Crystal Plasticity Finite Element Research Articles

An integrated computation framework for predicting mechanical performance of single-phase alloys manufactured using laser powder bed fusion: A case study of CoCrFeMnNi high-entropy alloy

Establishing a process-structure-property (PSP) relationship is crucial for understanding and optimizing the mechanical properties of components via laser powder bed fusion (L-PBF) additive manufacturing (AM). However, the parameters pertinent to the PSP relationship are encapsulated in a “black box” with a high dimension, resulting in relying on trial-and-error approaches to elucidate hidden associations becoming impracticable, while the acquisition of microscopic data proves financially burdensome. Thus this paper presents an integrated computation framework based on machine learning (ML) for predicting the tensile yield strengths and post-yield hardening rates of single-phase alloys fabricated through L-PBF, for efficient process optimization purposes. Research herein focuses on single-phase alloys to be built via L-PBF, taking CoCrFeMnNi high-entropy alloy as a study case, and provide an efficient integrated computation solution. The methodology proposed in this paper generates as-built microstructures associated with the varying L-PBF process parameters via cellular automata (CA). Subsequently, the mechanical responses of these microstructures are estimated by employing crystal plasticity finite element (CPFE) simulations. In addition, the approach raised in the paper leverages particle-level microstructure descriptors instead of average feature descriptors for the entire representative volume element (RVE) structure in an ML framework to predict the characteristics of the newly randomly growing grains. This research demonstrate the practicality and instructiveness of the methodology for modeling realistic grains. Then, trained ML model exhibits promising accuracy for the prediction of mechanical properties. This work showcases an integrated computation framework combining advanced materials science and ML techniques for enhancing understanding of the L-PBF process and offering valuable insights into process optimization for L-PBF-built diverse materials.

Study on Microstructure and Tensile Behavior of X70 Dual-Phase Steel in Different Directions: Experiments and Crystal Plasticity Finite Element Method

Study on Microstructure and Tensile Behavior of X70 Dual-Phase Steel in Different Directions: Experiments and Crystal Plasticity Finite Element Method

Advanced Computational Analysis of Cobalt-Based Superalloys through Crystal Plasticity.

This study introduces an advanced computational method aimed at accelerating continuum-scale processes using crystal plasticity approaches to predict mechanical responses in cobalt-based superalloys. The framework integrates two levels, namely, sub-grain and homogenized, at the meso-scale through crystal plasticity finite element (CPFE) platforms. The model is applicable across a temperature range from room temperature up to 900 °C, accommodating various dislocation mechanisms in the microstructure. The sub-grain level explicitly incorporates precipitates and employs a dislocation density-based constitutive model that is size-dependent. In contrast, the homogenized level utilizes an activation energy-based constitutive model, implicitly representing the γ' phase for efficiency in computations. This level considers the effects of composition and morphology on mechanical properties, demonstrating the potential for cobalt-based superalloys to rival nickel-based superalloys. The study aims to investigate the impacts of elements including tungsten, tantalum, titanium, and chromium through the homogenized constitutive model. The model accounts for the locking mechanism to address the cross-slip of screw dislocations at lower temperatures as well as the glide and climb mechanism to simulate diffusions at higher temperatures. The model's validity is established across diverse compositions and morphologies, as well as various temperatures, through comparison with experimental data. This advanced computational framework not only enables accurate predictions of mechanical responses in cobalt-based superalloys across a wide temperature range, but also provides valuable insights into the design and optimization of these materials for high-temperature applications.

The role of microstructure in the thermal fatigue of solder joints

Thermal fatigue is a common failure mode in electronic solder joints, yet the role of microstructure is incompletely understood. Here, we quantify the evolution of microstructure and damage in Sn-3Ag-0.5Cu joints throughout a ball grid array (BGA) package using EBSD mapping of localised subgrains, recrystallisation and heavily coarsened Ag3Sn. We then interpret the results with a multi-scale modelling approach that links from a continuum model at the package/board scale through to a crystal plasticity finite element model at the microstructure scale. We measure and explain the dependence of damage evolution on (i) the β-Sn crystal orientation(s) in single and multigrain joints, and (ii) the coefficient of thermal expansion (CTE) mismatch between tin grains in cyclic twinned multigrain joints. We further explore the relative importance of the solder microstructure versus the joint location in the array. The results provide a basis for designing optimum solder joint microstructures for thermal fatigue resistance.

Digital twin-based probabilistic prediction of microcrack initiation and propagation in the weld zone of orthotropic steel deck

Orthotropic steel deck (OSD) has become the primary bridge deck structure for steel bridges, but it is vulnerable to fatigue cracks in the weld zone of OSD under traffic loading. This study proposes a digital twin (DT)-based framework to give the probabilistic prediction of microcrack initiation and propagation in the weld zone of OSD. The DT-based framework couples crystal plasticity finite element model (CPFEM) simulations with fatigue tests through Dynamic Bayesian Network (DBN). The fatigue tests of the specimen (physical entity) cut from the weld zone of OSD and sliced to the centimeter scale are carried out using the standard dynamic test system together with optical microscope. The CPFEM simulations are used to develop a multiscale virtual entity to map the physical entity. The role of the DBN is to integrate the uncertainties into a hierarchical network. After completing the updating of uncertainties in the virtual entity via DBN, the microcrack propagation is predicted probabilistically by the DBN inference, and the microcrack initiation is predicted probabilistically by the inverse DBN inference. The results demonstrate the feasibility and accuracy of the DT-based framework for a full prediction of microcrack initiation and propagation in the weld zone of OSD.

Interpretation of Frequency Effect for High-Strength Steels with Three Different Strength Levels via Crystal Plasticity Finite Element Method.

The fatigue behavior of a high-strength bearing steel tempered under three different temperatures was investigated with ultrasonic frequency and conventional frequency loading. Three kinds of specimens with various yield strengths exhibited obvious higher fatigue strengths under ultrasonic frequency loading. Then, a 2D crystal plasticity finite element method was adopted to simulate the local stress distribution under different applied loads and loading frequencies. Simulations showed that the maximum residual local stress was much smaller under ultrasonic frequency loading in contrast to that under conventional frequency at the same applied load. It was also revealed that the maximum local stress increases with the applied load under both loading frequencies. The accumulated plastic strain was adopted as a fatigue indicator parameter to characterize the frequency effect, which was several orders smaller than that obtained under conventional loading frequencies when the applied load was fixed. The increment of accumulated plastic strain and the load stress amplitude exhibited a linear relationship in the double logarithmic coordinate system, and an improved fatigue life prediction model was established.

On the interaction of grain-scale and hydride-scale stresses in hydrogen enriched zirconium alloy nuclear cladding via combined discrete dislocation plasticity and crystal plasticity finite element modelling

The interaction of Zircaloy fuel cladding components with coolant water in a nuclear reactor leads to embrittlement and potentially delayed hydride cracking (DHC). We explore rate controlling mechanisms for the detrimental DHC process via Discrete Dislocation Plasticity (DDP) modelling of an intragranular δ-hydride, informed by Crystal Plasticity Finite Element (CPFE) analysis of a notched Zircaloy-4 (Zr-4) polycrystal. It is believed that nano-hydride plasticity occurs under a background (polycrystalline) stress state that depends on the grain-scale stress re-distribution associated with plastic deformation at a notch. We find that depending on grain size the background stresses can enhance plasticity during hydride growth (cooling), enhancing the residual hydrostatic stresses on hydride dissolution (heating), which encourages local hydrogen accumulation and re-precipitation. This ‘memory effect’ can be enhanced further by obstacles preventing dislocations from gliding backwards and annihilating during dissolution, highlighting that the discrete nature of plasticity can play important role in the DHC process. Our analysis provides a stepping-stone to modelling interacting nano-hydrides and irradiation effects for supporting the design of better nuclear materials.

Crystal plasticity modeling of grain boundary softening and fatigue in U75V pearlite steel under low strain conditions: A study of cyclic rolling contact fatigue

Grain boundaries (GBs) exhibit fatigue-induced softening under low strain conditions, making them the weakest and most vulnerable regions within the material. This phenomenon significantly influences plastic deformation, plastic strengthening, and the initiation and propagation of microcracks, leading to material fatigue failure. This investigation presents a comprehensive model for the rolling contact fatigue (RCF) damage mechanism of U75V railway steel. Leveraging data from Electron Backscatter Diffraction (EBSD) and employing the Crystal Plasticity Finite Element Method (CPFEM), intragranular mechanical responses are elucidated. A modified bilinear Traction Separation Law (TSL) Cohesive Zone Model (CZM) is developed to capture the impact of GBs fatigue. Integrating this CZM with CPFEM, mechanical properties, scalar stiffness degradation (SDEG), fatigue damage factors, and crack evolution patterns are analyzed to explore the effects of grain morphology, orientation, GB angle, and area on GB fatigue damage and crack initiation. Results indicate a significant increase in GBs damage with increasing GBs angle or decreasing GBs area, highlighting the potential for reducing RCF damage through deliberate grain morphology design. Additionally, GBs are found to impede crack propagation, suggesting that grain refinement can mitigate crack propagation rates. This study enhances our understanding of intergranular fracture, mechanical responses, and microstructure evolution in U75V rail steel under cyclic rolling contact loading, offering novel methodologies for investigating metallic materials' deformation behavior concerning GB fatigue.

Crystal plasticity modeling and analysis for the transition from intergranular to transgranular failure in nickel-based alloy Inconel 740H at elevated temperature

The precipitation-strengthened Nickel-based alloy Inconel® 740H® (IN740H) exhibits increased ductility at higher applied strain rates during quasi-static tensile tests at an elevated temperature of 760 °C. The examination of fracture surfaces in this context reveals a noteworthy transition of underlying fracture mechanisms from transgranular to intergranular fracture as the applied strain rate decreases from 1×10−3/s to 0.83×10−4/s. To thoroughly understand the mechanical response of IN740H under these conditions, this study develops a crystal plasticity finite element (CPFE) model. This model incorporates various deformation mechanisms including dislocation slips, climb, and grain boundary sliding, which are relevant to the test conditions. The model is calibrated using data from both tensile tests at different strain rates and creep tests across a broad stress range at 760 °C, enabling the accurate determination of model parameters for each mechanism. Simulation results well captured the experimental observations of different failure modes. At higher strain rates, the model shows a dominance of dislocation slip leading to heterogeneous plastic deformation and formation of transgranular shear bands causing the failure, while at lower strain rates, an increased activity of grain boundary sliding causes grain boundaries crack leading to intergranular failure.

The mechanistic origins of heterogeneous void growth during ductile failure

In 1969, Rice and Tracey proposed that the rate of void growth during ductile failure is a strong function of the hydrostatic stress state. Numerous in-situ x-ray computed tomography (XCT) studies demonstrated that the average rate of void growth is well-predicted by modified versions of the Rice-Tracey equation. However, recent in-situ XCT studies of void growth demonstrated that individual voids grow in highly heterogeneous manners in a way that is not predicted by Rice-Tracey or similar models. Model-based studies using crystal plasticity finite element (CP-FE) suggest that local effects of grain orientation play a strong role during void growth, but we lack experimental data to test this hypothesis. The present study leverages recent advances in laboratory-based diffraction contrast tomography (Lab-DCT) and in-situ XCT to systematically examine the effects of grain orientation on void growth experimentally in an Al-2219 alloy. CP-FE modeling was used to assess the local stress states associated with voids and their influence on void growth rates. These data indicate that void growth is not simply controlled by the local hydrostatic stress or stress triaxiality. Additionally, no clear relationship between void growth rates and grain orientation were observed. Instead, void growth rates were highly stochastic in ways that could not be directly linked to the local stress or strain states. The combination of experimental and modeling data suggests that our current assumptions regarding the mechanisms of void growth are flawed and that additional factors, which may include the local dislocation density, affect the rate of void growth.

Formation of plate-like high-strain region in polycrystalline α-titanium and its relation to high-strain bands on surface

The investigation of heterogeneous deformation mechanisms in materials is important for understanding fracture mechanisms. In this study, uniaxial tensile deformation of polycrystalline α-titanium was numerically reproduced by three-dimensional crystal plasticity finite element analysis, and the following were revealed for the first time: (i) plate-like high-strain regions form inside the specimen, which are typically observed as band-like high-strain regions (high-strain bands: HSBs) on the surface of and cross-sections in α-titanium specimen, and (ii) the formation of HSBs also affects the work-hardening rate near the yielding point. The reasons for the difference in the formation mechanism of HSBs between the surface and inside were also discussed. The results obtained showed that active slip systems that contribute to the formation of HSBs may differ between the surface and inside of specimen, and strain in HSBs on the specimen surface is higher than that inside. The distributions of HSBs at the surface of and inside the specimen are determined by distributions of resolved shear stress. These results are important for understanding the differences in the fracture mechanisms between the surface and interior of materials.

In situ measurement of three-dimensional intergranular stress localizations and grain yielding under elastoplastic axial-torsional loading

The three-dimensional grain-averaged response of solid bar samples under non-proportional (NP) elastoplastic axial-torsional loading was investigated using in situ high energy diffraction microscopy (HEDM) and companion crystal plasticity finite element (CPFE) modeling. Important stress metrics including applied shear (σθZ) and axial (σZZ) stress tensor components, stress and stress deviator tensor invariants (I1, J2, and J3), von Mises equivalent stress (), maximum resolved shear stress (mRSS), stress triaxiality (η), and lode angle parameter () values were tracked for ∼ 300 grains under two different loading conditions: (1) Torsion-dominated loading (low NP) and (2) Tension-torsion loading (high NP) in equiatomic NiCoCr, a representative multicomponent face-centered cubic (FCC) superalloy. Overall, significant stress localizations existed within both samples as evidenced by the radial dependence of grain-resolved σθZ, , and J2; by comparison, I1, J3, η, and metrics did not show discernable trends within the volume. These stress localizations reveal a complex interplay between axial and shear stress components (e.g., stress coupling) resulting in grain yielding near the sample surface largely driven by shear stress, whereas internal grain yielding was largely accommodated by axial stress. Grain-resolved stress localization trends were described well by the CPFE model, although some discrepancies in magnitude occurred, particularly for volumetric stress metrics (I1 and η) due to initial type II residual stress distributions. The superposition of initial residual stress states onto CPFE grain-resolved data significantly improved model accuracy for η. This suggests that residual stresses more strongly influence the simulation of volumetric rather than deviatoric (yield) stress metrics.

Modeling of crack tip fields and fatigue crack growth in fcc crystals

Predicting the mechanical behavior of polycrystalline materials containing a crack under both monotonic and cyclic loading conditions is crucial for accurately assessing the integrity of engineering materials. This study focuses on the deformation characteristics of face-centered cubic (fcc) grains within the crack tip field and their significant role in governing the driving force for fatigue crack growth during cyclic loading. We employ a cyclic crystal plasticity finite element (CPFE) model to analyze the mechanical response of austenitic 316L stainless steel polycrystals by accounting for nonlinear kinematic hardening effects. Through CPFE simulations, we investigate the deformation fields in 316L grains at the crack tip, considering two different grain orientations under plane strain conditions. Our CPFE results under monotonic loading align consistently with previous theoretical and experimental findings, particularly in comparing CPFE-simulated and experimentally observed plastic sectors consisting of different slip traces on the specimen surface near the crack tip. Based on a critical plastic work criterion for crack advancement, cyclic CPFE simulations are used to determine the fatigue crack growth rate as a function of stress intensity factor range for the two crack tip grain orientations in stainless steel. The simulated Paris law exponent matches experimental values. Furthermore, we compare cyclic CPFE results with those from cyclic J2 plasticity finite element simulations. This study demonstrates a cyclic CPFE approach for determining crack tip fields, accounting for crystallographic effects on plastic deformation of crack tip grains. Our approach can be applied to effectively evaluate fatigue crack growth rates in fcc polycrystalline metals.

Transverse difference of activation slip/twin system in wide AZ31 alloy plate during its rolling

The macroscopic finite element method (FEM) and the crystal plasticity finite element method (CPFEM) were combined to study the transverse difference of activation slip/twin system in wide AZ31 magnesium alloy plates during rolling. The macro-deformation and micro-texture evolution along the transverse direction of the plate during rolling were analyzed experimentally. The microscopic CPFEM was developed on the basis of the thermo-force coupling behavior during plate rolling obtained from macroscopic FEM. The CPFEM parameters were fitted by uniaxial compression experiments. This combination of two scale simulations accurately predicted the texture evolution during the rolling process and had been experimentally validated. Further examination of the deformation mechanism reveals that the transverse spread action of the plate is stronger at the edge region compared to center, and this transverse spread action has a more significant impact on the activation of the {10 1‾ 2} tension twin. The comparison of the activation and extension of pyramidal <a> slip in granular and plate-like grains reveals that plate-like grains are more prone to generate slip bands through the grain, leading to cracking of the grain along the slip activation band and further formation of sub-grains.

Experimental and modeling study on irradiation effect of A508-Ⅲ steel

Irradiation can induce microscopic defects in reactor pressure vessel (RPV) steel, resulting in macroscopic hardening and embrittlement. This paper proposes a micro-meso-macroscale calculation framework for the mechanical properties of irradiated RPV steel based on experimental and numerical investigations. The mean size and number density of Fe-ion-irradiation-induced dislocation loops were measured using transmission electron microscopy (TEM). These parameters were described by a power-function relationship with the irradiation dose at various temperatures and were used as input parameters for the crystal plasticity finite element model (CPFEM). Nano-indentation tests of A508-Ⅲ steel under different irradiation conditions were successfully simulated. In addition, microstructural characterization and molecular dynamics (MD) simulations revealed the phenomenon of dislocation pinning and the sweeping of irradiation defects during dislocation migration, implying that the dislocation-loop interactions could be responsible for the formation of dislocation channels and curved dislocation lines. Furthermore, increase in yield stress and the ductile-brittle transition temperature (DBTT) at various temperatures were investigated. Results indicated that yield stress, DBTT, and the degree of irradiation hardening and embrittlement increased with the irradiation dose and decreased with irradiation temperature. Finally, the adjusted reference temperature (ART), a significant design parameter for nuclear reactors, was calculated and evaluated using the multiscale framework. The framework can serve as a reference text for extending the life of nuclear reactors.

Crystal plasticity finite element method investigation of normal tensile deformation anisotropy in rolled pure titanium sheet

Industrial pure titanium with hexagonal close-packed (HCP) crystal structure has a high degree of anisotropy at room temperature. On the mesoscopic scale, this is due to the rolling texture presented by its crystal orientation. Tensile tests were performed on smooth specimens with five angles in the first quadrant at room temperature, and the central deformation region and fracture region were characterized using EBSD and SEM, respectively. The modified Salem anisotropic hardening model is incorporated into the crystal plasticity finite element method (CPFEM) framework in the form of incremental hardening to describe the initial strength and hardening increment evolution of each deformation system of pure titanium. Both slip dislocation and twinning mechanisms are considered in the CPFEM simulation. Three models with different meshing strategies are used to simulate the tensile conditions to capture the evolution of macro and micro variables of pure titanium sheet. The results show that there are anisotropy in stress-strain, system activity, cumulative shear strain, crystal orientation, twin volume fraction, stress triaxiality and Lode parameter. The purpose of this paper is to explore the anisotropy of macro-meso variables in different directions before damage occurs, so as to provide reference for the subsequent construction of related damage models.

Numerical and experimental investigation of the dynamic mechanical behavior of precipitation-strengthed NiCoCrSi0.3C0.048 medium-entropy alloy

An extended crystal plasticity model and an optimized neural network are established to investigate the mechanical behavior of CoCrNiSi0.3C0.048 Medium entropy alloy (MEA) with a three-level hierarchical precipitation structure under dynamic compressive deformation at a variety of ranges of strain rates. The interaction between the matrix and first-level precipitates is described by a presented hybrid representative volume element RVE model, involving the effects of volume fraction (Vf), radius and geometric distribution on heterogeneous deformation. Effects of second- and third-level precipitates are realized through the extended crystal plasticity constitutive model, reflecting the motion mechanism of dislocations near the precipitates in the form of initial slip resistance. Meanwhile, this study investigates the influence of the presence of primary precipitates on the initiation of slip systems within special grains with Goss or S orientations in the matrix. Additionally, it provides a more in-depth explanation of the underlying principles behind the suppression of Goss texture formation by the precipitates from the perspective of slip systems analysis. The changing of volume fractions affects flow stress evolution. Avoiding suffering from expensive computational consumption by the crystal plasticity finite element method, an artificial neural network model optimized through a genetic algorithm, is presented to predict stress-strain responses and texture evolution results under varying compression strain rates. A reliable dataset derived from crystal plasticity finite element models and experimental results is utilized to train, test, and validate the genetic algorithm-based artificial neural network model. This model demonstrates good prediction capability in dynamic mechanical behavior and texture evolution, showcasing the feasibility and efficacy of the proposed neural network model. Compared to the CPFEM method, neural network models can greatly improve computational efficiency.

Micro-mechanisms of anisotropic deformation in the presence of notch in commercially pure Titanium: An in-situ study with CPFEM simulations

This study investigates the impact of notch severity and initial texture on the micro-mechanisms during low strain deformation in commercially pure Titanium, exploiting in-situ electron back scatter diffraction (EBSD) experiments and crystal plasticity finite element model (CPFEM). In-situ tests were performed at different strain steps of un-notched and notched samples of transverse direction (TD) and rolling direction (RD) orientations. CPFEM, based on initial EBSD microstructures, predicted profuse prismatic slip traces and early activation of prismatic slip in notched sample, with RD orientation exhibiting higher activity. Further, CPFEM results revealed early activation of high CRSS slip systems as well as evidence of early twin activity at notch tip due to severely localized plastic deformation and steep strain gradient, as observed by GND maps causing higher stress at grain boundaries. At the notch tip, digital images correlation (DIC) at microscale indicated strain localization at 45∘ and 90∘ to the tensile axis for TD and RD orientations, respectively. Furthermore, 2.5D and 3D CPFEM confirmed distinct strain patterns at notch tip: TD orientation exhibited combined basal and prismatic slip influences, while RD orientation displayed dominant prismatic slip systems at localized strain. The model also successfully predicted anisotropic surface roughness, contributing to early necking in RD orientation.

Microstructural evolution modelling and low-stress fatigue performance of bimodal-structured Al-Mg-Sc-Zr alloy produced by laser powder bed fusion additive manufacturing

ABSTRACT Coarse – and fine-grained bimodal-structures in a Al-Mg base alloy with rare earth elements of Sc/Zr is produced due to the ultrafast nonequilibrium solidification occurs in laser-induced molten pools during laser powder bed fusion (LPBF) additive manufacturing. A novel high-fidelity cellular automaton (CA) algorithm incorporating numerical calculations of molt-pool temperature fields elucidates the formation and evolution of the bimodal-structure. Subsequent heat treatment induces precipitation of Al3(Sc/Zr) particles within the grains, synergistically enhancing strength and plasticity of the LPBF-processed alloy. The crystal plastic finite element method (CPFEM) is used to reveal the synergistic effect between the strength and plasticity during the material tensile procedure. The bimodal-structure exhibits good fatigue resistance but intriguing anisotropy under low stress cyclic loading. It is proved that differentiated distribution patterns relative to the principal stress direction of the bimodal-structure have a significant influence on its fatigue performance. Numerical evolutionary of the bimodal grain deformation reflects this phenomenon.

Experimental characterization and crystal plasticity finite element simulation of the microstructural evolution in CVD tungsten during multi-step rolling

Atmospheric pressure chemical vapor deposition (CVD) is a promising technique for the preparation of tungsten products with high purity, high density and almost unlimited thickness. The tungsten prepared by using the CVD method (CVD-W) usually has a columnar coarse grain microstructure with strong preferred orientations. Multi-step rolling at gradually decreased operating temperatures is an effective method to lower the ductile-to-brittle transition temperature in pure tungsten. So far, the microstructural evolutions of CVD-W during the multi-step rolling processing is still unclear. In this study, the microstructure evolution and texture development of CVD-W during multi-step rolling are investigated by the coupling of electron backscattering diffraction technique and full-field crystal plasticity finite element simulations. After multi-step rolling, the sample exhibits through-thickness texture gradient. A layered structure with elongated 〈100〉 // ND and 〈111〉 // ND grains is observed in the central region and Goss orientation mainly appears in the surface region. Crystal plasticity finite element simulations show that {001}〈110〉 is a stable orientation under the plane strain compression, which is realized by the rotation of {100} grains around ND. Meanwhile, the shear flow promotes the rotation of {100} grains around TD, leading to the formation of 〈111〉 // ND orientation. 〈110〉 // ND orientation is observed near the shear bands, which is generated through the rotation of {100} grains around <100> // RD axis. The rolled CVD-W exhibits crystallographic orientation dependent recrystallization behavior, which is related to the orientation dependent distortion energy generated in the rolling processing. Our studies provide fundamental insights into the microstructure evolution and texture development of CVD-W under the multi-step rolling processing.