Mean-field theory is extensively used in statistical physics, solid-state physics, and biophysics to compress a large number of interacting multi-body problems into an effective single-body problem, providing some insight into the system’s behavior at a lower computing cost. Nonetheless, the mean-field approximation always suppresses the non-local effects, hence obscuring the underlying mechanisms involving unit interactions between microscopic events, such as competition, co-evolution, and self-organized criticality. This paper presents a general, non-local mean-field approximation for the medium-long-range correlation of materials based on the finite element method, which has excellent compatibility and scalability with existing theories. It ties the evolution of a deformation unit to the status of other spatial domain elements, which is analogous to the fundamental principle of cellular automata. When applied to metallic glasses, the model demonstrates excellent spatial–temporal agreement between the shear band evolution measurements and simulation findings. Excitingly, the self-organized criticality of amorphous systems and the self-adaptive evolution mechanism of shear bands are realized in both two and three dimensions for the first time. Without restriction to amorphous systems, this work explores the application of mean-field theories to non-local phenomena. Future research into new mathematical types of medium-long range interaction is conceivable through multiscale simulation techniques.

Dislocation climb plays an important role in understanding plastic deformation of metallic materials at high temperature. In this paper, we present a continuum formulation for dislocation climb velocity based on densities of dislocations. The obtained continuum formulation is an accurate approximation of the Green’s function-based discrete dislocation dynamics method (Gu et al., 2015). The continuum dislocation climb formulation has the advantage of accounting for both the long-range effect of vacancy bulk diffusion and that of the Peach–Koehler climb force, and the two long-range effects are canceled into a short-range effect (integral with fast-decaying kernel) and in some special cases, a completely local effect. This significantly simplifies the calculation in the Green’s function-based discrete dislocation dynamics method, in which a linear system has to be solved over the entire system for the long-range effect of vacancy diffusion and the long-range Peach–Koehler climb force has to be calculated. This obtained continuum dislocation climb velocity can be applied in any available continuum dislocation dynamics frameworks. We also present numerical validations for this continuum climb velocity and simulation examples for implementation in continuum dislocation dynamics frameworks.

This paper proposes a modelling approach that combines the discrete element method (DEM) and a novel bonded contact model to characterise the fatigue response of cemented materials. While DEM is commonly used to simulate bonded materials undergoing cracking, the centrepiece of the present method is the development of the novel bonded fatigue model. This new model couples damage mechanics and bounding surface plasticity theory to capture fatigue crack growth in cement bridges between aggregates. Thanks to the incorporation of the bounding surface plasticity, the proposed model provides a smooth transition from static to fatigue damages and vice-versa in a unified manner, making it more flexible to capture damage responses of cemented materials under different loading conditions (i.e. monotonic and cyclic loadings). Moreover, the proposed approach automatically captures the hysteretic response in cement bridges between aggregates under fatigue loadings without ad-hoc treatments. More importantly, by removing the direct dependence of the fatigue damage variable on the number of loading cycles, the modelling approach can be applied to simulate the fatigue behaviour of cemented materials under cyclic variable load amplitudes. The proposed modelling approach is evaluated against several strength tests to examine its predictive capability. Satisfactory agreements with fatigue experiments are achieved for flexural modulus degradations, lifetimes and sensitivity of stress levels under constant and variable amplitude cycles. This result suggests that the proposed discrete modelling approach can be used to conduct numerical experiments for insights into the fatigue behaviour of cemented materials.

Achieving a high strength-ductility synergy in rolled Mg alloys remains a major challenge, especially for Mg alloys with high contents of rare earth (RE) elements, which are hard-to-deform and exhibit poor formability. In the present work, a bimodal grain structure consisting of fine grains (FGs) and coarse grains (CGs) has been achieved in a novel WE43 alloy sheet prepared by the hard-plate rolling (HPR) technique, which breaks the strength-ductility trade-off dilemma of the conventional WE43 alloy. Notably, the yield strength (YS) reaches as high as ∼312 MPa, presenting a remarkable improvement of YS (∼60 MPa) in comparison to conventionally rolled counterparts. Meanwhile, the ultimate tensile strength (UTS) and elongation-to-failure (EF) are ∼332 MPa and ∼11.8%, respectively, much higher than those of the wrought WE43 alloy reported in literature. Specifically, the disparate dislocation slips and dynamic precipitation behaviors in FGs and CGs have been studied in detail by combining EBSD and TEM analysis. The discrepancy of dynamic precipitation behavior in FGs and CGs is originated from the heterogeneous dislocation slip-dominated deformation behavior during HPR, related to initial grain orientations. It reveals that basal slips are dominant in the FG area, where equilibrium β-Mg14Nd2Y phase has precipitated along grain boundaries. In contrast, non-basal slips are prevalent and the metastable short rod-shaped β1 phase has formed within CGs. The enhanced YS of the present HPRed WE43 alloy sheet is mainly attributed to the formation of large amounts of extremely fine grains with an average size of ∼0.94 μm. The enhanced Orowan strengthening comes from the interaction between short rod-shaped β1 particles and non-basal dislocations (prismatic , pyramidal and pyramidal dislocations) in CGs. In particular, the interactions between β1 particles and pyramidal dislocations dominate the Orowan strengthening, leading to an increase of ∼34 MPa in the YS. Basal to basal slip transfers have been observed in FGs while non-basal slips are prevalent in CGs, which could be helpful for release the stress concentration near GBs. It is beneficial for preventing earlier fracture and thus enhancing the tensile strength combined with decent ductility.

Abstract not available

The ductility of polycrystalline aggregates is usually limited by two main phenomena: plastic strain localization and void coalescence. The goal of this contribution is to develop a new multiscale framework, based on the crystal plasticity finite element method (CPFEM), for the prediction of ductility limits set by these two phenomena for porous and non-porous polycrystalline aggregates. This numerical framework is based on the combination of crystal plasticity constitutive modeling with the periodic homogenization scheme. Within this strategy, the single crystal constitutive modeling follows a finite strain rate-independent approach, where the plastic flow is governed by the classical Schmid law. Thereby, the competition between the two aforementioned phenomena, which limit ductility, is thoroughly analyzed using the bifurcation theory and a strain-based coalescence criterion. To cover a wide range of mechanical states in this analysis, two types of loadings are applied to the studied aggregates: proportional triaxial stress paths and proportional in-plane strain paths. The developed CPFEM-based framework is well suited to account for essential microstructural features: pre-existence of spherical voids, crystallographic and morphological anisotropy, matrix polycrystallinity and interactions between grains and their surrounding medium. Extensive sensitivity studies are performed to analyze the impact of these microstructural features on the ductility limit predictions. The main trends obtained by classical phenomenological frameworks are extended here within the framework of crystal plasticity constitutive modeling.

High entropy alloys (HEAs) have received widespread attention as structural and functional materials owing to their large atomic lattice distortion and vast compositional space. Recently, nanoscale HEAs have been proven to exhibit exceptional combinations of mechanical properties, thermal stability, and oxidation resistance. The structural and functional stabilities of nanoscale HEAs under practical loading conditions are vital to their applications. Here, based on a grain boundary (GB) design strategy, we introduced custom-designed low-angle GBs (LAGBs) into quinary face-centered cubic HEA nanocrystals, intending to improve the mechanical stability of nanoscale HEAs under external loading through molecular dynamics simulations. Using CuCoNiPdFe and FeNiCrCoCu HEAs as examples, we reveal two distinct LAGB-mediated deformation behaviors of nanoscale HEAs, which stem from the differences in lattice distortion and shear modulus of the materials. In the case of CuCoNiPdFe, the LAGB is composed of separate Shockley dislocations, endowing the material with extraordinary plastic deformability and structural stability. In the case of FeNiCrCoCu, the LAGB contains a series of parallel stacking faults cross-linked immobile dislocation segments, which severely damages the plastic deformability of the material. Based on the atomistic understanding of LAGB structure and migration behavior, we have screened out a range of material systems with small lattice distortion and shear modulus, realizing superb plastic deformability and structural recoverability in HEAs designed with LAGBs. These findings promote the understanding of GB-mediated deformation mechanisms in HEAs and provide insights into the structural and composition design of HEA nanomaterials.

Boosting the applications of high nitrogen steels requires delicate control of detrimental brittle AlN precipitates which often initiate cracking and thus degrade overall mechanical performance. Here we report that stacking faults in nano-sized AlN precipitates can be activated by martensitic transformation during quenching in a high nitrogen martensitic stainless bearing steel. Atomic-scale structure and strain analyses illuminate that the planar deformation mode, which is rarely seen in inorganic AlN ceramic precipitates, is stimulated by the martensitic transformation of the steel matrix to accommodate the transformation stresses and strains at the precipitate/matrix interfaces. The critical resolved shear stresses derived from the density functional theory study are consistent with the stress arising from the martensitic transformation obtained from the phenomenological theory of martensitic crystallography combined with phase field modeling, further validating the martensitic transformation induced plastic deformation in AlN nanoprecipitates. Our finding paves a new way to mitigate the harmful effect of AlN precipitates in high nitrogen steels and enables the production of high-quality high nitrogen steels with an upper limit of Al content raised to the normal steelmaking level, which offers new guidelines for effectively reducing the production costs of high nitrogen steels.

It is challenging to precisely model the complicated plastic deformation of metals, including anisotropy in strength and plastic deformation, strength differential effect, anisotropic hardening, etc. A new approach is proposed to extend anisotropic yield functions into asymmetric ones by introducing a Lode dependent function. The approach is applied to the Hill48 function with a Lode-dependent function in a form of the normalized third stress invariant. The proposed Lode-dependent anisotropic-asymmetric (LAA) is applied to characterize the anisotropic hardening behaviors under both tension and compression of QP1180, DP980, AA2008 T4 and α-Ti to verify its performance. The convexity of yield surface evolution with plastic deformation is investigated by a geometry-inspired numerical convex analysis method. The application shows that the proposed LAA function precisely characterizes the anisotropy in tension and compression and its evolution with plastic deformation. It is therefore suggested to model the anisotropic-asymmetric plastic behavior with its applications to metal forming.

Understanding and controlling the performance of additively manufactured aluminum alloys containing scandium (Sc) and zirconium (Zr) elements heavily relies on knowledge of their microplasticity and macroplasticity behavior. However, this aspect has received very little attention. In this investigation, we examined the microplasticity and macroplasticity behavior of additively manufactured Al-Mg-Sc-Zr alloys before and after aging, using in-situ synchrotron X-ray diffraction and full-field crystal plasticity modeling. Our study provides a quantitative assessment of the transitions from elasticity to microplasticity and then to macroplasticity and analyzes the development of the initial microstructure, particularly the dislocations. We constructed crystal plasticity fast-Fourier-transform models based on dislocation densities. The predicted evolutions of macroscopic stress-strain curves, lattice strains, and dislocation densities agree with in-situ measurements. The present findings provide deep insights into controlling the performance of AM Al-Mg-Sc-Zr alloys. Besides, the micromechanical model developed in this investigation paves the way for predicting the microplasticity and macroplasticity behavior of various metallic materials.

This study proposes a machine learning-based constitutive model for anisotropic plasticity in sheet metals. A fully connected deep neural network (DNN) is constructed to learn the stress integration procedure under the plane stress condition. The DNN utilizes the labeled training data for feature learning, and the respective dataset is generated numerically based on the Euler-backward method for the whole loading domains with one element simulation. The DNN is trained sufficiently to learn all the incremental loading paths of the input-output stress pair by using advanced anisotropic yield functions. Its performance with anisotropy is evaluated for the predictions of r-values and normalized yield stress ratios along 0–90 ° to the rolling direction. In addition, the trained DNN is then incorporated in user material subroutine UMAT in ABAQUS/Implicit. Thereafter, the DNN-based anisotropic constitutive model is tested with a cup drawing simulation to evaluate earing profile. The obtained earing profile is compatible with the one from the trained anisotropic yield function.

The present work uses a full-field crystal plasticity model with a first principles-informed dislocation density (DD) hardening law to identify the key microstructural features correlated with micromechanical fields localization, or hotspots, in polycrystalline Ni. An ensemble learning approach to machine learning interpreted with Shapley additive explanation was implemented to predict nonlinear correlations between microstructural features and micromechanical stress and strain hotspots. Results reveal that regions within the microstructure in the vicinity of grain boundaries, higher Schmid factors, low slip transmissions and high intergranular misorientations, are more prone to being micromechanical hotspots. Additionally, under combined loading and large plastic deformations, slip transmissions take precedence over intergranular misorientations in formation of both strain and stress hotspots. The present work demonstrates a successful integration of physics-based crystal plasticity with DD-based hardening into machine learning models to reveal the microscale features responsible for the formation of local stress and strain hotspots within the grains and near the grain boundaries, as function of applied deformation states, grain morphology/size distribution, and microstructural texture, providing insights into micromechanical damage initiation zones in polycrystalline metals.

Helium migration is an important mechanism of helium embrittlement in irradiated metallic materials, which can severely affect their service reliability. Despite many efforts to reveal the mechanism of helium migration during plastic deformation, a mechanistic understanding of helium transport through dislocation motion is still lacking. In this work, we developed a theoretical model within the coupled framework of crystal plasticity and helium diffusion, to account for the helium transport due to the bidirectional dislocation motion. Our simulation results show that, for austenitic stainless steel, such motion has a significant impact on helium migration, leading to an enriched helium concentration on the grain boundaries (GBs), and thus resulting in a higher risk of intergranular fracture. Besides, our results also indicate that temperature and irradiation defect affect the helium concentration on the GBs by regulating the intragranular helium distribution. The present study reveals the key role of dislocation motion in regulating helium migration, a firm step toward a more comprehensive understanding over the failure mechanisms of irradiated metallic material.

In this paper, we investigate plasticity in irradiated FeCrAl nanopillars using discrete dislocation dynamics simulations (DDD), with comparisons to transmission electron microscopic (TEM) in situ tensile tests of ion- and neutron-irradiated commercial C35M FeCrAl alloy. The effects of irradiation-induced defects, such as a/2 and a type loops and composition fluctuations representative of phase separation in irradiated FeCrAl alloys, are investigated separately as well as superposed together in simulations. We explore the effects of defects on the stress-strain behavior, specifically yield strength and hardening response, of FeCrAl nanopillars. Our simulations confirm the widely accepted fact that irradiated alloys exhibit a stress-strain response with higher yield strength as compared to unirradiated alloys. However, our DDD calculations reveal an atypical superposition of the hardening contributions due to composition inhomogeneity and irradiation loops wherein composition inhomogeneity annihilates the hardening due to irradiation loops at small scales. As a result, we observe that the yield strength in irradiated alloys, after taking into consideration the effects of both composition inhomogeneity and irradiation loops, is smaller than the yield strength of the alloys with only irradiation loops and is approximately same for the alloy with composition inhomogeneity alone. This is referred to as “destructive interference” between the hardening contributions due to composition fluctuations and irradiation loops in the paper. We also identify this destructive interference in the superposition in our parallel TEM in situ tensile tests on unirradiated, ion-irradiated, and neutron-irradiated C35M FeCrAl alloy. This destructive interference in the hardening contributions contrasts with the dispersed barrier hardening (DBH) models widely utilized by the experimental community to model the hardening contributions due to different irradiation induced defects. The effects of the loading orientations on the yield strength and hardening are investigated and the mechanisms for the hardening in irradiated FeCrAl alloys are also reported.

We demonstrate the ability to synergistically enhance strength and toughness in metals by tailoring the dominant plasticity mechanisms from impact-induced heterogeneous nanostructures. Using a laser-induced projectile impact testing apparatus, we impact initially dislocation-free single crystal microcubes at high velocities to induce grain size and dislocation density gradients. These gradient nanostructures exhibit heterogeneous deformation under subsequent quasi-static loading leading to enhanced strength and toughness. Transmission Kikuchi diffraction (TKD) analyses show that the synergistic property improvement arises from the complimentary intragranular and intergranular plasticity mechanisms: the pronounced intragranular dislocation plasticity within coarse grained regions provides increased strain hardening and toughness while the nanograined regions with high dislocation densities provide high strength and supplemental toughness enhancement through cooperative grain rotation and grain boundary migration. These plasticity mechanisms are activated to different extents depending on the specific impact-induced nanostructures, which depend on the orientation of the single crystal upon impact. Controlled [100]-face, [110]-edge, and [111]-corner impact of single crystal microcubes, subsequent quasi-static mechanical testing, and pre- and post-compression nanostructural characterization provide a fundamental understanding of the comprehensive process-structure-property relations in heterogeneous nanostructured metals.

The designed low-carbon ultra-high strength martensite seamless tube steel was manufactured by hot rolling and quenching-tempering processes. The multiple strengthening mechanisms are evaluated depending on the microstructure and co-precipitation evolution mechanism of Cu and NiAl, and the toughening mechanisms associated with multiscale microstructures are systematically discussed. The results show that the microstructure of the experimental steel in the quenched state consists of 87.8% lath martensite (LM) and 12.2% granular bainite (GB), while the microstructure in the QT state includes tempered martensite (TM), GB and a small amount of reversed austenite. The TEM morphology of QT steel shows three types of nanoparticles co-precipitated by Cu-rich, NiAl and Cu-NiAl, and the nanoparticles coarsen significantly and the number density decreases dramatically as the aging temperature increases from 500 °C to 650 °C. The co-precipitation evolution mechanism of nanoparticles elucidates that high density of small-sized BCCCu and B2-NiAl particles is optimal for strengthening increment. The experimental steel has an maximum yield strength of 1332.5 MPa aged at 500 °C, which is attributed to high precipitation strengthening of 651.2 MPa (general superposition of shear strengthening and Orowan strengthening) and dislocation strengthening of 454.8 MPa. The experimental steel has obvious low-temperature toughening, and the impact energy at -40 °C increases from 5 J to 237 J as the aging temperature increases from 500 °C to 650 °C. The excellent low-temperature toughness is attributed to the reduction of dislocation density, the weakening of the shear mechanism and the transformation of a small amount of reversed austenite to increase the crack nucleation energy, and the increase of the number fraction of HAGB and the significant plastic deformation increase the crack propagation energy.

Slip transfer mechanism is studied based on in-situ tensile tests performed on an Al-Mg alloy and high-throughput computing. A statistical analysis of slip transfer is performed for over 1180 grain boundaries and 155,250 slip pairs while considering the local lattice rotation, grain boundaries, and slip system geometries. Two new slip transfer parameters, N and B, representing the alignment of the slip planes and the activation of slip systems in adjacent grains, are proposed. A decision tree model is built to evaluate the prediction accuracy of the slip transfer parameters. The optimized results of the decision tree classifiers show that the two new parameters are more effective than the Luster–Morris parameter, m′. The improvement in the classification accuracy is attributable to the information regarding the slip plane geometry and orientation evolution contained in N and B. The new slip transfer parameters improve our understanding of the slip transfer mechanism and can be integrated into plasticity models to predict the deformation and fracture behaviors of polycrystalline materials.

Detwinning of martensite accounts for the macroscopic deformation in shape memory alloys, yet the corresponding microstructural and crystallographic evolution remains less understood. Here, the detwinning behaviors of hierarchically twinned non-modulated (NM) martensite in a directionally solidified Ni54Mn24Ga22 alloy under uniaxial tension along the A direction of austenite are systematically investigated. Based on the interrupted in-situ EBSD measurements, it is demonstrated that tensile loading leads to the thickening of favorable variants with the NM parallel to the loading direction through intensive detwinning, which follows the route of detwinning of internal nanotwins as well as collective detwinning of internal nanotwins and inter-plate major-major variant pairs. Besides, the internal detwinning is also coupled with the rigid body rotation owing to the constraints of inter-plate boundaries, resulting in the refinements in the inter-plate correlation as the variation of thickness ratio of nanotwins. Consequently, the hierarchically twinned microstructure finally evolves into a single-variant state with the NM along the loading direction. This work provides clear demonstrations on the detwinning behaviors of hierarchically twinned NM martensite induced by tensile loading, which allows us to gain deep crystallographic insights into the stress-induced rearrangement of martensite variants in association with the macroscopic deformation.

In this paper, we have investigated void growth in von Mises materials which contain realistic porous microstructures. For that purpose, we have performed finite element calculations of cubic unit-cells which are subjected to periodic boundary conditions and include porosity distributions representative of three additively manufactured metals. The initial void volume fraction in the calculations varies between 0.00564% and 1.75%, the number of actual voids between 14 and 5715, and the pores size from 2.3μm to 110μm. Several tests with different void sizes and positions have been generated for each of the three porous microstructures considered, and for each test we have performed several realizations with different spatial arrangement of the voids. The simulations have been carried out with random spatial distributions of pores and with clusters of the same size and different void densities. The macroscopic stress state in the unit-cell is controlled by prescribing constant triaxiality and Lode parameter throughout the loading. Calculations performed exchanging the loading directions for a given distribution of void sizes and positions have shown that the porous microstructure makes the macroscopic strain softening of the unit-cell (slightly) anisotropic. Moreover, the results obtained with the realistic porous microstructures have been compared with unit-cell calculations having an equivalent single central pore, and with calculations in which the material behavior is modeled with Gurson plasticity. It has been shown that both initial void volume fraction and spatial and size distribution of voids affect the macroscopic response of the porous aggregate and the void volume fraction evolution. Moreover, the calculations with random spatial distribution of voids have brought out that different tests of the same microstructure carry significant variations to the effective behavior of the porous aggregate, and that the interaction between neighboring pores dictates the volume evolution of individual voids, especially at higher macroscopic triaxiality. The calculations with clusters have shown that pores clustering promotes localization/coalescence due to increased interaction between the voids, which results in an increased growth rate of voids in clusters with large number of pores. Moreover, the results for the evolution of the distribution of plastic strains in the unit-cell have provided quantitative indications of the role of porous microstructure on the development of heterogeneous plastic strain fields which promote macroscopic strain softening. Namely, the accelerated growth rate of the plastic strains near the voids which indicates the onset of localization/coalescence has been shown to occur earlier as the number of voids in the microstructure increases.

Gurson-Tvergaard-Needleman (GTN) model is one of the most famous and classical criterions widely used in modelling the ductile fracture process of metal. However, the existence of grain size effect affects the ductile fracture prediction in micro-scaled plastic deformation of nickel-based superalloy ultrathin sheet. In the pulsed current assisted (Pca) forming process, the current has a healing effect on the micro-void of metal due to the existence of local Joule heat, yet the strain has a promotion on the micro-void growth, and the coupled effect between grain size and electrical field is complicated, which makes it difficult to predict the fracture for the traditional GTN model in Pca forming process. To solve this problem, the authors added pulsed current parameters to the GTN model to describe the healing effect of pulsed current on the voids in the material. The parameters of the GTN model were calibrated by the finite element inverse identification method. The modified GTN model was embedded into Abaqus by VUMAT, and the Backward Euler algorithm was employed to integrate the constitutive equation. The validity of the model was verified by comparing the true stress-strain curves with the simulation results and comparing the void volume fraction (VVF) measured by three-dimensional X-ray computerized tomography (3DCT). The model provides a new method for ductile fracture prediction of multiphase alloys under a discontinuous energy field. Meanwhile, it is confirmed that the behaviour of fracture and necking in the Pca forming process is affected by the coupling effect of pulsed current and grain size effect, which provides a new idea for studying the Pca forming process.