Institute of Fundamental Technological Research

This paper describes an application of a machine learning approach for parameter optimization. The method is demonstrated for the elasto-viscoplastic model with both isotropic and kinematic hardening. It is shown that the proposed method based on long short-term memory networks allowed a reasonable agreement of stress–strain curves to be obtained for cyclic deformation in a low-cycle fatigue regime. The main advantage of the proposed approach over traditional optimization schemes lies in the possibility of obtaining parameters for a new material without the necessity of conducting any further optimizations. As the power and robustness of the developed method was demonstrated for very challenging problems (cyclic deformation, crystal plasticity, self-consistent model and isotropic and kinematic hardening), it is directly applicable to other experiments and models.

crystal plasticity, optimization, machine learning, long short-term memory networks, self-consistent modeling, Eshelby solution, cyclic deformation, low cycle fatigue

Recently developed single-phase concentrated solid-solution alloys (CSAs) contain multiple elemental species in high concentrations with different elements randomly arranged on a crystalline lattice. These chemically disordered materials present excellent physical properties, including high-temperature thermal stability and hardness, with promising applications to industries at extreme operating environments. The aim of this paper is to present a continuum plasticity model accounting for the first time for the behaviour of a equiatomic five-element CSA, that forms a face-centred cubic lattice. The inherent disorder associated with the lattice distortions caused by an almost equiatomic distribution of atoms, is captured by a single parameter that quantifies the relative importance of an isotropic plastic contribution to the model. This results in multiple plasticity mechanisms that go beyond crystallographic symmetry-based ones, common in the case of conventional single element metals. We perform molecular dynamics simulations of equiatomic CSAs: NiFe, NiFeCr, NiFeCrCo, and Cantor alloys to validate the proposed continuum model which is implemented in the finite element method and applied to model nanoindentation tests for three different crystallographic orientations. We obtain the representative volume element model by tracking the combined model yield surface.

High entropy alloys, Nanoindentation, Molecular dynamics, Finite element method, Crystal plasticity

The review starts by highlighting the significance of nuclear power plants in the contemporary world, especially its indispensable role in the global efforts to reduce CO2 emissions. Then, it describes the impact of irradiation on the microstructure and mechanical properties of reactor structural materials. The main part provides the reader with a thorough overview of crystal plasticity models developed to address the irradiation effects so far. All three groups of the most important materials are included. Namely, the Zr alloys used for fuel cladding, austenitic stainless steels used for reactor internals, and ferritic steels used for reactor pressure vessels. Other materials, especially those considered for construction of future fission and fusion nuclear power plants, are also mentioned. The review also pays special attention to ion implantation and instrumented nanoindentation which are common ways to substitute costly and time-consuming neutron irradiation campaigns.

irradiation, crystal plasticity, indentation, ion implantation, neutron, metallic materials, nuclear reactor, structural materials

Identification of elastic and plastic properties of materials from indentation tests received considerable attention in the open literature. However, unambiguous and automatic determination of parameters in the case of the crystal plasticity (CP) model is still an unsolved problem. In this paper, we investigate the possibility to unambiguously identify the CP parameters from spherical indentation tests using finite element method simulations combined with evolutionary algorithm (EA). To this aim, we check the efficiency and accuracy of EA while fitting either load–penetration curves, surface topographies, or both at the same time. By fitting the results against simulation data with known parameters, we can verify the accuracy of each parameter independently. We conclude that the best option is to fit both load–penetration curve and surface topography at the same time. To understand why a given fitting scheme leads to correct values for some parameters and incorrect values for others, a sensitivity analysis was performed.

crystal plasticity,optimization,evolutionary algorithm,indentation

Evolutionary algorithms have become an extensively used tool for identification of crystal plasticity parameters of hexagonal close packed metals and alloys. However, the fitness functions were usually built using the experimentally measured stress–strain curves. Here, the fitness function is built by means of numerical comparison of the simulated and experimental textures. Namely, the normalized texture difference index is minimized. The evolutionary algorithm with the newly developed fitness function is tested by performing crystal plasticity parameter optimization for both pure zinc and zinc-magnesium alloy. These materials are promising candidates for bioabsorbable implants due to good biocompatibility and optimal corrosion rate. Although their mechanical properties in the as-cast state do not fulfill the requirements, they can be increased by means of hydrostatic extrusion. The developed modeling approach enabled acquisition of the crystal plasticity parameters and analysis of the active deformation mechanisms in zinc and zinc-magnesium alloy subjected to hydrostatic extrusion. It was shown that although slip systems are the main deformation carrier, compressive twinning plays an important role in texture evolution. However, the texture is also partially affected by dynamic recrystallization which is not considered within the developed framework.

The paper reports experimental and numerical study of different deformation mechanisms activated in the AZ31B mag nesium alloy sheet subjected to cyclic in-plane tensile – compressive deformation. The influence ofslip, twinning and detwinning upon the mechanical response and texture evolution of the material is thoroughly investigated. The regime of twinning and detwinning activity is assessed based on the variation of hardening modulus in the course of the process. Velocity-based large strain crystal plasticity model accounting for twinning and detwinning is formulated. The crystal plasticity model parameters are identified using the implementation of the evolutionary algorithm. Predicted activity of deformation mechanisms is discussed with respect to the experimental data.

twinning, detwinning, crystal plasticity, magnesium alloys, AZ31B, evolutionary algorithm

The goal of the present work is to identify and model the elastic-viscoplastic behavior of electrodeposited copper films under tension-compression loadings. From the experimental point of view, as proposed in the literature, a film of copper is electrodeposited on both sides of an elastic compliant substrate. The overall specimen is next subjected to tensile loading-unloadings. As the substrate remains elastic, the elastic–plastic response of copper under cyclic loading is experimentally determined. A clear kinematic hardening behavior is captured. To model the mechanical response, a new elastic-viscoplastic self-consistent scheme for polycrystalline materials is proposed. The core of the model is the tangent additive interaction law proposed in Molinari (2002). The behavior of the single grain is rate dependent where kinematic hardening is accounted for in the model at the level of the slip system. The model parameters are optimized via an evolutionary algorithm by comparing the predictions to the experimental cyclic response. As a result, the overall response is predicted. In addition, the heterogeneity in plastic strain activity is estimated by the model during cyclic loading.

electrodeposited copper, self-consistent scheme, elasto-viscoplasticity, kinematic hardening, experiments

The paper presents the simulations of texture evolution of the AZ31B Mg alloy subjected to equal channel angular pressing (ECAP) and rotary swaging (RS) processes. It is shown that using the crystal plasticity (CP) parameters obtained by curve fitting conducted on simple mechanical tests with the aid of the evolutionary algorithm, it is possible to correctly predict the texture evolution in both processes. The influence of the initial texture as well as the CP parameters is discussed.

crystal plasticity, rotary swaging, ECAP; magnesium alloys, AZ31B, severe plastic deformation

Texture and twinning-induced anisotropy of the yield stress and hardening of AZ31B extruded rods is investigated. The multidirectional compression tests involving strain path changes are performed in order to: i. assess which slip and twinning systems are active in the polycrystalline sample with a strong texture, ii. analyze the influence of the preliminary deformation upon twin formation, iii. observe the resulting change of the mechanical response. In order to fulfil these goals mechanical testing is supplemented by microstructure analysis. Experimental observations are used to validate the proposed crystal plasticity framework when it is combined with the viscoplastic self-consistent scheme. On the other hand, the results of numerical simulations are used to confirm an advocated interpretation of experimental findings. Finally, the experimental and numerical results are discussed with respect to the theoretical study of slip and twinning activity on the basis of the generalized Schmid criterion. It is concluded that twinning activity influences the mechanical response predominantly by the texture change and to lesser extent by modification of strain hardening due to slip-twin interactions.

crystal plasticity, anisotropy, plastic deformation, twinning, hcp

In this paper, the recently developed three-scale crystal plasticity model is applied to simulate microstructural evolution of austenitic and ferritic stainless steels subjected to large plastic strains. It is shown that the model is able to correctly predict both texture and misorientation angle distributions in the materials studied. Moreover, it can correctly capture the grain-refinement kinetics and the influence of the stacking fault energy. Finally, it is confirmed that the 3SCP model is a computationally attractive alternative for reliable modeling of microstructural evolutions in metals and alloys.

Microstructure evolution in crystalline materials subjected to different loading conditions is regularly studied using crystal plasticity finite element simulations. Accurate and reliable description of the microstructure, particularly in the case of large deformations, requires the usage of remeshing procedures and the mapping of the material state from the distorted mesh onto a new mesh. In this work, we evaluate three different solution mapping schemes, viz. closest point projection (CPP), sequential spherical linear interpolation (SLERP), and weighted spherical averages, all of which are based on the mapping of crystal plasticity variables. The results show that the mapping with CPP is generally acceptable, whilst the sequential SLERP is a more robust method with little additional computing effort.

crystal plasticity, solution mapping, remeshing, severe plastic deformation SPD, equal channel angular pressing ECAP

The goal of the paper is to report the successful simulations of the nanoindentation problem. The finite-strain isotropic elasto-plasticity and crystal elasto-plasticity models used for the simulations are described. The developed contact formu-lation describing the contact with rigid surface approximating pyramidal indenter is presented. Both tensile stress-strain and indentation load-penetration curves obtained with a single set of material parameters are presented to be in the satisfactory agreement with experimental data. It seems that such a result is presented for the first time.

crystal plasticity, indentation, Al 6061-T6, nanoindentation, Vickers, Berkovich, CPFEM

A three-scale crystal plasticity model is applied to simulate microstructure evolution in hcp titanium subjected to cold rolling. Crystallographic texture and misorientation angle development, as an indicator of grain refinement, are studied. The impact of twinning activity on both phenomena is accounted for by combining the original three-scale formulation with the probabilistic twin-volume consistent (PTVC) reorientation scheme. The modeling results are compared with available experimental data. It is shown that the simulated textures are in accordance with the experimental measurements. The basic components of misorientation angle distribution, especially in the range of high angle boundaries, are also well reproduced.

Grain refinement due to severe plastic deformation is simulated using the crystal plasticity finite element method in the total Lagrangian setting. A rate-independent model with the regularized Schmid law is applied. As an example, a single pass of the equal channel angular pressing process is considered. Texture evolution, misorientation angle distributions and maps of new grains are presented. A special algorithm for tracking the creation of new grains in finite element simulations is developed. The results are analysed with respect to experimental data available in the literature. The possible mechanisms leading to the fragmentation of grains in a face centred cubic material are discussed. The influence of the quality of the microstructure representation on the simulation results is assessed

crystal plasticity, severe plastic deformation, grain refinement, finite element method

A new three-scale model of polycrystal accounting for grain refinement is proposed. The model is embedded into the crystal plasticity framework. With the experimental reference to the development of the dislocation induced cell substructure, a single crystallite in the representative grain aggregate is initially subdivided into subdomains with the crystallographic orientations slightly misoriented with respect to the nominal orientation of a parent grain. The predicted misorientation evolution of subgrains with respect to the reference orientation of a crystallite is an indicator of grain refinement. The correlation between the increase of a misorientation angle and a slip activity pattern is analyzed. The model predictions are compared with available experimental data.

Crystal plasticity, Severe plastic deformation, Grain refinement

Texture evolution in commercially pure titanium deformed by equal-channel angular pressing (ECAP) and extrusion with forward–backward rotating die (KoBo) is studied both experimentally and numerically. New results are provided that demonstrate the effects of distinct and complex deformation paths on the texture in the ultra-fine grained (UFG) material obtained after severe plastic deformation (SPD). The numerical simulations are based on the self-consistent viscoplastic method of grain-to-polycrystal scale transition. A recently proposed modification of the probabilistic scheme for twinning is used that provides consistent values of the twin volume fraction in grains. The basic components of the experimentally observed texture are reasonably well reproduced in the modelling. The numerical simulations provide an insight into the internal mechanisms of plastic deformation, revealing substantial activity of mechanical twinning in addition to the basal and prismatic slip in titanium processed by ECAP.

Texture evolution, UFG materials, SPD processes, Crystal plasticity, Twinning

A computationally efficient procedure for modelling of microstructural changes on complex and spatially nonuniform deformation paths of severe plastic deformation (SPD) is presented. The analysis follows a two-step procedure. In the first step, motivated by saturation of material hardening at large accumulated strains, the steady-state kinematics of the process is generated for a non-hardening viscoplastic model by using the standard finite element method for a specified SPD scheme. In the second step, microstructural changes are investigated along the deformation-gradient trajectories determined in the first step for different initial locations of a material element. The aim of this study is to predict texture evolution and grain refinement in a non-conventional process of cold extrusion assisted by cyclic rotation of the die, called KOBO process, which leads to an ultra-fine grain structure. The texture evolution is calculated for fcc and hcp metals by applying crystal visco-plasticity combined with the self-consistent scale transition scheme. In parallel, by applying the simplified phenomenological model of microstructure evolution along the trajectories, grain refinement is modelled. The results are compared with available experimental data.

SPD processes, Texture evolution, UFG materials, Crystal plasticity, Grain refinement

Texture evolution and grain refinement in materials subjected to severe plastic deformation (SPD), in particular the ECAP and KoBo extrusion processes are examined in this work. The well known ECAP process consists in extruding a billet through an angular channel. In the KOBO process material is extruded with assistance of cyclic rotation of a die. Both processes lead to considerable grain refinement and often to strong texture evolution [2,5]. The VPSC code itself provides different variants of self-consistent (SC) micro-macro transition scheme. It was combined with the proposed crystal plasticity framework and has been used to simulate texture evolution. However, this model is two-scale and does not predict the grain refinement. In order to examine the latter phenomenon three-scale model of microstructure evolution was developed. The model is able to combine two micro-macro transition schemes to simulate the evolution of orientations inside a grain and decide if the formation of subgrains has occurred.

texture evolution, grain refinement, SPD processes, crystal plasticity, micromechanics

Micromechanical modelling of magnesium alloys is presented. The applied model combines the crystal plasticity framework accounting for twinning with the self-consistent grain-to-polycrystal scale transition scheme. The mechanical response of the material in the experiments involving the strain path changes is studied, together with the prediction of the accompanying texture evolution. It is demonstrated that the evolution of microstructure has an important impact on the overall material behaviour. The model predictions will be verified in experiments performed on the rolled sheets made of AZ31B alloy

micromechanics, crystal plasticity, twinning, texture evolution

Microstructure evolution in hcp polycrystals subjected to severe plastic deformation, in particular in the KOBO extrusion and the equal channel angular pressing (ECAP) processes, are examined in this work, using the crystal plasticity framework. Modelling approach combines the large strain crystal plasticity model accounting for twinning and the tangent variant of the self-consistent (SC) scale transition scheme.

hcp polycrystals, twinning, SPD processes, crystal plasticity, self-consistent model, microstructure evolution