Crystal Plasticity Finite Element Analysis Research Articles

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.

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 Finite Element Analyses on the Formability of AA6061 Aluminum Alloy with Different Ageing Treatments

Different ageing treatments have been developed to achieve targeted properties in aluminum alloys through altering microstructures. However, there is a lack of understanding regarding the effect of ageing treatments on the formability of these alloys. In this study, we employed crystal plasticity finite element (CPFE) modeling, in conjunction with the Marciniak-Kuczynski (M-K) approach, to investigate the effects of ageing treatments on the mechanical properties and formability of AA6061 aluminum alloy. The as-received sheet was in the T6 heat treatment state, which was subjected to artificial ageing and pre-ageing, respectively, to achieve two age-hardened alloys with modified precipitation states. The microstructures and crystallographic textures of the three alloys were measured using the electron backscattering diffraction (EBSD) technique, and uniaxial tensile tests were performed along the rolling direction (RD), transverse direction (TD), and diagonal direction (DD, 45° to the RD) for each alloy. The forming limit curve (FLC) of the as-received alloy was determined using the Nakazima test. The dependence of mechanical strength, tensile ductility, and work-hardening behavior on the ageing treatments was clarified. Then, the tensile test results were utilized to calibrate the modeling parameters used in the CPFE model, whereas the FLC predictability of the developed model was validated with the experimental one. In the formability analysis, the effects of the ageing treatment on the FLC exhibit a notable dependency on loading paths, and the pre-aged alloy exhibits better formability than the other two at the plane strain tension state, thanks to its high work-hardening levels. In addition, the deformed textures along the different loading paths and the effects of the initial texture on the FLC are also discussed.

Comparison of Linear and Nonlinear Twist Extrusion Processes with Crystal Plasticity Finite Element Analysis.

The mechanical characteristics of polycrystalline metallic materials are influenced significantly by various microstructural parameters, one of which is the grain size. Specifically, the strength and the toughness of polycrystalline metals exhibit enhancement as the grain size is reduced. Applying severe plastic deformations (SPDs) has a noticeable result in obtaining metallic materials with ultrafine-grained (UFG) microstructure. SPD, executed through conventional shaping methods like extrusion, plays a pivotal role in the evolution of the texture, which is closely related to the plastic behavior and ductility. A number of SPD processes have been developed to generate ultrafine-grained materials, each having a different shear deformation mechanism. Among these methods, linear twist extrusion (LTE) presents a non-uniform and non-monotonic form of severe plastic deformation, leading to significant shifts in the microstructure. Prior research demonstrates the capability of the LTE process to yield consistent, weak textures in pre-textured copper. However, limitations in production efficiency and the uneven distribution of grain refinement have curbed the widespread use of LTE in industrial settings. This has facilitated the development of an improved novel method, that surpasses the traditional approach, known as the nonlinear twist extrusion procedure (NLTE). The NLTE method innovatively adjusts the channel design of the mold within the twist section to mitigate strain reversal and the rotational movement of the workpiece, both of which have been identified as shortcomings of twist extrusion. Accurate anticipation of texture changes in SPD processes is essential for mold design and process parameter optimization. The performance of the proposed extrusion technique should still be studied. In this context, here, a single crystal (SC) of copper in billet form, passing through both LTE and NLTE, is analyzed, employing a rate-dependent crystal plasticity finite element (CPFE) framework. CPFE simulations were performed for both LTE and NLTE of SC copper specimens having <100> or <111> directions parallel to the extrusion direction initially. The texture evolution as well as the cross-sectional distribution of the stress and strain is studied in detail, and the performance of both processes is compared.

Micromechanical analysis of anisotropy and asymmetry in pure titanium using electron backscatter diffraction and crystal plasticity finite element modeling

Commercially pure titanium (CP Ti) with a hexagonal close-packed structure exhibits large anisotropy and asymmetry at room temperature. While several reasons have been put forth to explain such unique behavior, the deformation mechanism responsible for the observed anisotropy and asymmetric yielding and hardening is not clearly understood. In this study, to understand the deformation mechanism of CP Ti and investigate the origin of such unusual mechanical behavior, a micromechanical analysis was conducted using electron backscatter diffraction (EBSD) and crystal plasticity finite element analyses. Representative volume elements of titanium sheets were generated using statistical data related to the microstructure, as analyzed using EBSD. Crystal plasticity model parameters corresponding to different deformation modes, including prismatic, basal, pyramidal <c+a> slip, {101‾2} tensile twinning, and {112‾2} compressive twinning, were calibrated using the macroscopic behavior in various loading conditions. Finally, the roles of different deformation modes in dictating the anisotropic and asymmetric behavior of CP Ti are discussed.

Temperature change and fatigue crack initiation associated with local cyclic slip deformation in a single crystal material

AbstractEvaluating the fatigue limit by measuring temperature changes via infrared thermography has attracted significant interest because of its potential for rapid assessments. However, the physical background and validity of this technique are not yet fully understood. In this study, notched specimens of a single crystal Ni‐base superalloy with different crystallographic orientations are subjected to cyclic loading to investigate crack initiation and temperature change. Local slip deformation is quantified using crystal plasticity finite element analyses. It is found from the experimental and analytical results that the distribution of the temperature change and the local slip deformation (a plastic shear strain on the most active slip system) are affected by the crystallographic orientation. However, the correlation between the plastic shear strain and the second harmonic amplitude, as well as the threshold values of these parameters for crack initiation, is independent of the crystallographic orientation.

Crystallographic rotation of Ti-6Al-4V alloy with a fiber texture component under isothermal forging through experimental and CPFEM analyses

This study examined the crystallographic rotation behavior of α phase in a Ti-6Al-4V alloy under isothermal uniaxial forging at 800 ℃ and 850 ℃ with changing strain rates. The base material of a Ti-6Al-4V alloy bar comprised a strong <101¯0> fiber texture component along the longitudinal direction (designated as the Z-direction in this study). Compression tests (until a height reduction of 50%) were conducted along the Z-direction and radius direction, which is perpendicular to the Z-direction (hereafter designated as the Y-direction). Microstructural conversions for the forging conditions with strain rates lower than 10−1 s−1 occurred under continuous dynamic recrystallization in which grain sizes became finer under deformation. However, only at the high strain rate condition of 1 s−1, grain refinement accompanied by significant crystallographic rotations of [0001] from the radius direction to the longitudinal direction occurred when compressed parallel to the Z-direction. This study investigates the origin of the significant rotation of [0001] observed during compression along the Z-direction at a high strain rate of 1 s−1 through experimental and crystal plasticity finite element analyses. The results show that the anisotropic dislocation glides among prismatic <a>, basal <a>, and pyramidal <c+a> led to the significant rotation of [0001] under isothermal forging at a high strain rate of 1 s−1. Furthermore, the possibility of the frequent occurrence of twinning is discussed, and it was determined to be lower than that of the anisotropic dislocation glide for the origin of the significant rotation of [0001] observed during forging at a high strain rate of 1 s−1. Alternatively, a sub-grain formation and its rotation occurred at strain rates below 1 s−1, corresponding to the process condition of the enhanced thermally activated process.

The effect of small orientation deviation from [001] to [011] on high-temperature creep properties of nickel-based single crystal

Having regard to the inherent crystal anisotropy characteristic of nickel-based single crystal and the actual industrial manufacture, and application of the turbine blade, a trade-off between orientation deviation and performance demands that attention should be paid to estimating the influences of orientation deviation from [001] to [011] on the mechanical properties of the nickel-based single crystal. The present study conducted the creep tests of nickel-based single crystals with orientation deviation under 980 °C/260 MPa and 1050 °C/169 MPa. Results show that the orientation deviation effect of nickel-based single crystals under high temperature and low stress gradually decreases with the temperature increase. A crystal plasticity finite element method based on stress, Schmid factor, γ/γ' phase, and dislocation is employed to investigate the orientation-deviation-affected creep mechanisms. The influence of orientation deviation on creep performance is summarized by combining the macroscopic mechanical properties, fracture profile morphology, and crystal plasticity finite element analysis.

Prediction of Fatigue Crack Initiation of 7075 Aluminum Alloy by Crystal Plasticity Simulation.

The 7075 aluminum alloy is a promising material for the aerospace industry due to its combination of light weight and high strength. This study proposed a method for predicting fatigue crack initiation of the 7075 aluminum alloy by crystal plasticity finite element analysis considering microstructures. In order to accurately predict the total fatigue life, it is necessary to calculate the number of cycles for fatigue crack initiation, small crack growth, and long crack growth. The long crack growth life can be estimated by the Paris law, but fatigue crack initiation and small crack growth are sensitive to the microstructures and have been difficult to predict. In this work, the microstructure of 7075 aluminum alloy was reconstructed based on experimental observations in the literature and crystal plasticity simulations were performed to calculate the elasto-plastic deformation behavior in the reconstructed polycrystalline model under cyclic deformation. The calculated local plastic strain was introduced into the crack initiation criterion (Tanaka and Mura, 1981) to predict fatigue crack initiation life. The predicted crack initiation life and crack morphology were in good agreement with the experimental results, indicating that the proposed method is effective in predicting fatigue crack initiation in aluminum alloys. From the obtained results, future issues regarding the prediction of fatigue crack initiation were discussed.

Temperature dependent transition from Mode I to crystallographic cracking in a Ni-base single crystal superalloy

To study the temperature dependent transition from Mode I to crystallographic cracking, fatigue crack propagation tests at room temperature, 300 °C and 450 °C, and crystal plasticity finite element analysis are conducted for a Ni-base single crystal superalloy by adopting compact specimens with four different crystallographic orientations. Through experimental examination, the stress intensity factor range (ΔKI) at the critical point of transition scatters for different crystallographic orientations and cannot explain the transition behavior. The slip plane for transition at different temperatures keeps the same. By crystal plasticity finite element assessment, the slip systems on the slip plane for transition are quite activated comparing with other slip systems. The distributions of the plastic shear strains along 12 slip systems at the critical point of transition exhibit the same pattern at different temperatures, which explains the slip plane for transition at different temperatures keeping the same. A damage parameter considering slip plane activity and normal stress on the slip plane can explain the transition regardless of crystallographic orientations. The damage parameter at the critical point of transition increases with the temperature, which indicates that the resistance for transition to crystallographic cracking increases with the temperature.

Formation mechanism of high-strain bands in commercially pure titanium

In textured α-Ti, band-like high-strain regions at approximately 45° to the loading direction are commonly observed under tensile deformation. Herein, such high-strain regions were called high-strain bands (HSB), and the reasons for the formation mechanism of HSBs were investigated by a uniaxial tensile test and crystal plasticity finite element (CPFE) analyses. First, we conducted a uniaxial tensile test of commercially pure titanium (CP–Ti) with a TD-split texture, where aggregates of (0001) split and incline in the transverse direction, and changes in strain distributions with deformation were observed by digital image correlation. The strain distributions showed that HSBs of approximately 45° to the loading direction were formed from the initial stage of deformation. Second, a geometric model including crystal orientation information was constructed from the crystal orientation map of the CP-Ti specimen obtained by electron back-scattered diffraction, and the cause of the formation of HSBs was investigated by CPFE analysis. The stress–strain relationship and strain distributions obtained by CPFE analysis correlated well with those obtained experimentally, and the HSBs were successfully reproduced. Finally, CPFE analyses were conducted when the loading conditions, critical resolved shear stress (CRSS), or elastic constants were changed. These results show that the HSBs formed from the initial stage of deformation and the distributions formed by elastic deformation changed depending on the elastic anisotropy. However, the distribution of HSBs after plastic deformation was unchanged by elastic anisotropy. This may be because the directions of easy deformation by elastic and plastic deformation coincided. Elastic anisotropy did not affect the distributions of HSBs formed by plastic deformation, and elastic and plastic deformations were predominantly determined by elastic constants and CRSS, respectively. Curved HSBs were also observed when plastic deformation-resistant regions occupied a large area in the specimen. In this case, the distributions of HSBs, caused by elastic deformation did not coincide with those of the plastic deformation.

Simulation of strain induced abnormal grain growth in aluminum alloy by coupling crystal plasticity and phase field methods

A mesoscale modeling methodology is proposed to predict the strain induced abnormal grain growth in the annealing process of deformed aluminum alloys. Firstly, crystal plasticity finite element (CPFE) analysis is performed to calculate dislocation density and stored deformation energy distribution during the plastic deformation. A modified phase field (PF) model is then established by extending the continuum field method to consider both stored energy and local interface curvature as driving forces of grain boundary migration. An interpolation mapping approach is adopted to transfer the stored energy distribution from CPFE to PF efficiently. This modified PF model is implemented to a hypothetical bicrystal firstly for verification and then the coupled CPFE-PF framework is further applied to simulating the 2D synthetic polycrystalline microstructure evolution in annealing process of deformed AA3102 aluminum alloy. Results show that the nuclei with low stored energy embedded within deformed matrix tend to grow up, and abnormal large grains occur when the deformation is close to the critical plastic strain, attributing to the limited number of recrystallized nuclei and inhomogeneity of the stored energy.

Cyclic stress–strain response and crystal plasticity finite element analysis of AISI 9310 steel in biaxial fatigue loading

AbstractThere are still many gaps in the research on the multiaxial fatigue failure mechanism of the gear shaft. In this paper, cyclic stress–strain response and biaxial fatigue damage characteristics of gear steel AISI 9310 were investigated. The specimens showed obvious cyclic softening characteristics at all phase angles, and the softening rate was directly associated with the initiation and propagation of cracks. The fractographies at different phase angles revealed that the specimens under out‐of‐phase loading suffered fatigue failure caused by a single crack source on the surface, while the fatigue crack under in‐phase loading was gathered together by the propagation of different crack sources. Finally, the established crystal plastic finite element model showed a good prediction of the plastic strain energy density at different phase angles, and the maximum error was 13.03%. Furthermore, a biaxial fatigue life prediction method was proposed, with a maximum error of 39.5%.

A crystal plasticity finite element analysis on the effect of prestrain on springback

An incremental elasto-visco-plastic self-consistent polycrystal model was directly interfaced with a finite element (FE) code and applied to simulations of a mild steel sample subjected to 3-point-bending (3 PB). Emphasis is put in applying this strategy, for the first time, to predict springback responses after various amounts of prestrains. The crystallographic orientation distribution obtained from an EBSD scan was used to assign the initial polycrystalline aggregate for each FE integration point. The RGVB dislocation-density-based hardening model was adopted as the constitutive law, and the parameters were characterized by fitting uniaxial tension and tension-compression flow stress curves. The numerical reliability of the FE simulation results was evaluated via a systematic numerical study in terms of the mesh size, the numbers of grains sampled per each FE integration point and the cross-section points. The model successfully predicts the effect of prestrain on the springback, thus implying that the current modeling approach can be directly applied to industrial forming and springback predictions.

In situ study on plastic deformation mechanism of Al0.3CoCrFeNi high-entropy alloys with different microstructures

Al0.3CoCrFeNi high-entropy alloys (HEAs) have attracted the attention of researchers owing to their excellent mechanical properties. In this study, Al0.3CoCrFeNi HEAs with typical grain microstructures were fabricated and subjected to tensile tests, along with in situ scanning electron microscopy–electron backscatter deformation (SEM–EBSD), to determine the relationship between the grain microstructure, plastic deformation, and mechanical properties. The in situ EBSD analysis showed that the HEA sample with fine grains (FGs) exhibited more significant grain boundary deformation than that with coarse grains (CGs). The FG sample had a more uniform dislocation density distribution than the CG sample, and no noticeable excessive dislocation density was observed inside the grain. This indicates that the plastic deformation of the FG sample could be distributed more homogeneously without a prominent local stress concentration. Based on the grain structures from EBSD scans, crystal plasticity finite element modeling (CPFEM) and analysis were conducted to analyze the grain-level stress and strain heterogeneities. The results showed that during the tensile process, high stress was initially distributed near the B2 phase and subsequently at the grain boundaries of the HEA with increase in tensile deformation. The local stress distribution in the matrix was significantly affected by the B2 phase. Although high stress was distributed near the B2 phase during plastic deformation, the probability of crack initiation at the phase boundaries was low. This can be partly attributed to the formation of deformation twins at the junction of the B2 phase and FCC matrix, which releases the stress.

Microstructure evolution and mechanical behavior of copper through‑silicon via structure under thermal cyclic loading

The through‑silicon via (TSV) technique is widely applied in the latest highly integrated circuits packaging. However, one of the prevalent failure modes is caused by thermal cyclic loading from power fluctuations of the chip. Different thermal expansion coefficients of Cu and Si could cause a mismatch of thermal stresses under temperature cycling, which will lead to thermal fatigue failure of structure. In the current study, thermal cycling experiments are performed on Cu-TSV samples to investigate the effect of temperature cycling on microstructure evolution and mechanical behavior. The electron backscatter diffraction analysis is conducted to investigate the grain size, local texture and microstructure evolution of Cu. Based on the crystal plasticity theory, a constitutive model considering temperature and grain size effect is developed, and the parameters are calibrated. Combining crystal plasticity theory and finite element analysis, the effects of grain orientation and different grain sizes on the stress distribution and plastic work evolution of TSV structure under thermal cyclic loading are investigated.

Influence of particle content on the ductility of extruded non-recrystallized aluminium alloys subjected to shear loading

In-plane shear tests were conducted on two extruded 6000-series aluminium alloys to investigate the influence of constituent particles on ductile fracture. The two alloys have previously been characterized and found to have different area fraction of constituent particles while having similar grain structure, crystallographic texture, strength, and work hardening. Specimens of both alloys were machined from flat profiles with their gauge section oriented along either the extrusion direction or the transverse direction. The specimens were loaded in shear until fracture and an experimental-numerical approach was employed to analyse the stress and strain fields, which involved digital image correlation and crystal plasticity finite element analysis. The fracture mode was determined by examining digital images captured during the experiment, while the fracture surface of representative specimens was examined in a scanning electron microscope. The shear strain across the gauge section at failure was substantially lower for the alloy with higher fraction of constituent particles, and the negative effect of the particle content on the ductility was found to be more pronounced for the tests in the transverse direction. The crystal plasticity finite element analyses showed an extensive texture development within the gauge region and that the local shear strain at failure was somewhat different in the two loading directions.

Numerical prediction of [formula omitted] compression twin activation in commercially pure titanium under uniaxial tension

In this study, the criteria for {112‾2} compression twinning in commercially pure titanium (CP–Ti) were investigated by uniaxial tensile tests, crystal plasticity finite element (CPFE) analyses, and slip operation factor (SOF) calculations. First, the aggregates of the [0001] axes of CP-Ti were inclined in the rolling direction (RD), implying its RD-split texture. The development of the crystal orientation distribution with deformation was observed by electron back-scattered diffraction (EBSD). Active slip systems were identified by kernel average misorientation (KAM) and intergranular misorientation axis (IGMA) analyses. The dominant slip system was prismatic <a>, whereas the non-prismatic <a> slip systems were activated near the grain boundary. Active twin systems were also identified by the rotation angles of the [0001] axes between the twin and matrix. The dominant active twin system was the {112‾2} compression twin, although a uniaxial tensile load was applied. Second, the positions of {112‾2} twinning were predicted by CPFE analysis using the resolved shear stress (RSS) criterion while considering plastic deformation. SOF analysis was also employed for the prediction. The CPFE and SOF analyses yielded almost the same level of prediction accuracy. However, these calculations do not completely predict the twinning positions. Finally, the criteria for {112‾2} twinning were discussed, and it was revealed that hydrostatic pressure and RSS are possible criteria for {112‾2} twinning in the continuum model.

Crystal plasticity finite element analysis of size effect on the formability of ultra-thin ferritic stainless steel sheet for fuel cell bipolar plate

The present study investigated the size effect on the formability of ultra-thin metallic bipolar plate for proton exchange membrane (PEM) fuel cell by crystal plasticity finite element method (CPFEM) in conjunction with the Marciniak-Kuczynski (MK) model. Mechanical behavior and crystallographic texture of a 0.08 mm-thick ferritic stainless steel (FSS) sheet were characterized by uniaxial tensile test and electron backscatter diffraction (EBSD) measurement. Nakazima formability test was carried out to measure the forming limit diagram (FLD) of ultra-thin FSS sheet. A hybrid cellular automata–Monte Carlo (CA–MC) model was developed to generate a ‘realistic’ representative volume element (RVE) that accurately reconstructed the measured texture and grain boundary misorientation distribution (GBMD). The predicted FLD by the CPFEM–MK model with the realistic RVE shows a good agreement with the experimental results. In order to explore the size effect on the formability, the forming limit analyses were performed using RVEs with various thickness-to-grain size ratios (t/d = 2∼10). The results reveal a significant degradation of the formability of the ultra-thin FSS sheet as t/d decreases. With decreasing number of grains through the thickness, the stress and strain heterogeneities in the surface grains are noticeably increased due to the less constraint by the subsurface grains, which plays an important role in the size effect. Furthermore, it is found that the surface strain hot spots in the material with low t/d can act as the geometrical imperfection to accelerate the failure, together with the increased stress triaxiality in the surface grains as the results of the localized strains and premature necking during the deformation. This attributes the decrease of forming limit strains to the early plastic flow instability in the ultra-thin sheet material with low thickness-to-grain size ratio.

Multiscale mechanical characterization of 601 nickel-based superalloy fabricated using wire-arc additive manufacturing

The anisotropy in the mechanical properties of 601 nickel-based superalloy fabricated using wire-arc additive manufacturing (WAAM) was investigated through multiscale tensile testing combined with crystal plasticity analysis. Micrometer-scale and millimeter-scale tensile tests were performed to obtain single crystal properties and deformation behavior as the layered structure, respectively. Tensile tests on millimeter-scale specimens, composed of columnar grains grown along [001], exhibited anisotropy in the fracture strain and work-hardening behavior despite the fact that the yield stress was approximately constant regardless of the loading axis. Tensile tests on micrometer-scale specimens, which were single crystals with dendrites, exhibited a critical resolved shear stress (CRSS) of 116 ± 3 MPa. This value was close to 110 MPa for the CRSS of the wire sample without dendrites, which indicates limited influence of dendrite formation on the yielding behavior of columnar grains. Crystal plasticity finite element analysis was carried out to reproduce the experimental deformation behavior depending on the loading direction of the millimeter-scale tensile tests. Based on the numerical results of the simplified analysis models, the possible mechanism of the dependence of loading direction on the deformation behavior is explained by three newly proposed factors related to the Schmid factor of the primary slip system (PSF) for the characterization of non-uniform deformation in multiple crystals. A significant variation difference existed depending on the loading direction, owing to the superposed contributions of the crystallographic orientations and geometrical configurations of the columnar grains.