Crystal Plasticity Simulations Research Articles

Deformation inhomogeneity evolution and crack formation mechanism analysis in ultra-high strength steel by crystal plasticity simulations

Understanding deformation inhomogeneity and the formation mechanism of crack are crucial for fully exploiting the potential of ultra-high strength steel (UHSS). In this paper, the deformation inhomogeneity and microscopic crack formation mechanism of UHSS were investigated by combining high-fidelity crystal plasticity models with microscopic experiments. The simulation results at grain level shows that the deformation strain of the UHSS is non-uniform, characterized by distinct deformation bands. A broad deformation band extends between multiple grains at an angle of approximately 40 degrees to the rolling direction, while a sharp deformation band is observed within a single grain. These features are intricately linked to the initial orientation (Taylor factor) distribution of the grains and their rotational behavior. The locations with greater Taylor factor deviations become potential crack initiation sites. In addition, as the deformation proceeds, the α- fiber reinforcement exacerbates the deformation inhomogeneity of the UHSS.

Dynamic strength differential and Bauschinger effects in an extruded AZ80 magnesium alloy

Quasi-static and high-rate tension and compression properties of an extruded AZ80 Mg alloy rod were investigated at loading rates of 0.001 and 500 s−1. Acquired stress – strain results show that tension and compression plastic deformations of AZ80 rod are asymmetric, and such strength differential effect is dependent of strain rate and loading orientation. Strength differential effect is weakened at 500 s−1 when the sample was loaded along the extrusion direction. Crystal plasticity simulations on the basis of the visco-plastic self-consistent method were performed. Numerical results indicate that the rate and orientation dependency of strength differential effect in AZ80 alloy is related to {101‾2} extension twinning. High-rate tests for pretension, unloading and reverse compression were realized to investigate the dynamic Bauschinger effect. Experimental results show that Bauschinger effect of AZ80 alloy is anisotropic and sensitive to the strain rate. A Bauschinger effect parameter considering strength differential effect was proposed, and it was found that the Bauchinger effect in the extrusion direction is reduced significantly at 500 s−1.

Mechanical anisotropy induced by the competition between twinning and basal slip of AZ31 magnesium alloy under biaxial tension

The mechanical behavior of a hot-rolled Mg AZ31 plate was studied under biaxial tensions along two perpendicular loading axes of x and y in the ND-TD plane, with the x-axis aligned at a 45° counterclockwise angle from the TD (ND and TD refer to the normal direction and transverse direction). A complex strain partitioning in two loading axes is observed with the variation of stress ratio σxx:σyy. For σxx:σyy= 1:1 and 1:1.5, the strains along the x- and y-axes, εxx and εyy, are both positive. However, With the stress ratio of σxx:σyy= 1:3, εyy remains positive, while εxx becomes negative. Interestingly, for σxx:σyy = 1:2, εxx changes from negative during the early stage of loading to positive upon failure. Crystal plasticity simulations and theoretical calculations reveal that the observed strain transition. The reasons for the strain transition with stress ratio is related to the competition between {101¯2} twinning and basal slip. For {101¯2} twinning, the accommodated strains by most of the twins are εxx>0 and εyy>0 for all the stress ratios considered. For basal slip, most of the basal variants accommodate a positive y-axis strain, while for loading cases with low stress ratios, most of the basal variants result in a negative x-axis strain. As the stress ratio decreases, basal slip becomes more active, while the activity of {101¯2} twinning gradually decreases, leading to the observed strain transition. For σxx:σyy = 1:2, the transition from negative to positive is related to the increasing activity of {101¯2} twinning with strain. Theoretical calculations reveal that the competition of basal slip and {101¯2} twinning under biaxial tension is determined by the variation of their Schmid factors with σxx:σyy.

Crystal Plasticity Finite Element Modeling of the Influences of Ultrafine-Grained Austenite on the Mechanical Response of a Medium-Mn Steel

Medium manganese (medium-Mn) steel, one of the third-generation advanced high-strength steels (AHSS), delivers impressive mechanical properties such as high yield strength, ultimate tensile strength, and uniform elongation. One notable feature of medium-Mn steels is the presence of ultrafine-grained (UFG) austenite, achieved through phase transformation from the parent martensite phase during intercritical annealing. While, in general, UFG is considered a strengthening mechanism, the impact of UFG austenites in medium-Mn steel has not been fully studied. In this manuscript, we advance our previous work on crystal plasticity simulation based on the Taylor model to consider fully resolved high-fidelity microstructures and systematically study the influence of the UFG austenites. The original microstructure with UFG is reconstructed from a set of serial electron backscatter diffraction (EBSD) scans, where the exact grain morphology, orientation, and phase composition are preserved. This microstructure was further analyzed to identify the UFG austenites and recover them to their parent martensite before the intercritical annealing. These two high-fidelity microstructures are used for a comparative study using dislocation density-based crystal plasticity finite modeling to understand the impact of UFG austenites on both the local and overall mechanical responses.

Machine learning-based fatigue life prediction of lamellar titanium alloys: A microstructural perspective

Fatigue life prediction based on the traditional empirical formulation in large fatigue regimes is limited and prone to over-fitting. In this regard, we propose an integrated approach for fatigue life prediction of lamellar titanium alloys incorporating crystal plasticity simulations and a variety of machine learning methods from a microstructural perspective. Firstly, various defect shapes and distinct lamellar distributions are employed to characterize fatigue performance under different microstructural features. By utilizing fatigue indicator parameters (FIPs) to get an expanded dataset, this work employs algorithms including artificial neural networks (ANN), random forests regression (RFR), support vector regression (SVR), and particularly convolutional neural networks (CNN) to predict fatigue life. The results indicate that CNN outperforms the previously mentioned algorithms in prediction accuracy, due to its ability to directly extract microstructural features from images. Our proposed approach provides a microstructural perspective for fatigue life prediction of lamellar titanium alloys, broadening the way for life assessment of materials with diverse microstructures.

Machine learning-based sampling of virtual experiments within the full stress state

This paper presents a new machine learning-based approach to investigate anisotropic yield surfaces of sheet metals by means of virtual experiments. The new sampling approach is based on the machine learning technique known as active learning, which has been adapted to efficiently sample virtual experiments with respect to the full stress state in order to identify parameters of anisotropic yield functions. The approach was employed to sample virtual experiments based on the crystal plasticity finite element method (CPFEM) for a DX56D deep drawing steel and compared with two state-of-the-art sampling methods taken from the literature. The resulting points on the initial yield surface for all three sampling methods were used to identify parameters of the anisotropic yield functions Hill48, Yld91, Yld2004–18p and Yld2004–27p. These parameters were then applied to a cylindrical cup drawing simulation to analyse the effect of the three sampling methods on a typical sheet forming simulation. The results show that the new machine learning-based sampling approach has a higher sampling efficiency than the two state-of-the-art sampling methods. Consequently, fewer computationally expensive crystal plasticity simulations are required. By comparing different variants of the Hill48, Yld91, Yld2004–18p and Yld2004–27p yield surfaces, it was also found that identifying parameters of anisotropic yield functions based on virtual experiments sampled within the full stress state can lead to a degraded representation of the in-plane anisotropy. With respect to DX56D deep drawing steel, this degradation was observed for the Yld2004–18p yield function. The negative implications following from this degraded in-plane representation were further demonstrated by the results of the cylindrical cup drawing process. As a consequence, the representation of the in-plane anisotropy must be carefully reviewed when taking the full stress state into account. In this context, Yld2004–27p was identified as being sufficiently flexible to simultaneously represent the plastic anisotropy of DX56D with respect to the in-plane and out-of-plane behaviour with high accuracy.

A Full-Field Crystal Plasticity Study on the Bauschinger Effect Caused by Non-Shearable Particles and Voids in Aluminium Single Crystals

In the present work, the goal is to use two-scale simulations to be incorporated into the full-field open software DAMASK crystal plasticity framework, in relation to the Bauschinger effect caused by the composite effect of the presence of second-phase particles with surrounding deformation zones. The idea is to achieve this by including a back stress of the critical resolved shear stress in a single-phase simulation, as an alternative to explicitly resolving the second-phase particles in the system. The back stress model is calibrated to the volume-averaged behaviour of detailed crystal plasticity simulations with the presence of hard, non-shearable spherical particles or voids. A simplified particle-scale model with a periodic box containing only one of the spherical particles in the crystal is considered. Applying periodic boundary conditions corresponds to a uniform regular distribution of particles or voids in the crystal. This serves as an idealised approximation of a particle distribution with the given mean size and particle volume fraction. The Bauschinger effect is investigated by simulating tensile–compression tests with 5% and 10% volume fractions of particles and with 1%, 2%, and 5% pre-strain. It is observed that an increasing volume fraction increases the Bauschinger effect, both for the cases with particles and with voids. However, increasing the pre-strain only increases the Bauschinger effect for the case with particles and not for the case with voids. The model with back stress of the critical resolved shear stress, but without the detailed particle simulation, can be fitted to provide reasonably close results for the volume-averaged response of the detailed simulations.

Texture formation under control of S phase characteristic and tensile property of hot-rolling 2A12 aluminum alloy improved by Brass texture

In this paper, 2A12-T3 aluminum alloy is first solution-treated and then experienced an artificial aging for different time to induce different S phase characteristics. By using this method, the texture formation behavior solely contributed from S phase characteristic could be determined during hot rolling. It is found that the increase of S phase in size and density has a positive effect on Brass texture formation, which is attributive to the increased Dislocation Shear Slipping (DSS) near S/Al interface. The relative slip tendency factor (Msx) is proposed to quantitatively evaluate the impact of S phase characteristic on Brass formation. It is revealed that Brass volume fraction (VBrass) has a better positively linear relationship with Msx than texture intensity. Then, the effect of Brass texture on tensile property is analyzed in details. Crystal plasticity simulation shows that Brass texture can improve the yield stress and tensile strength and simultaneously keep the elongation. Comparatively, the rolling sheet aged for 3 h obtains an excellent combination of strength and ductility.

Mechanism of high temperature mechanical properties enhancement of Ni-based superalloys repaired by laser directed energy deposition: Microstructure analysis and crystal plasticity simulation

The high-temperature tensile and fatigue performance play a crucial role in the applications of repaired Ni-based superalloys by Laser directed energy deposition (LDED). This work investigates the effect of microstructure on the high temperature (650 °C) mechanical behaviors of GH4169 superalloys repaired by LDED with the microstructure characterizations and crystal plasticity modelling. Results indicate that the solution and aging heat treatment (STA) is necessary to homogenize the distributions of precipitations. Microstructure characterizations and crystal plasticity modelling imply that the plasticity deformations occur mainly in columnar dendrites of fusion area and twin grains of substrate, which enhance the tensile strength and elongation rate of repaired area and demonstrates comparable characteristics with the casting alloy. At the same time, the existence of the Laves phase and carbide cannot eliminate the dynamic strain aging phenomenon of repaired material. Similarly, under high stress levels (850– 950 MPa), the fatigue performance of repaired material is primarily influenced by the plastic deformation and exhibits similarity to that of the substrate; however, under low stress levels (650– 750 MPa), it is primarily influenced by the presence of defects, resulting in an obviously longer fatigue life for the substrate.

Investigation of Grain Misorientation on Creep Void Nucleation in P91 Heat-Resistant Steel by Experimentation and Crystal Plasticity Simulation

Investigation of Grain Misorientation on Creep Void Nucleation in P91 Heat-Resistant Steel by Experimentation and Crystal Plasticity Simulation

Accurate simulation of texture evolution and mechanical response of cubic and hexagonal structural alloys using self-consistent polycrystal plastic method

Simulating the evolution of microstructures and the mechanical response of alloys with cubic and hcp structures is crucial for the industrial manufacturing of key alloy components. In this work, a modified Voce (ME-Voce) model is proposed, based on the extended Voce hardening model, to depict the variations of hardening rate with cumulative shear strain. Also, an orientation-dependent weight that describes the neighboring grain-induced ‘drag’ effect is evaluated. These improvements are numerically implemented in a standard viscoplastic self-consistent (VPSC) model. The ME-Voce parameters are determined through multi-parameter optimization using Matlab software. The influences of grain shape and neighboring grains on the hot deformation behavior of alloys are investigated. The proposed ME-Voce model is validated through hot compression experiments of alloys with cubic and hcp structures. The results show the VPSC embedded in the ME-Voce can reasonably predict the mechanical response under different deformation conditions. This enhances the predictive capability of the VPSC model and provides more options for crystal plasticity simulation of alloys with different crystal structures.

Nonlinear optimization for compact representation of orientation distributions based on generalized spherical harmonics

An orientation distribution is a necessary input in any crystal plasticity simulation. The computational time involved in crystal plasticity simulations scales linearly with the number of crystal orientations in the input distributions. Reducing the number of crystal orientations in representing the input orientation distributions quantitatively is a critical and necessary requirement for performing computationally efficient crystal plasticity simulations of deformation processes. A procedure for the compaction of orientation distribution functions (ODFs) relying on a spectral representation using series of generalized spherical harmonics (GSH) basis functions was recently developed. Linear fitting of the spectral representation of an ODF containing a compact set of weighted orientations towards a full-size ODF containing many crystal orientations was in the core of the procedure. This paper advances the compaction procedure by replacing the linear with a nonlinear optimization in Matlab for which a suitably defined error, gradient, and Hessian matrix are derived to allow for more efficient, accurate, and greater compactions. The utility of the new procedure is to allow for not only fitting the weights of a compacted set of orientations but to allow for optimizing weighted orientations or a combination of optimizing weights and orientations. The new compaction procedure has been successfully applied to compactions of large ODFs of cubic, hexagonal, and orthorhombic polycrystalline metals. In doing so, the evolution of texture, twinning, and stress-strain are predicted at large plastic strains with compact ODFs to agree with the corresponding full size ODFs using crystal plasticity models. In closing, guidance for effective texture compaction trading off the accuracy and computational gains are provided.

Crystal plasticity simulations reveal cooperative plasticity mechanisms leading to enhanced strength and toughness in gradient nanostructured metals

Heterogeneous deformation is thought to provide the strengthening in gradient nanostructured metals, but the underlying plasticity mechanisms and optimal gradient structures for attaining improved mechanical performance remain elusive. Through crystal plasticity simulations of three-dimensional heterogeneous nanostructures, we reveal the heterogeneous-deformation-induced plasticity mechanisms which evoke increased flow strength and strain hardening. We have developed a synthetic microstructure generation algorithm which replicates both the microstructural features and external geometry of experimentally characterized samples—providing a direct comparison between the mechanical response recorded in simulations and experiments. Aligning well with experiments, the simulations show synergistically enhanced mechanical properties. High strain hardening rates directly correlate to large stress gradients that emerge due to heterogeneous deformation. Samples with smooth grain size gradients exhibit the most extreme stress gradients and correspondingly higher strain hardening rates. Large increases in dislocation density—especially within larger grains—and high intra- and inter-granular crystal rotation are plasticity mechanisms common to samples which exhibit high mechanical performance. Although the nanostructural gradients have pronounced influence over the mechanical performance, samples with the same grain size and dislocation density gradients exhibit varied mechanical properties. We show that the distribution of initial grain orientations and the microstructural constraints placed on larger grains also influence the active plasticity mechanisms providing improved mechanical properties.

Deformation mechanisms in the α phase of the Ti-6Al-2Sn-4Zr-2Mo titanium alloy: In situ experiments and simulations

Titanium alloys are widely employed in aerospace applications due to an outstanding combination of properties. The variety of loading conditions and microstructures encountered in industrial components is urging the development of microstructure sensitive modeling capabilities. In particular, reliable predictions require a good knowledge of operating deformation mechanisms. The present study aims at providing a thorough characterization of deformation mechanisms in the near-α Ti-6Al-2Sn-4Zr-2Mo alloy using experiments and simulations. The sequential activation of deformation mechanisms in the α phase was monitored in situ during a tensile test carried out in a scanning electron microscope using a combination of slip traces analysis and electron back-scattered diffraction. Basal slip is activated first, and prismatic slip activity, which proceeds at a higher macroscopic stress level, is needed for a significant creep/relaxation to occur. While little evidence of 〈a〉-type pyramidal slip was found, 〈c + a〉 pyramidal slip involved first-order pyramidal planes and operates at stress levels near or above the 0.2% proof stress. Atomic force microscopy characterization of the features of the different slip modes revealed that 〈a〉 slip is coarser and wavier than 〈c + a〉 slip. Twinning, which is usually neglected in such alloys within this strain regime, was observed to be slip stimulated at a plastic strain as low as 0.5%. Crystal plasticity parameters leading to an accurate simulation of the activation sequence of deformation mechanisms were then determined. For this purpose, critical resolved shear stress values were derived for the different slip and twinning modes using specific approaches and subsequently validated using crystal plasticity simulations based on fast-Fourier transforms.

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.

An effective anisotropic visco-plastic model dedicated to high contrast ductile laminated microstructures: Application to lath martensite substructure

In particular types of layer- or lamellar-like microstructures such as pearlite and lath martensite, plastic slip occurs favorably in directions parallel to inter-lamellar boundaries. This may be due to the interplay between morphology and crystallographic orientation or, more generally, due to constraints imposed on the plastic slip due to the lamellar microstructural geometry. This paper proposes a micromechanics based, computationally efficient, scale independent model for a particular type of lamellar microstructures containing softer lamellae which are sufficiently thin to be considered as discrete slip planes embedded in a matrix representing the harder lamellae. Accordingly, the model is constructed as an isotropic visco-plastic model which is enriched with an additional orientation-dependent planar plastic deformation mechanism. This additional mode is activated when the applied load, projected on the direction of the soft films, induces a significant amount of shear stress. Otherwise, the plastic deformation is governed solely by the isotropic part of the model. The response of the proposed model is assessed via a comparison to an infinite periodic two-phase laminate. It is shown that the yielding of the model follows the same behavior as the reference model. The proposed model is highly anisotropic, and the degree of anisotropy depends on the contrast between the slip resistance of the planar mode versus that of the isotropic part. The framework is applied to the substructure of lath martensite with thin films of inter-lath retained austenite, and exploited in a mesoscale simulation of a dual-phase steel microstructure. The results are compared with those of a standard isotropic model and a full crystal plasticity model which does not have the additional planar plastic mechanism. Predictions made with the proposed model show distinct differences compared with the crystal plasticity results, while keeping the computational cost comparable to that of the isotropic model — and significantly lower than that of the crystal plasticity simulation.

Crystal plasticity approach for predicting mechanical responses in wire-arc directed energy deposition of NbZr1 refractory alloy

The refractory alloy, such as Niobium-1 wt% Zirconium (NbZr1) alloy, is a promising candidate for diverse applications in extreme environments. This study investigates an integrated experimental and computational methodology that can predict the mechanical properties of wire-arc directed energy deposited (DED) refractory NbZr1 alloy. The effect of large columnar grains with strong texture induced by the wire-DED process has been successfully incorporated into the representative volume element (RVE). Performing crystal plasticity (CP) simulation on RVE of NbZr1, deformation behavior and stress-strain relationship are predicted to explore the process-structure-property (PSP) relationship. The RVE has been created in synthetic microstructure generation software utilizing the grain statistics derived from electron backscatter diffraction (EBSD) analysis, capturing essential microstructural features. A phenomenological constitutive model and appropriate boundary conditions have been applied and solved, using the CP fast Fourier transform method. The CP model has been calibrated and validated utilizing the tensile test data along the build direction and deposition direction, respectively. The error in predicting yield strength and ultimate tensile strength is 0.91% and 0.67%, respectively, for the calibration simulation, whereas these values are 2.51% and 1.81% for the validation simulation. The results suggest strong agreement between the simulation and experimental observation. Even though global deformation behavior remains consistent across multiple RVEs with the same microstructural features, local stress-strain values vary, indicating structural anisotropy, which is also consistent with the digital image correlation (DIC) result. It is proven that this proposed CP method can effectively predict the mechanical responses of components with large grains and strong textures resulting from the wire-arc DED.

Advances in Fatigue Performance of Metal Materials with Additive Manufacturing Based on Crystal Plasticity: A Comprehensive Review.

Using metal additive manufacturing processes can make up for traditional forging technologies when forming complex-shaped parts. At the same time, metal additive manufacturing has a fast forming speed and excellent manufacturing flexibility, so it is widely used in the aerospace industry and other fields. The fatigue strength of metal additive manufacturing is related to the microstructure of the epitaxially grown columnar grains and crystallographic texture. The crystal plasticity finite element method is widely used in the numerical simulation of the microstructure and macro-mechanical response of materials, which provides a strengthening and toughening treatment and can reveal the inner rules of material deformation. This paper briefly introduces common metal additive manufacturing processes. In terms of additive manufacturing fatigue, crystal plasticity simulations are summarized and discussed with regard to several important influencing factors, such as the microstructure, defects, surface quality, and residual stress.

Micromechanical response of dual-hardening martensitic bearing steel before and after rolling contact fatigue

Material decay in bearing steels under rolling contact fatigue (RCF) leads to fatigue initiation and failure. This study examines the local structure-property relationship in decayed material through in-situ compression testing of micropillars prepared from a dual-hardening martensitic bearing steel (Hybrid 60) before and after RCF testing. The results demonstrate a pronounced enhancement in local yield strength for decayed regions (2200–2340 MPa) as compared to non-decayed regions (1755–1780 MPa). The higher initial stress for dislocations glide in the decayed regions and their discontinuous yield behavior are attributed to the presence of ferrite microbands. Crystal plasticity simulations corroborated these findings, showingincreased critical resolved shear stress (CRSS) and reduced strain hardening in decayed samples.

Predicting the in-plane mechanical anisotropy of 7085 aluminum alloys through crystal plasticity simulations and machine learning

The crystallographic texture of rolled 7xxx series aluminum alloys may lead to mechanical properties anisotropy which undermines the formability and performance of the material. This article aims to explore the quantitative relationship between texture and the in-plane anisotropy of 7085 aluminum alloy. A comprehensive computational method combining crystal plasticity simulation with machine learning and experiment was used to establish an analytical model and train a machine learning model to predict the anisotropy of 7085 aluminum alloys. We first performed a full-field crystal plasticity spectral simulations using fast Fourier transformation (CPFFT) to predict the anisotropy of 7085 aluminum alloy at different annealing times. Then, based on the CPFFT simulation data, the quantitative relationship between texture and the in-plane anisotropy of the r-value was established by using the multiple linear regression and gradient boosting regressor model. The results indicate that CPFFT simulation can effectively capture the influence of texture changes on anisotropy, and the model established through the gradient boosting regressor model is in good agreement with experimental results, providing effective guidance for improving the performance of 7085 aluminum alloy sheets.