Crystal Plasticity Finite Element Model Research Articles

Research on the evolving yielding behaviour and micro-mechanism in biaxial deformation of DP1180 sheet based on crystal plasticity finite element model

Dual-phase steels (DP steels) consist of ferrite and hard martensitic phase. For the high strength and good formability, they are widely used in automotive applications. Compared with the DP steels with lower strength, DP1180 is more special for the volume fraction of martensite is higher than that of ferrite. In this paper, the evolving plastic yielding behaviours and insight into their microscale mechanisms of DP1180 were studied by biaxial tension experiments and crystal plasticity finite element method. The representative volume element (RVE) model of DP1180 taking the dual phase fraction, grain size and texture into consideration is established and the relevant parameters of crystal plasticity are reverse calibrated by the uniaxial tensile test stress strain curve. The simulated biaxial tension tests were conducted by the established RVE model to investigate the yielding micro-mechanisms of DP1180 steel, and the obtained yield loci matches well with the test results. The simulation results show that the texture has a significant effect on the contours of the yield loci. The soft ferrite grains weaken the kinetic constraints to the polycrystalline matrix and further free the rotation and plastic deformation of the neighbouring grains. This study thus provides a comprehensive understanding of the effect of the microstructure (crystal structure, texture and dual phase fraction) on the yielding behaviour of DP1180 steel as well as a method of virtual experiment to get the yield loci of metallic materials.

The effect of phase distribution of constituent-fiber structure on the deformation heterogeneity of TRIP-assisted lean duplex stainless steel

The cold-rolled TRIP-assisted lean duplex stainless steel (TLDX) showed the directional distribution of constituent-fiber structure. The effect of phase distribution of constituent-fiber structure on the deformation heterogeneity during tensile tests and deep drawing of cylindrical cup was investigated through crystal plasticity finite element model (CPFEM) involved in the martensitic transformation. The results showed that the strain for the plastic instability was lower in the transverse direction (TD)-loaded case (true strain εT ∼0.408) compared with the rolling direction (RD)-loaded case (εT ∼0.485). Also, the strain localization bands formed at a lower strain (engineering strain εE ∼40%) in the TD-loaded case than that in the RD-loaded case (εE ∼55%). At the same strain, the volume fraction of transformed martensite of the TD-loaded case was relatively less than that of the RD-loaded case. For the transformed martensite, it only accommodated a low proportion (<5%) of global strain in the two cases. The proportion of partitioned strain into austenite (Pεγ) in the RD-loaded case was always higher than that in the TD-loaded case, while the partitioned strain into ferrite (Pεα) showed a converse law, which indicated that the deformation heterogeneity in the TD-loaded case is more pronounced. Similarly, the high risk of cracking of deep-drawn cylindrical cups with different sizes also always formed at the specific zones corresponding to the TD-loaded case.

Experimental investigation and micromechanical modeling of load partitioning behavior of duplex stainless steel 2205 during cyclic hardening

This paper aims to understand the load partitioning behavior between austenite and ferrite of duplex stainless steel 2205 under cyclic loading by experiments, including a series of low cycle fatigue tests and electron back scattered diffraction observation. Meanwhile, a crystal plasticity finite element model was developed to predict the cyclic micromechanical response of two constituent phases. The results show that more slip bands were found within the austenite. The cyclic plasticity of 2205 started within the austenite, and gradually translated into the ferrite with the elevation of applied cyclic amplitude. The plastic deformation within the austenite was inclined to form at the phase boundaries, while it promoted at grain boundaries in the ferrite. The micromechanical elasto-viscoplastic parameters of two constituent phases were calibrated accurately. The proposed crystal plasticity finite element model has a great ability of predicting not only the time- and amplitude- macroscopic cyclic hardening behavior but also the micro-deformation within two constituent phases, even the cyclic hardening of 2205 with different phase ratios can also be reproduced accurately. The prediction error on cyclic stress amplitude of 2205 during cyclic hardening can be controlled within 3.2%.

Slip localization behavior at triple junctions in nickel-base superalloys

Incipient slip localization in the vicinity of hundreds of grain boundary triple junctions (TJs) in a lightly deformed nickel-base superalloy IN718 is studied using a combination of three-dimensional (3D) crystal plasticity finite element (CPFE) modeling, high resolution digital image correlation (HR-DIC) and 3D electron back-scatter diffraction tomography (3D EBSD). A 3D reconstruction method enables identification of thousands of TJs and correspondence of any observed slip bands with their originating TJ lines below the specimen surface. We present a large-scale CPFE model of the experimental 3D microstructure composed of high-fidelity representation of the TJ lines and the boundaries and interiors of the parent grains and use it to calculate the local micromechanical response and slip activity of all TJs at the onset of macroscopic yielding. Statistical analysis of the calculated quantities reveal TJs develop larger stress concentration and grain-average re-orientation than grain interiors and grain boundaries, however no substantial differences in cumulative slip were found among these microstructural regions. We find that TJs with observed slip bands generate lower grain-average re-orientation, fewer active slip systems, and more localized slip on a single system than those without. The distinctions in the reorientation and slip activity are stronger in TJs that experience more intense slip.

Study on microstructural characterization and local stress–strain behavior of transition zone within K-TIG welded SAF2205/Q235 dissimilar joints

Dissimilar metal welded joints are increasingly and widely applied in any field of manufacturing. Meanwhile, a novel keyhole gas tungsten arc (K-TIG) welding technology presents the advantages of high productivity, high precision as well as low cost. This paper investigated microstructural characterization of K-TIG welded SAF2205/Q235 dissimilar joints with different welding torch deviations. Moreover, evolution of local microstructure and stress–strain behavior from transition zone was discussed by means of crystal plasticity finite element modeling. The results show that solid–solid phase transformation mode in the weld metal changes due to the change of constituent alloy elements. Noted that transition zone on the Q235 side includes compact martensite with high hardness, and the elements and mechanical properties present a severe gradient distribution. Transition zone with high strength has a greater resistance to plastic deformation. In addition, a large strain gradient takes place near the transition zone and on the side of an austenite grain with a high Schmid factor. Besides, the twin boundary is prone to deform at a lower stress level, which leads to a new strain partition. Therefore, stress–strain incompatibility caused by a difference in both mechanical properties and crystal structure is the root cause of K-TIG DMWJs failure.

Microstructure- and damage-nucleation-based crystal plasticity finite element modeling for the nucleation of multi-type voids during plastic deformation of Al alloys

During deformation of aluminum (Al) alloys, there are three kinds of voids being formed by distinct mechanisms, i.e., matrix-cracking voids (MCVs), particle-cracking voids (PCVs), and interface-debonding voids (IDVs), due to mesoscale heterogeneous deformation. The three kinds of void nucleation have different effects on the subsequent void growth, void coalescence, and ductile fracture of Al alloys. To determine the complex nucleation behavior of the three kinds of voids under mesoscale heterogeneous deformation, a microstructure- and damage-nucleation-based crystal plasticity finite element (MDNCPFE) model considering different nucleation mechanisms was established. To realize the MDN-CPFE modeling, the deformation and void nucleation of the matrix, particle, and their interface in Al alloys were described by a non-local dislocation density CP constitutive model and a local stored energy density criterion, an elastic constitutive model and a maximum principal stress criterion, and a cohesive zone model and fracture energy criterion, respectively. The developed MDN-CPFE model was validated by the nucleation locations and quantitative variations of the three kinds of voids in an in-situ tensile test. Using the developed model, the nucleation characteristics of the three kinds of voids during the small deformation of Al alloys were analyzed. It is found that PCVs are likely to nucleate within particles that are located at the deformation bands and with greater shape irregularity; IDVs are prone to nucleate at the interfaces around smaller particles in the deformation bands; MCVs tend to nucleate within grains with a higher Schmid factor and aspect ratio. The void area fractions (VAFs) of the three kinds of voids all evolve with an incubation stage and then followed by an exponentially increasing stage during deformation. The duration of the incubation stage for the three kinds of voids, designated by the nucleation strain, presents the following sequence: PCV < IDV < MCV; while, their VAFs and quantities present the opposite sequence. Additionally, the effects of the particle volume fraction and grain size on the nucleation strain, total VAF, and proportion of VAFs of the three kinds of voids were unraveled.

Surface hardening through oxygen diffusion in niobium: The defining role of stress inhomogeneity in tensile embrittlement

Surface hardening, through oxygen diffusion, enforced significant tensile embrittlement of a commercial niobium (Nb) alloy (C-103). This was explored with microscopic digital image correlation and crystal plasticity finite element (CPFE) modeling. In particular, the presence of an oxygen-rich surface layer provided a gradient in hardness and elastic stiffness. These coincided with an increase in yield and tensile strength but a significant drop in ductility. The latter was reflected in the strain localization(s) and crack(s) on the hard gauge region, which ultimately led to a brittle failure. Full-field CPFE simulations were conducted on the actual microstructures. Our model, without crack and damage initiation, predicted extreme stress inhomogeneity during the tensile deformation. In brief, ∼5 times higher stress concentration was noted in the oxygen-rich hard surface grains. This appeared to be responsible for the subsequent crack initiation and embrittlement.

Effect of tempering process on the cryogenic impact toughness of 13Cr4NiMo martensitic stainless steel

The effects of tempering process on the cryogenic impact toughness of 13Cr4NiMo martensitic stainless steel (13-4MSS) were investigated by experiments and crystal plasticity finite element modeling (CPFEM). The tempering structure mainly includes tempered martensite lath, reversed austenite and M23C6 carbide. The tempered martensite lath is refined by the tiny new martensite transformed by reversed austenite, and the refinement degree increases with the tempering temperature. The nucleation of reversed austenite depends on the new martensite and carbide generated during tempering, and more reversed austenite is obtained by double tempering. The cryogenic impact toughness of the material changes nonlinearly with the increase of tempering temperature. It indicates that fine martensitic lath and inverse austenite are beneficial to improve the cryogenic impact toughness of the material, while carbide particles play the opposite role. The results of CPFEM show that reversed austenite coordinates the impact force of the surrounding martensite through large plastic deformation, and eases the stress concentration. Reversed austenite even occurs DIMT behavior under large plastic deformation to further reduce the stress concentration and prevent the initiation and propagation of cracks. As a hard particle, carbide causes the stress concentration, leading to cracks initiation and propagation along the martensite boundary.

Mechanical Anisotropy of Selective Laser Melted Ti-6Al-4V Using a Reduced-order Crystal Plasticity Finite Element Model

In this study, a reduced-order crystal plasticity finite element (CPFE) model was developed to study the effects of the microstructural morphology and crystallographic texture on the mechanical anisotropy of selective laser melted (SLMed) Ti-6Al-4V. First, both hierarchical and equiaxed microstructures in columnar prior grains were modeled to examine the influence of the microstructural morphology on mechanical anisotropy. Second, the effects of crystallographic anisotropy and textural variability on mechanical anisotropy were investigated at the granular and representative volume element (RVE) scales, respectively. The results show that hierarchical and equiaxed CPFE models with the same crystallographic texture exhibit the same mechanical anisotropy. At the granular scale, the significance of crystallographic anisotropy varies with different crystal orientations. This indicates that the present SLMed Ti-6Al-4V sample with weak mechanical anisotropy resulted from the synthetic effect of crystallographic anisotropies at the granular scale. Therefore, combinations of various crystallographic textures were applied to the reduced-order CPFE model to design SLMed Ti-6Al-4V with different mechanical anisotropies. Thus, the crystallographic texture is considered the main controlling variable for the mechanical anisotropy of SLMed Ti-6Al-4V in this study.

Gaussian process autoregression models for the evolution of polycrystalline microstructures subjected to arbitrary stretching tensors

Crystal plasticity finite element models (CPFEM) have shown tremendous potential for simulating the microstructure evolution paths in polycrystalline aggregates subjected to large plastic strains. However, their high computational cost has hindered their broader deployment in design efforts where large process design spaces need to be explored. In this work, a novel machine learning framework is developed to establish low-computational cost reduced-order models for predicting the details of microstructure evolution in face-centered cubic (FCC) polycrystalline microstructures subjected to arbitrary stretching tensors. Within this framework, the previously established feature engineering of polycrystalline materials within the material knowledge system (MKS) framework is extended such that it is applicable to the highly deformed microstructures obtained during large deformations. Gaussian process autoregression (GPAR) approaches combined with Bayesian design of experiment strategies are employed for building the desired surrogate models to optimize the generation of the computationally expensive training data (produced using CPFEM). It is demonstrated that a relatively small training set of 1400 datapoints is adequate to produce a high-fidelity reduced-order model for predicting the details of the microstructure evolution in a very broad set of FCC polycrystalline aggregates subjected to arbitrary macroscopically imposed stretching tensors.

The Effect of Laser Shock Peening on Back Stress of Additively Manufactured Stainless Steel Parts

Abstract This work studies the use of laser shock peening (LSP) to improve back stress in additively manufactured (AM) 316L parts. Unusual hardening behavior in AM metal due to tortuous microstructure and strong texture poses additional design challenges. Anisotropic mechanical behavior complicates application for mechanical design because 3D printed parts will behave differently than traditionally manufactured parts under the same loading conditions. The prevalence of back-stress hardening or the Bauschinger effect causes reduced fatigue life under random loading and dissipates beneficial compressive residual stresses that prevent crack propagation. LSP is known to improve fatigue life by inducing compressive residual stress and has been applied with promising results to AM metal parts. It is here demonstrated that LSP may also be used as a tool for mitigating tensile back-stress hardening in AM parts, thereby reducing anisotropic hardening behavior and improving design use. It is also shown that the method of application of LSP to additively manufactured parts is key for achieving effective back-stress reduction. Back stress is extracted from additively manufactured dog bone samples built in both XY and XZ directions using hysteresis tensile. Both LSPed and as-built conditions are tested and compared, showing that LSPed samples exhibit a significant reduction to back stress when the laser processing is applied to the sample along the build direction. Electron backscatter diffraction (EBSD) performed under these conditions elucidates how grain morphologies and texture contribute to the observed improvement. Crystal plasticity finite element (CPFE) modeling develops insights as to the mechanisms by which this reduction is achieved in comparison with EBSD results. In particular, the difference in plastic behavior across build orientations of identified crystal planes and grain families are shown to impact the degree of LSP-induced back-stress reduction that is sustained through tensile loading.

Low-cycle fatigue behavior and life prediction of TA15 titanium alloy by crystal plasticity-based modelling

It is of significance to reveal the low-cycle fatigue deformation mechanism of titanium alloy with tri-modal microstructure for improving its properties. This work developed a crystal plasticity finite element model based on realistic microstructure to predict the low-cycle fatigue behavior of TA15 titanium alloys with tri-modal microstructure containing primary α (αp), secondary lamellar α (αl) and transformed β (βt). During modelling, plastic strain accumulation (PSA) and energy dissipation were used as the fatigue indicator parameter (FIP) to predict fatigue damage and life. It is found that the fatigue deformation prefers to localize at the interfaces of αp/β, αl/β and at triple junctions, which leads to the initiation of fatigue crack. In addition, the soft geometry of αl will also contribute to the strain localization inside αl grains causing fatigue damage. This is because the local lattice rotation is more prone to occur at these locations due to the tension-compression asymmetry of lattice rotation, which induces the occurrence of the microtexture and aggravates the heterogeneity of the lattice rotation, leading to the localized PSA and the total energy dissipation. And the asymmetry of lattice rotation in each cycle also leads to the tension-compression asymmetry of flow behavior. Both of the two FIPs can effectively predict fatigue life. With the strain amplitude increasing, the PSA-based model shows a relatively higher predictive accuracy of fatigue life than that of the accumulated energy dissipation-based model. The predicted fatigue life is in accordance with the C-M model.

Kink band formation mechanism in α/β Ti-9Cr two-phase alloy

A combination of experimental and numerical studies was carried out to understand the microstructure and formation mechanism of kink bands in α/β two-phase titanium alloys. A deformation kink band was introduced in a Ti-9Cr alloy after uniaxial compression test. The strength changes of the α and β phases inside and outside the kink band were evaluated by nanoindentation tests. A potential hardening effect was revealed in the α phase inside the kink band, while a possible softening effect was located in the β phase at the kink boundaries. Microstructural examination of the kink band was conducted by electron backscatter diffraction measurement. The crystal rotation axis was found to be perpendicular to both the (0001) basal plane of the α phase and one of the (110) planes of the β phase. The crystallographic features were characterized by transmission electron microscopy observation, revealing a prismatic 〈a〉 slip that occurred during the compression to accommodate the rotations around the c-axis. Nanoindentation tests were performed on an undeformed specimen to calibrate the crystal plasticity model. A crystal plasticity finite element model was developed and {110}β-rotation-type kink bands were reproduced in the simulation and confirmed the prismatic slip activity.

Crystal Plasticity Finite Element Modeling on High Temperature Low Cycle Fatigue of Ti2AlNb Alloy

Ti2AlNb alloy is a three-phase alloy, which consists of O phase, β phase and α2 phase. Because of the difference in the mechanical characteristics between phases, Ti2AlNb alloy often exhibits deformation heterogeneity. Based on EBSD images of the Ti2AlNb alloy, a crystal plasticity finite element model (CPFEM) was built to study the effects of O phase and β phase (dominant phases) on stress and strain distribution. Four types of fatigue experiments, and the Chaboche model with 1.2%~1.6% total strain range were conducted to verify the CPFEM. The simulation results showed that the phase boundary was the important position of stress concentration. The main reason for the stress concentration was the inconsistency deformation of grains which resulted from the different deformation abilities of the O and β phases.

Research on the effect of micro-voids on the deformation behavior and crack initiation lifetime of titanium alloy under cyclic loading by crystal plasticity finite element method

Micro-voids defects associated with materials formed by diffusion bonding and super-plastic connection limit their usage in the aerospace industry. A crystal plasticity finite element (CPFE) model was established in the current work to investigate the relationship between local stress concentration and the micro-void defects, and predict the fatigue crack initiation lifetime. Based on the concept of the curvature of the crack tip, the shape and size of the voids are strictly separated, so that the influence of the single parameter of voids on the microplasticity deformation behavior is better obtained. It's found that the micro-voids lead to the stress concentration phenomenon in the material, the effect of the curvature of the void tip surface is greater than that of the void size. Stress concentration tends to occur in the hard grains. When L/d is greater than 2.0, stress concentration factor reaches a constant small value. The simulated results based on the Manson-Collin law and Fatemi-Socie parameter show that when the void tip curvature is greater than 0.4 μm−1 or L/d is less than 2.0, the fatigue crack initiation lifetime is less than 106 cycles, indicating that the influence of such micro-voids on fatigue crack initiation is small. This work has a good guiding significance for properties and lifetime prediction of the material with defects.

Hardening mechanisms of “cold” rolled tungsten after neutron irradiation: Indentation and finite elements modelling

The mechanical properties of “cold” rolled tungsten sheet after neutron irradiation at high temperature are investigated by instrumented indentation and crystal plasticity finite element modelling (CPFEM). Neutron irradiation to a dose of 0.2 displacements per atom was performed in the temperature range from 600 to 1200 °C in the Belgian material test reactor BR2 at SCK CEN, Mol. The contribution of the irradiation damage in the constitutive laws has been deduced by utilizing the load-depth curves of the indentation measurements and incorporating microstructural information from transmission electron microscopy measurements. The simulated load-depth curves are in very good agreement with the experimental data indicating that the model can characterize the plastic deformation of the irradiated W material. It is found that the irradiation temperature has almost no effect on the load-depth curves and the hardness increase, of around 19% after irradiation, is temperature independent within errors. The formation of voids after irradiation is the main cause of irradiation induced hardening while the dislocation loops have a much lower influence. Indentation tests at low and high loading rates showed that the void dominated microstructure is more sensitive to the increase of the deformation rate.

An artificial neural network-based model for roping prediction in aluminum alloy sheet

Roping is a common macroscopic surface defect in AA6XXX aluminum alloy sheets resulting from the three-dimensional (3-D) spatial distribution of specific textures. The crystal plasticity finite element model (CPFEM) has been applied to study roping behavior and achieves good agreement with experimental observations but suffers from expensive computational consumption due to large-area and multi-layer characteristics of the roping phenomenon. In the present work, an artificial neural network-based (ANN) model is developed to predict thickness strain and corresponding surface roping under tensile deformation. A 3-D artificial orientation map generation algorithm is proposed and combined with CPFEM to produce reliable datasets to train, test, and validate the ANN model. The layer-by-layer random texture replacement strategy is adopted for dataset generation and facilitates the ANN model to capture the effects of individual layer textures on the thickness strain. A novel exponential weight loss function is also introduced to solve the imbalance problem of texture components. The ANN-based model demonstrates good prediction capability and generalizability in multiple validation cases with various artificial and experimental textures. The proposed ANN-based model provides an efficient and accurate alternative to the conventional physics-based method for roping analysis in aluminum alloy and can be also applied to similar microstructure-related deformation prediction in other materials.

Predicting residual stress in a 316L electron beam weld joint incorporating plastic properties derived from a crystal plasticity finite element model

Electron beam welding is an advanced joining technique which induces narrow weld region with minimal heat affected zone and weld-induced distortion. This reduces residual stresses in the joints which can be detrimental to structural performance of components in safety critical industries. Being an autogenous process, electron- beam welding generates a highly textured, columnar microstructure in the weld zone which have distinct properties when compared to the parent material region. Determining mechanical properties of the weld material assists in accurate assessment of the joint. However, extracting weld material specimens to determine plastic properties becomes increasingly cumbersome in thinner weld joints. An alternate approach has been demonstrated in this work wherein mechanical properties were derived using the weld microstructure in a crystal plasticity finite element (CPFE) framework. The initial calibration of the CPFE parameters was done using experimental data from thick weldment. These calibrated values were used to obtain the elastic and elastic-plastic properties of thinner weld materials by deforming corresponding synthetic microstructures whose attributes were determined by Electron Backscatter Diffraction analysis. The resultant properties were incorporated in a finite element (FE) based weld simulation to determine the residual strain. These results were compared with the residual strain data obtained using X-ray diffraction and good agreement was observed.

Diffusion and redistribution of hydrogen atoms in the vicinity of localized deformation zones

The presence of hydrogen atoms in the lattice of polycrystalline metals can lead to hydrogen embrittlement. The diffusion of hydrogen atoms and formation of hydrides depend on several parameters such as the microstructure of the metal alloy, the presence of stress risers, and the applied loading condition. In this study, a non-local crystal plasticity finite element model is coupled with hydrogen diffusion equations to study the effects of such parameters on the stress-assisted diffusion of hydrogen atoms in zirconium polycrystals. The concentrations of hydrogen atoms in the lattice and dislocation trap sites under different scenarios are studied to deconvolute the effects of texture, microstructure, and applied strain on hydrogen diffusion. It is shown that the concentration of hydrogen in the lattice peaks in the vicinity of grain boundaries and most importantly, at the triple-junction points. It is further shown that in localized deformation zones, such as twin or notch tips where dislocations concentrate, the effects of trapped hydrogen content can be significant.

Microstructure-texture-micro-strain evolution during tensile deformation of α+β titanium alloy using in-situ Synchrotron X-ray diffraction and CPFEM simulation

The evolution of micro-strain and crystallographic texture of each phase of α+β Ti-6Al-4V titanium alloy generated during tensile deformation has been estimated numerically and then compared with the experimental results. It has been carried out based on the Crystal Plasticity Finite Element Model (CPFEM) simulation of the stress-strain curve till the uniform elongation for the equiaxed microstructure is generated synthetically. The synthetic microstructure of Ti-6Al-4V has been developed using the microstructure feature parameters (such as grain size, phase fraction, and grain orientation). The polycrystal stress-strain behaviour for the same has been simulated using the representative orientation distribution function data obtained from the electron backscatter diffraction (EBSD) scans. The present investigation discusses the mechanism of strain-partitioning during uniform elongation using CPFEM simulation in conjunction with EBSD-based experimental misorientation data to rationalize our observation.