Two of the microstructural parameters most influential in the properties of polycrystalline materials are grain size and crystallographic texture. Although both properties have been extensively studied and there are a wide range of analysis tools available, they are generally considered independently, without taking into account the possible correlations between them. However, there are reasons to assume that grain size and orientation are correlated microstructural state variables, as they are the result of single microstructural formation mechanisms occurring during material processing. In this work, the grain size distribution and orientation distribution functions are combined in a single multivariate grain size orientation distribution function (GSODF). In addition to the derivation of the function, several examples of practical applications to low carbon steels are presented, in which it is shown how the GSODF can be used in the analysis of 2D and 3D electron backscatter diffraction data, as well as in the generation of representative volume elements for full-field models and as input in simulations using mean-field methods.@en

Crystal plasticity models attempt to reproduce the complex deformation processes of polycrystalline metals based on a virtual representation of the real microstructure. When choosing this representation, a compromise must be made between level of detail at the local level and statistical significance of the aggregate properties, also taking into account the computational cost of each solution. In this work, the correlation between crystallographic orientation and grain size is considered in the definition of virtual microstructures for the simulation of the mechanical behavior of AISI 420 stainless steel (consisting of a ferrite matrix with large carbide precipitates), in order to improve the accuracy of the solution without increasing model complexity or computation time. Both full-field (DAMASK) and mean-field models (Visco Plastic Self Consistent (VPSC)) are used together in combination with experimental results to study the validity of the assumptions done in each of the models.@en

This work presents an advanced crystal plasticity model for the simulation of the mechanical behavior of multiphase advanced high-strength steels. The model is based on the Visco-Plastic Self-Consistent (VPSC) model and uses information about the material’s crystallographic texture and grain morphology together with a grain constitutive law. The law used here, based on the work of Pantleon, considers how dislocations are created and annihilated, as well as how they interact with obstacles such as grain boundaries and inclusions (carbides). Additionally, strain rate sensitivity is implemented using a phenomenological expression derived from literature data that does not require any fitting parameter. The model is applied to the study of two bainitic steels obtained by applying different heat treatments. After fitting the required parameters using tensile experiments in different directions at quasi-static and high strain rates, formability properties are determined using the model for the performance of virtual experiments: uniaxial tests are used to determine r-values and stress levels and biaxial tests are used for the calculation of yield surfaces and forming limit curves.@en

This article details the ESAFORM Benchmark 2021. The deep drawing cup of a 1 mm thick, AA 6016-T4 sheet with a strong cube texture was simulated by 11 teams relying on phenomenological or crystal plasticity approaches, using commercial or self-developed Finite Element (FE) codes, with solid, continuum or classical shell elements and different contact models. The material characterization (tensile tests, biaxial tensile tests, monotonic and reverse shear tests, EBSD measurements) and the cup forming steps were performed with care (redundancy of measurements). The Benchmark organizers identified some constitutive laws but each team could perform its own identification. The methodology to reach material data is systematically described as well as the final data set. The ability of the constitutive law and of the FE model to predict Lankford and yield stress in different directions is verified. Then, the simulation results such as the earing (number and average height and amplitude), the punch force evolution and thickness in the cup wall are evaluated and analysed. The CPU time, the manpower for each step as well as the required tests versus the final prediction accuracy of more than 20 FE simulations are commented. The article aims to guide students and engineers in their choice of a constitutive law (yield locus, hardening law or plasticity approach) and data set used in the identification, without neglecting the other FE features, such as software, explicit or implicit strategy, element type and contact model.@en

A cellular automaton algorithm for curvature-driven coarsening is applied to a cold-rolled interstitial-free steel's microstructure - obtained through electron backscatter diffraction (EBSD). Recrystallization nucleation occurs naturally during the simulation, due to the highly heterogeneous and hence competitive growth among pre-existing (sub) grains. The spatial inhomogeneity of the subgrain growth that takes place derives from the large local variations of subgrain sizes and misorientations that comprise the prior deformed state. The results show that capillary-driven selective growth takes place to the extent that the prior elongated and deformed grains are replaced by equiaxed grains with no interior small-angle boundaries. Additionally, during the simulation certain texture components intensify and others vanish, which indicates that preferential growth occurs in a fashion that relates to the crystal orientations’ topology. The study of the early stages of recrystallization (i.e. nucleation) shows that the pre-existing subgrains that eventually recrystallize, exhibit certain topological characteristics at the prior deformed state. Successful nucleation occurs mostly for pre-existing matrix subgrains abutting shear bands or narrow deformation bands and particularly at regions where the latter intersect.@en

This study proposes a new approach to determine phenomenological or physical relations between microstructure features and the mechanical behavior of metals bridging advanced statistics and materials science in a study of the effect of hard precipitates on the hardening of metal alloys. Synthetic microstructures were created using multi-level Voronoi diagrams in order to control microstructure variability and then were used as samples for virtual tensile tests in a full-field crystal plasticity solver. A data-driven model based on Functional Principal Component Analysis (FPCA) was confronted with the classical Voce law for the description of uniaxial tensile curves of synthetic AISI 420 steel microstructures consisting of a ferritic matrix and increasing volume fractions of M23C6 carbides. The parameters of the two models were interpreted in terms of carbide volume fractions and texture using linear mixed-effects models. @en

The third generation of advanced high strength steels shows promising properties for automotive applications. The macroscopic mechanical response of this generation can be further improved by a better understanding of failure mechanisms on the microstructural level and micro-mechanical behavior under various loading conditions. In the current study, the microstructure of a multiphase low silicon bainitic steel is characterized with a scanning electron microscope (SEM) equipped with an electron backscatter diffraction detector. A uniaxial tensile test is carried out on the bainitic steel with martensite and carbides as second phase constituents. An extensive image processing on SEM micrographs is conducted in order to quantify the void evolution during plastic deformation. Later, a new post-mortem electron backscatter diffraction-based method is introduced to address the correlation between crystallographic orientation and damage initiation. In this multiphase steel, particular crystallographic orientation components were observed to be highly susceptible to micro-void formation. It is shown that stress concentration around voids is rather relaxed by void growth than local plasticity. Therefore, this post-mortem method can be used as a validation tool together with a crystal plasticity-based hardening model in order to predict the susceptible crystallographic orientations to damage nucleation.@en

Bainitic steels, as a third generation of advanced high strength steels, are potential steel grades for automotive applications. Two grades of bainitic steels with low and high silicon content, with three different thermal treatments per grade and therefore different second phase constituents, are examined under quasi-static and high strain rate deformations. Microstructures are studied by advanced characterization techniques, including X-ray diffraction and scanning electron microscope equipped with an electron backscatter diffraction detector. Subsequently, the quasi-static and dynamic mechanical responses of the steels are correlated to the microstructures. A positive effect of the strain rate is observed for all the examined materials: when the strain rate is increased, both the tensile stress and deformation levels increase, thus also the energy absorption capacity. However, it is shown that the higher the fraction of second phase constituents, the lower the effect of strain rate becomes. In addition, the grain size directly correlates to the strain rate effect too. The phenomenological hardening model of Johnson-Cook is used to simulate the quasi-static and dynamic flow behaviors, allowing to quantify the strain rate sensitivity for each material. A comprehensive literature survey on the strain rate sensitivity of various steel grades reveals that steels with higher strength demonstrate a lower strain rate sensitivity factor. This trend can be approximated by a power law function which clearly is followed by the materials under consideration in this study.@en

Bainitic steels, as a third generation of advanced high strength steels, are potential steel grades for automotive applications. Two grades of bainitic steels with low and high silicon content, with three different thermal treatments per grade and therefore different second phase constituents, are examined under quasi-static and high strain rate deformations. Microstructures are studied by advanced characterization techniques, including X-ray diffraction and scanning electron microscope equipped with an electron backscatter diffraction detector. Subsequently, the quasi-static and dynamic mechanical responses of the steels are correlated to the microstructures. A positive effect of the strain rate is observed for all the examined materials: when the strain rate is increased, both the tensile stress and deformation levels increase, thus also the energy absorption capacity. However, it is shown that the higher the fraction of second phase constituents, the lower the effect of strain rate becomes. In addition, the grain size directly correlates to the strain rate effect too. The phenomenological hardening model of Johnson-Cook is used to simulate the quasi-static and dynamic flow behaviors, allowing to quantify the strain rate sensitivity for each material. A comprehensive literature survey on the strain rate sensitivity of various steel grades reveals that steels with higher strength demonstrate a lower strain rate sensitivity factor. This trend can be approximated by a power law function which clearly is followed by the materials under consideration in this study.@en

In this article, the capacity of the Visco-Plastic Self-Consistent model (VPSC) as a constitutive model for the simulation of cold-rolled Ti–6Al–4V under a diverse set of loading conditions is investigated. The model uses information about the material crystallographic texture and grain morphology obtained with EBSD together with a grain constitutive model that is sensitive to strain rate and temperature. The ability of the model to capture the macroscopic response and underlying microstructural phenomena is critically assessed considering various sets of hardening parameters, obtained applying different fitting procedures to tensile experiments in different directions on the sheet plane. In order to validate the fitted parameters, the obtained model is applied to the simulation of experiments in a wide range of testing conditions, including uniaxial, plane strain and simple shear loading modes at strain rates ranging from 10−4s−1 to 103s−1 and temperatures between −10°C and 70°C. High strain rate experiments were performed using a Split Hopkinson Bar setup, with specimens designed to achieve the desired loading mode, while isothermal experiments were performed with the help of a fluid cell to keep a constant temperature. A good agreement between experimental and simulation results is obtained.@en

Multiphase bainitic steels, as a third generation of advanced high strength steels, show promising properties for automotive applications. Understanding the micro-mechanisms of damage initiation during plastic deformation is a key to further mechanical properties enhancement. The topological effect of martensite as a second phase constituent on local damage nucleation activity is significant. This effect has been studied in two different martensite banded microstructures produced by two various annealing cycles. The postmortem damage analysis by a scanning electron microscope on uniaxial loaded samples, revealed more damage nucleation along the dispersed and fragmented martensite phase within martensite banded regions. More pronounced strain partitioning was observed in coarse bainitic grains between adjacent martensite blocks. It is shown that the fracture strain is not controlled by local damage activities, implying that earlier damage initiation or an increased volume fraction of voids does not give rise to a reduced ductility.@en

Plastic deformation of metallic materials is an inherently anisotropic process as a result of the presence of preferential orientations in their crystallographic texture. Crystal plasticity modeling, which allows simulating the response of polycrystal aggregates taking into account their texture and other microstructural parameters, has been extensively used to predict this behavior. In this work, crystal plasticity models are used to deal with the opposite problem: given a desired behavior, determine how to modify a texture to approximate this behavior in the most efficient way. This goal can be expressed as an optimization problem, in which the objective is to find the texture with the best formability properties among all the possible ones. An incremental optimization method, based on the gradient descent algorithm, has been developed and applied to different initial textures corresponding to typical steel and aluminum sheet products. According to expectations, the textures found present a stronger γ fiber component. Moreover, the method sets the basis for the development of more complicated optimization schemes directed toward optimizing specific materials and forming processes.@en

Recently, the third generation of advanced high strength steels (AHSSs) show promising properties for automotive applications. The improvement of macroscopic mechanical performance is not feasible without a deep understanding of the micromechanical behavior and failure micro-mechanisms involved during its response under various loading conditions. In this study, a uniaxial tensile test is conducted on a low silicon bainitic steel with second phase constituents (martensite and carbides). A comprehensive image processing on SEM micrographs is performed in order to quantify the damage evolution as a function of plastic deformation. A new methodology is examined to address the correlation between crystallographic orientation and damage initiation. In this multiphase steel, it appears that orientation dependence of damage initiation is blurred by the presence of different phases and hence there is not an obvious preferential orientation from where damage has initiated.@en