Grain-scale Simulations Research Articles

Temperature dependent deformation behavior and texture evolution in AA6082 aluminum alloy: An integrated experimental and crystal plasticity simulation approach

This research provides a comprehensive analysis of the texture and temperature dependent deformation behavior of the aluminum alloy AA6082. The study is performed using a combination of experimental deformation tests and computational simulations using a crystal plasticity (CP) framework. The primary objective is to identify the critical influence of temperature on local stress states and dislocation density within the material during tensile tests. From an experimental perspective, the study employs ex-situ deformation tests and subsequent electron backscatter diffraction (EBSD) data in combination with energy dispersive x-ray spectrometer (EDS) analysis at 200 °C and 400 °C. The experimental EBSD data are adopted, preprocessed and converted into a geometry file for the numerical simulations. On the computational front, a dislocation density-based material model is adopted for CP simulations. The physical and fitting parameters of the model are calculated, adopted from the literature, or calibrated by comparing the global simulation results with experimental stress-strain observations under uniaxial tensile load at room temperature, 200 °C and 400 °C. Empirical functions for solid solution strengthening, dislocation density, fitting parameters controlling mean free path and dislocation annihilation have been derived that can be used to quickly interpolate them for any intermediate temperature. These functions combined with other model parameters can now be used for temperature-dependent CP modeling of AA6082. The isothermal grain-scale simulation and ex-situ experimental results confirmed a noteworthy texture transformation at higher temperatures, characterized by a reduction in the primary Cube orientation and its transition into a Copper orientation due to the stretching process. The correlation between the experimental results and the simulations on macro- and micro-scales is reasonable, indicating the accuracy and effectiveness of the CP approach in predicting the temperature dependent deformation behavior and texture evolution in aluminum alloys.

A grain-scale modeling on the surface burning and agglomeration of the metalized solid propellants

This study delves into the dynamic behavior of reactive grains within metalized propellants during surface deflagration. Our grain-scale simulations account for both fast and slow deflagration processes involving two distinct metal fuels, namely zirconium and magnesium, with potassium perchlorate (KClO4) as the common oxidizer. Our primary goal is to develop a model and numerical technique capable of replicating the surface reactions observed in experiments. To achieve this, we utilize the compressible Navier–Stokes equations, incorporating the Arrhenius rate law and Johnson-Cook stress model. We pay particular attention to the melt layer, where surface burning occurs in an open atmosphere, and we develop a mechanism to describe the interaction between reactive grains and exhaust gases. We differentiate between two limiting scenarios: convective burning, where unreacted particles experience high-speed compression waves leading to reduced thermal diffusion within the cold reactant, and diffusive burning, characterized by insufficient pressure from particles undergoing both reaction and deformation to erode the burning surface. This results in pronounced agglomeration and the formation of gaseous metal oxides above the melt layer. The results shed light on critical factors influencing surface combustion, including the thermal softening of reactive particles, the time required for particle agglomerations, and tangential forces at multi-element interfaces within the grain-scale simulation domain.

Data-driven breakage mechanics: Predicting the evolution of particle-size distribution in granular media

This paper presents a model-free data-driven framework for breakage mechanics. In contrast with continuum breakage mechanics, the de facto approach for the macroscopic analysis of crushable granular media, the present framework does not require the definition of constitutive models and phenomenological assumptions, relying on material behavior that is known only through empirical data. For this purpose, we revisit the recent developments in model-free data-driven computing for history-dependent materials and extend the main ideas to materials with particle breakage. A systematic construction of the modeling framework is presented, starting from the closed-form representation of continuum breakage mechanics and arriving at alternative model-free representations. The predictive ability of the data-driven framework is highlighted and contrasted with continuum breakage mechanics on different boundary value problems. Moreover, an application to a real experimental test in crushable sand is presented, where the data is furnished by high-fidelity grain-scale simulations, indicating that the proposed framework provides an accurate prediction of the mechanics of crushable materials including the state of comminution.

Anomalous Scaling of Aeolian Sand Transport Reveals Coupling to Bed Rheology

Predicting transport rates of windblown sand is a central problem in aeolian research, with implications for climate, environmental, and planetary sciences. Though studied since the 1930s, the underlying many-body dynamics is still incompletely understood, as underscored by the recent empirical discovery of an unexpected third-root scaling in the particle-fluid density ratio. Here, by means of grain-scale simulations and analytical modeling, we elucidate how a complex coupling between grain-bed collisions and granular creep within the sand bed yields a dilatancy-enhanced bed erodibility. Our minimal saltation model robustly predicts both the observed scaling and a new undersaturated steady transport state that we confirm by simulations for rarefied atmospheres.

Enhancing Lithium-Ion Battery Aging Simulations By Coupling a High-Resolution, 3D, Grain-Scale Electromechanical Model to a Single Particle Model

One of the main goals in modeling lithium-ion batteries is to improve/predict longevity and resilience of new chemistries. Unfortunately, this requires simulation of thousands of charge/discharge cycles, which can be rather time consuming depending on the fidelity of the simulation. The purpose of this talk is to discuss a new modeling framework that couples a high-resolution, continuous damage model (CDM) to a single particle model (SPM) resulting in a good combination of speed and fidelity.In previous work, a 3D, continuum-level chemo-mechanical model was developed to investigate cracking within a single cathode particle comprised of hundreds to thousands of randomly oriented grains. The CDM predicted that particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. Essentially, when neighboring grains were misaligned, they expanded different rates relative to one another leading to high stresses and ultimately the formation of intraparticle cracks. The model predicted that small particles with large grains develop significantly less damage than larger particles with small grains. Finally, the model predicted most of the chemo-mechanical damage accumulates in the first charge after formation. This chemo-mechanical “damage saturation” effect indicated that initial particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced. This led to a need for simulating fatigue-like mechanism that degrade the battery over longer time scales.In order to reach the time scales, need to resolve fatigue-like degradation, the CDM needs to be complemented by a faster model. Therefore, recent efforts have been focused on using results from the CDM to inform parameters within the SPM. These parameters are homogenization factors that are associated with diffusion, particle radius, and/or exchange current density. By coupling the CDM to the SPM, the aging simulation is broken up into two domains: short-term and long-term degradation. The short-term degradation occurs over a single cycle and is handled by the CDM due of its high fidelity, but relatively expensive computational cost. Such mechanism include break-in crack caused by mismatches in grain orientation. The long-term degradation occurs over tens of cycles and is handled by the SPM due it’s computational efficiency. Most of the fatigue-like mechanism fall into this category.The eventual goal of this modeling framework is to upscale to a psudo-2D model allowing for full electrode simulation, which are informed by high-fidelity grain-scale simulations. Figure 1

Temperature-dependent constitutive modeling of a magnesium alloy ZEK100 sheet using crystal plasticity models combined with in situ high-energy X-ray diffraction experiment

A multiscale crystal plasticity model accounting for temperature-dependent mechanical behaviors without introducing a larger number of unknown parameters was developed. The model was implemented in elastic-plastic self-consistent (EPSC) and crystal plasticity finite element (CPFE) frameworks for grain-scale simulations. A computationally efficient EPSC model was first employed to estimate the critical resolved shear stress and hardening parameters of the slip and twin systems available in a hexagonal close-packed magnesium alloy, ZEK100. The constitutive parameters were thereafter refined using the CPFE. The crystal plasticity frameworks incorporated with the temperature-dependent constitutive model were used to predict stress–strain curves in macroscale and lattice strains in microscale at different testing temperatures up to 200 °C. In particular, the predictions by the crystal plasticity models were compared with the measured lattice strain data at the elevated temperatures by in situ high-energy X-ray diffraction, for the first time. The comparison in the multiscale improved the fidelity of the developed temperature-dependent constitutive model and validated the assumption with regard to the temperature dependency of available slip and twin systems in the magnesium alloy. Finally, this work provides a time-efficient and precise modeling scheme for magnesium alloys at elevated temperatures.

Evaluation and prediction of pore effects on single-crystal mechanical and damage properties of selective laser melted Inconel-718

Pore defects inescapably occur during the selective laser melting (SLM) process of metallic materials, which are difficult to be eliminated even by advanced process optimizing and post-treatment technologies. Properties of SLM-fabricated materials depend on the influence of pores, while the effect mechanism is not clearly understood. To clarify the pore effects and achieve reliable forecasting, a statistical-theory-based grain-scale simulation work was performed. Taking Inconel-718 as the example, actual pore defects were detected and classified into three types i.e., gas pore, keyhole pore and lack-of-fusion (LOF) pore, which were then fitted by single or multiple ellipsoids. The volume, shape and posture of pores were characterized by independent parameters, and single-pore-included single-crystal simulations were carried out. Furthermore, overall pore effects were divided into single-ellipsoidal effects, sub-pore quantity effects and sub-pore intersection effects, and the influence mechanisms of pore characteristics on the mean tensile strength and the maximum damage driving force were clarified through partial correlation analysis. Eventually, single-crystal mechanical and damage property prediction models for the grain with an internal pore defect were developed and verified, which show good accuracy with 8–22% relative deviation for damage resistance predictions, and show excellent accuracy with lower than 0.3% relative deviation for strength property predictions.

From Blowing Wind to Running Water: Unifying Sediment Transport

Laboratory experiments and grain-scale computer simulations during the past decade have led to a more universal understanding of flow-driven sediment transport across flows in oil, water, and air.

Morphodynamics of a dense particulate medium under radial explosion

In this paper, we investigate the initiation and growth of instability patterns arising from the shock loaded internal surfaces of granular rings confined in a Hele-Shaw cell using both experimental and numerical approaches. A variety of patterns are formed in granular media consisting of grains with varying morphologies. When the particle shape becomes increasingly irregular, and/or the gap in the Hele-Shaw cell becomes narrower, it is increasingly hard for confined particles to fluidize. Consequently the emergent pattern transitions from a smooth circle with trivial undulation which grows in a self-similar manner to an unstable finger-like structure with significant tip-splitting. The distinct growth mode of the well-defined instability pattern is closely associated with its inception phase alongside the transmission of the compaction front. The runaway growth of the incipient perturbations gives rise to the unstable growth of the late-time finger-like instabilities. Conversely the minimal growth of the perturbations in the inception phase guarantees the ensuing self-similar growth of the instability patterns featuring insignificant corrugation. The grain-scale simulations reveal the fundamental role played by the heterogeneous non-linear force network inherent to granular media in the stable-to-unstable transition of the instability pattern. The present work reveals the correlation between the grain-scale physics underpinning the formation of surface instability upon shock loading granular media and the nature of the resulting macro-scale instability patterns. The macroscopic flowability of particles through the confined space is found to be the foremost indicator of the nature of the shock induced granular instability pattern.

Screw dislocation interaction with irradiation defect-loops in α-iron: Evaluation of loop-induced stress field effect using dislocation dynamics simulations

Plastic strain spreading in post-irradiated Fe grains takes the form of wavy shear bands, where mobile dislocations interact with the radiation defect dispersions. In actual Fe grains, dislocation/loop interactions involve several contributing factors including: screw dislocation cross-slip and loop-induced stress. The loop-induced stress effect is here evaluated by systematic simulation case comparisons, using adapted dislocation dynamics simulations. Namely, dislocation/loop simulation cases are systematically compared with equivalent dislocation/facet simulation cases, under room temperature straining conditions. The facets have exactly the same size and orientation as in the reference loop cases, however; the facets have no associated stress field. It is thereby found that in presence of cross-slip the total reaction time and reaction strain associated with various dislocation/facet cases is close to their dislocation/loop counterparts (within 15% and 12%, respectively). In the present investigation context, loop-induced stress field contribution is thus a second order effect, regardless of the considered loop type and orientation. In this situation, the calculation-intensive dislocation/loop interaction description can be replaced by the much faster dislocation/facet approach, for computationally intensive grain-scale simulations.

Laboratory measurements of the viscous anisotropy of olivine aggregates

A marked anisotropy in viscosity develops in Earth's mantle as deformation strongly aligns the crystallographic axes of the individual grains that comprise the rocks. On the basis of geodynamic simulations, processes significantly affected by viscous anisotropy include post-glacial rebound, foundering of lithosphere and melt production above subduction zones. However, an estimate of the magnitude of viscous anisotropy based on the results of deformation experiments on single crystals differs by three orders of magnitude from that obtained by grain-scale numerical models of deforming aggregates with strong crystallographic alignment. Complicating matters, recent experiments indicate that deformation of the uppermost mantle is dominated by dislocation-accommodated grain-boundary sliding, a mechanism not activated in experiments on single crystals and not included in numerical models. Here, using direct measurements of the viscous anisotropy of highly deformed polycrystalline olivine, we demonstrate a significant directional dependence of viscosity. Specifically, shear viscosities measured in high-strain torsion experiments are 15 times smaller than normal viscosities measured in subsequent tension tests performed parallel to the torsion axis. This anisotropy is approximately an order of magnitude larger than that predicted by grain-scale simulations. These results indicate that dislocation-accommodated grain-boundary sliding produces an appreciable anisotropy in rock viscosity. We propose that crystallographic alignment imparts viscous anisotropy because the rate of deformation is limited by the movement of dislocations through the interiors of the crystallographically aligned grains. The maximum degree of anisotropy is reached at geologically low shear strain (of about ten) such that deforming regions of the upper mantle will exhibit significant viscous anisotropy.

Influences of deformation strain, strain rate and cooling rate on the Burgers orientation relationship and variants morphology during β→α phase transformation in a near α titanium alloy

Abstract High temperature compression deformation studies of Ti–6Al–2Zr–1Mo–1V titanium alloy in full β phase region with different strains/strain rates and then with subsequent varied cooling rates were performed to understand the microstructure evolution. Crystal orientation information and microstructure morphology of all tested samples were investigated by electron backscatter diffraction (EBSD) measurements. The crystal orientations of prior high temperature β grains were estimated by reconstructing the retained β phase at room temperature. The theoretical crystal orientations of all possible α variants within an investigated prior β grain were calculated according to the Burgers orientation relationship (OR) between parent and product phase. The calculated and experimental results were then compared and analyzed. The influences of deformation strain, strain rate and cooling rate on the Burgers OR between prior β matrix and precipitated α phase were investigated. Full discussions have been conducted by combination of crystal plasticity finite element method (CP-FEM) grain-scale simulation results. The results indicate that external factors (such as deformation strain, strain rate and cooling rate) have a slight influence on the obeying of Burgers OR rule during β → α phase transformation. However, strain rate and cooling rate have a significant effect on the morphology of precipitated α phase.

Incorporating atomistic data of lattice friction into BCC crystal plasticity models

Despite the technological importance of body-centered cubic (BCC) metals, models of their plastic deformation are less common than those of face-centered cubic (FCC) metals, due in part to the complexity of slip in BCC crystals caused by the thermal activation of screw dislocation motion. This paper presents a physically based crystal plasticity model that incorporates atomistic models and experimental measurements of the thermally activated nature of screw dislocation motion. This model, therefore, reproduces the temperature, stress, and strain rate dependence of flow in BCC metals in a simple formulation that will allow for large, grain-scale simulations. Furthermore, the results illustrate the importance of correctly representing mechanistic transitions in materials with high lattice friction.

Experimental characterisation of (localised) Deformation Phenomena in Granular Geomaterials from Sample Down to Inter-and Intra-grain Scales

This paper outlines some recent advances in the full-field experimental characterisation of the mechanics of granular geomaterials (in particular, sands) using a range of methods that provide characterisation at different scales, from the sample-scale down to the inter- and intra-grain scale. The techniques used are “full-field” approaches involving in-situ x-ray micro-tomography, 3D-volumetric digital image analysis/correlation and grain ID-tracking, in-situ 3D x-ray diffraction and in-situ, spatially-resolved neutron diffraction. These methods provide new data on the mechanics of sand at different scales, including continuum measures of strain, porosity, and fabric plus discrete measures of particle kinematics and force transmission. The results of such measurements might be used to advance higher-order continuum theories, and provide the necessary input parameters, or to calibrate discrete grain-scale simulations of sand behaviour to explore loading paths that are inaccessible in the laboratory.

Multi-scale modeling of low-temperature deformation in b.c.c. metals

The deformation of body-centered cubic (b.c.c.) metals such as W, Ta, and Mo is complicated both by complex deformation mechanisms at the atomic scale and by microstructural variations at the microscale. In this paper, we develop a multiscale model for low-temperature deformation in b.c.c. metals. This model integrates atomic-scale observations into a single crystal constitutive relationship that is implemented in a polycrystal plasticity grain-scale simulation. We determine that the details of deformation at the microscale differ substantially between b.c.c. and f.c.c. metals.

Simulation of polycrystal deformation with grain and grain boundary effects

Modeling the strengthening effect of grain boundaries (Hall–Petch effect) in metallic polycrystals in a physically consistent way, and without invoking arbitrary length scales, is a long-standing, unsolved problem. A two-scale method to treat predictively the interactions of large numbers of dislocations with grain boundaries has been developed, implemented, and tested. At the first scale, a standard grain-scale simulation (GSS) based on a finite element (FE) formulation makes use of recently proposed dislocation-density-based single-crystal constitutive equations (“SCCE-D”) to determine local stresses, strains, and slip magnitudes. At the second scale, a novel meso-scale simulation (MSS) redistributes the mobile part of the dislocation density within grains consistent with the plastic strain, computes the associated inter-dislocation back stress, and enforces local slip transmission criteria at grain boundaries. Compared with a standard crystal plasticity finite element (FE) model (CP-FEM), the two-scale model required only 5% more CPU time, making it suitable for practical material design. The model confers new capabilities as follows: (1) The two-scale method reproduced the dislocation densities predicted by analytical solutions of single pile-ups. (2) Two-scale simulations of 2D and 3D arrays of regular grains predicted Hall–Petch slopes for iron of 1.2 ± 0.3 MN/m 3/2 and 1.5 ± 0.3 MN/m 3/2, in agreement with a measured slope of 0.9 ± 0.1 MN/m 3/2. (3) The tensile stress–strain response of coarse-grained Fe multi-crystals (9–39 grains) was predicted 2–4 times more accurately by the two-scale model as compared with CP-FEM or Taylor-type texture models. (4) The lattice curvature of a deformed Fe-3% Si columnar multi-crystal was predicted and measured. The measured maximum lattice curvature near grain boundaries agreed with model predictions within the experimental scatter.

Frictional granular mechanics: A variational approach

AbstractThe mechanical properties of a cohesionless granular material are evaluated from grain‐scale simulations. Intergranular interactions, including friction and sliding, are modeled by a set of contact rules based on the theories of Hertz, Mindlin, and Deresiewicz. A computer‐generated, three‐dimensional, irregular pack of spherical grains is loaded by incremental displacement of its boundaries. Deformation is described by a sequence of static equilibrium configurations of the pack. A variational approach is employed to find the equilibrium configurations by minimizing the total work against the intergranular loads. Effective elastic moduli are evaluated from the intergranular forces and the deformation of the pack. Good agreement between the computed and measured moduli, achieved with no adjustment of material parameters, establishes the physical soundness of the proposed model. Copyright © 2009 John Wiley & Sons, Ltd.