Single Crystal Plasticity Model Research Articles

Bridging microscale to macroscale mechanical property measurements of FeCrAl alloys by crystal plasticity modeling

FeCrAl alloys are candidates for accident tolerant fuel cladding of light water reactors. In this work, a microstructure- and temperature-dependent crystal plasticity model is employed to bridge microscale to macroscale mechanical property measurements of FeCrAl alloys. With the visco-plastic self-consistent (VPSC) polycrystal plasticity framework, a mechanism-based single crystal plasticity (MSCP) model adopts the Arrhenius type rate equation to describe the dependence of the critical resolved shear stress for dislocation slips on their temperature-dependent intrinsic frictional resistance and the microstructure-dependent irradiation hardening. The intrinsic frictional resistance associated with {110}<111> and {112}<111> slip systems were measured by in-situ micromechanical testing on unirradiated/irradiated samples at 25-500 °C. The irradiation hardening is estimated by the Bacon-Kocks-Scattergood (BKS) model with density and size of radiation-induced defects measured from microstructural characterization. Several features associated with thermo-mechanical behavior of unirradiated/irradiated polycrystalline FeCrAl alloys are captured. High density of deformation-induced dislocations and radiation-induced defects results in obvious hardening at room temperature, which is weakened at high temperature, and facilitates damage evolution during deformation. Moreover, both high temperature and radiation-induced defects, which facilitate dislocation multiplication, trigger large hardening rate. The proposed method together with application of accelerator-based ion irradiation technique is a surrogate approach to simulate neutron damage, improving the efficiency associated with evaluation of mechanical properties of FeCrAl alloys exposed to temperature, stress and radiation conditions.

Influence of Local Microstructural Variations on the Bendability of Aluminum Extrusions: Experiments and Crystal Plasticity Analyses

Abstract The bendability of extruded profiles of an age hardenable aluminum alloy is investigated using mechanical tests on flat tensile specimens and bending specimens. Two profile geometries are considered, where the profiles exhibit different grain structures. The microstructure of the profiles in terms of the crystallographic texture and constituent particles is otherwise comparable. While the tensile properties are not that different for the two profiles, their bendability is strongly dependent on the grain structure and is about twice as high for one profile than for the other. A newly proposed coupled damage and single crystal plasticity model is used in finite element analyses of the mechanical tests to investigate the influence of the grain structure on the bending behavior, and the numerical results are compared to the experimental tests. The crystallographic texture and the grain morphology of the profiles, found by the electron back-scatter diffraction technique, are explicitly represented in the finite element models. The crystal plasticity simulations capture the difference in the bendability of the two profiles, and in agreement with the experiments predict a considerably higher bendability for one of the profiles. It is found that the grain structure affects the shear band formation in these profiles, but also the local texture where the shear bands are located is important for crack initiation and propagation as grains with certain crystallographic orientations may have a higher fracture resistance.

Microstructure-sensitive finite-element analysis of crack-tip opening displacement and crack closure for microstructural short fatigue cracks

In this paper, the effect of the polycrystalline microstructure on crack-tip opening displacement and crack closure is investigated for microstructural short plane strain fatigue cracks using the finite-element method. To this end, cracks are introduced in synthetically generated microstructures and the grain properties are described using a single crystal plasticity model with kinematic hardening. Additionally, finite-element calculations without resolved microstructure and von Mises plasticity with kinematic hardening are performed. Fully-reversed strain-controlled cyclic loadings are considered under large-scale yielding conditions as typical for low-cycle fatigue problems. The crack opening stress and the cyclic crack-tip opening displacement are significantly influenced by the local grain structure. While the stabilized crack opening stresses obtained with the microstructure-based finite-element model are in good accordance with the von Mises plasticity results, the differences in the cyclic crack opening displacement are addressed to the asymmetric plastic strain fields in the plastic wake behind the crack-tip of the microstructure-based model. The asymmetric plastic strain fields result in discontinuous and premature contact of the crack flanks.

On fracture anisotropy in textured aluminium alloys

The yielding, plastic flow and fracture of textured aluminium alloys depend on their microstructure formed during the thermo-mechanical processing. In this work, we investigate two extruded aluminium alloys with different yield strength, work hardening, grain structure, crystallographic texture and tensile ductility. To study the fracture anisotropy of these alloys, i.e., the variation in the failure and fracture strain with loading direction, finite element simulations of an axisymmetric smooth tensile specimen are compared to experimental tests in five in-plane directions with respect to the extrusion direction. A newly proposed coupled damage and single crystal plasticity model is used in three-dimensional finite element analyses of the tensile tests. The tensile tests are simulated in Abaqus/Explicit, where each grain is explicitly modelled. This modelling framework is able to capture the effects of the heterogeneous yielding and plastic flow on ductile fracture, caused by the differences in the crystallographic orientation between grains, such as shear bands which may promote strain localization and ductile fracture. The overall agreement between the experimental and numerical results with respect to the plastic anisotropy, i.e., the anisotropy in yielding, plastic flow and work hardening, highlights the important role played by the crystallographic texture. Plastic anisotropy is found to have a marked influence on the tensile ductility and to induce fracture anisotropy. By particularly accounting for the crystallographic texture, the finite element simulations are able to capture the fracture anisotropy observed in the experimental tests.

Bauschinger effect and latent hardening under cyclic micro-bending of Ni-base Alloy 718 single crystals: Part II. Single crystal plasticity modeling with latent kinematic hardening

In this paper, the Bauschinger effect and latent hardening of single crystals are assessed in finite element calculations using a single crystal plasticity model with kinematic hardening. To this end, results of cyclic micro-bending experiments on single crystal Alloy 718 in different crystal orientations (single slip and multi slip) with respect to the loading direction are used to determine the slip system related material properties of the single crystal plasticity model. Two kinematic hardening laws are considered: a kinematic hardening law describing latent hardening and a kinematic hardening law without latent hardening. For the determination of material properties for both hardening laws, a gradient-based optimization method is used. The results show that the different strength levels observed for micro-bending tests on different crystal orientations can only be described with latent kinematic hardening well, whereas the pronounced Bauschinger effect is described well by both kinematic hardening laws. It is concluded that cyclic micro-bending experiments on single crystals using different crystal orientations give an appropriate data base for the determination of the slip system related material properties of the single crystal plasticity model with latent kinematic hardening.

Bauschinger effect and latent hardening under cyclic micro-bending of Ni-base Alloy 718 single crystals: Part I. Experimental analysis of single and multi slip plasticity

Cyclic micro-bending tests on fcc single crystal Ni-base Alloy 718 cantilevers with different crystal orientations were performed to analyze the influence of activated slip systems on dislocation plasticity, latent hardening and the Bauschinger effect. The investigations indicate that plasticity in single crystal micro-cantilevers is significantly influenced by two phenomena - dislocation interaction and dislocation pile-up at the neutral plane. Both phenomena occur at the same time. Their ratio seems to be determined by the activated slip systems. Slip trace analysis indicates that the activation of only one slip system leads to a strong localization of plasticity to a limited number of parallel slip bands. This results in low dislocation interaction and consequently pronounced pile-ups at the neutral plane. In multi slip orientation, the second slip system leads to activation of significantly more dislocation sources, causing a much earlier and more homogeneous elastic-plastic transition zone. In stress-strain hysteresis loops during bending, pronounced dislocation interaction in multi slip orientation leads to a more pronounced latent hardening. The results suggest that on a microstructural length scale, plasticity behavior is strongly affected by activated slip systems, which determine local dislocation phenomena. Based on the results presented in this paper, a finite element analysis of latent hardening and the Bauschinger effect using a single crystal plasticity model with latent kinematic hardening is presented in Part II.

X-ray diffraction data from shock-compressed copper: Some consequences of metallurgical texture

We report the measurements of in situ Debye–Scherrer x-ray diffraction from copper foils shock compressed at the Orion laser facility to pressure in the range of 10–40 GPa. Our objective was to record distortion (variation of scattering angle at peak intensity, 2θ, with azimuthal position, φ, around the diffraction ring) of the Debye–Scherrer rings. We intended to measure the anisotropy of elastic strain and infer the effective strength of copper at a high strain rate. However, our measured diffraction data from all crystallographic reflection planes considered together are not consistent with a simple model that assumes homogeneous elastic strain. Consideration of both the β-fiber metallurgical texture of the rolled copper foil that we used as the sample material and the measured diffraction linewidths provides an empirical understanding of the data. We extend our understanding by using a Taylor-type, single-crystal plasticity model in which the total strain of each grain is assumed to be identical to that of the whole sample. This model reproduces many features of our experimental data and points to the importance of accounting for the plastic anisotropy of single-crystal grains, which can, in turn, lead to inter-grain elastic strain inhomogeneity and complex distortions of the diffraction rings.

On the coupling of damage and single crystal plasticity for ductile polycrystalline materials

A crystal plasticity model accounting for damage evolution and ductile failure in a single crystal due to the presence of voids or micro-cracks is presented. An accurate, robust and computationally efficient single crystal implementation is extended and applied to model the behaviour of different aluminium alloys in the cast and homogenized condition and the extruded condition. A total of four different materials are investigated, in which the yield strength, work hardening, grain structure, crystallographic texture and tensile ductility are unique for each alloy. The coupled damage and single crystal plasticity model is used in three-dimensional polycrystalline finite element analyses of one smooth and two notched axisymmetric tensile specimens for each material. The tensile tests are analysed in Abaqus/Explicit, where each grain is explicitly modelled. An efficient procedure for calibrating the work-hardening parameters for single crystal plasticity models is proposed and used to determine the material parameters from the tension tests of the smooth tensile specimen with high accuracy. The capability of the proposed crystal plasticity model is demonstrated through comparison of finite element simulations and experimental tests. A good agreement is found between the experimental and numerical results, and the various shapes of the failed specimens are well predicted by the crystal plasticity finite element analyses. For one of the extruded aluminium alloys, a diamond-shaped fracture surface is observed in the experiments of the notched tensile specimens and also this unusual shape is captured by the crystal plasticity analyses.

Modeling Microstructural Effects on Heterogeneous Temperature Fields within Polycrystalline Explosives

AbstractThe paper addresses the role of crystal anisotropy on the evolution of heterogeneous temperature fields in plastic‐bonded explosives (PBXs) under conditions of weak shock. The modeling approach is based on simplified idealizations of PBX microstructure including RDX grains and estane binder regions subjected to velocity boundary conditions representative of impact conditions in situ. The constitutive description of the microstructure constituents includes a dislocation‐based, anisotropic, single crystal plasticity model for the explosive grains and a linear viscoelastic model to represent the estane binder. Large suites of simulations were used to systematically study the correlation in heating of the grains with local wave dynamics, crystal orientation, and the microstructural neighborhood. These correlations were identified through the selection of characteristics of crystal anisotropy including oriented wave speeds and Taylor factor. A key observation is that the wave dispersion within a certain distance from the impact interface plays a dominant role in the temperature field. Beyond this distance, individual crystal orientations play a more dominant role, but cannot entirely account for the observed heterogeneity without consideration of the local microstructure neighborhood.

A single crystal plasticity finite element formulation with embedded deformation twins

Deformation twinning is an important plastic deformation mechanism in some polycrystalline metals such as titanium and magnesium. In this paper, we present a novel crystal plasticity finite element framework that accounts for deformation twinning explicitly, in addition to crystallographic slip. Within this computational framework, deformation twins are treated as weak discontinuities embedded within individual finite elements, such that a jump in the velocity gradient field is introduced (via the discretized gradient operator) between the twinned and untwinned crystalline regions, taking into account compatibility and traction continuity conditions at the interface between these two regions. The deformation gradient is multiplicatively split into elastic and plastic parts in the untwinned region, as is customary in finite-deformation crystal plasticity formulations. A different multiplicative decomposition of the deformation gradient into elastic, plastic (slip), and twinning parts is adopted in the twinned region, allowing deformation twinning to be accounted for as an additional mode of plastic deformation. A stochastic model is used to predict twin nucleation at grain boundaries, and the evolution of the length and thickness of the twinned region under subsequent deformation is taken into account. The linearization of the single-crystal plasticity model, required in order to enforce traction continuity at the interface between the twinned and untwinned regions using a Newton iterative scheme, is described in detail. Simulations of the initiation and propagation of {101¯2} tensile twins in hexagonal close packed (HCP) titanium are presented to demonstrate the capabilities of the proposed computational framework.

Springback prediction for a mechanical micro connector using CPFEM based numerical simulations

The bending process of an industrial connector is considered and investigated via numerical simulation using a crystal plasticity finite element model (CPFEM). The process consists of sequentially bending a 0.1 mm thick copper-based alloy (CuBe2) with progressive tools into a miniature cylindrical connector of around 1 mm in diameter. The paper focuses on the prediction of springback through the influence of several key-parameters of the numerical simulations. The finite element characteristics, single crystal plasticity model features and the number of grains in the sheet thickness are investigated in order to highlight relevant and influential parameters in CPFEM based microforming process simulations. The influence of the elastic properties is analyzed and a modification of the Peirce-Asaro-Needleman single crystal hardening law is taken into account in order to improve the description of reverse strain path changes. Finally, the numerical results are discussed and compared to the springback measured during the industrial process of the cylindrical connector. It is demonstrated, through the very good agreement with the experimental results, that such approach can be useful to simulate industrial processes.

Machine Learning Approach for Identification of Microstructure–Process Linkages

The present work addresses a machine learning approach to study the linkage between deformation processing and microstructural texture evolution. The texture evolution is represented with a one-point probability descriptor, orientation distribution function (ODF) by employing a rate-independent single-crystal plasticity model. The ODF relates to the volume densities of different orientations in a microstructure, and thus it quantifies the texture during processing. First, a database of microstructural textures and deformation processes is built to generate the training dataset. The Latin hypercube sampling method is implemented to create uniformly distributed ODF values that represent the initial texture. Next, the crystal plasticity simulations using the initial ODF samples are performed for different deformation processes such as tension, plane strain compression, shear, shear, and shear; and the final texture information is stored in the database. Transductive learning is employed by using the training data to predict the label (optimum process) that can produce a given unlabeled texture. Two example process design applications are discussed for a galfenol alloy. In the first problem, the transductive learning approach is verified by using the previously optimized ODF solutions for a vibration tuning problem. In the second example, the process design is performed for a multiphysics optimization problem.

Crystal plasticity modeling of strain rate and temperature sensitivities in magnesium

This paper develops a single-crystal plasticity model with Johnson–Cook-type hardening laws to examine the strain rate and temperature sensitivities of magnesium (Mg). Slip, twinning and their interactions are deemed the dominant plastic mechanisms. The twinning-induced lattice reorientation is implemented by taking the initial grain after reorientation as a “new” grain with an updated orientation. Distinct strain rate and temperature dependences are considered for different slip and twinning modes. Non-basal slip is believed strain rate and temperature dependent, while compression twinning (CT) is assumed to exhibit temperature sensitivity in a certain temperature range. To validate the proposed model, plane-strain compression tests of Mg crystals under different strain rates and temperatures are simulated. The experimental data available in the literature are compared with the predicted results, and the tendencies of stress–strain curves are analyzed based on the corresponding evolution of slip and twinning. It is found that twinning-induced lattice reorientation significantly influences the mechanical behavior of Mg, especially when tension twinning (TT) dominates the plastic deformation. High temperatures and low strain rates enhance the activity of non-basal slip, and CT becomes easily activated as the temperature is increased beyond $$150\,^{\circ }\hbox {C}$$ , which coincides well with experimental observations. The strain rate sensitivity rising with temperature is also predicted by the model.

A physics-based single crystal plasticity model for crystal orientation and length scale dependence of machining response

Abstract Crystal plasticity model with physics-based dislocation kinetics and hardening relations is presented in this work. The model is applied to simple shearing of machining to determine the shear angle by work minimization that is similar to the Merchant's principle. Model reveals crystal orientation dependence of cutting specific pressure during machining of single crystals in addition to the machining parameters such as friction coefficient, uncut chip thickness, rake angle, temperature, and cutting speed. The length scale dependence of machining forces is linked to the physical length of the shear plane which is treated as a limit for the mean-free-path. A unified approach is developed for the first time to account for a wide range of strain rates for machining process. Taylor-based rate insensitive model is also implemented and applied to the same problem. Taylor-based model captures the four-fold symmetry of the force patterns yet with incorrect prediction of force peak locations. The physics-based model predicts the values of cutting forces and its pattern more accurately than the Taylor-based rate-insensitive model. The significantly better results are obtained because of the treatment of stress on the shear plane in full tensor form, the strain hardening and its anisotropy, and the effect of temperature and strain-rate by the physics-based model.

A phase-field model for creep behavior in nickel-base single-crystal superalloy: Coupled with creep damage

This paper focuses on the simulation of microstructural evolution during the three stages of creep in nickel-base single-crystal superalloys. A phase-field model coupled with a single-crystal plasticity model is developed in this paper. The creep damage and γ′-shearing during tertiary creep are considered in the phase-field model for the first time. The complete evolutions of γ′/γ phases during all three stages of creep are primarily simulated, and the simulated creep curve shows typical three creep deformation stages. The distribution of plastic strain is illustrated to analyze the morphological evolution and creep mechanism.

A dislocation climb/glide coupled crystal plasticity constitutive model and its finite element implementation

The glide and climb of dislocations are two important plastic deformation mechanisms of the metallic crystals at elevated temperatures. In this work, a new dislocation density-based constitutive model for single crystal plasticity with explicit consideration of both dislocation glide and climb is presented. Three contributions of dislocation climb to the plastic deformation are involved: the kinematics, the climb-enhanced dislocation mobility and the climb-induced dislocation annihilation. A fully implicit time-integration scheme for this model is given and implemented by a user material subroutine in software ABAQUS. Then, the compression tests of 〈110〉 single crystalline aluminum at high temperature and low strain rate are simulated, showing good agreements with the experimental results. Moreover, this model is used to predict the creep deformation of single crystalline aluminum at different temperatures and applied stress levels. The results show that the present model can capture the power law creep behavior of single crystalline aluminum and the predicted creep exponent falls within the range suggested by earlier research.

Existence result for a dislocation based model of single crystal gradient plasticity with isotropic or linear kinematic hardening

We consider a dislocation-based rate-independent model of single crystal gradient plasticity with isotropic or linear kinematic hardening. The model is weakly formulated through the so-called primal form of the flow rule as a variational inequality for which a result of existence and uniqueness is obtained using the functional analytical framework developed by Han-Reddy.

Crystal Plasticity Modeling and Experimental Validation with an Orientation Distribution Function for Ti-7Al Alloy

An orientation distribution function based model is used for micromechanical modeling of the titanium-aluminum alloys, Ti-0 wt % Al and Ti-7 wt % Al, which are in demand for many aerospace applications. This probability descriptor based modeling approach is different than crystal plasticity finite element techniques since it computes the averaged material properties using upper bound averaging. A rate-independent single-crystal plasticity model is implemented to compute the effect of macroscopic strain on the polycrystal. An optimization problem is defined for calibrating the basal, prismatic, pyramidal slip system and twin parameters using the available tension and compression experimental data. The crystal plasticity parameters of Ti-7 wt % Al are not studied extensively in literature, and therefore the optimization results for the crystal plasticity model realization produce unique data, which will be beneficial to future studies in the field. The sensitivities of the slip and twin parameters to the design objectives are also investigated to identify the most critical slip system parameters. Using the optimum design parameters, the microstructural textures, during the tension test, are predicted by the crystal plasticity finite element simulations, and compared to the available experimental texture and scanning electron microscope—digital image correlation data.

A reduced micromorphic single crystal plasticity model at finite deformations. Application to strain localization and void growth in ductile metals

A micromorphic single crystal plasticity model is formulated at finite deformations as an extension of Mandel’s classical theory based on a multiplicative decomposition of the deformation gradient. It involves a single microslip degree of freedom in addition to the usual displacement components. Two main variants of the constitutive equations are proposed. The first one relies on a Lagrangian microslip gradient and leads to a Laplace term in the isotropic hardening law. In contrast, the second formulation, based on a generalized strain measure defined with respect to the intermediate configuration, is shown to induce both isotropic and kinematic enhanced hardening. The first formulation is implemented in a 3D finite element code. The model is applied first to strain localization phenomena in a single crystal in tension undergoing single slip. The regularization power of the model is illustrated by mesh-independent simulations of the competition between kink and slip bands. The model is then used to investigate void growth and coalescence in FCC single crystals. Cylindrical and spherical voids are considered successively. The simulations show, for the first time in the case of spherical voids embedded in a single crystal matrix, that smaller voids grow slower than bigger ones, and that the onset of void coalescence is delayed for smaller voids. These results are related to the fact that the field of plastic slip is found to be more diffuse around smaller voids.

Void growth and coalescence in triaxial stress fields in irradiated FCC single crystals

Void growth and coalescence, known as main mechanisms of ductile fracture, are investigated for irradiated FCC single crystals. Finite element simulations of voided unit cells are performed with a single crystal plasticity model accounting for strain hardening and softening associated with irradiation-induced defects. The simulations predict a rather brittle overall behavior for the voided irradiated single crystal at high stress triaxiality, with a large amount of local plastic deformation, which is consistent with experimental observations reported in the literature for stainless steels irradiated in fast reactors. Compared with unirradiated single crystals, irradiated crystals exhibit a higher void growth rate leading to an earlier void coalescence, which is caused by a stronger plastic slip localization in the region near the voids.