Crystal Plasticity Finite Element Method Research Articles

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

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.

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 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.

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.

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.

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.

Advances in Understanding the Evolution Mechanism of Micropore Defects in Metal Materials under External Loads

Micropores are one of the critical factors affecting materials’ performance and service life. As the need for a deeper understanding of micropore evolution and damage mechanisms grows, assessing the mechanical properties of materials containing micropores and predicting the lifespan of related metal structural components becomes increasingly complex. This paper focuses on the evolution process, regularities, and research methods of micropores in metal materials. Based on recent research and practical applications, the key stages of micropore evolution are discussed, encompassing nucleation, growth, coalescence, collapse, interaction, and the influence of other microstructures. Firstly, the advantages and limitations of commonly used characterization methods such as scanning electron microscopy, transmission electron microscopy, and X-ray computed tomography are introduced in the study of micropore evolution. Subsequently, critical theoretical models for micropore evolution, such as the Gurson model and its extensions, are summarized. By using a multiscale approach combining the crystal plasticity finite element method, dislocation dynamics, and molecular dynamics, the factors influencing the micropore evolution, such as external stress conditions, internal microstructures, and micropore characteristics, are specifically elaborated, and the basic physical mechanisms of micropore evolution are analyzed. Finally, a comprehensive review and summary of current research trends and key findings are provided, and a forward-looking perspective on future research directions is presented.

Experimental and numerical study on high-cycle fatigue performance of austenitic stainless steel with pre-charged hydrogen

High-cycle fatigue performance is one of the crucial issues for hydrogen diaphragm compressors, as hydrogen embrittlement affects the components in a high pressure hydrogen environment. In this study, the high-cycle fatigue response of MP7, a novel material of austenitic stainless steel designed for hydrogen diaphragm compressors, is investigated by tests and by numerical ways using the Crystal Plasticity Finite Element Method (CPFEM). The uniaxial tensile tests and fatigue tests are carried out on MP7 specimens with different levels of pre-charged hydrogen. The analysis indicates that, even for MP7 with the improved hydrogen resistance performance, both the ductility and the fatigue limit are still affected by the pre-charged hydrogen in a considerable way. Based on the principles of crystal plasticity theory, a CPFEM model is established and a fatigue life prediction model for austenitic stainless steel with pre-charged hydrogen is proposed. This model successfully predicts the fatigue life under different hydrogen contents and stress amplitudes, and the predicted fatigue lives are well-fitted to S-N curves within a two-fold error band.

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.

Improving the fatigue property of diffusive film cooling holes in nickel-based single crystal superalloy via ultrashort pulse laser drilling coupled with abrasive flow machining

A novel hole-making technique, which combines ultrashort pulse (UP) laser drilling with abrasive flow machining (AFM), has been developed to enhance the surface quality and fatigue resistance of diffusive holes in nickel-based single crystal (NBSC) superalloys. This study conducted a comprehensive analysis of the surface morphology and metallurgical characteristics of the hole wall, evaluated by fatigue testing at elevated temperatures and fractography analysis. The findings demonstrate that AFM can effectively eliminate the solidified debris generated during UP laser drilling, significantly reducing surface roughness and inducing a rounded effect at the outlet acute zone of the diffusive hole. Such improvements have been shown to increase the fatigue life of the holes by up to 50.6 % compared to those without polish. Furthermore, the crystal plasticity finite element method (CPFEM) was employed to investigate the localized stress concentration and the accumulation of plastic slip around the diffusive hole, elucidating the mechanisms behind fatigue failure in NBSC superalloys. The study also discusses the influence of the different hole-making technology on the fatigue properties of diffusive holes, integrating CPFEM results with analyses of surface quality and fatigue fractography. The study conducted in this study can provide valuable guidance for the fabrication of diffusive holes in turbine blades. Furthermore, it can also improve our understanding of the fatigue failure mechanism of diffusive holes in NBSC superalloy.

Texture evolution and stress formation behaviour during tensile deformation using crystal plasticity finite element method

In this work, a three-dimensional crystal plasticity (CP) model was constructed to study the texture evolution behaviour and stress distribution of AA2024 alloy under uniaxial tensile conditions. After parameter calibration, the accuracy of simulated stress–strain curve reached 98.82%, and with good convergence. It was found that the {111} plane dots of Brass in (111) pole figure predominantly prolong at an angle of approximately 35.8° with respect to the RD, while those of Copper, S, Goss and Cube scatter towards almost all directions by the way in a circular augmentation. Moreover, it was revealed that Brass orientation is more conducive to alleviating stress during deformation process, while Copper is the least effective. The situations for Cube and Goss orientations are similar.

Microscopic-plastic deformation behavior of grain boundary precipitates in an Al–Zn–Mg alloy

The nano-precipitates with minimal misfit strengthen Al–Zn–Mg alloys by impeding dislocation motion. However, grain boundary precipitates (GBPs) are known to have a completely incoherent relationship with the matrix, making them less effective in strengthening the alloys. Instead, GBPs are recognized for preoccupying elements such as Zn or Mg, thereby diminishing the quantity of nano-strengthening phases. GBPs significantly influence the deformation and fracture behaviors of Al–Zn–Mg alloys by accelerating stress localization and crack formation. In this study, we investigated how the accumulation of dislocations in the GBP areas leads to stress localization and subsequent cracking, using micropillar tests and crystal plasticity finite element method (CP-FEM) analysis. The dislocation pile-up in the GBPs causes stress localization around the grain boundaries, inducing crack initiation and leading to intergranular fracture. These findings enhance our understanding of the role of GBPs in the deformation and cracking of Al–Zn–Mg alloys and may pave the way for new concepts in managing GBPs.

In-situ study of microstructure and mechanical properties of GH3536 alloy manufactured by selective laser melting at 750 °C

Nickel-based GH3536 alloy exhibits high strength but low ductility when produced by selective laser melting (SLM), which hinders its widespread application in aerospace. This paper employed a ‘two-step’ method of heat treatment to optimize the microstructure of the SLM GH3536 alloy and investigated the mechanical properties. Tensile tests were conducted on SLM GH3536 alloy before and after heat treatment at 750 °C, using an in-situ high-temperature tensile stage. The relationship between the microstructural evolution and deformation behavior of the alloys was investigated by combining the in-situ tensile experiments and crystal plasticity finite element method (CPFEM). The results suggested that the elongation can be increased by 80% without a significant reduction in tensile strength. The improved elongation is attributed to the complete recrystallization, formation of annealed twins and serrated grain boundaries after heat treatment. The study also investigated the deformation behavior and fracture mode of the alloy before and after heat treatment. Discussion was done on the influence of the microstructure, particularly the twin and serrated grain boundaries on the alloy's plastic deformation. This study enhanced the understanding of plastic deformation of SLM GH3536 alloy and provided a valuable reference for the design and post-treatment of superalloy.

A machine learning constitutive model for plasticity and strain hardening of polycrystalline metals based on data from micromechanical simulations

Machine learning (ML) methods have emerged as promising tools for generating constitutive models directly from mechanical data. Constitutive models are fundamental in describing and predicting the mechanical behavior of materials under arbitrary loading conditions. In recent approaches, the yield function, central to constitutive models, has been formulated in a data-oriented manner using ML. Many ML approaches have primarily focused on initial yielding, and the effect of strain hardening has not been widely considered. However, taking strain hardening into account is crucial for accurately describing the deformation behavior of polycrystalline metals. To address this problem, the present study introduces an ML-based yield function formulated as a support vector classification model, which encompasses strain hardening. This function was trained using a 12-dimensional feature vector that includes stress and plastic strain components resulting from crystal plasticity finite element method (CPFEM) simulations on a 3-dimensional RVE with 343 grains with a random crystallographic texture. These simulations were carried out to mimic multi-axial mechanical testing of the polycrystal under proportional loading in 300 different directions, which were selected to ensure proper coverage of the full stress space. The training data were directly taken from the stress–strain results obtained for the 300 multi-axial load cases. It is shown that the ML yield function trained on these data describes not only the initial yield behavior but also the flow stresses in the plastic regime with a very high accuracy and robustness. The workflow introduced in this work to generate synthetic mechanical data based on realistic CPFEM simulations and to train an ML yield function, including strain hardening, will open new possibilities in microstructure-sensitive materials modeling and thus pave the way for obtaining digital material twins.

Special texture evolution behavior of strip-cast non-oriented electrical steel combined with in-situ experiment and CPFEM

The impact of shear deformation on texture evolution in strip-cast Fe-1.5%Si non-oriented electrical steel was studied combined with in-suit experiments and crystal plasticity finite element method (CPFEM). Throughout the deformation process, the texture evolution predominantly follows a traditional route: transitioning from {211}<036> and {411}<148> to {111}<112> orientation. In certain regions with specific stress conditions, orientation evolution shifts from {310}<236> to {411}<148>, {100}<021>, and finally to {100}<001> orientation. Crystal plasticity finite element (CPFE) simulation results show that the rotation of {310}<236> through {411}<148> to {100}<021> orientation, {211}<236> and {112}<110> orientations transition to {111} and {110} orientations, respectively, which is consistent with the experimental observations. Recrystallization texture mainly includes favorable λ and near-λ (<100>∥ND, normal direction) textures, with detrimental γ (<111>∥ND) texture essentially diminishing. In-situ heating experiments revealed {411}<148> as the primary recrystallization orientation, the mechanism involves both oriented nucleation and growth. In the edge region lacking stress constraints, the Schmid factor (SF) reaches up to 0.48, the (21-3)[111] slip system is preferentially activated, with shear bands appearing earlier in the same region. Indicating that when slip mechanism alone are inadequate for sustaining plastic deformation, the shear deformation becomes the favored mode of activation. {411}<148> orientation can serve as a transitional orientation for transitioning to {100} orientation, and further as an advantageous transitional orientation during the nucleation and growth of recrystallization. Due to the texture improvement, superior magnetic properties were achieved, with the average magnetic induction (B50) and iron loss (P1.5/50) being 1.77 T and 4.25 W/kg, respectively.

Surface roughness evolution and heterogeneous plastic deformation of austenitic stainless steel during micro deep drawing: Modeling and experiment

The present work involves the numerical simulation and experimental study on the surface roughness evolution and heterogeneous plastic deformation (strain localization and concomitant surface morphology evolution) in grain scale of micro deep drawn parts of austenitic stainless steel (ASS) 304 foils. A three-dimensional modeling framework was used to simulate the micro deep drawing (MDD) process. The simulation involved the development of a Voronoi-based polycrystalline geometry model (VPGM), a multi-stress-strain response model, and a crystal plasticity finite element methods (CPFEM) model. The results indicate that CPFEM model exhibits higher accuracy in the localized stress and strain, thickness distribution fluctuation and surface roughness evolution of the fabricated parts compared to multi-stress-strain response model. Therefore, the plastic deformation heterogeneity in MDD is in-depth discussed based on CPFEM model. The results show that the coarse-grained foils correspond to the intense strain localization, which is the main cause of surface roughening. Considering the average grain size is close to the thickness of ASS foils, mounding features on the rough surface may readily develop further into potentially fractured sites during deformation. On the other hand, crystal orientation influence plastic deformation by affecting the slip behavior of materials. The effect of crystal orientations including {011} 〈211〉 (Brass), {011} 〈100〉 (Goss), and {112} 〈110〉 components on deformation is discussed. The results indicate a strong correlation between the magnitude of the Schmid's factor and the ease of deformation. Additionally, variations in Schmid's factor across different directions result in differences in deformation accumulation, which affects the thickness distribution along the radial direction and the distribution of earrings and wrinkles along the circumferential direction of the fabricated micro parts.

Microscopic mechanism of plastic heterogeneous deformation of columnar-grained polycrystalline ice

Studying ice deformation starting from crystal scale can provide insight into the microscopic mechanisms of ice deformation. In this paper, a crystal plasticity constitutive model of ice considering the dislocation slip mechanism and grain-size dependence was implemented within the finite element framework, and a modeling approach starting from ice single crystals based on the crystal plasticity finite element method (CPFEM) was proposed to study the elastic-viscoplastic deformation of polycrystalline ice samples. Finite element models of ice single crystals and columnar-grained polycrystalline ice characterizing the microstructure were established successively, and the proposed method was validated by comparing the uniaxial compression prediction results of ice single crystals and columnar-grained polycrystalline ice with the existing experimental data. Finally, the microscopic mechanism of plastic heterogeneous deformation of columnar-grained polycrystalline ice under constant strain rate compression conditions was analyzed. The results indicate that the modeling approach from ice single crystals to polycrystalline ice samples based on CPFEM can reasonably describe the mechanical properties of ice deformation. The deformation of columnar-grained polycrystalline ice globally exhibits apparent slip bands around 30° - 60° relative to the loading direction and locally presents intragranular localization bands parallel or perpendicular to the C-axis. This plastic heterogeneous deformation phenomenon is related to the elastic-viscoplastic anisotropy of ice single crystals and the interaction of neighboring grains at grain boundaries (GBs).

Investigation of the Behavior of Surface Roughness Suppression Orientation on the Inner Surface of Metal Microtubes Using Crystal Plasticity Finite Element Method

The objective of this study was to clarify whether the surface roughness suppression orientation actually suppresses surface roughness by using the crystal plasticity finite element method (CPFEM), which is based on the relationship between the surface roughness suppression orientation and deformation in the inner surface direction that we have clarified in the past. In order to simplify the calculation and reduce the computational cost, a model was created by embedding cylinders in a rectangular body, which was then divided into 1/4 for the analysis. A dislocation density increase model that takes work hardening into account was applied to the model, and values obtained from tensile tests were used for material constants. The model was divided into 2130 elements. The simulation results show that the surface roughness suppression orientation is actually more difficult to deform than its surroundings.

Investigation of the effect of morphological and crystallographic textures on the ductility limits of thin metal sheets using a CPFEM-based approach

The current contribution investigates the effect of some relevant microstructural parameters (specifically, morphological and crystallographic textures) on the ductility limits of polycrystalline aggregates using the Crystal Plasticity Finite Element Method (CPFEM). The polycrystalline aggregates are assumed to be representative of thin metal sheets and their macroscopic behavior is determined from that of their constituent single crystals on the basis of the periodic homogenization technique. The single crystal behavior is described by a finite strain elastoplastic framework in which the plastic flow rule obeys the classical Schmid law and plastic deformation is solely attributed to the slip on the crystallographic slip systems. The CPFEM is implemented within and in connection with ABAQUS/Standard finite element code. The ductility limits are predicted by the Rice bifurcation theory where strain localization is detected when the macroscopic acoustic tensor becomes singular. Three grain morphologies (namely, cube, random, and elongated morphology) and three initial crystallographic textures (namely, cube, random, and copper orientation) are considered to investigate the effect of morphological and crystallographic textures on the onset of plastic strain localization. The numerical results indicate that the effect of initial crystallographic texture is much more pronounced than that of grain morphology on the predicted ductility limits. In addition, the impact of grain size and sheet thickness are thoroughly analyzed. The research reveals that the trends of the predicted ductility limits are strongly dependent on the size effects.