Crystal Plasticity Simulations Research Articles

Anisotropic tensile behaviour of additively manufactured Ti-6Al-4V simulated with crystal plasticity

The anisotropic behaviour of laser powder bed fusion (LPBF) Ti-6Al-4V under uniaxial tension is investigated through crystal plasticity simulations. A periodic multi-scale representative volume element (RVE) is calibrated against quasi-static tensile tests carried out on dog-bone specimens, printed in different orientations. This fitting procedure results in an anisotropic crystallographic texture and a minimum set of crystal plasticity constitutive parameters which are able to reproduce the experimental behaviour. The synthetic RVE consists of primary grains with a realistic aspect ratio and an internal lamellar structure, that approximates the α′ martensite microstructure observed in micrographs of as-built Ti-6Al-4V. The Young’s modulus, yield strength, and hardening behaviour observed experimentally, could be precisely captured using a very limited number of model parameters. Thereby, this work contributes to a deeper understanding of the interplay between micro-structure and macroscopic behaviour, and with a new set of crystal plasticity parameters specific for α′ dominated LPBF Ti-6Al-4V.

The impact of heterogeneous microstructural features on crystal plasticity modeling of plastic anisotropy

Crystal plasticity finite element models typically assume each grain starts with a spatially uniform dislocation distribution, meaning each grain is initialized with a single lattice orientation and all grains share the same slip resistance. This study assessed that assumption by comparing crystal plasticity simulations of tensile tests against experiments on an extruded aluminum 7079 alloy. The simulations utilized computational microstructures with ‘pancaked’ grains and a significant degree of crystallographic texture, consistent with experimental measurements. In one case, the computational microstructures were assigned a single slip resistance and a single lattice orientation for each grain prior to the tension tests. In another case, the extrusion process prior to the tension tests was simulated to cause nonuniform slip resistances, nonuniform crystal orientations within each grain, and nonuniform slip resistances at each material point. Both approaches produced reasonably accurate predictions of the measured yield stress and lateral strain ratio anisotropy, but the predictions considering the initial nonuniformity exhibited less prediction error. Other factors, such as latent vs self hardening of slip systems and fine vs coarse grains, did not have as large an impact. These results suggest that dislocation heterogeneity should be experimentally characterized and fed into future crystal plasticity simulations.

Simulation of dynamic crystal plasticity with a Lagrangian discontinuous Galerkin hydrodynamic method

We present a new Lagrangian modal discontinuous Galerkin (DG) hydrodynamic method that supports a dynamic dislocation based crystal plasticity model for simulating the mechanical behavior of crystallographic materials, both single crystal and polycrystalline, under dynamic conditions. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated by Taylor series polynomials of varying degree. These polynomials describe macro-scale hydrodynamic behavior while their evolution is determined by evaluating the dynamic crystal plasticity model at material points within the element. The dynamic crystal plasticity model is sensitive to the time increment size, with too large of time increments leading to instability in the model. To mitigate this, the temporal evolution of the dynamic crystal plasticity model is achieved with the combination of a sub-incrementing scheme with Heun’s third-order time integration scheme, which is also used to temporally evolve the governing equations. The implementation of the dynamic crystal plasticity model within the DG framework is tested using a 2D approximation of the Taylor impact test with a single crystal material, using quadratic elements that have faces that can bend. In addition to the standard continuous material modeling, we propose a new simulation method that would represent the heterogeneous behavior of polycrystalline microstructures within an element by varying the position and material properties of the material points within the element. This method is demonstrated using random orientation distributions on materials points that are arranged in both structured and random configurations.

A Crystal Plasticity Simulation on Strain-Induced Martensitic Transformation in Crystalline TRIP Steel by Coupling with Cellular Automata

In transformation-induced plasticity (TRIP) steel, the strain-induced martensitic transformation (SIMT) has a close relationship with the shear band formation. At a small length scale such as that of a crystal, the explicit analysis of the shear band structure with the formed microstructure is quite important for an adequate understanding of the SIMT. Here, a study on the microstructures formed by SIMT, related to shear band formation in both single and polycrystal TRIP steels, is presented. The constitutive equation for single crystal TRIP steel considering the transformation strain on each variant system is derived based on a rate-dependent crystal plasticity theory. To express the martensitic transformation, the cellular automata approach, including a transformation criterion acting as a local rule, is introduced. Numerical simulation is conducted with patterning processes of the martensitic phase at an infinite medium under the plane strain tension. It is found that the similar distributions of the plastic strain and the martensitic phase are dependent on the initial crystal orientation and appear as the shear band structures. In addition, the sizes of embryo and cell strongly influence the shear band formation and the martensitic volume fraction of crystal TRIP steel.

Simulation Study of Hatch Spacing and Layer Thickness Effects on Microstructure in Laser Powder Bed Fusion Additive Manufacturing using a Texture-Aware Solidification Potts Model

Microstructure control in the laser powder bed fusion additive manufacturing processes is a topic of major interest because of the submillimeter length scale at which the manufacturing process occurs. The ability to control the process at the melt pool scale allows for microstructure control that few other manufacturing techniques can match. The majority of work on microstructure control has focused on altering laser parameters to control solidification conditions (Ref (R.R. Dehoff, M.M. Kirka, W.J. Sames, H. Bilheux, A.S. Tremsin, L.E. Lowe, and S.S. Babu, Site Specific Control of Crystallographic Grain Orientation through Electron Beam Additive Manufacturing, Mater. Sci. Technol., 2014, 31(8), p 931–938. R. Shi, S.A. Khairallah, T.T. Roehling, T.W. Heo, J.T. McKeown, and M.J. Matthews, Microstructural Control in Metal Laser Powder Bed Fusion Additive Manufacturing Using Laser Beam Shaping Strategy, Acta Mater., 2020, 184, p 284–305, https://doi.org/10.1016/j.actamat.2019.11.053.)). Other machine parameters, besides the laser parameters, have also been shown to affect the microstructure of AM parts (Ref (N. Nadammal, S. Cabeza, T. Mishurova, T. Thiede, A. Kromm, C. Seyfert, L. Farahbod, C. Haberland, J.A. Schneider, P.D. Portella, and G. Bruno, Effect of Hatch Length on the Development of Microstructure, Texture and Residual Stresses in Selective Laser Melted Superalloy Inconel 718, Mater. Des., 2017, 134, p 139–150, https://doi.org/10.1016/j.matdes.2017.08.049. F. Geiger, K. Kunze, and T. Etter, Tailoring the Texture of IN738LC Processed by Selective Laser Melting (SLM) by Specific Scanning Strategies, Mater. Sci. Eng. A, 2016, 661, p 240–246, https://doi.org/10.1016/j.msea.2016.03.036.)). We propose an investigation of the effects of hatch spacing and layer thickness on microstructure development in laser powder bed fusion additive manufacturing. A Monte Carlo Potts model with textured solidification capabilities is used to study the effects of these parameters on a unidirectional scan strategy. The simulation results reveal substantial changes in grain morphology as well as texture. Additionally, EVP-FFT crystal plasticity simulations were performed to evaluate the effect of the microstructural shifts on mechanical response. The conclusions from this work elucidate the effects of these parameters on part microstructure as predicted by the texture-aware solidification Potts model and inform understanding of how bulk texture is predicted by the simulation approach.

Accessing pore microstructure–property relationships for additively manufactured materials

AbstractUnderstanding structure–property (SP) relationships is essential for accelerating materials innovation. Still being in the state of ongoing research and development, this is especially true for additive manufacturing (AM) in which process‐induced imperfections like pores and microstructural variations significantly influence the material's properties. That is why, the present work aims at proposing an approach for accessing pore SP relationships for AM materials. For this purpose, crystal plasticity (CP) simulations on reconstructed domains based on experimental measurements are employed to allow for a microstructure‐sensitive investigation. For the considered Ti–6Al–4V specimen manufactured by laser powder bed fusion, the microstructure and pore characteristics are obtained by utilizing light microscopy and X‐ray computed tomography at the microscale. Employing suitable statistical analysis and reconstruction, statistical volume elements with reconstructed pore distributions are created. Using them, microscale CP simulations are performed to obtain fatigue indicating parameters. Employing a further statistical analysis, fatigue ranking parameters are derived for a comparison of different microstructures. Additionally, a comparison with the empirical Murakami's square root area concept is made. Results from first numerical studies underline the potential of the approach for understanding and improving AM materials.

Large-deformation crystal plasticity simulation of microstructure and microtexture evolution through adaptive remeshing

The capability of high-resolution modeling of crystals subjected to large plastic strain is essential in predicting many important phenomena occurring in polycrystalline materials, such as microstructure, deformation localization and in-grain texture evolution. However, due to the heterogeneity of the plastic deformation in polycrystals, the simulation mesh gets distorted during the deformation. This mesh distortion deteriorates the accuracy of the results, and after reaching high local strain levels, it is no longer possible to continue the simulation. In this work, two different adaptive remeshing approaches are introduced for simulating large deformation of 3D polycrystals with high resolution under periodic boundary conditions. In the first approach, a new geometry with a new mesh is created, and then the simulation is restarted as a new simulation in which the initial state is set based on the last deformation state that had been reached. In the second approach, the mesh is smoothened by removing the distortion part of the deformation, and then the simulation is continued after finding a new equilibrium state for the smoothed mesh and geometry. The first method is highly efficient for conducting high-resolution large-deformation simulations. On the other hand, the second method’s primary advantage is that it can overcome periodicity issues related to shear loading, and it can be used in conjunction with complex loading conditions. The merits of the methodologies are demonstrated using full-field simulations performed using a dislocation-density-based crystal plasticity model for Interstitial free (IF-) steel. Particular emphasis is put on studying the effect of resolution and adaptive meshing. The algorithms presented have been implemented into the free and open-source software package, DAMASK (Düsseldorf Advanced Material Simulation Kit).

Experimental and simulated investigations of low cycle fatigue behavior in a nickel-based superalloy with different volume fractions of δ phase

The fatigue crack initiation life and damage mechanisms of three heat-treated nickel-based alloy with different volume fractions of δ phase have been investigated based on experiment and crystal plasticity simulation. With the help of fatigue indicator parameters (FIPs), the predicted fatigue lives are agreed well with experimental results, where energy dissipation based FIP shows more accurate life prediction than plastic slip based FIP does. Maximum fatigue damage sites shift from grain boundary to δ phase boundary by increasing δ phase and applied strain level. Furthermore, the existence of δ phase leads to the increase of plastic slip accumulation and decrease of localized stress level.

The role of plastic strains on variant selection in ausformed bainitic microstructures studied by finite elements and crystal plasticity simulations

Abstract The mechanisms driving variant selection phenomena in ausformed bainitic microstructures are not fully controlled yet. Previous results are not congruent among them, as they cannot be explained by the same rule. In this work, we aimed to understand the mechanisms governing variant selection in a medium carbon-high silicon steel subjected to ausforming treatments. To do so, the microstructural characterization in different regions of barreled samples has been combined with the simulation of the stress and strain state at the macro and micro level, by finite elements simulations and crystal plasticity simulations, respectively. The main conclusion is that the variant selection shown in these microstructures can be explained by understanding the distribution of the plastic strains at the macro and micro level. The selection of crystallographic variants is more pronounced in the regions which have been more deformed. Also, the deformation distributes along deformation microbands, where the most promoted variants seem to grow, in good agreement with previous results in ausformed lath martensite.

A new ANN based crystal plasticity model for FCC materials and its application to non-monotonic strain paths

Machine learning (ML) methods are commonly used for pattern recognition in almost any field one could imagine. ML techniques can also offer a substantial improvement in computational time when compared to conventional numerical methods. In this research, a machine learning- and crystal plasticity-based framework is presented to predict stress–strain behaviour and texture evolution for a wide variety of materials within the face-centred cubic family (FCC). Firstly, the process of the framework design is described in detail. The proposed framework was designed to be built of ensemble of artificial neural networks (ANN) and a crystal-plasticity based algorithm. Next, the dataset constituent of crystal plasticity simulations was collected. The dataset consisted of examples of monotonic deformation cases, was prepared for training using mathematical transformations, and finally used to train ANNs used in the framework. Then, the ML framework was demonstrated to predict full stress–strain and texture evolution of different FCC single crystals under uniaxial tension, compression, simple shear, equibiaxial tension, tension–compression–tension, compression–tension–compression, and, finally, for some arbitrary non-monotonic loading cases. The proposed framework predicts the stress–strain response and texture evolution with a high degree of accuracy. The results demonstrated in this research show that the proposed machine learning- and crystal plasticity-based framework exhibits a tremendous computational advantage over conventional crystal plasticity model. Finally, one of the most important contributions of this work is to show the framework’s feasibility. The work demonstrates that machine learning methods can help predict complex strain paths without having to train machine learning models on the infinite set of possible non-monotonic loading scenarios.

Temperature-dependent fatigue response of a Fe44Mn36Co10Cr10 high entropy alloy: A coupled in-situ electron microscopy study and crystal plasticity simulation

The fatigue behavior of Fe44Mn36Co10Cr10 high entropy alloy (HEA) at room temperature and 300 °C was studied by in-situ SEM observation, electron back-scattered diffraction (EBSD) and crystal plasticity simulation. The microstructure evolution and deformation process was observed by in-situ SEM fatigue experiment. The misorientation and geometrically necessary dislocation (GND) density was analyzed by EBSD. A crystal plasticity finite element (CPFE) modeling method based on the real grain morphology was proposed. The cumulative plastic strain, dominant slip system and dominant slip plane distributions were obtained. CPFE simulation shows multiple dominant slip systems being activated, which agrees with the multiple slip phenomena observed by in-situ SEM.

Mechanical behavior predictions of additively manufactured microstructures using functional Gaussian process surrogates

Relational linkages connecting process, structure, and properties are some of the most sought after goals in additive manufacturing (AM). This is desired especially because the microstructural grain morphologies of AM components can be vastly different than their conventionally manufactured counterparts. Furthermore, data collection at the microscale is costly. Consequently, this work describes and demonstrates a methodology to link microstructure morphology to mechanical properties using functional Gaussian process surrogate models in a directed graphical network capable of achieving near real-time property predictions with single digit error magnitudes when predicting full stress–strain histories of a given microstructure. This methodology is presented and demonstrated using computationally generated microstructures and results from crystal plasticity simulations on those microstructures. The surrogate model uses grain-level microstructural descriptors rather than whole microstructure descriptors so that properties of new, arbitrary microstructures can be predicted. The developed network has the potential to scale to predict mechanical properties of grain structures that would be infeasible to simulate using finite element methods.

Micromechanism involved in ultrafine grained ferrite/martensite dual phase steels strengthened by nanoscale Cu-rich precipitates

The strengthening effects of grain refinement and nano-sized coherent precipitation are effective strengthening mechanisms in the development of low-cost advanced high-strength steels. In the present work, low carbon dual phase steels with ultrafine grains and nanoscale copper rich precipitates were produced by a combination of warm deformation and isothermal aging processes. Then, the microstructure and plastic deformation behavior were explored using the EBSD technique and crystal plasticity simulations, and the precipitation mechanism of nanoscale Cu-rich particles was investigated by HRTEM, atom-probe tomography in combination with first-principles calculations. The results indicate that the formation and compositional evolution of the Cu-rich particles are associated with the mixing enthalpy of alloying elements and the attractive interaction between the solute atoms. Besides the precipitation hardening effect, grain refinement improve both strength and ductility of the steels significantly, while more severe deformation will result in the heterogeneous distribution of martensite, then intensify the plastic heterogeneities and early hardening of ferrite grains during tension deformation, thus give rise to a decrease in ductility.

Discrepancy Between Crystal Plasticity Simulations and Far-Field High-Energy X-ray Diffraction Microscopy Measurements

Discrepancy Between Crystal Plasticity Simulations and Far-Field High-Energy X-ray Diffraction Microscopy Measurements

A crystal plasticity finite element model embedding strain-rate sensitivities inherent to deformation mechanisms: Application to alloy AZ31

The fundamental power-law relationship representing the flow rule in crystal visco-plasticity ensures uniqueness in the selection of slip systems accommodating imposed plastic strain-rates. The power-law relationship also introduces an artificially high strain-rate sensitivity in crystal plasticity simulations, unless a high value of the power-law exponent is used. However, the use of high values for the exponent is limited by numerical tractability. This paper presents a numerical method implemented in a crystal plasticity finite element (CPFE) model for embedding any value of the power-law exponent reflecting the true material strain-rate sensitivity. Importantly, the method does not increase computation time involved in the simulations. The enhanced CPFE model is used to interpret and predict a complex strain-rate sensitive response and microstructural evolution of AZ31 Mg alloy. Measured values of strain-rate sensitivity for slip and twinning modes are used in the simulations. Calculations show that the model successfully captures the phenomena pertaining to the effect of changing applied strain-rate on the mechanical response including flow stress and evolution of texture and twinning for a broad range of strain-rates ranging from 10−3 s−1 to 103 s−1 and loading orientations in tension and compression. It is shown that such predictions are a consequence of not only relative amounts of slip and twinning activities driven by a set of accurately characterized hardening law parameters but also values of the strain-rate sensitivities inherent to individual deformation mechanisms. Besides, the model validates the measured strain-rate dependency of deformation mechanisms while accurately reproducing the mechanical data. Hence, the model can be used to verify and further refine or infer measured strain-rate sensitivity per deformation mechanism by reproducing experimental data.

On crystallographic aspects of heterogeneous plastic flow during ductile tearing: 3D measurements and crystal plasticity simulations for AA7075-T651

Crystallographic aspects of heterogeneous plastic flow during ductile tearing are assessed experimentally by combining in situ synchrotron laminography imaging of notched flat samples with a full-field measurement technique and numerical simulations with the crystal plasticity finite element method (CP-FEM). Advantage is taken of the plane strain condition in the region ahead of the notch root (i.e., in the plane normal to the crack propagation direction) to perform two-dimensional image correlation in the material bulk. Intermetallic particles provide image contrast that is registered during the correlation analyses. They reveal the early onset of slant strained bands along which the final slant crack propagated. Two-dimensional plane strain CP-FEM simulations using the grain shape and crystallographic orientations of the studied material show the same trends as those observed experimentally, namely, the appearance of early slant strained bands that cross tens of grains and that remain stable over the loading history. The ratio of the strains within and outside the bands is also similar to that observed experimentally.

Using Macrotexture Map to Visualize Texture Heterogeneity in Polycrystalline Aggregate

Abstract A new tool, macrotexture map, was developed to represent and visualize texture heterogeneity in polycrystalline aggregate. This is a critical tool for microstructure representation, useful in risk analysis, performance simulation, and hotspot identification. In contrast to the orientation imaging microscope (OIM) map where each color represents a crystal orientation, each color in this macrotexture map represents a texture. Different colors represent different textures, and similar textures shall have similar colors. The macrotexture map provides a unique function to quantitatively evaluate texture heterogeneity of large components, leading to a first-hand understanding of property heterogeneity and anisotropy. For an experienced user, these maps serve the same purpose in identifying high-risk locations in the investigated component as medical imaging maps do for diagnosis purpose. This method will also serve as a starting point in mesoscale simulation with meshing sensitivity based on the texture heterogeneity. It will provide a bridge between texture characterization and behavior simulation of components with texture heterogeneity. The macrotexture map will offer a linkage between crystal plasticity simulation in small length scale and finite element/difference simulation in large length scale.

Measurement and crystal plasticity simulation of plastic deformation behavior of 5052 aluminum alloy sheet subjected to various loading modes

Measurement and crystal plasticity simulation of plastic deformation behavior of 5052 aluminum alloy sheet subjected to various loading modes

A method for determining r-value of aluminum sheets with the Portevin-Le Chatelier effect

Abstract Lankford coefficient (r-value) is an important parameter for metal sheet. For sheet metals with obvious Portevin-Le Chatelier (PLC) effect, the r-values are difficult to measure owing to the occurrence of inhomogeneous deformation. In this paper, the PLC bands of AA3104-H19 sheet were investigated by uniaxial tensile test with digital image correlation (DIC) technology. The result showed that inclination of the PLC band keeps invariable with respect to loading direction with straining. The constancies of PLC band angle and r-value are result from the limit of texture evolution during tensile test. Additionally, an analytic relationship between the PLC band inclined angle and r-value was derived based on the observation of zero-expansion along the PLC band direction. Accordingly, a novel r-value determining method based on the PLC band was proposed. The accuracy of the new method was evaluated by comparing with the extensometer method, DIC method and crystal plasticity simulation.

Crystal Plasticity Simulation of Magnesium and Its Alloys: A Review of Recent Advances

Slip and extension twinning are the dominant deformation mechanisms in Magnesium (Mg) and its alloys. Crystal plasticity is a powerful tool to study these deformation mechanisms. Different schemes have incorporated crystal plasticity models to capture different properties, which vary from the simple homogenization Taylor model to the full-scale crystal plasticity finite element model. In the current study, a review of works available in the literature that addresses different properties of Mg and its alloys using crystal plasticity modes is presented. In addition to slip and twinning, detwinning is another deformation mechanism that is activated in Mg and its alloys. The different models that capture detwinning will also be addressed here. Finally, the recent experimental frameworks, such as in-situ neutron diffraction, 3D high energy synchrotron X-ray techniques, and digital image correlation under scanning electron microscopy (SEM-DIC), which are incorporated along crystal plasticity models to investigate the properties of Mg and its alloys, are addressed. Future research directions towards improving the deformation response of Mg and its alloys are identified, which can lead to increased deployment of the lightest structural metal in engineering applications.