Crystal Plasticity Model Research Articles

The crack propagation behaviors, microstructure and mechanical properties of T-welded joints for TIGW with crystal plasticity model and XFEM

In view of the significant impact of welding defects on the fracture behaviors involving the strength, stress concentration and bearing capacity of welded joint, etc., the propagation behaviors and mechanical properties of welded joints with porosity and micro crack are deeply investigated using a multiscale method. In this work, a crack nucleation and propagation model based on crystal plasticity theory, combined with the extended finite element method (XFEM), is established for the T-welded joint. The maximum slip on the predominant slip system method is applied to predict the crack propagation path of pores and micro cracks in the weld zone (WZ), and the effect of crystal orientation on crack growth is explored. Then, a continuous model is used to analyze the micro and macro fracture behaviors near the weld under tensile load, combined with the maximum principal stress method. The WZ and heat affected zone (HAZ) are observed using electron backscatter diffraction (EBSD) to study the microstructure evolution. Considering grain boundaries, the image information of crystal morphology is processed through binary image analysis for FE modeling. The local mechanical properties testing is carried out using micro-specimens of HAZ and WZ to calibrate the crystal plastic parameters. The results show that the resolved shear stress of the predominant slip system of crack initiation and propagation elements is increased by pore and crack defects. The fracture positions of tensile specimens through numerical simulation are in good agreement with the macroscopic experimental results. It will provide an analysis basis for preventing fracture failure and improving the service performance of thin-walled structures in future.

Revealing the fatigue strengthening and damage mechanisms of surface-nanolaminated gradient structure

Extending the fatigue life of metals is a critical concern for maintaining material and component integrity in engineering systems. The integration of gradient structures within materials represents a highly promising approach to enhance the fatigue properties in metallic materials, while a detailed mechanistic understanding of the fatigue damage evolution of such structures is yet to be developed. Here, we report that the surface-nanolaminated gradient structure comprised of nanolaminates and hierarchical twins imparts remarkable resistance to both low-cycle and high-cycle fatigue. A dislocation-based strain gradient crystal plasticity model is developed to investigate the strengthening and damage mechanisms of our gradient structure. The size dependence of the initial dislocation density, its evolution and back stress hardening are taken into account and verified by the experimental data. The simulation results reveal that the strain delocalization and back stress hardening induced by the structure gradient significantly mitigate the fatigue damage accumulation. Additionally, in contrast to conventional gradient structures, the mechanical stability of the present structure enables these strengthening mechanisms to persist until crack initiation. These effects, combined with the sequential toughening mechanisms activated in the surface-nanolaminated gradient structure, ensure a marked life extension under low-cycle fatigue (by a factor of four), outperforming conventional gradient and other microstructural design strategies. Finally, a multiscale anti-fatigue design principal for damage homogenization is given based on the prior quantitative analysis.

Digital twin-based identification of crystal plastic material parameters for weld joints of orthotropic steel decks

The identification of crystal plasticity (CP) material parameters is indispensable for using CP models to simulate and understand the microcrack initiation and propagation of orthotropic steel decks (OSD). This study proposes a digital twin (DT)-based framework for identifying CP material parameters of weld joints of OSD by fusing multiscale CP finite element model (CPFEM) with macroscale stress–strain material tests. The material tests of the specimen (physical entity) cut from the weld joints of OSD and sliced to the centimeter scale are carried out using the standard dynamic test system. The CPFEM simulation is used to develop a multiscale virtual entity to map the physical entity. The particle swarm optimization algorithm is used to fuse the CPFEM simulation with the material test data to identify CP material parameters and produce a DT. The results demonstrate that the CP material parameters identified by the proposed framework are more accurate than those identified by a single representative volume element method. The results also show that the DT-based identification of CP material parameters has high applicability.

Two-way coupled modeling of dislocation substructure sensitive crystal plasticity and hydrogen diffusion at the crack tip of FCC single crystals

Dislocation substructure-sensitive crystal plasticity (DSS-CP) modeling accounts for the evolution of mesoscale structures using dislocation-based parameters informed by experiments and computation at various lower length scales. To a first-order approximation, DSS-CP model parameters are affected by hydrogen (H) concentration, accounting for both H-dependent yield strength and strain hardening rate. This H-affected DSS-CP model is two-way coupled with H-diffusion to explore both effects of plastic deformation on H-diffusion and effects of H on yield strength and strain hardening in the DSS-CP model. Crack tip simulations are performed for face-centered cubic (FCC) metals under monotonic loading conditions with and without H. Enhanced maximum plastic deformation in the vicinity of the crack tip (i.e., localization or intensification of plastic strain) and crack tip opening displacement (CTOD) are predicted in the presence of H, consistent with experimental observations. In spite of increased initial strength due to H, subsequent reduction of the rate of strain hardening in the presence of H is shown to enhance localization of crack tip plasticity. Furthermore, this modeling framework predicts that higher H-diffusivity (leading to a larger H-affected zone) will enhance the crack tip plasticity, making use of the two-way coupling algorithm implemented in this work. On the other hand, we find that the H-sensitivity of crack tip strain localization response, based only on modification of model parameters, is too weak to explain typical experimental observations. This points to the need to develop more advanced DSS-CP constitutive relations that consider highly complex dislocation interactions with point defects.

Texture optimization based on crystal plasticity modeling to improve strength and control anisotropy in heat treated additive manufactured Al-Mn-Sc alloy

Texture optimization based on crystal plasticity modeling to improve strength and control anisotropy in heat treated additive manufactured Al-Mn-Sc alloy

Creep condition-oriented design of molybdenum alloys with La2O3 addition assisted by microstructure-based crystal plasticity modeling

Molybdenum (Mo) alloys are essential for applications requiring outstanding mechanical properties at high temperatures across various industrial sectors. Understanding and predicting the creep properties of Mo alloys is crucial for service safety and the design of new materials. This study introduces a physics-based crystallographic creep model dedicated to the characteristic hierarchical microstructure of Mo–La2O3 alloys. By sourcing most parameters from existing literature and calibrating others within recommended ranges, the model efficiently predicts creep behavior beyond its initial calibration scope. Through the integration of microstructure descriptors, we systematically explored the impact of different microstructural features on the creep behavior and identified the underlying mechanisms. This analysis yielded two pivotal concepts: the minimum acceptable grain size and the necessary nanoparticle number density. These metrics, readily obtainable from the model, quantify the requisite grain size and nanoparticle content to achieve the target steady-state creep rates for operational demands, thus providing essential insights for the creep condition-oriented design of Mo–La2O3 alloys. The model is also expected to be adaptable for developing other Mo alloys reinforced by second phase particles, aimed at achieving desired creep properties under specified conditions, assuming that relevant parameters are accessible through literature or lower-scale simulations.

Crystal plasticity modeling of prior austenite orientation effects on deformation behaviors of martensitic steels under different strain paths

The influence of prior austenite grain (PAG) orientation on the deformation behavior of a low-carbon martensitic steel is investigated using crystal plasticity (CP) modeling with hierarchical representative volume elements (RVEs). The Kurdjumov-Sachs (K-S) relationship is refined for accurate PAG reconstruction in martensitic steel. A robust calibration strategy for CP parameters based on nanoindentation tests is developed by integrating analytical calculations with inverse methods. Virtual polycrystalline aggregates are subsequently generated by manipulating initial PAG orientations. The simulations reveal that assigning cube texture to PAGs enhances strain hardening of martensite under plane strain tension. Moreover, the RVEs with brass and copper orientated PAGs exhibit similar deformation behavior, and a more homogeneous strain distribution is realized in the RVE with PAG cube orientation. The influence of PAG orientation on stress and strain fields is correlated with lattice rotation behavior during deformation. Notably, different strain paths elicit distinct lattice rotation trajectories, wherein uniaxial tension and plane strain tension favor grains reorientation toward hard γ-fiber, whilst equi-biaxial tension drives the crystal matrix to concentrate on 〈001〉 and 〈011〉 directions. These findings provide insights into the intricate relationship between microstructural orientation and deformation behavior in martensitic steels, which is crucial for performance optimization.

High strain-rate strength response of single crystal tantalum through in-situ hole closure imaging experiments

The properties of crystalline materials often depend on directionality and operating conditions. Specifically, the strength of materials can depend anisotropically on crystal direction and the loading condition. To probe these effects, a preliminary series of high strain-rate (>105/s) strength plate-impact hole closure experiments were performed on high purity single crystal tantalum cubes. The orientation of the single crystals with respect to impact/loading were varied to provide data to inform crystal plasticity modeling efforts. The experiments consist of in-situ high-resolution X-ray radiographic imaging of the hole collapse under dynamic compression conditions to infer the material strength via its resistance to closure at increasing levels of plastic strain. The experiments are compared against hydrocode simulation predictions. A comparison with simple elastic perfectly plastic strength model predictions is presented to elucidate the response of the different crystal orientations at high strain-rate and large plastic strains.

A crystal plasticity-based creep model considering the concurrent evolution of point defect, dislocation, grain boundary, and void

Creep poses a significant threat to the integrity and longevity of structural components at high-temperature. The most current understanding of creep mainly focuses on the coupled dynamics of point defects and dislocation, which may well describe the first and second stage of creep. However, the behavior of the three stages of creep is jointly controlled by point defect (vacancy) diffusion, dislocation glide, dislocation climb, grain boundary (GB) sliding, and void evolution. A critical knowledge gap still exists regarding how these different creep mechanisms are simultaneously coupled during the three stages of creep. In this work, a multi-physical mechanisms-based crystal plasticity model is proposed to consider the concurrent evolution of point defect, dislocation, GB, and void based on a unified thermodynamic framework. In-situ scanning electron microscope creep experiments and macroscopic creep experiments of Ti-6Al-4V were conducted to validate our model. The in-situ creep experiment directly revealed the GB sliding creep failure behavior of Ti-6Al-4V for the first time. The proposed model well predicts both the microscopic and macroscopic experimental behavior of creep. The contribution of different microstructure evolutions is discussed, and a phase diagram of the dominated creep mechanism is obtained. An in-depth analysis was conducted on the coupling effects and microstructure characteristics of different creep mechanisms. This work not only deepens our understanding of the micro creep mechanism but also offers valuable insights for designing materials with specific microstructures to enhance their creep resistance.

On the plastic deformation mechanism of Al0.6CoCrFeNi high entropy alloy: In-situ EBSD study and crystal plasticity modeling

In this study, in-situ tensile tests with electron back-scattered diffraction (EBSD) were conducted to reveal the microstructural effects on the plastic deformation behavior of dual-phase Al0.6CoCrFeNi high entropy alloys (HEAs). The in-situ EBSD results demonstrated a uniform distribution of dislocation density in the fine grain (FG) samples, whereas high dislocation density was predominantly localized near body-centered cubic (BCC) phases in the coarse grain (CG) samples. The difference in mechanical properties between face-centered cubic (FCC) and BCC phases caused stress concentration and cracking at the boundaries during tension. The FCC phase within FG samples exhibited excellent plasticity, effectively impeding the propagation and coalescence of microcracks emanating from the BCC phase into longer cracks. For CG samples, brittle cracks formed in BCC phases are easy to merge, thus evolving into long cracks. Crystal plasticity finite element analysis revealed that as the strain increases, stress distribution in FG samples tended to become more homogeneous, whereas for CG samples high stress concentration consistently occurred within BCC phases. The deformation characteristics of FG were attributed to the synergistic effect generated by the FCC phase with heterogeneous grain size and the BCC phase characterized by small grain size.

Interpretation of the stress dip test as a means of characterizing backstress: Experiments and backstress-aided crystal plasticity modeling of polycrystalline tantalum

Backstresses, associated with certain dislocation arrangements and their inter-dislocation long-range stresses, are known to contribute significantly to deformation response of metals, including kinematic hardening, the Bauschinger effect (BE) and the Hall-Petch effect. Various methods have been employed to quantify these backstresses at the macro-scale. One of these approaches, which has received relatively little attention, is the stress dip test. The strain rate observed during a load dip and hold, after previous plastic deformation, can be positive or negative, depending upon the level at which the load is held, and the relative magnitudes of competing friction and backstresses. The most direct interpretation of previously reported tests indicates a surprisingly high level of backstress in common materials, and which is generally also higher than the value extracted from an unload-reload test. In this paper, stress dip tests are performed on pure polycrystalline tantalum, along with unload-reload tests. A plateau is seen in the strain rate observed during the stress dip test, which has not been previously reported. If the backstress is interpreted to correspond with the stress level associated with the middle point of the plateau, in line with the friction/backstress model of the unload-reload test, the resulting backstress obtained from both tests are very similar. A novel crystal plasticity model, incorporating backstress, reversible dislocations and non-Schmid effects, is used to help justify this new approach. The model predicts the observed plateau in strain rate, and provides a slip-level interpretation of the macroscopically observed backstress. The slip-level backstress (when considered as a fraction of the stress prior to the dip) is reasonably similar to the values interpreted from the dip test experiment. The ∼23% lower value in the simulation may be due to the lack of certain aspects of the actual physics in the model.

Effect of strain state on the surface roughening for hydroforming of aluminum alloy tube based on cross-scale numerical modeling

The complex deformation behavior would result in surface roughening such as orange peel defect during the hydroforming process of aluminum alloy tubular parts. In order to control the surface quality of hydroformed tubular parts, the effect of strain state on the surface roughening for 2219 aluminum alloy tube was analyzed based on a cross-scale model. The model combined the crystal plasticity model and macroscopic finite element model. During the uniaxial tension, the surface morphology reveals an equiaxed pattern characteristic of orange peel due to the strain incompatibilities between grains, and the peak and valley are stretched along the tensile direction. The surface roughness under tension-compression plane strain state is the lowest due to the low through-thickness strain. In the biaxial tension region, the change rate of surface roughness gradually increases with the decrease of the second principal strain especially in the late deformation stage, and the surface features evolve from an orange peel pattern to a ridging pattern. The forming limit diagram under different strain states based on surface roughness was established to guide the optimization of hydroforming process. Compared with the one-step hydroforming, the surface roughness of the bulging peak of 2219 aluminum alloy tube using multi-step hydroforming with the axial self-feeding decreases obviously from 16.3 to 10.8 μm due to the significant reduction of the equivalent strain.

On the grain level deformation of BCC metals with crystal plasticity modeling: Application to an RPV steel and the effect of irradiation

Capturing realistic deformation behavior in BCC metals at the polycrystal scale is an important aspect of predicting the material’s strength and failure. Furthermore, local deformation/strength heterogeneity also influences the lifetime and its assessments in reactor pressure vessel (RPV) steels, especially with accumulating irradiation doses during long-term operational conditions. This work utilizes a micromorphic crystal plasticity (CP) model for BCC materials with the capability to address temperature-dependent stress–strain response and irradiation effects relevant to RPV materials. The microstructure of the investigated material was characterized prior to and during testing using electron microscopy experiments, which are used for finite element model generation and simulation result validation. To analyze the validity of the model to predict strain localization under monotonic tensile loading, micro digital image correlation (DIC) was employed jointly with the CP simulations. Different modeling choices, such as the use Schmid/non-Schmid laws and gradient based CP modeling, greatly affected the capability of the model to represent similar magnitudes in strain localization and grain reorientation. The requirement for experimental measurements, including image based analyses, on a microstructural level as a validation tool for CP modeling is clearly demonstrated.

The Overload Effect on the Crack Tip Damage Mechanism in a 7075 Aluminum Alloy.

In the serviced components of a 7075 aluminum alloy, the propagation of fatigue crack can be retarded because of the overload effect; however, the corresponding retardation mechanisms are complex. To provide further insights into the retardation mechanisms of 7075 aluminum alloys, this study addresses the crack tip damage response of a cracked 7075 aluminum alloy under an overload effect. Based on the dual-scale modeling approach and the damage-coupled crystal plasticity model, the effect of the microstructure of a 7075 aluminum alloy on the damage behavior ahead of the crack tip under an overload was studied. The factors affecting fatigue damage accumulation ahead of the crack tip, such as dislocation density, the variation in the activities of slip systems, and the orientation effect of the nearest neighbor grains, are described. The results show that for the 7075 aluminum alloy, the compressive residual stress induced by the overload effect not only decreases the number of activated slip systems, but also lowers the rate of increase in dislocation density. This causes a decrease in fatigue damage accumulation during deformation. Moreover, the overload effect decreases the slip system activity as well as the resultant plastic slip; however, the decrease in plastic slip varies with the grain orientation, indicating that the overload effect depends on the grain orientation. It can also be found that both the damage strain energy release rate and lattice strain are influenced by the orientation of the nearest neighbor grains, which can eventually affect the overload effect. These findings contribute to understanding the retardation mechanisms from a microscopic perspective and provide guidance on improving the material design of a 7075 aluminum alloy to some extent.

Crystal plasticity analysis of tensile plastic behavior and damage mechanisms of additive manufactured TiAl alloy under elevated temperatures

A crystal plasticity model based on Electron Backscatter Diffraction (EBSD) experimental data has been developed to simulate the tensile behavior of additively manufactured TiAl alloys at various temperatures. To accurately capture the activity of different slip systems and their contribution to the material's plasticity, multiple slip systems across different phases are considered. The validity of the model is verified by comparing the simulation results, such as microscopic properties, with experimental and test data. Additionally, a continuous damage model is incorporated to analyze the damage behavior of additively manufactured TiAl alloys at different temperatures. Compared to experimental data, the crystal plasticity model incorporating damage effectively simulates the tensile failure behavior of TiAl alloys across a range of temperatures.

Direct application of elasto-visco-plastic self-consistent crystal plasticity model to U-draw bending and springback of dual-phase high strength steel

The incremental elasto-visco-plastic self-consistent polycrystal model (ΔEVPSC) was utilized to describe the constitutive behavior of dual-phase 980 (DP980) steel. A simple baseline modeling approach was chosen: the hardening behavior of each constituent phase in the DP980 steel was described by a simple Voce hardening law without explicitly considering the back stress; and it was assumed that using the same single crystal elastic modulus for ferrite and martensite is sufficiently representative. The adequacy of this baseline modeling approach was evaluated by comparing various mechanical experimental data with model predictions in terms of the stress vs. strain curves obtained from uniaxial tension, tension-compression, and loading-unloading-loading (LUL) tests. Additionally, the evolution of experimental lattice strain data reported in literature was used to validate the phase-specific Voce hardening parameters. Despite its minimalistic modeling description, the baseline ΔEVPSC model successfully captured key features: 1) the Bauschinger effect, 2) the decrease in chord modulus, and 3) the non-linearity in the stress vs. strain curves resulting from the LUL test. All three mentioned characteristics are crucial for accurate prediction of springback in sheet metals. The ΔEVPSC model, interfaced with a finite element solver (Abaqus/standard) as the user material subroutine, was employed to simulate the Numisheet93 benchmark problem. The strip of DP980 was first U-drawn followed by springback. The model-predicted springback profile aligned well with the experimental results only when stress relaxation was properly considered, resulting in improved predictive accuracy compared to predictions based on a distortional plasticity model.

Modeling local deformation, damage distribution, and phase transformation in zirconia particle-reinforced TRIP steel composites

This study investigates tensile deformation, damage analysis, and the effect of microtexture on a 10 % vol. zirconia particle-reinforced TRIP steel composite. In situ tensile tests and simulations were conducted, with sequential SEM images captured during tensile loading tests and electron backscatter diffraction (EBSD) providing initial crystal orientation data. SEM images were utilized in digital image correlation (DIC) analysis to calculate the local plastic strain distribution using VEDDAC software. Initial micrographs and EBSD data were transformed into geometry files for simulations, employing crystal plasticity with a dislocation density-based model and a newly proposed phase field approach-based ductile-brittle damage criterion for both austenite and ceramic particles. MATLAB's image processing functions were used to compare and validate experimentally observed damage instances with simulation predictions. The effect of microtexture combined with various physical quantities was explored using MTEX. The results show that the simulations accurately predict strain concentration around ceramic particles, with a higher strain observed in the middle region compared to the DIC observations. The simulated strain in the austenitic matrix is found to be 1.4 times higher than the DIC measurements. Quantitative analysis of damage pixels reveals that the proposed critical plastic strain value aligns closely with experimental results, showing an error of - 0.25 % compared to 1.121 % for a smaller strain case. This comprehensive analysis provides insight into the effect of microstructural attributes on material performance and behavior under tensile deformation, leading to a validated microstructural-informed damage-inclusive crystal plasticity model.

Investigating grain-resolved evolution of lattice strains during plasticity and creep using 3DXRD and crystal plasticity modelling

Microstructure-informed crystal plasticity finite element models have shown great promise in predicting plastic and creep deformation in polycrystalline materials. These models can provide substantial insight into the design, fabrication and lifetime assessment of critical metallic components during operation, for instance, in thermal power plants. However, to correctly incorporate damage prediction into models, the microstructural strain simulated at the grain level must be accurately predicted with suitable validation. For this reason, a 3D X-ray Diffraction (3DXRD) experiment was carried out on 316H stainless steel, a material commonly used in thermal power plants, to obtain the per-grain strain response during plastic and creep deformation at 550°C. Several hundred grains within a probed X-ray volume were tracked and measured whilst loading in-situ, obtaining per-grain centre-of-mass positions, crystallographic orientations, and average lattice strain over individual grains. These data were used to calibrate a crystal plasticity model to study the plastic and creep deformation using macroscopic stress-strain and stress-relaxation data. Subsequently, the model was used to predict the average elastic strain in different grains during the cyclic creep experiment, which was validated by 3DXRD datasets. The model results reveal that {100} or {311} grain families are strongly sensitive to microstructure, thereby a polycrystal model that describes specific orientation and neighbourhood characteristics is essential to predict the local response of these grain families. Whereas, self-consistent models are suitable for {110} and {111} grain families. This study shows that only with a suitable calibration of subsurface grain behaviour, crystal plasticity models reveal grain characteristic-dependent micromechanical behaviour.

A monolithically implicit time-integration approach for a dislocation-density-based b.c.c. single crystal plasticity model

A monolithically implicit time-integration approach for a dislocation-density-based b.c.c. single crystal plasticity model

Crystal-plasticity modelling of the yield surfaces and anelasticity in the elastoplastic transition of metals

The paper presents a full-field crystal-plasticity computational investigation of 10με small-strain-offset yield surfaces with pointed vertexes that are seen in the elastoplastic transition of pre-strained polycrystal metals. It is concluded that the shape of these yield surfaces obtained with a full-field spectral solver compares reasonably well with calculated ones by a simple aggregate Taylor model. The influence of material strength, work hardening, and texture are discussed. An assessment is made of the origin of anelasticity and Bauschinger effects at small strains, considering two mechanisms. Firstly, there is a built-in composite effect in crystal elastoplastic simulations due to the mixture of elastically and plastically loaded grains. Secondly, kinematic hardening of reverse slip systems will contribute to the Bauschinger effect. Based on analyses of the computed selected cases and comparison to previously published measurements, it is concluded that both mechanisms are important.