Crystal Plasticity Simulations Research Articles

A virtual laboratory based on full-field crystal plasticity simulation to characterize the multiscale mechanical properties of AHSS

In this work, we proposed a virtual laboratory based on full-field crystal plasticity (CP) simulation to track plastic anisotropy and to calibrate yield functions for multiphase metals. The virtual laboratory, minimally, only requires easily accessible EBSD data for constructing the highly-resolved microstructural representative volume element and macroscopic flow stress data for identifying the micromechanical parameters of constituent phases. An inverse simulation method based on a global optimization scheme was developed to identify the CP parameters, and a nonlinear least-squares method was employed to calibrate yield functions. Mechanical tests of advanced high strength steel sheet under various loading conditions were conducted to validate the virtual laboratory. Three well-known yield functions, the quadratic Hill48 and non-quadratic Yld91 and Yld2004-18p yield functions, were selected as the validation benchmarks. All the studied functions, calibrated by numerous stress points of arbitrary loading conditions, successfully captured both the deformation and strength anisotropies. The full-field CP modeling correlated well the microscopic deformation mechanism and plastic heterogeneity with the macromechanical behavior of the sheet. The proposed virtual laboratory, which is readily extended with physically based CP models, could be a versatile tool to explore and predict the mechanical property and plastic anisotropy of advanced multiphase materials.

Combinatorial synchrotron diffraction-constitutive modelling-crystal plasticity simulation framework for direct metal laser sintered AlSi10Mg alloy

Combinatorial synchrotron and electron backscatter diffraction experiments coupled with constitutive modelling and fast Fourier transform crystal plasticity simulations have been employed to capture the mechanical behaviour of direct metal laser sintered AlSi10Mg alloy for different microstructures obtained by heat treatment. The microstructure of the as-printed sample with Al-Si eutectic cellular network transforms to coarse silicon particles on solutionising treatment at 510 °C for 1 h along with decrease in dislocation density that contributes to a decrease in strength and increase in ductility post solution heat treatment. Ageing of the solutionised specimen at 160 °C for 6 h leads to reprecipitation of silicon and improvement in strength with little change in ductility. The deformation behaviour at different length scales is captured by synchrotron diffraction and EBSD, while constitutive modelling using the Kocks-Mecking approach provides a mechanistic perspective on strain hardening of the alloy. Crystal plasticity simulations using fast Fourier transform solver are able to capture stress and strain hot spots in the as printed cellular and post solution treated non-cellular microstructures and provide information on the stress and strain evolution in the microstructure. A high throughput experimental and computational modelling protocol is established in the present investigation that can help rapidly screen different microstructures to establish processing-microstructure-mechanical property paradigm in direct metal laser sintered AlSi10Mg.

Mechanical response and texture evolution prediction of AZ31 magnesium alloy during CVCDE process using crystal plasticity finite element method

Continuous variable channel direct extrusion (CVCDE) is one of the effective methods for the fabrication of high-performance light alloy, which can realize the cooperative control of the shape and properties of extruded components with short process in a single pass. However, in consideration of the closed cavity in CVCDE, it is difficult to observe the microstructure in real time, and it is characterized by strong nonlinear and complex deformation path. Therefore, CPFEM (Crystal Plasticity Finite Element Method) was established based on VPSC-PTR to study texture evolution under complex conditions. The texture evolution law under different forming conditions was stated, and the experiments data were compared with the simulation results. The results were consistent with the simulation results. By means of crystal plasticity simulation, the material deformation and strain distribution at different positions in the CVCDE process were revealed. The simulation results based on this model show that during the 2-interim CVCDE process, the edge region of AZ31 magnesium alloy is subjected to obvious shear strain, which promotes the initiation of non-basal plane <c+a> slip system, and the basal axis orientation of grain is deflated, and the material texture is significantly different from that in the center deformation region.

Strain localization and crack initiation behavior of a PM Ni‐based superalloy: SEM‐DIC characterization and crystal plasticity simulation

AbstractThe strain localization and crack initiation behavior of a powder metallurgy (PM) nickel‐based superalloy FGH4098 under low cycle fatigue (LCF) loads at room temperature is investigated by combining scanning electron microscope (SEM)‐digital image correlation (DIC) characterization with crystal plasticity simulation. The elastic anisotropy near annealing twin boundaries contributes to strain localization and results in high propensity of LCF failure. The effect of local microstructure on the fatigue crack initiation at {111} slip bands and tortuous crack propagation is revealed. Meanwhile, local crystal plasticity finite element cyclic deformation simulation is carried out based on explicit microstructure reconstructed from electron backscatter diffraction (EBSD) characterization. Four metrics of accumulated shear strain, effective plastic strain, shear strain energy dissipation density, and Fatemi–Socie parameter are selected as fatigue indicator parameters to predict crack initiation site. Fatemi–Socie parameter is proved to be a promising metric for crack initiation prediction.

Microstructure of laser cladding nickel-based superalloy: characterization, finite element modeling, and fatigue analysis

Abstract After laser cladding, the mechanical response of nickel-based single crystal superalloy is more complex when the loading direction is perpendicular to the columnar grain growth direction. In order to understand the deformation at grain level, a representative volume element (RVE) model based on the randomness of columnar grain texture was established for DD6 single crystal alloy, and the finite element model simulation of crystal plasticity (CPFEM) was performed. The results show that the stress and strain responses of the cladding microstructure are related to the grain distribution. The orientation difference between columnar grains in the epitaxial growth microstructure leads to non-uniform deformation and local stress concentration. The greater the crystal orientation difference is, the more obvious the stress concentration phenomenon is. On this basis, the statistical standard deviation of strain component is chosen to represent the fatigue damage of material, and the relationship between the statistical standard deviation of strain component and the external load strain is studied, which has certain reference value for the fatigue damage research of micro-cladding.

Surface roughness influence in micromechanical fatigue lifetime prediction with crystal plasticity models for steel

Although surface roughness significantly influences fatigue, most micromechanical models using crystal plasticity only consider bulk behavior. In this work, a framework is described to include surface roughness in crystal plasticity simulations with emphasis on enabling extensive computational studies. This is achieved by the utilization of a statistical surface roughness generator and the prescription of appropriate boundary conditions. Fatigue lifetimes of a high-strength steel are evaluated for three surface conditions, with the models appropriately parameterized by surface measurements. It is shown that fatigue lifetime prediction considering surface roughness is qualitatively in agreement with experimental observations regarding their mean values and scatter.

Effects of temperature and microstructure on low cycle fatigue behaviour of a PM Ni-based superalloy: EBSD assessment and crystal plasticity simulation

The macro and mesoscale deformation and damage of the PM nickel-based superalloy FGH4098 under low cycle fatigue loading at elevated temperatures were investigated using both SEM/EBSD characterization and crystal plasticity finite element (CPFE) simulations. The results indicate that higher temperature leads to more severe macroscale damage i.e. larger areas of hysteresis loops and shorter fatigue life with transgranular failure mode at both 650 °C and 750 °C. The misorientation parameters derived from EBSD characterization show similar deformation at both temperatures, but more intense localized deformation in the crack initiation region at 750 °C. Based on the accumulated shear-strain energy dissipation density and Fatemi-Socie fatigue indicator parameter, the distribution and evolution of fatigue damage are shown to be strongly affected by local stress–strain state and temperatures, and more severe and homogeneous damage is found at 750 °C. The CPFE simulation results also show higher damage propensity, as indicated by the fatigue indicator parameters used here, in the vicinity of annealing twin boundaries with high difference in elastic modulus.

Influence of Non-Metallic Inclusions on Local Deformation and Damage Behavior of Modified 16MnCrS5 Steel

This work investigates a ferrite matrix with multiple non-metallic inclusions to evaluate their influence on the global and local deformation and damage behavior of modified 16MnCrS5 steel. For this purpose, appropriate specimens are prepared and polished. The EBSD technique is used to record local phase and orientation data, then analyze and identify the size and type of inclusions present in the material. The EBSD data are then used to run full phase crystal plasticity simulations using DAMASK-calibrated material model parameters. The qualitative and quantitative analysis of these full phase simulations provides a detailed insight into how the distribution of non-metallic inclusions within the ferrite matrix affects the local stress, strain, and damage behavior. In situ tensile tests are carried out on specially prepared miniature dog-bone-shaped notched specimens in ZEISS Gemini 450 scanning electron microscope with a Kammrath and Weiss tensile test stage. By adopting an optimized scheme, tensile tests are carried out, and local images around one large and several small MnS inclusions are taken at incremental strain values. These images are then processed using VEDDAC, a digital image correlation-based microstrain measurement tool. The damage initiation around several inclusions is recorded during the in situ tensile tests, and damage initiation, propagation, and strain localization are analyzed. The experimental results validate the simulation outcomes, providing deeper insight into the experimentally observed trends.

Texture transition of shear bands in initially Goss–oriented grains in Fe–3 wt%Si alloy

Texture transition of shear bands in Goss–oriented grains of normalized Fe–3 %Si sheets with different diffused angles along φ2 axis during cold rolling was investigated by quasi in–situ electron back–scatter diffraction (EBSD) analysis. The diffused angle along φ2 axis of {111} 〈112〉 deformed matrix from initial Goss grains with φ2 axis diffusion below 10° decreases after cold rolling. Shear bands formed in {111} 〈112〉 deformed matrix have a similar diffusion along φ2 axis to the deformed matrix, and the diffused angle along φ1 axis is insignificant. The φ2–diffused angle evolution of shear band and deformed matrix in initially diffused Goss grains during cold rolling were analyzed using a crystal plasticity simulation.

Crystal Plasticity Simulation of the Microstructural Effect in Powder Metallurgy Superalloys under Dwell Fatigue Loading

The microstructural effect, including γ’ precipitate morphology and twin grains, of dwell fatigue behavior in a powder metallurgy nickel-based superalloy, was studied using crystal plasticity modeling. Strain rate and dwell sensitivities of 923 K were quantitatively investigated. The strain accumulations, under normal and dwell fatigue loading, showed γ’ precipitate size-dependence. Strong load shedding can be observed between parent and twin grains, which was attributed to local plastic heterogeneity. Local stress and strain evolution are both faster than the macroscopic values, which threatens the safety of engine components.

Synchronous involvement of topology and microstructure to design additively manufactured lattice structures

This article presents a methodical approach to optimize microstructure (e.g., the crystallographic texture) and topology (e.g., unit cell and struts) concurrently to improve the mechanical properties of additively manufactured metallic lattice structures (AMLS), i.e., yield strength and plastic flow stress. Full-field elasto-viscoplastic Fast Fourier Transform (EVP-FFT) crystal plasticity (CP) simulations are employed to determine the optimal microstructure. The CP model parameters were calibrated to measured macroscopic stress–strain response and microstructural data for polycrystalline samples of additively manufactured (AM) Inconel 718 with solution treated and aged (STA) microstructure. Since the crystallographic orientation of the constituent single-crystal grains with respect to the loading direction has a significant impact on the mechanical behavior of the material, stress projection factor analysis was used to determine four candidate textures to explore in for a given unit cell topology. Full-field crystal plasticity simulations were used to determine macroscale yield surface parameters for each of the considered textures, thereby enabling macroscale lattice unit cell simulations that account for the underlying microstructure. The calibrated microstructure-dependent yield surfaces are used to investigate the effect of different microstructures on the mechanical response of different LS topologies with the same relative density. The results show that in a texture with <111> crystallographic direction, parallel to the loading direction, the tensile and compressive yield strength are 20% and 58% larger, respectively compared to the AM STA IN718 texture. Furthermore, when this texture is used in conjunction with the Rhoctan topology, the results demonstrate 50% improvement in both the yield strength and modulus of elasticity relative to previously optimized AMLS designs that did not directly account for microstructure. This simultaneous consideration of microstructure and topology during optimization, thus, significantly enhances the structural integrity of the AMLS.

Understanding slip activity and void initiation in metals using machine learning-based microscopy analysis

The use of machine learning techniques to supplement traditional data analysis in mechanics and materials research can improve the understanding of microstructure-property relationships. Identification of key microstructural features or correlation between deformation mechanisms and material response can be discerned that might otherwise have been overlooked. Motivated by the possibilities of gaining additional insight into the process of void nucleation in polycrystalline metals, several machine learning techniques are applied to the analysis of mesoscopic deformation mechanisms as determined by experimental characterization and modeling. Results from crystal plasticity modeling, experimental microstructural analysis, and theoretical models of slip transmission are combined to test a hypothesis regarding fatigue-induced void nucleation. Unsupervised spectral clustering was used with results from crystal plasticity simulations to characterize slip system activity for different crystallographic orientations. The slip system activity as determined by the clustering analysis was then fed into a K-nearest neighbor classifier to quantify the probability of slip transmission across different grain boundaries of interest and analyze grains containing fatigue-induced voids. An unique and unanticipated result from the unsupervised clustering analysis shows that including a group of partially-active slip systems was more appropriate than using the binary classification of active/non-active. Predicted slip activity behavior in a face-centered cubic material was shown to differ significantly from that of a body-centered cubic material due to non-Schmid effects. The outcome of the overall analysis was that grains containing fatigue-induced voids were more likely to be surrounded by grains with orientations that inhibited slip transmission according the Lee-Robertson-Birnbaum (LRB) criteria. Finally, it is demonstrated that smaller datasets using limited simulation results were equally effective at predicting a similar outcome when additional physical descriptors for the slip system activity are used.

A crystal plasticity model that accounts for grain size effects and slip system interactions on the deformation of austenitic stainless steels

To ensure a more representative simulation of meso‑scale and macro-scale deformation, it is important the underlying constitutive relations are advanced to more effectively incorporate the micro-mechanisms such as those operative near the grain boundaries. Critical features necessary for accurate predictions include the influence of grain size, morphology, and misorientation on the local deformation. In this study, a length scale dependence is incorporated into classical crystal plasticity simulations. The implementation is based on the influence of dislocation slip pile-up at grain boundaries based on the Hall-Petch theory in materials. This was achieved by applying a purpose-built algorithm to extract the slip distance in adjacent grains along each slip direction. This extracted data was used to adjust the critical resolved shear stress within the grain. The adjusted slip law was then implemented in constitutive models to predict the yield stress and hardening evolution of material for different grain sizes. The interaction of the slip systems between grains was also considered, which resulted in the adjustment in the extent of slip transfer permitted between grains based on misorientation. The proposed approach can be applied in both finite element and spectral methods for solving the continuum differential equations. The accuracy of the proposed model was investigated by considering the meso‑scale predictions using two-dimensional simulations, in addition to macro-scale predictions using three-dimensional models. Furthermore, the validity of the method was experimentally supported by tracking the development of intragranular residual elastic stresses, measured via high-resolution electron backscatter diffraction. The discussed results highlight a new potential of enhancing the way in which complex grain boundary interactions contribute to local deformation in crystal plasticity simulations.

Crystal Plasticity Simulation of Yield Loci Evolution of SUS304 Foil.

The deformation process of metal foils is usually under a complex stress status, and the size effect has an obvious influence on the microforming process. To study the effect of grain orientation and grain size distribution on the yield loci evolution of SUS304 stainless steel foils, three representative volume element (RVE) models were built based on the open source tools NEPER and MTEX. In addition, the yield loci with different grain sizes are obtained by simulation with Duisseldorf Advanced Material Simulation Kit (DAMASK) under different proportional loading conditions. The initial yield loci show a remarkable difference in shape and size, mainly caused by the distinct texture characteristics. By comparing the crystal plasticity simulation with the experimental results, the model with normal grain size distribution and initial texture based on Electron Back-scattered Diffraction (EBSD) data can more accurately describe the influence of the size effect on the shape and size of yield loci, which is the result of the interaction of grain size distribution and texture. However, the enhancement of grain deformation coordination will weaken the impact of the size effect on yield loci shape if the grain size distribution is more uniform.

Anisotropic yield surfaces of additively manufactured metals simulated with crystal plasticity

The mechanical anisotropy created by additive manufacturing (AM) is not yet fully understood and can depend on many factors, such as powder material, manufacturing technology and printing parameters. In this work, the anisotropic mechanical properties of as-built, laser powder bed fusion (LPBF) austenitic stainless steel 316L and titanium alloy Ti-6Al-4V are investigated through crystal plasticity simulations. Periodic representative volume elements (RVEs) are used that are specific to each material. The RVE for austenitic stainless steel consists of FCC crystals with a crystallographic texture measured by X-ray diffraction. The α′ martensite microstructure of Ti-6Al-4V is captured with a multi-scale RVE, including internal lamellar structures, using HCP crystals and a synthetically generated texture. For both materials, the crystal plasticity parameters are calibrated against tensile tests carried out on dog-bone specimens printed in different orientations. The RVEs, calibrated to experiments, are applied in virtual material testing and subjected to multiple load cases to generate the Hill-48 and Yld2004-18p yield surfaces of the materials.

Developing parametrically upscaled constitutive and crack nucleation models for the [formula omitted] Ti64 alloy

This paper develops Parametrically Upscaled Constitutive Model (PUCM) and the Parametrically Upscaled Crack Nucleation Model (PUCNM) for a commercially used α/β-phase Ti64 alloy. These thermodynamically consistent macroscopic constitutive models bridge spatial scales through the explicit representation of Representative Aggregated Microstructural Parameters (RAMPs). The PUCNM is an indicator of the probability of crack nucleation in the local underlying microstructure. A symbolic regression-based machine learning method operates on data-sets generated by image-based micromechanical crystal plasticity simulations to derive constitutive coefficients as functions of the RAMPs. The PUCM/PUCNMs development (both calibration and validation) uses data from microstructural characterization as well as mechanical tests, including constant strain-rate, creep, and strain-controlled dwell tests for the Ti64 alloy. Parametric study is conducted with the experimentally-validated PUCM and PUCNM to investigate the effect of RAMPs on dwell fatigue crack nucleation life. Finally, the combined PUCM/PUCNM tool is used for examining the impact of microstructure on fatigue crack nucleation in an engine blade model under simulated operating conditions. The results from these examples clearly exhibit the promise of the PUCM/PUCNM models in predicting fatigue crack nucleation in the microstructure of real structural applications, as well as demonstrating the microstructural influence.

Multiscale analysis of crystalline defect formation in rapid solidification of pure aluminium and aluminium-copper alloys.

Rapid solidification leads to unique microstructural features, where a less studied topic is the formation of various crystalline defects, including high dislocation densities, as well as gradients and splitting of the crystalline orientation. As these defects critically affect the material’s mechanical properties and performance features, it is important to understand the defect formation mechanisms, and how they depend on the solidification conditions and alloying. To illuminate the formation mechanisms of the rapid solidification induced crystalline defects, we conduct a multiscale modelling analysis consisting of bond-order potential-based molecular dynamics (MD), phase field crystal-based amplitude expansion simulations, and sequentially coupled phase field–crystal plasticity simulations. The resulting dislocation densities are quantified and compared to past experiments. The atomistic approaches (MD, PFC) can be used to calibrate continuum level crystal plasticity models, and the framework adds mechanistic insights arising from the multiscale analysis.This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Simulation of Crystal Plasticity in Irradiated Metals: A Case Study on Zircaloy-4

Simulation of Crystal Plasticity in Irradiated Metals: A Case Study on Zircaloy-4

Nano-Structuring of a High Entropy Alloy by Severe Plastic Deformation: Experiments and Crystal Plasticity Simulations

Nano-Structuring of a High Entropy Alloy by Severe Plastic Deformation: Experiments and Crystal Plasticity Simulations

双晶の体積分率に依存する流れ応力を考慮した双晶誘起塑性モデルに基づく結晶塑性解析

Recently, TWIP steels have been focused on because of their excellent ductility and strength. One approach to formulating the behavior of materials containing deformation twins in terms of crystal plasticity is a model in which each material point in the material is represented by a mixture law based on the volume fractions of the twin and matrix phase. Such kind of approach cannot express the macroscopic mechanical property more precisely because the influence of twin boundaries is neglected. In this study, the mechanical property under the existence of twin boundaries is researched by using crystal plasticity simulation. The analysis intended for a material with a laminar structure made of twin phase and matrix phase reproduces the accumulation of dislocations at twin boundaries. By investigating the influence of twin boundaries on several models with different volume fractions of each phase, the relationship between the volume fractions of the twin phase and the influence of twin boundaries was determined.