Dislocation Density-based Crystal Plasticity Model Research Articles

Sequential Dual-Scale Approach for Microstructure-Informed Ductile Fracture Prediction

This study presents a novel dual-scale finite element method to establish a microstructure-informed ductile fracture criterion for ferrite–martensite dual-phase (DP) steel. At the macroscale, an anisotropic plasticity model with rate-dependent hardening was employed to simulate the material's deformation history. Simultaneously, at the microscale, a dislocation density-based crystal plasticity model was utilized to simulate deformation within a representative volume element (RVE) of the dual-phase steel, constructed using tomography aided by a plasma-focused ion beam/electron backscatter diffraction system.The material properties of the ferrite and martensite phases were determined through X-ray diffraction (XRD) analysis and load-displacement measurements obtained via nanoindentation for each phase. The RVE simulation results were validated against experimentally measured mechanical properties and microstructural changes. The local deformation history at the fracture initiation site, extracted from the macroscale model, was used as boundary conditions for the microscale RVE simulation; sequential dual-scale approach. The models were applied to specimens with varying notch radii, generating different local stress triaxialities and accumulated shear strains at fracture onset. This process allowed the establishment of a ductile fracture criterion, which was further tested in a hole expansion experiment, demonstrating close alignment with experimental data.This sequential dual-scale analysis effectively predicts the deformation behavior of multiphase metallic materials by incorporating realistic microstructures while minimizing computational costs. Consequently, the proposed ductile fracture prediction technique offers a robust method with broad applicability across various metallic materials.

Phasing effects on thermo-mechanical fatigue damage investigated via crystal plasticity modeling

Nickel (Ni)-based superalloys have high strength at elevated temperatures, making them ideal candidates for aerospace components exposed to thermo-mechanical loads. Thermo-mechanical fatigue's (TMF) influence on material failure is highly dependent on the temperature-load phase profile as a consequence of path-dependent thermo-mechanical plasticity. In order to understand the direct influence phasing effects have on TMF performance, a microstructure-based fatigue model has been developed to connect damage mechanisms to crack initiation events. In this work, in-phase (IP) TMF, out-of-phase (OP) TMF, and iso-thermal (ISO) loading profiles are investigated with a temperature-dependent, dislocation density-based crystal plasticity model to pinpoint a relationship between microstructural damage and TMF phasing effects. A crystal plasticity modeling framework with capabilities to isolate phasing (IP, OP, and ISO) effects is presented to locate fatigue damage in a set of statistically equivalent microstructures (SEMs) with an energy-based damage indicative parameter. Local stress, accumulated damage, intragranular misorientiation, grain interactions, and slip alignment activity at the damaged regions are studied under the various temperature-load phase profiles to connect microstructural material damage to TMF performance. Based on the local microstructural material damage, it is postulated the material's stiffness at maximum load influences OP TMF performance, whereas the hardening/plasticity at maximum load influences IP TMF. The results from the presented framework is consistent with experimental evidence that at high mechanical strain amplitudes IP TMF has a shorter life as a consequence of hardening/plasticity influencing path-dependent thermo-mechanical plasticity, whereas at low strain amplitudes OP TMF has a shorter life due to stiffness influencing path-dependent thermo-mechanical plasticity.

Insights into the deformation mechanisms of an Al1Mg0.4Si alloy at cryogenic temperature: An integration of experiments and crystal plasticity modeling

In this work, we investigated the mechanical properties and corresponding deformation mechanisms of an Al1Mg0.4Si alloy, which exhibited significantly higher strength and outstanding strain hardening capacity at 77 K compared to its counterparts at 298 K. The deformation mechanisms responsible for the excellent strength-ductility synergy and extraordinary strain hardening capacity at cryogenic temperature were elucidated through a combined experimental and simulation study. The results reveal the presence of numerous slip traces and microbands throughout grain surfaces during deformation at 298 K, whereas at 77 K, vague grain surfaces dominate, indicating the simultaneous operation of multiple slip systems. Transmission electron microscopy (TEM) analysis using the two-beam diffraction technique demonstrates the presence of dislocations with several different Burgers vectors inside a grain at cryogenic temperature, confirming the activation of multiple slip systems. The accumulation of dislocations facilitated by these multiple slip systems, combined with the high dislocation density, contributes to strain hardening and remarkable uniform elongation at 77 K. A modified dislocation density-based crystal plasticity model, incorporating the effect of grain boundary hardening (GBH) and temperature, was developed to gain a better understanding of the underlying mechanisms governing alloy's strength and plasticity. The GBH effect significantly enhances statistically stored dislocation (SSD) density and screw dislocation proportion, which promote homogeneous deformation and enhance strain hardening capacity at cryogenic temperature. These findings deepen the understanding of plastic deformation at cryogenic temperatures and pave the way for the development of ultrahigh-performance metallic materials for cryogenic applications.

A dislocation density-based crystal plasticity damage model for rolling contact fatigue of gradient grained structures

A dislocation density-based crystal plasticity damage model is presented for a numerical study on the spalling behavior of gradient grained structures under rolling contact fatigue loading. The topology of the gradient grained structure is constructed using Voronoi tessellations. The fatigue damage is coupled into a dislocation density-based crystal plasticity model where the evolutions of the dislocation density and fatigue damage are considered. The process of spalling is characterized by the evolution of fatigue damage in the polycrystalline structures. The evolutions of contact pressure, stresses, dislocation density, plastic strain, and fatigue damage of gradient grained structures with regard to rolling cycles are investigated. Moreover, the effect of the gradient form and residual stress on the rolling contact fatigue behavior is studied. The simulation results reveal that the gradient grained structures and the residual stress influence the rolling contact fatigue resistance.

Grain interactions under thermo-mechanical loads investigated with coupled crystal plasticity simulations and high-energy X-ray diffraction microscopy

Nickel (Ni)-based superalloys are used for safety-critical components in the aerospace industry because of their high strength at elevated temperatures. These materials are subjected to complex thermal and mechanical cycling due to service conditions, which leads to thermo-mechanical fatigue (TMF) failure. The failure mechanisms associated with TMF are dependent on microstructural characteristics and loading parameters, such as temperature, strain range, and strain-temperature phasing, requiring a large set of experimental test matrices to study TMF failure. One means to reduce the necessity of extensive and exhaustive testing for material qualification is with model-based approaches. In this work, to study the complexities of micromechanical TMF damage, a temperature-dependent, dislocation density-based crystal plasticity model for a Ni-based superalloy is generated with uncertainty quantification. The capabilities of the model's temperature dependency are examined via direct instantiation and comparison to a high-energy X-ray diffraction microscopy (HEDM) experiment under coupled thermal and mechanical loads. Unique loading states throughout the experiment are investigated with both crystal plasticity predictions and HEDM results to study early indicators of TMF damage mechanisms at the grain scale. Via a crystal plasticity-based failure metric that can predict likely sites for crack initiation, regions of extreme values indicate the spatial location of microstructural damage, while showing correlation with high strain gradients. The results also indicate that the extreme value of thermo-mechanical damage accumulation is influenced by the surrounding grains characteristics including slip system activity, lattice curvature, and neighboring grain compatibility interactions, quantified via a grain interaction strength-to-stiffness ratio orthogonal to the grain boundary.

A fundamental understanding of how dislocation densities affect strain hardening behavior in copper single crystalline micropillars

Under mechanical loading, the strain hardening behavior of crystalline face-centered cubic (FCC) metals is of critical importance in determining fracture behavior and overall mechanical performance. While strain hardening is typically accompanied by a decrease in ductility, it can also simultaneously enhance the material's resistance to plastic deformation and improve its load bearing capacity. Hence, we conducted a detailed study using copper (Cu) single-crystal micropillars as a model system to investigate and delineate the relationship between strain hardening and defect behavior. We employed in situ compression in a scanning electron microscope (SEM) and dislocation density-based crystal plasticity (DCP) modeling. The strain hardening rate varied with the compression crystallographic orientation, ranging from negligible values (of approximately 80 MPa) to relatively high hardening rates (of approximately 1150 MPa) for nominal strains of up to 15%. Various analysis methods were applied, including slip trace characterization, electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), and transmission Kikuchi diffraction (TKD). These techniques allowed us to identify the distributions of active slip systems, dislocation structures after compression, and correlated internal lattice rotations. Furthermore, the DCP model was developed to specifically understand how serration events are related to dislocation-density evolution or strain bursts, and this was validated with the micropillar experiments. This integrated experimental and modeling investigation offers valuable insights and predictions regarding the evolution of both total and partial dislocations, including Hirth and Lomer junctions, as well as lattice rotations.

Computational homogenization based crystal plasticity investigation of deformation behavior of AA2024-T3 alloy at different strain rates

PurposeModeling of material behavior by physically or microstructure-based models helps in understanding the relationships between its properties and microstructure. However, the majority of the numerical investigations on the prediction of the deformation behavior of AA2024 alloy are limited to the use of phenomenological or empirical constitutive models, which fail to take into account the actual microscopic-level mechanisms (i.e. crystallographic slip) causing plastic deformation. In order to achieve accurate predictions, the microstructure-based constitutive models involving the underlying physical deformation mechanisms are more reliable. Therefore, the aim of this work is to predict the mechanical response of AA2024-T3 alloy subjected to uniaxial tension at different strain rates, using a dislocation density-based crystal plasticity model in conjunction with computational homogenization.Design/methodology/approachA dislocation density-based crystal plasticity (CP) model along with computational homogenization is presented here for predicting the mechanical behavior of aluminium alloy AA2024-T3 under uniaxial tension at different strain rates. A representative volume element (RVE) containing 400 grains subjected to periodic boundary conditions has been used for simulations. The effect of mesh discretization on the mechanical response is investigated by considering different meshing resolutions for the RVE. Material parameters of the CP model have been calibrated by fitting the experimental data. Along with the CP model, Johnson–Cook (JC) model is also used for examining the stress-strain behavior of the alloy at various strain rates. Validation of the predictions of CP and JC models is done with the experimental results where the CP model has more accurately captured the deformation behavior of the aluminium alloy.FindingsThe CP model is able to predict the mechanical response of AA2024-T3 alloy over a wide range of strain rates with a single set of material parameters. Furthermore, it is observed that the inhomogeneity in stress-strain fields at the grain level is linked to both the orientation of the grains as well as their interactions with one another. The flow and hardening rule parameters influencing the stress-strain curve and capturing the strain rate dependency are also identified.Originality/valueComputational homogenization-based CP modeling and simulation of deformation behavior of polycrystalline alloy AA2024-T3 alloy at various strain rates is not available in the literature. Therefore, the present computational homogenization-based CP model can be used for predicting the deformation behavior of AA2024-T3 alloy more accurately at both micro and macro scales, under different strain rates.

Hydrogen-assisted intergranular fatigue crack initiation in metals: Role of grain boundaries and triple junctions

In this work, small-scale, low-cycle fatigue experiments on hydrogen charged nickel specimens are performed that highlight particular grain boundaries (GBs) and triple junctions as potential intergranular crack initiation sites. To understand the micromechanics and underlying physics, a dislocation density-based crystal plasticity model coupled with slip-rate based hydrogen transport model is developed. A fatigue indicator parameter (FIP) is also developed that models the crack initiation process by considering the contributions of accumulated plastic slip, GB normal stress, and local hydrogen concentration. Depending on the diffusivity, hydrogen binding energy, and misorientation, GBs are categorized as ‘special’ or ‘random’, and their role on hydrogen distribution is analysed using a model microstructure. Special GBs are ones with low diffusivity and high hydrogen binding energy whereas the random GBs have high diffusivity but low hydrogen binding energy. Complying with the experimental observations, the evolution of FIP with load cycles suggests certain triple junction configurations in the microstructure involving in the crack initiation process. For the case of uniform initial hydrogen concentration, special GBs are found to retain more hydrogen with load cycles primarily due to their low hydrogen diffusivity whereas the random GBs diffuse hydrogen out quickly to the bulk. The high hydrogen concentration and favourable stress state in the form of high hydrostatic stress spots generally found at triple junction of special/random GBs fulfil the necessary condition leading to an intergranular crack initiation.

Modelling of hydrogen-assisted damage at the deforming single crystal crack-tip

A coupled framework of dislocation density-based crystal plasticity model and slip-rate based hydrogen transport model is developed to simulate hydrogen-assisted damage at the deforming crack-tip. Chemical potential-based boundary conditions and mobile dislocation-assisted hydrogen transport account for the evolving hydrogen concentration. A novel fracture indicator parameter is proposed to quantify the damage that considers the combined effect of local hydrogen concentration, accumulated plastic slip and stress triaxiality. Experimentally-informed critical value for hydrogen concentration is considered to model the crack initiation. Depending on the crystal orientation, the damage is shown to be associated either with an individual hydrogen embrittlement mechanism (hydrogen-enhanced localized plasticity, and hydrogen-enhanced decohesion) or their synergistic effect at the crack tip.

Finite strain crystal plasticity-phase field modeling of twin, dislocation, and grain boundary interaction in hexagonal materials

Twin, dislocation, and grain boundary interaction in hexagonal materials, such as Mg, Ti, and Zr, has critical influence on the materials’ mechanical properties. The development of a microstructure-sensitive constitutive model for these deformation mechanisms is the key to the design of high-strength and ductile alloys. In this work, we have developed a mechanical formulation within the finite strain framework for modeling dislocation slip- and deformation twinning-induced plasticity. A dislocation density-based crystal plasticity model was employed to describe the dislocation activities, and the stress and strain distributions. The model was coupled with a multi-phase-field model to predict twin formation and twin-twin interactions. The coupled model was then employed to study twin, dislocation, and grain boundary interactions in Mg single- and polycrystals during monotonic and cyclic deformation. The results show that twin-twin interactions can enhance the strength by impeding twin propagation and growth. The role of dislocation accommodation on twin-twin interactions was twofold. Dislocation slip diminished twin-twin hardening by relieving the development of back-stresses, while it effectively relaxed the stress concentration near twin-twin intersections and thus may alleviate crack nucleation. The plastic anisotropy in each grain and the constraints imposed by the local boundary conditions resulted in stress variations among grains. This stress heterogeneity was responsible for the observed anomalous twinning behaviour. That is, low Schmid factor twins were activated to relax local stresses and accommodate the strain incompatibility, whereas the absence of high Schmid factor twins was associated with slip band-induced stress relaxation.

Coupled diffusion-mechanics framework for simulating hydrogen assisted deformation and failure behavior of metals

Understanding of years-old multifaceted hydrogen-assisted damage evolution necessitates efforts to model the coupled diffusion-mechanics response in metallic materials. Informed by the dislocation-hydrogen interactions, understood earlier via experiments and/or multi-scale modeling techniques, this work presents a dislocation density-based crystal plasticity model coupled with a hydrogen diffusion/trapping model to simulate the hydrogen-assisted deformation and failure under the HELP mechanism of hydrogen embrittlement. The important role of hydrogen on dislocation multiplication, annihilation and dislocation interaction weakening are included in the presented framework. Two possible scenarios under HELP mechanism, leading to H-induced macroscopic softening or hardening as a result of trade-off between the hydrogen-induced weakening of dislocation interactions and hydrogen-induced increased dislocation density emerges from the simulation studies. These finding points towards the inevitable role of HELP mechanism to cause early failure in metals either working independently or in support with additional mechanisms.

Crystal plasticity modelling of stability of residual stresses induced by shot peening

Gas turbine components are often shot-peened to improve surface integrity and fatigue capability. Compressive Residual Stress (CRS) and increased surface hardness are the key outcomes of shot peening. But the CRS is observed to relax during the service life, and its stability depends on the amount of cold work during the shot peening process and the applied load during service life. This study develops a numerical framework capable of accurately estimating the amount of cold work using a dislocation density-based crystal plasticity model. The proposed framework captures the evolution of microstructure during the shot peening process, incorporating the effects of grain size, orientation, and strain rate. The simulation methodology is used to investigate the influence of loading conditions on work hardening and relaxation. The numerical predictions are shown to agree with available experimental observations. The proposed method demonstrates the capability to optimize microstructure and shot peening parameters to reduce the relaxation of CRS during service life.

An insight into size effect on fracture behavior of Inconel 718 cross-scaled foils

Product miniaturisation has increased the demand for cross-scaled components with various sized features covering the macroscale (mm-scale) and mesoscale (μm-scale). During the sheet metal forming process, the feature size of cross-scaled components, such as foil thickness, changes from macroscale to mesoscale. The fracture behavior of the cross-scaled components varies from that of the macroscale components due to the size effect, leading to a high scrap rate and unacceptable cost in manufacturing. To reveal size effect on fracture and predict the fracture occurring of the cross-scaled components is still a challenge urgently to be solved. Thus, taking Inconel 718 superalloy cross-scaled foils as the case material, firstly, the cross-scaled foils were prepared with the thicknesses from 0.05 to 1.5 mm, the ratio of thickness to grain size (t/d) from 1.07 to 24.26. Uniaxial tensile tests and in-situ tensile tests were performed to reveal the fracture mechanism of the superalloy cross-scaled foils. Then, several uncoupled fracture criteria were implemented into the crystal plasticity finite element modeling (CPFEM) with the cross-scaled geometric modeling and random texture to predict the fracture behavior of the cross-scaled components. The uncoupled fracture criteria include Freudenthal criterion, Cockcroft & Latham(C&L) criterion, Normalized C&L, Brozzo criterion, Ayada criterion, Rice & Tracy criterion, Tresca criterion, equivalent stress criterion, equivalent strain criterion and maximum principal strain criterion. The phenomenological crystal plasticity model and dislocation density-based crystal plasticity model were compared in terms of calculation accuracy and efficiency. Thirdly, the size effect related fracture mechanisms of the cross-scaled foils were revealed, and the relationship between the fracture strain, fracture stress and t/d were obtained. Generally, the fracture strain and stress drop with a decrease in t/d. Consequently, an abnormal phenomenon occurs where the plasticity and strength increase with the decrease of t/d in some areas. The random textures lead to fluctuations in the strength and plasticity of the cross-scaled foils. Finally, the equivalent stress fracture criterion (ESFC) was determined where the fracture threshold is less affected by random texture. The relationship between the fracture threshold of ESFC and t/d was found, and the CPFEM-ESFC model was established considering the random textures induced scattering of the fracture threshold due to random textures. The scattering distribution function of cross-scaled component fracture behavior under different t/d was obtained through CPFEM-ESFC model and hundreds of random textures designs. The study provides a statistical method to avoid the forming scattering and a theoretical basis for the process design of cross-scaled components.

Experiments and Crystal Plasticity Simulations on Plastic Anisotropy of Naturally Aged and Annealed Al–Mg–Si Alloy Sheets

The influence of the heat treatment on the plastic anisotropy of an Al–Mg–Si sheet was investigated by experiments and crystal plasticity simulations. Uniaxial tension tests were conducted for the naturally aged (T4 temper) and annealed (O temper) Al–Mg–Si sheets. Solute atoms Mg and Si form clusters in the T4 temper sheet, while they bind to form precipitates in the O temper sheet. It is found that the in-plane variation of the R value, texture, and grain size are almost identical for both sheets. By contrast, the anisotropy of the flow stress is clearly dissimilar; the flow stress is the highest in the diagonal direction for the O temper sheet, whereas the flow stress in that direction is nearly lowest for the T4 temper sheet. Thus, the heat treatment alters the anisotropy of the flow stress. The plastic behaviors of the specimens were simulated using the dislocation density-based crystal plasticity model. The influence of the dislocation interaction matrix on the plastic anisotropy was examined. The orientation dependence of the flow stress is found to be sensitive to the interaction matrix. The flow stresses predicted by the interaction matrix determined based on the dislocation dynamic simulation agree with the experimental results for the O temper sheet. Whereas this interaction matrix does not reproduce the flow stress anisotropy for the T4 temper sheet. When the interactions among the dislocations are set to equivalent—i.e., the interaction matrix is filled with unity—the crystal plasticity simulation results in the flow stress anisotropy that is similar to the experimental trend of the T4 temper sheet. In contrast to the flow stress, the R value is insensitive to the interaction matrix, and the predicted R values agree with the experimental results for both specimens.

Modeling cyclic deformation of austenitic stainless steels at elevated temperatures using a physically-based mesoscale crystal plasticity framework

Austenitic stainless steels demonstrate significant changes in key macroscale deformation responses at elevated temperatures; these changes are relatively well-understood at micro- and macroscales in the framework of dynamic strain aging (DSA). At the microscale, temperature-dependent behavior is attributed to enhanced solute mobility and subsequent pinning of dislocations by solute atmospheres. At the macroscale, phenomenological equations are used to approximate microscale material behavior. However, the connection between unit dislocation processes at the microscale and macroscale deformation behaviors is unclear. In the current study, a dislocation density-based crystal plasticity model is used to relate micro- and macroscale responses for cyclic loading of austenitic stainless steels at elevated temperatures. Specifically, the variation in deformation behavior at elevated temperatures is attributed to modifications in the heterogenous distribution of dislocations on the mesoscale. The proposed framework demonstrates good agreement with experiments for strain- and stress-controlled cyclic loading scenarios. The model is also shown to be able to address key phenomena associated with DSA, i.e., negative strain rate sensitivity and stress-strain curve serrations.

On the crystallographic anisotropy of plastic zone size in single crystalline copper under Berkovich nanoindentation

Aiming at revealing plastic deformation mechanisms of nanoindentation tests, we investigate the crystallographic orientation-influenced indentation size effect in the Berkovich nanoindentation tests of single crystalline copper, by using the nonlocal crystal plasticity finite element approach and specifically designed experiments. In our simulation model of nanoindentation, a new geometrically necessary dislocation density-based crystal plasticity model is proposed, and the utilized model parameters are calibrated by fitting the measured load-displacement curves of indentation tests. Then the size of plastic zone of indentation tests is defined by the surface pile-up profile, i.e. the diameter of a circle consisting of material points with half of maximum pile-up height. It is found that the modified plastic zone model incorporated with the newly developed scaling factor provides good predication of the indentation depth-dependent hardness of single crystalline copper.

Hydrogen distribution in metallic polycrystals with deformation

To understand hydrogen embrittlement and predict probable damage sites based on high hydrogen segregation, it is important to identify hydrogen distribution mechanisms in metallic microstructure with deformation. Hydrogen segregation in metals is affected by various factors such as grain-size, the character of grain boundaries (GBs), loading direction and strain-rate. To this end, a computational framework consisting of non-local dislocation density-based crystal plasticity model coupled with slip-rate based hydrogen transport model is presented to study the role of (i) grain-size, (ii) loading direction, (iii) strain-rate and (iv) GB character on hydrogen distribution and segregation in the pre-charged metallic microstructure. The computational framework is capable of accounting for the change in local hydrogen concentration due to prevailing hydrostatic pressure, trapping by dislocations, GB energetics and local slip-rates in the metallic microstructure. The difficulty in dislocation motion at the inter-granular regions of polycrystal due to high cross-hardening offered by geometrically necessary dislocations (GNDs) is incorporated in the model as additional isotropic hardening, whereas the back stress due to the GND pileups is included as a kinematic term in the flow rule. In addition, GNDs act as hydrogen trap sites leading to increased hydrogen concentration in the inter-granular regions. The strain-rate factor initially provided by Krom & Bakker (1999) is modified in the present work to make it compatible with the dislocation density-based coupled framework, which is able to calculate trapped hydrogen in dislocations along the slip systems. Plastically deformed polycrystals of various grain-sizes, along different directions, with varying strain rates and containing Σ3[11¯0](111) and Σ5[001](210) GBs show that the gradients of hydrostatic pressure and GB character are major factors controlling hydrogen segregation in the microstructure.

Deformation behavior and anisotropic response of 2060 Al-Cu-Li alloy: experimental investigation and computational homogenization-based crystal plasticity modeling

Since AA2060-T8 was launched the past few years, it was crucial to understand the deformation behavior and to establish a multi-scale model that can link the microstructural state of this alloy with its mechanical behavior. Thus, a computational homogenization-based crystal plasticity modeling was proposed to predict the deformation behavior and capture the anisotropic response of AA2060-T8 at different deformation conditions. Uniaxial tensile tests were accomplished at room temperature and strain rates of 0.001 and 0.1s−1 using samples with different fiber orientations to experimentally investigate the deformation behavior and anisotropic response of AA2060-T8. Thereafter, to clarify the details of the in-grain deformation features, a representative volume element was established to describe the real microstructure of AA2060-T8 in which each grain was discretized using many finite elements. Afterwards, a dislocation density-based crystal plasticity model was developed to describe the behavior of grains and simulate the plastic deformation of AA2060-T8. The material parameters utilized in the crystal plasticity model was determined from the stress–strain curves of the samples tested at loading direction of 30° with respect to rolling direction and strain rate of 0.001s−1. Additionally, a periodic boundary condition was modified to consider both geometrical and deformation induced anisotropy. The achieved results from the proposed computational homogenization method are in remarkable agreement with that obtained from experimental work. This means that the proposed computational homogenization method is able to predict the deformation behavior and capture the anisotropic response of AA2060-T8 at various deformation conditions.

Computational homogenization of tensile deformation behaviors of a third generation Al-Li alloy 2060-T8 using crystal plasticity finite element method

A computational homogenization procedure based on the crystal plasticity model was proposed herein to predict the tensile deformation behavior and investigate the anisotropic response of a novel third generation Al-Li alloy (AA2060-T8) at room temperature and different deformation conditions. To elucidate the in-grain deformation features, a representative volume element was constructed to reveal the microstructure of the real AA2060-T8 (polycrystalline material) in which each grain was discretized by many finite elements. Afterward, numerical results were assigned to each grain to explore the pre-texture formed by previous thermomechanical processes. A dislocation density-based crystal plasticity model was developed to infer the constitutive equation of each grain and simulate the plastic deformation of AA2060-T8 alloy. The material parameters used in the dislocation density-based crystal plasticity model were calibrated against a tensile stress-strain curve deformed at 30° with respect to rolling direction. The results obtained from the proposed computational homogenization method are in line with those obtained from experimentation. This indicates that the proposed computational homogenization method can definitely predict the tensile deformation behavior and capture the anisotropic responses of AA2060-T8 (polycrystalline materials) originating from deformation induced texture as well as the initially anisotropic texture.

An integrated crystal plasticity–phase field model for spatially resolved twin nucleation, propagation, and growth in hexagonal materials

Typical hexagonal engineering materials, such as magnesium and titanium, deform extensively through shear strains and crystallographic re-orientations associated with the nucleation, propagation, and growth of twins. To accurately predict their deformation behavior it is, therefore, critical for constitutive models to incorporate these mechanisms. In this work an integrated approach for modeling the concurrent dislocation mediated plasticity and heterogeneous twinning behavior in hexagonal materials is presented. A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1¯012} tensile twins. A stochastic model is used to nucleate twins at grain boundaries, and their subsequent propagation and growth are driven by the Ginzburg–Landau relaxation of the system free energy which includes the orientation dependent twin interfacial energy and the elastic strain energy. Application of this novel and fully coupled model to the cases of magnesium single crystal, bicrystal, and polycrystal deformation is shown to demonstrate its predictive capability. Numerical simulations predict, in accordance with experimental observations, twin nucleation at grain boundaries followed by twin propagation into the grain interior and subsequent transverse twin thickening. Through this new combination of modeling approaches it is possible to systematically study the twin induced strain fields, the stress distribution along twin boundaries, and the spatial evolution of dislocation density within twins and parent grains.