incorporate the atomic features into the continuum theory,therefore provide an alternative way to understand the dislocation core properties.The numerical simulation of the collective motion and interactions of dislocations,known as dislocation dynamics,is becoming a more and more important tool for the investigation of the plastic behaviors of materials.Several simulation methods for dislocation dynamics are also reviewed in this article.

Effect of Dislocation Mechanism on Elastoplastic Behavior of Crystals with Heterogeneous Dislocation Distribution

Gradient structures have excellent mechanical properties,such as synergetic strength and ductility.It is desirable to reveal the connection between the gradient structure and mechanical properties.However,few studies have been conducted for materials with heterogeneous dislocation distribution.In the present study,we use the discrete dislocation dynamics(DDD)method to investigate the effect of dislocation density gradient on the elastoplastic behavior of single crystals controlled by source activation.In contrast to the intuitive expectation that gradient structure affects the mechanical properties,the DDD simulations show that the elastic moduli and yield stresses of three gradient samples(i.e.,no gradient,low gradient,and high gradient)are almost identical.Different from the progressive elastic-plastic transition in the samples controlled by Taylor hardening(i.e.,the mutual interaction of dislocation segments),the flow stresses of source activation ones enter into a stage of nearly ideal plasticity(serrated flow)immediately after yielding.The microstructure evolution demonstrates that the mean dislocation spacing is relatively large.Thus,there are only a few or even one dislocation source activated during the plastic flow.The intermittent operation of sources leads to intensive fluctuation of stress and dislocation density,as well as a stair-like evolution of plastic strain.The present work reveals that the effect of dislocation density gradient on the mechanical response of crystals depends on the underlying dislocation mechanisms controlling the plastic deformation of materials.

Fast Multipole Accelerated Boundary Integral Equation Method for Evaluating the Stress Field Associated with Dislocations in a Finite Medium

In this paper,we develop an efficient numericalmethod based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated with dislocations in a finite medium.Numerical examples are presented to examine the influence from material boundaries on dislocations.

Strengthening of tungsten by coherent rhenium precipitates formed during low fluence irradiation

Experimental data show that the accumulation of rhenium and osmium from transmutation reactions severely affect the microstructural evolution and property degradation of tungsten-based materials under neutron irradiation.Theory and modeling have confirmed that Re atom transport in W is by irradiation-produced migrating self-interstitial atoms.With this diffusion mode in operation,a specific microstructure evolution is realized when at relatively low neutron fluence the Re-rich precipitates are formed,while the void and interstitial loop population development is suppressed,affecting the mechanical properties.This research shows the effect of small coherent Re-rich precipitates on the dislocation glide under stress,investigated using the molecular dynamics approach with empirical interatomic potentials.The results are compared with an earlier simulation of void hardening in W.It is demonstrated that small coherent Re-rich precipitates of less than 6 nm diameter represent relatively weak obstacles for moving edge dislocations.The implication of these results on the interpretation of experimental results is discussed.