This combined experimental and theoretical study examines the impact of ferrite/martensite (F/M) interface on the hardness/indentation depth curve during nanoindentation tests on a Dual-Phase (DP) steel. Depth-dependent hardness measurements are performed and compared with the classical Indentation Size Effect (ISE), which typically predicts a monotonic decrease in hardness with increasing indentation depth. However, in ferritic regions near martensite, the present experimental investigation reveals a non-monotonic nanohardness behavior with an initial decrease due to the classic ISE, followed by an increase from a critical indentation depth and a final decrease from a second critical depth. The intermediate stage with an increase in nanohardness between these two critical depths indicates a localized hardening mechanism, which is not captured by the classic ISE model equation. Using a large enough dataset of representative indents performed in ferritic grains close to F/M interfaces, the experimental study demonstrates that this localized hardening is attributed to these specific interfaces acting as strong barriers to plasticity. It is also shown that the increase in nanohardness follows a clear power-law dependence on the microstructural surface geometric distance between the indent position and the nearby F/M interface location. A model, based on Strain Gradient Plasticity (SGP) theory, and explicitly accounting for this distance, is used to explain this nanohardness increase and estimate the evolutions of geometrically necessary dislocation (GND) densities between both critical indentation depths at the origin of the pronounced size-dependent strengthening. These results shed new light on the plasticity mechanisms that control hardness variations at the nanoscale in DP steels due to ferrite/martensite interface, and provide a framework for better understanding the effects of phase boundaries on localized plasticity.

Defect–grain boundary interactions have been proven essential for the development of tailored microstructures for high-performance materials. We aim to unravel the mechanical response of grain boundaries by investigating dislocation activity in the vicinity of a tensile twin boundary (TB) in Mg-Y. A combined approach of quasi in-situ nanoindentation, electron channeling contrast imaging (ECCI), and high-resolution electron backscattered diffraction (HR-EBSD) was employed to induce localized deformation and analyze the resulting TB response. Nanoindentation in the parent grain near the TB produces distinct pop-ins, indicating deformation events close to the boundary. Observed slip includes pyramidal 〈c+a〉 activity in the twin and prismatic slip in the parent grain. It is shown that dislocation pile-ups cause TB bulging rather than transmission, which is consistent with low slip transmission factors. However, limited slip transmission is observed. Peach–Koehler force calculations based on the Nye tensor and the elastic strain extracted from 2D HR-EBSD measurements confirm that TB motion may be induced by dislocation pile-ups.

Accurate representation of crystallographic orientation is critical for modeling the mechanical behavior of crystalline materials using Neural Network (NN)-based approaches. Traditional orientation descriptors, such as Euler angles and quaternions, suffer from discontinuities and non-uniqueness, especially in the presence of crystal symmetry, which limits the performance and generalization of machine learning models to these materials. This study introduces a family of physically-informed, symmetry-aware orientation representations tailored for NN modeling of crystalline materials. The proposed descriptors explicitly account for elastic and plastic crystallographic symmetry groups, allowing continuous and unique mapping of orientation information. Large datasets of polycrystalline microstructures were generated via periodic Voronoi tessellation, with mechanical properties computed using crystal plasticity-based Mesoscale Field Dislocation Mechanics model within an elastoviscoplastic FFT-based formulation (MFDM-EVPFFT). Artificial Neural Network (ANN) and three-dimensional Convolutional Neural Network (3D-CNN) were trained to predict key mechanical properties, such as yield stress and Young’s modulus, for face-centered cubic (FCC) and hexagonal close-packed (HCP) structures. Systematic comparison of input representations demonstrates that the optimal choice depends on the physical property and microstructural complexity, with symmetry-aware descriptors yielding superior accuracy and generalization compared to conventional methods. The developed approach provides a robust foundation for data-driven modeling of the mechanical properties of crystalline materials like single crystals, bicrystals and polycrystals.

The paper addresses the question of determining local stress fields using the numerically efficient Fast Fourier Transform (FFT) method as an application of the continuum defect theory in the presence of interfacial defects, and specifically High Angle Grain Boundaries (HAGBs). First, the Field Dislocation and Disclination Mechanics (FDDM) equations are reported highlighting the use of the Stokes-Helmholtz orthogonal decomposition for both elastic strain and curvature tensors which are involved for disclination-type defects. Then, following this decomposition, both incompatible and compatible fields can be solved. Second, the Green's function method for heterogeneous media is used to derive the stress polarization field, which integrates both dislocation and disclination densities. The compatible elastic strain tensor is numerically solved with the spectral method using the FFT (fast Fourier transform) algorithm together with finite difference (FD) schemes for computing first-and second-order spatial derivatives (FDDM-FFT). As applications of the method, the stress fields of two specific HAGBs (symmetric tilt GBs with [001] tilt axis), precisely 229(520)[001]46.40 degrees and 2149(1070)[001]20.02 degrees are obtained from the Disclination Structural Unit Model (DSUM). They are calculated assuming both isotropic and anisotropic elasticity with the present FDDM-FFT numerical method and assuming periodic disclination density tensors. Quantitative comparisons are first performed for both HAGBs with analytical solutions obtained from specific combinations of disclination dipole walls in linear isotropic elasticity. Then, the effect of anisotropic elasticity is analyzed for both HAGBS considering two different FCC metals, namely Al and Ag. Lastly, some comparisons between the FDDM-FFT-based results with molecular statics (MS) simulations, using the virial stress method and an interpolation method based on Gaussian kernel are reported for both HAGBs applied to Al and Ag. It is shown that, despite their relative simplicity in describing HAGB defect cores, the FDDM-FFT results reproduce the major trends of MS-based results for both hydrostatic and shear stress components.

Magnesium (Mg) and its alloys, known for their low density and high specific strength, are increasingly explored as lightweight structural materials across a broad range of industrial applications. However, their widespread application remains constrained by intrinsic mechanical limitations, fundamentally rooted in the nature of crystallographic defects. Atomic-scale modeling techniques are transforming our ability to unravel the structures, energetics, and dynamics of these defects and to explore their complex interactions, thereby guiding defect engineering in Mg alloys. However, the growing body of available data can make it difficult for researchers to identify critical knowledge gaps and promising areas for further exploration. To address this challenge, we highlight key research domains with significant potential for impactful advancements, aiming to illuminate these areas while inspiring innovative approaches and encouraging deeper exploration of pivotal topics that may shape the future of Mg alloy development. This review presents a comprehensive overview of the state-of-the-art in atomic-scale modeling of defects in Mg and its alloys. We introduce key simulation methodologies, including density functional theory and atomistic simulations, and highlight their applications to defect distribution, defect dynamics, and defect-defect interactions. By bridging fundamental insights in defects with alloy design strategies, this review aims to support and inspire the broader Mg research community and to underscore the growing impact of atomic-scale modeling in the accelerated development of high-performance Mg alloys.

This paper investigates the relationship between microstructural features and small-angle scattering (SAS) patterns in Ni-based superalloys using a combined phase-field and SAS simulation approach coupled with microstructure analyses. The simulated SAS patterns accurately capture key experimental observations previously reported in the literature, including the time-dependent transition from circular to square-shaped precipitates and the development of anisotropic SAS patterns. Importantly, our analysis reveals the correlations between characteristic length scales extracted from SAS profiles and microstructural descriptors, such as precipitate size and inter-precipitate distance. These findings provide a comprehensive understanding of the link between SAS profiles and microstructure evolution in Ni-based superalloys, offering valuable insights for materials characterization and design.1

Mean-field modeling based on the Eshelby inclusion problem poses some difficulties when the non-linear Maxwell-type constitutive law is used for elasto-viscoplasticity. One difficulty is that this behavior involves different orders of time differentiation, which leads a long-term memory effect. One of the possible solutions to this problem is the additive interaction law. Generally, mean field models solely use the mean values of stress and strain fields per phase, while variational approaches consider the second moments of stresses and strains. It is seen that the latter approach improves model predictions allowing to account for stress fluctuation within the phases. However, the complexity of the variational formulations still makes them difficult to apply in the large scale finite element calculations and for non-proportional loadings. Thus, there is a need to include the second moments within homogenization models based on the additive interaction law. In the present study, the incorporation of the second moments of stresses into the formulation of the additive Mori-Tanaka model of two-phase elastic-viscoplastic material is discussed. A modified tangent linearization of the viscoplastic law is proposed, while the Hill-Mandel's lemma is used to track the evolution of second moments of stresses. To study the model performance and efficiency, the results are compared to the full-field numerical calculations and predictions of other models available in the literature. Very good performance of the modified tangent linearization is demonstrated from these benchmarks for both monotonic and non monotonic loading responses.

A crystal plasticity elastoviscoplastic FFT (fast Fourier transform) formulation with a mesoscale continuum field dislocation mechanics model is presented, which incorporates a defect energy density that depends on GND densities and an associated material length scale. This allows to thermodynamically derive internal length scale dependent intra-crystalline backstress and Peach-Koehler force acting on GND densities. The model considers GND density evolution through a filtered numerical spectral approach, which is coupled with stress equilibrium through the elastoviscoplastic FFT algorithm. The discrete Fourier transform (DFT) method together with finite difference (FD) schemes is applied to solve both the backstress tensor and the Fourier-Green operator. Numerical results are first reported for two-phase laminate composites with plastic single crystal channels and elastic precipitates for shear loadings. Channel size effects are simulated and analyzed on the overall and local hardening behaviors during monotonous loadings. In addition, the evolutions of GND densities and the role of their associated backstress on size effects are examined during reversible shear loading. In a second part, the role of the defect energy internal length scale on polycrystal’s hardening during tension-compression is discussed. The results are compared to those obtained using FFT-based continuum field dislocation mechanics without defect energy.

A new plasticity-induced internal length mean field model (ILMF) is developed, based on statistical analyses of geometrically necessary dislocation (GND) densities and total dislocation densities estimated from EBSD and nanoindentation data, respectively. It is applied to a single phase ferritic Al-killed steel, which plastically deforms with the occurrence of heterogeneous intra-granular fields. During tensile tests up to 18 % of overall plastic strain, the deformation maps of GND densities due to intra-granular plastic strain gradients are obtained together with nano-hardness maps. The Nye tensor (or dislocation density tensor) is calculated from the 2D EBSD orientations to estimate the intragranular GND density, while a mechanistic model is used to estimate the intragranular total dislocation density from nano-hardness measurements. These data are quantified as a function of the distance to grain boundaries (GBs) to study the development of such plastic strain gradients in the vicinity of GBs. The novel methodology lies in extracting the evolution law of a single plasticity-induced internal length, denoted 7, from the statistical analysis of GND and total dislocation densities spatial distribution. Hence, it is introduced as an evolving variable in an elastoviscoplastic self-consistent model (EVPSC) for a twophase composite as a new internal mean field (ILMF) approach. Both experimentally quantified microstructural internal lengths defined by the mean grain size and the evolving layer 7, are considered to more realistically describe the macroscopic and phase response in terms of stress, GND density evolution and total dislocation density in each phase. An experiment/model comparison is also discussed regarding GND density evolution with plastic deformation.

Solute segregation towards grain boundaries is investigated by modeling solute atoms as elastic dipoles interacting with the strain fields of symmetric tilt low-angle grain boundaries (LAGBs). Elastic dipoles are determined using molecular statics (MS) considering both the permanent second-rank tensor and the fourth-rank polarizability tensor, which is needed to capture the elastic dipole dependence on external strain. For cubic lattices, the latter tensors are related to size and modulus effects, respectively. The strain fields of LAGBs are evaluated either through MS or by considering arrays of edge dislocations within the framework of linear isotropic elasticity or heterogeneous anisotropic elasticity using the Stroh formalism. The interaction energies arising from the coupling between elastic dipoles and LAGB strain fields are compared to segregation energies computed on a site-by-site basis using MS. These comparisons are made for three LAGBs and two cubic systems (Cu and Ag) with solute atoms in substitution (Ag and Ni, respectively). The results underscore the critical role of anisotropic elasticity in accurately modeling solute segregation. Notably, variations in behavior between grain boundaries having a same tilt angle are only captured when anisotropic elasticity is considered. Furthermore, despite the inherent limitations in addressing non-linear effects at defect cores, the elastic dipole approximation proves to be an effective method for approximating segregation energy spectra in LAGBs obtained through atomistic simulations. Lastly, the estimation of overall solute concentration at grain boundaries highlights the prominent influence of the modulus effect.

Grain boundary (GB) migration plays a crucial role in the microstructural evolution of polycrystalline materials, particularly in fine‐grained materials. This migration can be driven by shear forces or by an energy jump across a GB. Interestingly, GB migration processes during cyclic loading deformations have been observed to be fully reversible. This study focuses on understanding the impact and importance of shear driving forces, the free energy difference across a GB, and lattice dislocations on GB migration. These factors are key points for gaining deeper insights into the underlying mechanisms of GB migration. In this work, GB migration in cyclic loading deformations is demonstrated, and it is emphasized that it clearly depends on both the shear driving forces (attributed to the motion of disconnections) and the energy differential across the GB. Two cyclic micro‐experimental methods, accompanied by analytical and numerical simulations, have been employed to investigate the role of shear stresses and energy jump‐driving forces in GB migration. This investigation provides clear experimental evidence that GB migration, in particular for a high‐angle GB, is dependent on both stress and energy driving forces.

Nanoindentation is a promising tool for advancing the estimation of single crystal elastic constants in multiphase materials. In this study, a novel protocol is presented that couples high-speed nanoindentation mapping with the Vlassak and Nix's model and Bayesian inference simulations to statistically estimate the elastic constants of cubic materials. The originality lies in considering ratios of indentation modulus as input data. For cubic elasticity, these ratios depend solely on two dimensionless parameters, which can be chosen as the Zener ratio A and the directional Poisson's ratio v(< 100 >). Using ratios mitigates the influence of experimental calibration parameters. Only two constants are varied in the Bayesian simulations, and the computation time is further reduced by employing an optimized Vlassak and Nix's model. This approach has also the great advantage to bound the search domain of v(< 100 >) and A directly from elastic stability conditions. Furthermore, the method efficiency allows for continuous variation of the uncertainty considered in the experimental moduli, leading to stabilized Bayesian inference results. The choice of the finally retained values is thus simplified, converging to the uniqueness of the single crystal elastic constants. This method is successfully applied to high-purity Ni and Inconel 718, with the predicted elastic constants aligning well with literature data.

Titanium alloys exhibit complex microstructures containing heterogeneities at different length scales. Microtextured regions (MTRs), usually called “macrozones”, exhibit grains having the same or nearly the same crystallographic orientation. They are known to have a detrimental influence on the alloy performance under cyclic loadings and dwell fatigue. Recent numerical studies based on crystal plasticity evidenced an effect of the degree of macrozones on the yield strength and stress distributions in polycrystalline aggregates. In the present study, a fast Fourier transform-based crystal plasticity elasto-viscoplastic (CP-EVPFFT) code using MPI (Message Passing Interface) and the FFTW library, is used to perform massive calculations for the study of the mechanical response in the microplastic stage of large 3D polycrystalline aggregates containing macrozones. These macrozones are synthetically generated with three different features: crystallographic texture with different orientation and intensity, volume fraction, and morphology. The 3D microstructure is obtained from EBSD data measured on a Ti64 hot rolled and annealed plate. Using two metrics, namely the equivalent Von Mises stress and the normal stress to basal plane, which is important for fatigue damage, intra-granular stress hotspots are found to be affected by the presence of the different macrozone features. A slip analysis is reported for a macrozone with a lamina shape. The CP-EVPFFT model predicts an early activity at low strain for 1st order c + a pyramidal slip when the macrozone exhibit a strong 0002 texture component. The discussion concludes on a hierarchy of these macrozone features for mechanical performance of the Ti64 alloy.

The origin and mechanisms responsible for incipient plasticity in metals are still poorly understood. Moreover, the reasons for the recently reported large scattering of the initial pop-in load remain unclear. Hence, this study addresses these issues through a combination of nanoindentation tests and electron channelling contrast imaging characterisation considering a CrCoNi medium-entropy alloy. Experimental findings were also supported by elastic calculations that consider both the indentation and dislocation stress fields. A wide scatter in the maximum shear stress underneath the indenter, as expected, was observed for the analysis based on dislocation density. As a consequence, the spatial arrangement of dislocations within the indented region or local dislocation configuration is introduced as a new parameter to overcome overly simple analysis based on the dislocation density. The maximum shear stress underneath the indenter increased from 6 GPa for dislocation closer to the indentation axis to 11 GPa at 600 nm for dislocation far away from it. Additionally, elastic calculations revealed that the response to the incoming nanoindenter was different for dislocations with different configurations. Thus, the complex interactions of stress fields due to configurations of dislocations and indentation account for the large scatter of the maximum shear stress beneath the indenter.

A new microstructure-informed three-scale homogenization scheme for elasto-viscoplastic het-erogeneous materials is developed. It is applied to predict the mechanical behavior of cast duplex austenitic-ferritic (AF) steels, which are widely used in primary loop of pressurized water reactors (PWR). At the first scale (microscale), the elasto-viscoplastic behavior of single crystals for both phases is modeled using linear elasticity and a viscoplastic crystal plasticity model. An "affine" type formulation based on the first moments of stresses is applied to the inelastic non-linear part of the deformation. Then, at the second scale (mesoscale), an EBSD-informed two-phase austenite/ferrite laminate structure (LS) model is developed with {110}-type habit planes (HP) in ferrite and a Kurdjumov-Sachs orientation relationship (KS-OR) between both phases. At the third scale (macroscale), the model considers a single ferritic primary grain as an aggregate of spherical two-phase laminate structure domains corresponding to the 24 KS-OR variants. The elasto-viscoplastic self-consistent scheme (EVPSC) is used through the Translated Fields (TF) method to obtain the effective behavior at this scale. The TF-EVPSC scheme is also used for an ensemble of primary ferritic grains to identify materials parameters from experimental tensile curves corre-sponding to as received and aged specimen. From EBSD measurements, the crystallographic data are thoroughly analyzed to physically feed the three-scale model. The results are discussed in terms of stress/strain responses in ferrite and austenite, which are correlated to the different KS -OR variants and HP orientations. The effect of primary ferritic grain crystallographic orientation and aging is also studied regarding monotonic and cyclic tests to study the possible origins of backstress in this material.