Electroplastic effects in metals show measurable changes in the exerted force in deformation processes under certain electric current conditions, holding potential to facilitate metal forming. However, the application of these effects is hindered by the so far unclear image of the underlying mechanisms, and the corresponding contributions are debatable. This work aims to quantitatively elucidate the athermal mechanisms of electroplasticity in copper with experimental and computational methods combined. Temperature-controlled pulsed-current electricity-assisted deformation (EAD) tests were conducted to emphasize athermal contributions, while large-area EBSD, two-beam TEM, and high-resolution EBSD (HR-EBSD) measurements were used to characterize texture evolution, slip systems, and semi-quantitative dislocation density. Then, a crystal plasticity model, incorporating electroplasticity-related mechanisms with thermodynamic evolution formulas, was applied to support a mechanism-focused interpretation of the observed electroplastic responses from dislocation behaviors. Analysis reveals that the reduced work hardening observed in the stress-strain curves originates from fluctuations in the local response. These fluctuations exhibit a characteristic two-stage behavior, consisting of a “rapid drop” followed by a “slow decline” of stress response. The associated changes in maximum flow stress and macroscopic work-hardening rate arise from the cumulative effect of EAD-induced softening during current pulses, which is linked to the recovery of statistically stored dislocations (SSDs). By quantitatively connecting short-term information to macroscopic stress-strain evolution within an electricity-coupled crystal plasticity framework and comparing with experimental textures and dislocation densities, this work provides mechanistic interpretations of athermal mechanisms and consolidate the understanding of electroplasticity in metals.

This study examines the Portevin-Le Chatelier (PLC) effect in the nickel-based superalloy Inconel 718 through a combined experimental-computational approach using statistical indicators from nonlinear dynamical systems theory. We develop a finite element model incorporating the Kubin-Estrin-McCormick constitutive law to capture Dynamic Strain Ageing effects, accounting for machine stiffness influence, and reproduce various dynamics under both hard and soft loading conditions. Statistical analysis reveals that machine stiffness significantly affects serration morphology and dynamics, influencing mean amplitudes, stress drop periods, and dynamical indicators such as the correlation dimension and Lyapunov exponents. Comparison of simulated and experimental stress time series demonstrates chaotic behaviour for type B and C serrations across all strain rates, with no evidence of self-organised criticality in experimental data. However, simulations predict self-organised criticality at high strain rates corresponding to type A bands, consistent with literature references. Statistical indicators reveal power-law behaviour for stress drop amplitudes as a function of strain rate, with critical exponents dependent on band type. Multifractal analysis shows that simulations overestimate complexity relative to experimental observations, suggesting the need for additional internal variables and finer-scale dynamics in modelling. Additionally, multifractal analysis of spatio-temporal diagrams reveals power-law distributions of plastic strain rates with consistent critical exponents across all strain rates, demonstrating its potential for characterising PLC spatio-temporal dynamics. Statistical, dynamical, and multifractal indicators show consistent correlations, collectively capturing transitions between serration regimes and serving as reliable quantitative metrics for characterising PLC dynamics. The analysis is finally applied to the spatio-temporal strain fields measured by digital image correlation. The results demonstrate the value of multi-indicator analysis for assessing the agreement between experiment and simulation and subsequently improving constitutive model parameter identification.

The quantitative predictive capabilities of a recently developed plastic-distortion-based micromorphic approach are rigorously assessed through analysis, finite element simulations, and systematic comparison with experimental observations and discrete dislocation dynamics (DDD) predictions. This approach is based on multiple series decompositions of higher-order kinematic terms, and provides flexible control of the scaling effects via a penalty parameter constraining the micromorphic variable. A comprehensive analytical investigation is first conducted using an idealized constrained shear layer problem to elucidate scaling effects associated with both energetic and dissipative higher-order effects. The approach is subsequently applied to predict the orientation-dependent response of thin metallic layers under confined compression. In agreement with experimental observations from the literature, finite element simulations reveal pronounced size effects for layers oriented perpendicular to the loading direction, arising from both first-order and higher-order contributions, whereas negligible size effects are observed for the 45 degrees inclination. The formulation is further employed to capture the size effects in L-beam single-crystal specimens subjected to bending-torsion loading. Both energetic and dissipative higher-order contributions are incorporated, leading to good quantitative agreement with the experimentally observed responses, with a numerically predicted scaling exponent of 0.36 against the experimental value of 0.38. Finally, the model is applied to reproduce complex size-dependent responses obtained by DDD, under cyclic shear loading conditions. Good quantitative agreement is obtained, with a predicted scaling exponent of 0.26, fully consistent with the range [0.2, 0.3] reported in recent DDD studies. The results obtained in this work demonstrate the strong predictive capabilities of the employed formulation across diverse loading conditions and specimen geometries, highlighting the effectiveness of the relaxed micromorphic implementation for the quantitative modeling of size effects in small-scale crystalline materials.

High-speed nanoindentation mapping (HSNM), electron backscatter diffraction (EBSD), electron microprobe analyses (EPMA), and high resolution-microscale laser induced breakdown spectroscopy (HR-mu LIBS), were used to characterize the evolution of the elastic anisotropy of a commercially pure titanium (CP-Ti) having a gradient of oxygen concentration. CP-Ti samples were pre-oxidized in air at 655 degrees C for 120 h to create a 35 mu m-deep gradient of oxygen within Ti, the oxygen-rich layer (ORL). Wedge-cut samples were prepared to spread the ORL over hundreds of micrometers instead of tens of micrometers for cross-sections. EPMA and HR-mu LIBS were used to quantify the oxygen distribution within the ORL in a relative and absolute manner, respectively. The Vlassak-Nix theory was used for inverse identification of the stiffness matrix terms as a function of the oxygen content. The stiffness matrix as a function of the oxygen concentration was used to simulate the stress-strain distribution at the sub-grain level in the ORL under tensile macroscopic loading. Configurations with and without external oxide were numerically tested to investigate the role of the oxide layer on the stress distribution within the ORL as well as the crystallographic texture.

The objective of this study is twofold: (i) to comprehensively describe the deformation modes of zinc coatings depending on their crystallographic texture and (ii) to investigate the effect of L & uuml;ders banding occurring in the steel substrate on the coating deformation and cracking modes. Microscopic characterization and mechanical tests were conducted on three types of galvanized steel: a mild steel substrate and a high-strength low-alloy (HSLA) steel substrate known to exhibit the L & uuml;ders banding phenomenon, and a dual-phase steel substrate. The results reveal a direct correlation between the coating texture, plastic deformation modes, and the mechanical behavior of the respective substrates. Digital Image Correlation (DIC) was employed to measure the strain fields and characterize strain localization phenomena resulting from L & uuml;ders banding. The strain field measured on the galvanized substrate specimens showed that L & uuml;ders band propagation leads to accelerated plastic deformation and cracking in the Zn-Al-Mg coating. Finite element simulations were performed by considering the real coating microstructure and incorporating the macroscopic behavior of the substrate. The simulation results demonstrate that slip and twinning activities of the coating grains are strongly influenced by the underlying substrate behavior.

A novel plastic distortion based micromorphic model is proposed, incorporating higher-order multi-kinematic decomposition and generalized power-law defect energy to accurately capture size-dependent effects. For the first time in micromorphic modeling, higher-order dissipation effects are introduced, providing enhanced description of strengthening and hardening phenomena beyond existing micromorphic approaches. Analytical investigation of the proposed model reveals the crucial role of the micromorphic relaxation, governed by the penalty parameter, in reproducing realistic scaling behaviors. The model predicts two distinct asymptotic regimes for size effects at very large and very small geometrical sizes. At intermediate sizes, it yields realistic scaling relationships with adjustable scaling exponent between 0 and 2, allowing for a more precise description of size-dependent strengthening and hardening. Numerical simulations using the proposed model demonstrate its capability to reproduce complex cyclic responses with nonlinear hardening effects, capturing key microstructural mechanisms. Comparison with discrete dislocation dynamics (DDD) simulations under cyclic loading conditions shows excellent agreement for intermediate geometrical sizes, accurately reflecting size-dependent strengthening and hardening evolution. However, challenges remain in predicting cyclic responses at very small scales, indicating a restricted range of applicability in extreme miniaturized conditions. Despite this limitation, the proposed micromorphic framework provides a versatile and robust alternative to classical gradient plasticity theories, offering greater flexibility in modeling small-scale plasticity mechanisms. This work establishes the foundation for future refinements through systematic parameter identification, experimental validation, and broader comparisons with existing and emerging size-dependent plasticity models.

Plastic flow is conventionally treated as continuous in finite element (FE) codes, whether in isotropic, anisotropic plasticity, or crystal plasticity. This approach, derived from continuum mechanics, contradicts the intermittent nature of plasticity at the elementary scale. Understanding crystal plasticity at micro-scale opens the door to new engineering applications, such as microscale machining. In this work, a new approach is proposed to account for the intermittence of plastic deformation while remaining within the framework of continuum mechanics. We introduce a material parameter, the plastic deformation threshold, denoted as Delta p(min), corresponding to the plastic deformation carried by the minimal plastic deformation burst within the material. The incremental model is based on the traditional predictor-corrector algorithm to calculate the elastoplastic behavior of a material subjected to any external loading. The model is presented within the framework of small deformations for von Mises plasticity. To highlight the main features of the approach, the plastic strain increment is calculated using normality rule and consistency conditions, and is accepted only if it exceeds Delta p(min). To achieve this, a time-discontinuous generalization of the Karush-Kuhn-Tucker (KKT) conditions is proposed. The simulations show that the introduction of the plastic threshold allows for the reproduction of the spatiotemporal intermittence of plastic flow, capturing the self-organization of plastic flow in complex loading scenarios within an FE model.

Corrosion resistant alloys can exhibit oxidation induced damage in the long term for high temperature applications in air (>700 degrees C), e.g. in gas turbines, and also for elevated temperature applications in corrosive environments (>300 degrees C), e.g. in nuclear power plants. Observations show delayed brittle damage associated with stress corrosion cracking. Oxidation and damage phenomena occur in the form of oxide intrusions along grain boundaries due to local enhancement of oxygen diffusion. This work presents a comprehensive phase field and mechanical modelling framework which is capable of simulating the growth of oxide intrusions along grain boundaries. Oxide formation is accompanied by the development of anisotropic eigenstrains. Viscoplasticity in the oxide layer and in the intrusion allows for stress relaxation while a crystal viscoplasticity framework is assumed in the metallic substrate composed of two misoriented grains separated by a grain boundary (GB) subjected to oxide intrusion. The finite element simulations of a growing oxide intrusion predict distinct kinetics of the oxide layer and intrusion growth, and chromium depletion in the metallic substrate around the intrusion. Complex stress relaxation and redistribution are observed, leading to the generation of delayed positive normal tractions along the ghost grain boundary at the free surface and at the tip of the oxide intrusion. The framework also includes a constitutive GB damage model active in the actual grain boundary and in the ghost GB in the oxide layer. A novel crack initiation mechanism ahead of the oxide intrusion tip is proposed. The GB fracture stress values assumed in the simulation are such that the oxide is much more brittle than the metallic grain boundary. This, combined with the traction sign reversal ahead of the intrusion, results in crack initiation from the free surface which further enhances oxygen diffusion in the GB. This mechanism is thought to play a significant role in crack initiation and propagation during oxidation of metallic components.

Standard scalar-based strain gradient plasticity models generally incorporate the gradient of the cumulative plastic strain into the constitutive modeling. The following limitations of this approach have been pointed out in the literature: Unlimited enhanced hardening at large strains, unlimited cyclic hardening in bending, strain localization band broadening at large applied strains for softening materials with saturation, and possible vanishing of the yield stress for too high values of the Laplace term in the enhanced hardening function. The present work proposes an alternative scalar-based micromorphic approach that solves most of the listed difficulties. The theory incorporates the effect of the gradient of saturating variables instead of the gradient of ever-increasing cumulative plastic strain. A phenomenological theory is presented that includes an exponentially saturating internal variable and its gradient. The approach is also applied to dislocation density based plasticity where the dislocation density is known to saturate at large strains. The benefits of the new theory are demonstrated by finite element simulations of various boundary value problems: Monotonic and cyclic tension and simple glide of an infinite strip, strain localization in a plate, bending and torsion of bars. Both hardening and softening plasticity laws are addressed illustrating the size-dependent hardening in the former case and the evolution of the finite width of localization bands in the latter. Weak points of the approach, namely the possibility of negative dissipation and of negative yield stress, are also identified.

Most commercial Finite Element codes rely on hypo-elastoviscoplastic constitutive equations for structural computations at large deformations. Such formulations are known to suffer from physical and thermodynamical flaws but their versatility and ease of implementation made them ubiquitous. The paper presents an alternative systematic and thermodynamically consistent extension of anisotropic thermo-elastoviscoplastic constitutive equations at finite strain. The formulation is based on the well–known multiplicative decomposition of the deformation gradient into a thermoelastic and an inelastic part. This decomposition relies on Mandel’s isoclinic intermediate configuration. The present framework covers a wide range of multi-mechanism elastoplastic models so that it can advantageously replace the constitutive part of existing codes. The choice of a suitable hyperelastic potential, hardening variables and anisotropy evolution laws are discussed. The concept of plastic spin is used and can be either derived from general representation theorems or obtained from the normality rule. The effect of the plastic spin is discussed in the light of examples involving anisotropic plasticity. The response of the proposed formulation is compared to hypoelastic models in the case of several structural applications. The implementation of this methodology in a commercial FE object-oriented code is detailed. We show how to extend readily a wide range of small strain nonlinear constitutive models to finite deformations. The paper contains original features such as multimechanism based inelastic contributions, a Mandel-stress tensor based nonlinear kinematic hardening rule containing dynamic and static recovery terms, and a study of lattice rotation in single crystalline volume elements and turbine blades. The implementation is proved to be competitive with respect to existing hypo-elastoviscoplastic formulations in terms of CPU time.

During the plastic deformation of metallic materials, part of expended mechanical energy diffuses as heat. The fraction of plastic work converted into heat is called the Taylor–Quinney Coefficient (TQC), which is often assumed to be a constant parameter of about 0.9. The remaining portion of the plastic work is called stored energy. The stored energy is known as the main driving force for dynamic or static recovery and recrystallization. Therefore, numerical predictions and experimental measurements of the stored energy and TQC are essential to optimize thermomechanical material processing. An adequate prediction of the stored energy and the TQC using existing crystal plasticity models in line with the experimental measurements remains a challenging problem. In this work, a thermodynamic class of crystal plasticity models is used to predict the stored energy and TQC of copper and aluminum single crystals. Then, the numerical stored energy predictions are extended to polycrystalline austenitic steel 316L and compared with the experimental measurements from the literature. An ad-hoc factor is introduced in the numerical expression of stored energy in order to compensate for the difference with the experimental measurement. To this end, the contributions of statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) for the stored energy prediction are analyzed to understand the physical origin of the ad-hoc factor. The contribution of GNDs to stored energy and enhanced hardening is accounted for by means of a strain gradient plasticity model. The present systematic finite element crystal plasticity simulations also include specific interface conditions at grain boundaries. The presented computational analysis indicates that, compared to the experiment, there remains dark energy in the evaluation of energy storage as predicted by the proposed thermodynamically consistent crystal plasticity framework.

Thermomechanical processing of crystalline materials induces microstructural evolution such as grain nucleation and growth. In the numerical simulation of these processes, grain nucleation is generally treated as an additional ad hoc step in which circular or spherical grains are added in regions where a critical dislocation density, stress or strain are reached. In this paper, systematic finite element simulations are performed showing that the Kobayashi-Warren-Carter (KWC) phase field model and its coupling with Cosserat crystal plasticity predict spontaneous nucleation of new grains in single crystals in the presence of lattice orientation/rotation gradients. The numerical analysis of the stability of gradients of lattice rotation and dislocation-based stored energy indicates that a gradient of stored energy alone is not sufficient to trigger grain formation. As an application, the KWC-Cosserat model is used to simulate the torsion and annealing of a copper single crystal bar with a circular cross section. This mechanical loading produces a large, fairly uniform axial rotation gradient which induces nucleation in the form of a stack of cylindrical grains. Plastic strain gradients in cross-sections predicted by the 3D finite element simulation, are not strong enough to compete with the longitudinal nucleation process, as confirmed by experimental observations from the literature.

Materials can now be designed and architectured like structural components for targeted mechanical and physical properties. Structures and microstructures should not be studied independently and their design will benefit from a multiscale approach combining nonlinear continuum mechanics approaches and physical descriptions of elasticity, viscoplasticity, phase transformations and damage of microstructures, at various scales. The aim of the workshop was to gather outstanding junior and senior researchers in the various branches of mathematics, physics and engineering sciences suited to address the question of design of materials and structures by means of multiscale discrete and continuum approaches to their constitutive behavior. Examples include atomic or macroscopic lattices, random or periodic cellular materials, smart materials like shape memory alloys, 3D woven composites, acoustic and electromagnetic metamaterials, etc. Modern continuum mechanics relies on sophisticated constitutive laws for anisotropic materials exhibiting elastoviscoplastic behavior, still a field of intense research with new mathematical concepts. In particular size-dependent properties are addressed by resorting to generalized continua such as gradient or micromorphic and phase field models. The latter are attractive for the simulation of microstructure evolution coupled with mechanics, due to thermodynamic and metallurgical processes and damage. Scale transition and homogenization methods for continuous and discrete systems are required for the determination of effective material and structural behavior. Metamaterials are architectured materials specifically designed to achieve certain propagation and dispersion properties of elastic and plastic waves. Optimization strategies for the design of optimal architectures are involved in the design process. Target functions for optimization are now based on multicriteria (stiffness, strength, thermal expansion, transport properties, anisotropy etc.).

A number of experimental evidences indicate that the local response of polymer matrices near fibres is inadequately represented by classical continuum models relying on the bulk polymer behaviour. This results from size-dependency associated to large plastic strain gradients, complex interphase behaviour and/or changes of polymer structure. Classical multiscale models require artificial tuning of the properties to provide realistic macroscale predictions. We demonstrate that an unprecedented modelling approach based on a micromorphic theory is able to capture such size effects in long-fibre composites. The model is identified via nano digital image correlation strain fields and validated by predicting the strengthening found in transverse compression of UD composites, not captured by classical models. Micro-shear bands are properly regularised by the model, thus correctly handling the size-dependent plasticity and softening effects. The improved prediction of the strain localisation pattern in the matrix opens avenues to more accurately model interfacial failure and damage processes.

Chemically architectured high entropy alloys are a new concept of multi-scale microstructure originally including a 3D network of composition fluctuations, named interphase. To unravel the strengthening contribution of each entity of the microstructure, chemically architectured alloys were processed, their microstructure and mechanical properties were characterized and then they were modelled by the finite element method. Nanoindentation measurements reveal a local extra-hardening at the interphase. Conventional modelling, even when considering three phases in a full-field approach, could not reproduce the compression properties, indicating again the existence of an extra-hardening. Then, the chemical and plastic strain gradients effects were included in the model and an agreement was reached with experimental data. Both experimental and modelling results prove that chemical gradients are at the origin of a new strengthening mechanism. This chemical gradient strengthening depends on the many microstructural parameters of chemically architectured alloys and opens the way for tuning and optimization of mechanical properties.

An extensive study of size effects on the small-scale behavior of crystalline materials is carried out through discrete dislocation dynamics (DDD) simulations, intended to enrich strain gradient crystal plasticity (SGCP) theories. These simulations include cyclic shearing and tension-compression tests on two-dimensional (2D) constrained crystalline plates, with single- and double-slip systems. The results show significant material strengthening and pronounced kinematic hardening effects. DDD modeling allows for a detailed examination of the physical origin of the strengthening. The stress-strain responses show a two-stage behavior, starting with a micro-plasticity regime with a steep hardening slope leading to strengthening, and followed by a well-established hardening stage. The scaling exponent between the apparent (higher-order) yield stress and the geometrical size h varies depending on the test type. Scaling relationships of h( -02) and h( -03) are obtained for respectively constrained shearing and constrained tension- compression, aligning with some experimental observations. Notably, the DDD simulations reveal the occurrence of the uncommon type III (KIII) kinematic hardening of Asaro in both single- and double-slip cases, emphasizing the relevance of this hardening type in the realm of small-scale plasticity. Inspired by insights from DDD, two advanced SGCP models incorporating alternative descriptions of higher-order kinematic hardening mechanisms are proposed. The first model uses a Prager-type higher-order kinematic hardening formulation, and the second employs a Chaboche-type (multi-kinematic) formulation. Comparison of these models with DDD simulation results underscores their ability to effectively capture the observed strengthening and hardening effects. The multi-kinematic model, through the use of quadratic and non-quadratic higher-order potentials, shows a notably better qualitative congruence with DDD findings. This represents a significant step towards accurate modeling of small-scale material behaviors. However, it is noted that the proposed models still have limitations, especially in matching the DDD scaling exponents, with both models producing h -1 scaling relationships ( i.e., Orowan relationship for precipitate size effects). This indicates the need for further improvements in gradient-enhanced theories in order to guarantee their suitability for practical engineering applications.

Zn-Al-Mg coatings are characterized by a complex microstructure with dendritic and eutectic phases. This heterogeneous phase distribution contributes to multiple deformation and damage mechanisms. The presence of brittle phases promotes crack initiation and propagation. This study reveals a new deformation and damage mechanism of a Zn-Al-Mg coating, where twinning can induce crack initiation in the eutectic region. The chronology of different events leading to crack initiation and propagation is clearly established by in-situ tensile testing in a scanning electron microscope, which helps to establish a detailed characterization of the mechanical behavior of the coating.