Random Crystallographic Texture Research Articles

A machine learning constitutive model for plasticity and strain hardening of polycrystalline metals based on data from micromechanical simulations

Machine learning (ML) methods have emerged as promising tools for generating constitutive models directly from mechanical data. Constitutive models are fundamental in describing and predicting the mechanical behavior of materials under arbitrary loading conditions. In recent approaches, the yield function, central to constitutive models, has been formulated in a data-oriented manner using ML. Many ML approaches have primarily focused on initial yielding, and the effect of strain hardening has not been widely considered. However, taking strain hardening into account is crucial for accurately describing the deformation behavior of polycrystalline metals. To address this problem, the present study introduces an ML-based yield function formulated as a support vector classification model, which encompasses strain hardening. This function was trained using a 12-dimensional feature vector that includes stress and plastic strain components resulting from crystal plasticity finite element method (CPFEM) simulations on a 3-dimensional RVE with 343 grains with a random crystallographic texture. These simulations were carried out to mimic multi-axial mechanical testing of the polycrystal under proportional loading in 300 different directions, which were selected to ensure proper coverage of the full stress space. The training data were directly taken from the stress–strain results obtained for the 300 multi-axial load cases. It is shown that the ML yield function trained on these data describes not only the initial yield behavior but also the flow stresses in the plastic regime with a very high accuracy and robustness. The workflow introduced in this work to generate synthetic mechanical data based on realistic CPFEM simulations and to train an ML yield function, including strain hardening, will open new possibilities in microstructure-sensitive materials modeling and thus pave the way for obtaining digital material twins.

Augmenting the performance of friction stir back extruded AZ91 alloy using the gradient composite design technology

This study investigates the effect of extrusion speed during friction stir back extrusion on the microstructure, mechanical characteristics, and in vitro corrosion behavior of AZ91-3 vol % bioactive glass composite wire. To that end, the bioactive glass powder was inserted into the AZ91 matrix by drilling holes in the cross-section of the AZ91 rod. The results show that the extrusion speed strongly influenced the material's flow in the extruded wire's cross-section. By adding the bioactive glass powder to the processed wire, the ultimate tensile strength and corrosion resistance increased 5 and 23% compared to the additive-free wire. By decreasing the extrusion speed to 20 mm/min, the higher amount of discontinuous β-Mg17Al12 phase and α + β eutectic formed in the grain boundaries. By applying the friction stir back extrusion process on the AZ91 rod a random crystallographic texture formed in the extruded wires. In the composite samples extruded at a rotational speed of 1200 rpm, a traverse speed of 20 mm/min, a gradient distribution, and improvement of mechanical properties (ultimate tensile strength of 332.95 MPa, yield strength of 268.33 MPa, and elongation of 9.89%) and corrosion rate (1.879 mm/year) at simulated body fluid were achieved.

Energy-dispersive X-ray stress analysis under geometric constraints: exploiting the material's inherent anisotropy.

Two data evaluation concepts for X-ray stress analysis based on energy-dispersive diffraction on polycrystalline materials with cubic crystal structure, almost random crystallographic texture and strong single-crystal elastic anisotropy are subjected to comparative assessment. The aim is the study of the residual stress state in hard-to-reach measurement points, for which the sin2ψ method is not applicable due to beam shadowing at larger sample tilting. This makes the approaches attractive for stress analysis in engineering parts with complex shapes, for example. Both approaches are based on the assumption of a biaxial stress state within the irradiated sample volume. They exploit in different ways the elastic anisotropy of individual crystallites acting at the microscopic scale and the anisotropy imposed on the material by the near-surface stress state at the macroscopic scale. They therefore complement each other, in terms of both their preconditions and their results. The first approach is based on the evaluation of strain differences, which makes it less sensitive to variations in the strain-free lattice parameter a 0. Since it assumes a homogeneous stress state within the irradiated sample volume, it provides an average value of the in-plane stresses. The second approach exploits the sensitivity of the lattice strain to changes in a 0. Consequently, it assumes a homogeneous chemical composition but provides a stress profile within the information depth. Experimental examples from different fields in materials science, namely shot peening of austenitic steel and in situ stress analysis during welding, are presented to demonstrate the suitability of the proposed methods.

Role of Grain Size and Recrystallization Texture in the Corrosion Behavior of Pure Iron in Acidic Medium

This work investigates the role of grain size and recrystallization texture in the corrosion behavior of pure iron in 0.1 M sulfuric acid solution. Annealing heat treatment was applied to obtain samples with different average grain sizes (26, 53 and 87 µm). Optical microscopy, X-ray diffraction and electron backscatter diffraction techniques were used to characterize the microstructure. The EBSD data analysis showed ferrite phase with no inclusions and very low geometrically necessary dislocation density, indicating strain-free grains constituting all samples. The crystallographic texture analysis of the samples revealed that the 26 µm grain size sample had a high volume fraction of {111} oriented grains parallel to the sample surface, while other samples exhibited nearly random crystallographic texture. The electrochemical results from potentiodynamic polarization and electrochemical impedance spectroscopy showed a decrease in corrosion resistance from 87 µm to 53 µm grain size sample and then an increase for the 26 µm grain size sample. This increase was attributed to the dominant effect of recrystallization texture on the corrosion behavior of the sample. The cathodic hydrogen evolution reaction kinetics was found to play a decisive role in the corrosion behavior of iron.

The effect of heat treatments on mechanical properties of M789 steel fabricated by laser powder bed fusion

The microstructural evolution during the aging heat treatment of a newly developed steel (designed to be employed in the laser powder bed fusion), known as M789, was evaluated. The electron-backscatter diffraction (EBSD) analysis suggests that the as-printed sample contains a fully martensitic phase with random crystallographic texture. The samples were then solutionized at 1000 °C for 1 h, followed by aging at a temperature range of 400–600 °C and holding times from 40 to 120 min. The maximum hardness and tensile strength were achieved at aging temperatures of 450 °C and 500 °C for 2 h, with the latter temperature generated the highest amount of Ni3Ti precipitates (η-phase) with no traces of reverted austenite. Then, the heat-treated sample underwent transmission electron microscopy (TEM) and atom probe tomography (APT) analyses, which revealed the nano-scale, plate-like and spherical precipitates with number densities of 1.11 × 1024 m−3 and 0.93 × 1024 m−3, respectively. These precipitates contributed to the increase in tensile strength, from 1019 MPa (as-printed) to 1798 MPa (heat-treated), a net increase of 779 MPa. As a consequence of enhanced strength, the elongation decreased from 16% to 9%. Generally, the results of all experiments are consistent with simulations; the errors were identified to be less than 5%.

Crystallographic texture influences on the thermal stability of nanocrystalline materials

The influence of crystallographic texture on the total amount of solute segregated at the grain boundaries (Xgb,tot) and consequently the weighted grain boundary energy (γw) of a nanocrystalline material is investigated. Toward this end, two different 3D nanostructures, one with random crystallographic texture and the other with {111} texture, were generated. The grain boundary misorientation distribution was obtained from both the 3D nanostructures and converted into an equivalent grain boundary energy distribution using the data from Olmstead et al. It was found that both Xgb,tot and γw are higher for the nanostructure bearing random texture vis-a-vis the {111} texture. This has implications in the development of thermally stable nanocrystalline materials. The effect of texture is also discussed through a case study on the Ni–W system by invoking the nanocrystalline stability criterion proposed by Kalidindi and Schuh.

Grain refinement of stainless steel in ultrasound-assisted additive manufacturing

Metals and alloys fabricated by fusion-based additive manufacturing (AM), or 3D printing, undergo complex dynamics of melting and solidification, presenting challenges to the effective control of grain structure. Herein, we report on the use of high-intensity ultrasound that controls the process of solidification during AM of 316L stainless steel. We find that the use of ultrasound favours the columnar-to-equiaxed transition, promoting the formation of fine equiaxed grains with random crystallographic texture. Moreover, the use of ultrasound increases the number density of grains from 305 mm-2 to 2748 mm-2 despite an associated decrease in cooling rate and temperature gradient in the melt pool during AM. Our assessment of the relationship between grain size and cooling rate indicates that the formation of crystallites during AM is enhanced by ultrasound. Furthermore, the use of ultrasound increases the amount of constitutional supercooling during solidification by lowering the temperature gradient in the bulk of the melt pool, thus creating an environment that favours nucleation, growth, and survival of grains. This new understanding provides opportunities to better exploit ultrasound to control grain structure in AM-fabricated metal products.

High ductility and transformation-induced-plasticity in metastable stainless steel processed by selective laser melting with low power

A metastable austenitic Fe–Cr–Ni steel was processed by selective laser melting with low power, resulting in nearly random crystallographic texture. In-situ tensile loading and neutron diffraction experiments were undertaken and the results indicate high ductility, despite the presence of porosity, and pronounced strain-induced martensitic transformation. A secondary hardening is observed in the mechanical data due to the martensite carrying significant load, upon its formation. The pronounced martensitic transformation is discussed with respect to the initial and the evolving deformation texture and its affinity for forming martensite under uniaxial tensile loading.

On the numerical modeling of nucleation and growth of microstructurally short cracks in polycrystals under cyclic loading

Abstract

High Ductility and Transformation-Induced-Plasticity in Metastable Stainless Steel Processed by Selective Laser Melting with Low Power

A metastable austenitic Fe-Cr-Ni steel was processed by selective laser melting with low power, resulting in nearly random crystallographic texture. In-situ tensile loading and neutron diffraction experiments were undertaken and the results indicate high ductility, despite the presence of porosity, and pronounced strain-induced martensitic transformation. A secondary hardening is observed in the mechanical data due to the martensite carrying significant load, upon its formation. The pronounced martensitic transformation is discussed with respect to the initial and the evolving deformation texture and its affinity for forming martensite under uniaxial tensile loading.

Magnetic Properties of NdFeB Alloys Obtained by Gas Atomization Technique

Since Sagawa reported in [1]on the excellent hard magnetic properties of NdFeB permanent magnets, the utilization of anisotropic sintered NdFeB magnets in large motor and generator applications has grown spectacularly. Such hard magnetic material consists of a major tetragonal intermetallic compound (Nd 2 Fe 14 B), with excellent intrinsic hard magnetic properties, and a minor Nd-rich phase. Obviously, the magnetic behavior depends strongly on the microstructure of the magnet material, which in turn is determined by the production process. Microstructural factors affecting the hard magnetic character include the mean and the standard deviation of the grain size distribution, the orientation degree of the grains, the distribution of the Nd-rich phase, and the presence of a residual amount of other secondary phases (e.g. α-Fe, NdFe 4 B 4 , and other borides). All kind of defects in the microstructure, especially soft magnetic phases, can easily deteriorate the hard magnetic properties. It has been reported a slope change in the curve of magnetization as a function of temperature at around 150 K due to a spin reorientation transition (SRT) [2]. Such effect has been carefully analyzed for sintered magnets, since it is essential for the design of sensors, magnetic apparatus or magnetomechanical devices for cryogenic applications [3]. Alternative production routes of NdFeB magnets result in new microstructures whose impact on magnetic properties has to be carefully studied. Inert gas atomization is one of the novel processes under evaluation to produce NdFeB powders [4]. This technique consists on breaking a liquid metal stream into droplets by means of a high velocity inert gas flow. These droplets become spherical particles after solidification. The small size of the droplets, typically in the microns range, and the high velocity of the gas enable a fast heat transfer between both, resulting in high cooling rates and fine microstructures. Using this technique, we have produced several NdFeB alloys. After splitting the as-atomized powders in different size fractions by sieving, their microstructure and magnetic properties have been studied. In this work, we report the magnetic properties as a function of temperature, between 1.8 and 400 K, and of particle size. Fig. 1shows the characteristic microstructure of a single gas atomized NdFeB particle, whose main constituents are Nd 2 Fe 14 Bgrains of a few microns in size. The Inverse Pole Figure (IPF) demonstrates the random crystallographic texture of the material. The cooling rate of gas atomized particles increases when the particle size is reduced. As a result, larger particles exhibit higher microsegregation and, hence, the precipitation of soft magnetic α-Fe phase. On the other hand, smaller particles display finer microstructures. As for the coercive field, it was observed that it increases significantly when the particle size is reduced, reflecting a higher difficulty for reverse domain nucleation (less surface defects, finer grain size, lower volume fraction of secondary soft magnetic phases, etc.). Fig. 2shows the temperature dependency of the saturation magnetization, M s (T). The anomaly, i.e. a slope change of the M s (T) curve, observed around 150 K could be ascribed to the spin-reorentation transition (SRT) mentioned before, which has been reported to occur in the same temperature range when the magnetic field is applied parallel and perpendicularly to the sample direction [2]. In contrast with the measurements performed in single crystals and anisotropic sintered magnets, isotropic gas atomized powders exhibit an increment of saturation magnetization below the split tilt temperature of the SRT. This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 720838 (NEOHIRE project).

Influence of the initial state on the microstructure and mechanical properties of AX41 alloy processed by ECAP

This study investigates the influence of the initial state of the commercial AX41 magnesium alloy on the microstructure evolution and mechanical properties after equal-channel angular pressing. Two initial conditions, an as-cast one with a grain size of 200 μm and a random crystallographic texture, and an extruded one having a grain size of 10 μm and a strong fibre texture, are compared. ECAP processing was performed at the temperature of 220 °C up to 8 passes via route BC. A much smaller grain size was obtained in the ECAP-processed as-cast material compared to the extruded one. This difference was attributed to the different evolution of the dislocation density and its fractions in different slip systems. Consequently, different refinement mechanisms were dominant in the later stage of ECAP processing. It was shown that ECAP processing leads to the formation of similar crystallographic textures for both initial states, having dominant basal texture component. The mechanical properties investigation showed improvement in the microhardness, tensile strength and elongation in both ECAP-processed samples.

Bayesian inference of elastic properties with resonant ultrasound spectroscopy.

Bayesian modeling and Hamiltonian Monte Carlo (HMC) are utilized to formulate a robust algorithm capable of simultaneously estimating anisotropic elastic properties and crystallographic orientation of a specimen from a list of measured resonance frequencies collected via Resonance Ultrasound Spectroscopy (RUS). Unlike typical optimization procedures which yield point estimates of the unknown parameters, computing a Bayesian posterior yields probability distributions for the unknown parameters, and HMC is an efficient way to compute this posterior. The algorithms described are demonstrated on RUS data collected from two parallelepiped specimens of structural metal alloys. First, the elastic constants for a specimen of fine-grain polycrystalline Ti-6Al-4 V with random crystallographic texture and isotropic elastic symmetry are estimated. Second, the elastic constants and crystallographic orientation for a single crystal Ni-based superalloy CMSX-4 specimen are accurately determined, using only measurements of the specimen geometry, mass, and resonance frequencies. The unique contributions of this paper are as follows: the application of HMC for sampling the Bayesian posterior of a probabilistic RUS model, and the procedure for simultaneous estimation of elastic constants and lattice-specimen misorientation. Compared to previous approaches these algorithms demonstrate superior convergence behavior, particularly when the initial parameterization is unknown, and enable substantially simplified experimental procedures.

Influence of microstructure on work-hardening and ductile fracture of aluminium alloys

The effect of microstructure on the work-hardening and ductile fracture of aluminium alloys was studied using an experimental–numerical approach. Four aluminium alloys with different strength and particle content were tested in uniaxial tension after the following subsequent processing steps: (1) casting and homogenisation, (2) extrusion, and (3) cold rolling followed by heat treatment. The latter processing step was carried out to obtain a recrystallized grain structure with random crystallographic texture. The alloys were two AlFe alloys with different Fe content, one AlMn alloy and one AlMgSi alloy. The grain structure, particle distribution and crystallographic texture were determined for all combinations of alloy and processing route using optical and scanning electron microscopy. Tensile tests were carried out on axisymmetric samples to obtain the true stress–strain curves to failure and the true failure strain of the materials, using a laser-based measuring system. Based on numerical simulations of the tensile tests, the equivalent stress–strain curves were determined to failure, assuming J2 flow theory. The results showed that the microstructure had a marked effect on both work-hardening and ductility, whilst the ductile fracture mechanism remained unchanged. The plastic anisotropy, induced by the extrusion process and not entirely removed by the cold rolling and heat treatment, led to a wide range of fracture modes of the axisymmetric samples. The failure strain was markedly lower for the cast and homogenised material than for the extruded and the cold rolled and recrystallized materials of the same alloy. The failure strain was further found to decrease linearly with the yield stress for similar microstructure.

Fine grained Mg–3Al–1Zn alloy with randomized texture in the double-sided friction stir welded joints

The improvement in mechanical properties of the AZ31B Mg joint was achieved through texture control by the double-sided friction stir welding technique. The co-direction and counter-direction rotations of the upper and lower tools were adopted for comparison. The results of the microstructure observations showed that, although the grain refinement occurred in both the conventional friction stir welded joint and double-sided friction stir welded joints, the more complex material flows caused mainly by the double tools provided by a randomization of the crystallographic texture in the entire stir zone of the double-sided friction stir welded joints. Additionally, the formation of the {10–12} twin in the double-sided friction stir welded joints was observed and it has a significant effect on the grain reorientation. The results of the tensile test indicated that the random crystallographic texture in the double-sided friction stir welded joints hindered the fracture of the stir zone with low elongation of 18% in the friction stir welded joint. Therefore, relatively higher elongations of 28% and 24% with similar tensile strengths as the friction stir welded joint were achieved in the double-sided friction stir welded joints.

Hot working mechanisms and texture development in Mg-3Sn-2Ca-0.4Al alloy

Hot deformation mechanisms in Mg-3Sn-2Ca (TX32) alloy containing 0.4% Al are evaluated in the temperature and strain rate ranges of 300–500 °C and 0.0003–10 s−1 using processing map and kinetic analysis. The evolution of microstructure and texture during high temperature compression of the alloy has been studied using an electron back scatter diffraction (EBSD) technique. The processing map for hot working revealed two domains of dynamic recrystallization (DRX) occurring in the temperature and strain rate ranges of: (1) 300–360 °C and 0.0003–0.001 s−1 and (2) 400–500 °C and 0.005–0.7 s−1, which are the two safe hot workability windows for this alloy. A regime of flow instability occurs at higher strain rates and lower temperatures where adiabatic shear banding and flow localization are the microstructural manifestations. The onset of DRX during compression at lower temperatures and strain rates (Domain 1) resulted in a fine, partially recrystallized and necklaced grain microstructure along with a texture where the basal poles are spread along 30° from the compression direction. Specimens deformed at temperatures higher than 450 °C (Domain 2) resulted in a fully recrystallized microstructure and an almost random crystallographic texture, which was attributed to the significant occurrence of pyramidal slip and associated cross-slip.

Deformation Microstructures and Textures of Cast Mg-3Sn-2Ca Alloy under Uniaxial Hot Compression

The influence of deformation conditions on the microstructure and texture evolution during hot compression of Mg-3Sn-2Ca (TX32) has been studied. Cylindrical samples were compressed uniaxially at different combinations of temperatures and strain rates in the ranges 300-500 oC and 0.0003-10 s-1. The crystallographic orientation information of the as-cast and deformed specimens was obtained by EBSD micro-texture analysis. Activation of different slip systems was investigated using Schmid factor analysis and the results reinforce the importance of non-basal slip for deformation at high temperatures. Samples deformed at 500 oC/0.1 s-1 resulted in a fully recrystallized microstructure with near random crystallographic texture.

Microstructure and mechanical characteristics of bulk polycrystalline Ni consolidated from blends of powders with different particle size

Near fully dense polycrystalline nickel with a random crystallographic texture was consolidated by hot isostatic pressing of blends of nanocrystalline and conventional microcrystalline powders with different volume fractions. The transformation process resulted in a composite-like microstructure constituted by clusters of soft coarse grains regularly distributed in a hard ultrafine-grained matrix. It was found that the ultrafine-grained matrix hinders the coalescence of the coarse grains component during sintering resulting in a smaller grain size than in the fully coarse-grained counterpart in a sort of “barrier effect”. This effect was found to depend on the volume fraction of the ultrafine-grained matrix. Conversely, during the hot isostatic pressing, the plastic deformation of the coarse-grained fraction is preferred to that of the ultrafine-grained fraction, because of greater dislocation activity in the former type of grains, resulting in lower defect densities in the ultrafine-grained matrix (“shielding effect”). It is shown that as a result of the interplay between the coarse-grained and ultrafine-grained components during sintering, the mechanical behavior of the composite materials cannot be obtained by a linear interpolation between the characteristics of fully ultrafine-grained and coarse-grained counterparts.

Effect of homogenization on recrystallization in a twin-roll cast Al–Fe–Si alloy

The effect of homogenization treatment on the recrystallization process in a twin-roll cast AlFeSi alloy was investigated by means of calorimetry, microstructural analysis, electrical conductivity, and hardness measurements and cupping tests. The response to annealing of cold-rolled AlFeSi sheet processed with a homogenization treatment at the cast gauge is a typical two-stage, recovery and recrystallization process, while that processed without homogenization softens without recovery. The rather limited precipitation capacity in the former allows recrystallization to occur largely discontinously, favoring the annealing texture. The nucleation rate and the volume fraction of the discontinously recrystallized grains are largely reduced in the sheet processed without homogenization, owing to extensive dynamic precipitation. This reduces the strength of the annealing texture components and gives a more or less random crystallographic texture after annealing. With a relatively finer-grain structure and a nearly random crystallographic texture, AlFeSi sheet processed to soft temper at 1 mm without a homogenization treatment is an attractive foil stock material.

Dynamic recrystallization during high temperature deformation of magnesium

As a consequence of the high critical stresses required for the activation of non-basal slip systems, dynamic recrystallization plays a vital role in the deformation of magnesium, particularly at a deformation temperature of 200 °C, where a transition from brittle to ductile behavior is observed. Uniaxial compression tests were performed on an extruded commercial magnesium alloy AZ31 at different temperatures and strain rates to examine the influence of deformation conditions on the dynamic recrystallization (DRX) behavior and texture evolution. Furthermore, the role of the starting texture in the development of the final DRX grain size was investigated. The recrystallized grain size, measured at large strains (ɛ ∼ −1.4) seemed to be more dependent on the deformation conditions than on the starting texture. In contrast to pure magnesium, AZ31 does not undergo grain growth at elevated deformation temperatures, i.e. 400 °C, even at a low strain rate of 10 −4 s −1. Certain deformation conditions gave rise to a desired fully recrystallized microstructure with an average grain size of ∼18 μm and an almost random crystallographic texture. For samples deformed at 200 °C/10 −2 s −1, optical microscopy revealed DRX inside of deformation twins, which was further investigated by EBSD.