The incipient plasticity behavior of medium- and high-entropy alloys (MEAs/HEAs), particularly the “pop-in” phenomenon, has been noticed to be significantly influenced by the short-range orders (SROs). However, the existing models cannot uniformly characterize the effect of SROs on both homogeneous and heterogeneous dislocation nucleation mechanisms. To address this issue, a physical mechanism-based and statistically unified nucleation model is developed to elucidate the regulatory influence of SROs on the incipient plasticity of single crystalline MEAs. Specifically, for heterogeneous nucleation, the SROs are considered as potential heterogeneous nucleation sites, whose contribution is characterized by the nucleation source density and proportion coefficient in the model. For homogeneous nucleation, the contribution of SROs is incorporated by considering the influence on the generalized stacking fault energy. Additionally, an energy correction factor is introduced to achieve precise matching between the theoretical and actual nucleation energy barriers. Furthermore, the combined effect of these two nucleation mechanisms is quantitatively described by employing a weighting method. To help validate the proposed dislocation nucleation model, statistical distributions of the pop-in data are compared between experimental data and theoretical results for single crystalline CrCoNi MEAs under different heat treatments. A close agreement is achieved for all the considered data, indicating the good accuracy and rationality of the proposed model. Furthermore, corresponding dislocation nucleation mechanisms are discussed to help comprehend the pop-in behaviors affected by SROs.

In order to help comprehend the influence of short-range ordering (SRO) on the cyclic deformation behavior of N-containing austenitic high-manganese (high-Mn) steels, and reveal the underlying micromechanisms governing their low-cyclic fatigue performance, a microstructure-based crystal plasticity constitutive model is developed in this work, which covers the key deformation mechanisms including the evolution of dislocation microstructure, dynamic annihilation of Cr-N SROs, and the coupling effect of backstress evolution. An innovative model of dislocation evolution is proposed to characterize the transformation between mobile and immobile dislocations driven by the accumulated plastic strain, capturing the rearrangement of dislocation substructures (e.g., from tangled dislocations to walls or cells) that affects cyclic hardening/softening. Additionally, a dynamic framework for SRO annihilation is established to quantify the process where repeated dislocation shearing induces the destruction of Cr-N SROs, forming "softening channels" that enhance cyclic softening. Moreover, the model incorporates the coupling effect of backstress evolution to characterize the cyclic responses influenced by interstitial N atoms, which promote the SRO formation and reduce stacking fault energy, thereby altering the dislocation slip modes (e.g., planar slip). To help validate the proposed constitutive equations, the cyclic deformation behaviors of polycrystalline 00 N (0 wt% N) and 21 N (0.21 wt% N) high-Mn steels, including the evolution of stress amplitude, hysteresis loops, and microstructural changes such as the decay of SRO density and dislocation rearrangement, are compared between the experimental data and theoretical results. A good agreement is achieved that can help verify the proposed theoretical model and facilitate the comprehension of the underlying deformation mechanisms.

In this work, a creep rupture life prediction model is proposed by combining the creep constitutive laws and Monkman-Grant (M-G) relation to analyze the rupture time under thermal and irradiation creep. The model could simultaneously characterize the influence of testing temperature, applied stress and irradiation damage on the steady-state creep strain rate by taking into account corresponding microstructure evolution, accurately capture the mechanism transitions during creep, and then convert the steady-state creep strain rate into macroscopic rupture life via the M-G relation. Once the irradiation effect is ignored, the model can be degraded to predict the thermal creep rupture life. Model validation is achieved by comparing theoretical results with the experimental data of 15-15Ti, 316H, P92 and 304 steels for both thermal and irradiation creep. Related mechanism analyses indicate that the shortened thermal creep rupture life with increasing stress and temperature is mainly ascribed to the accelerated activity of dislocation climb that leads to the enhancement of dislocation mobility and acceleration of creep damage accumulation. Under irradiation creep, it is the elevated vacancy diffusion coefficient that leads to the enhanced activity of dislocation climb, and finally results in the shorter irradiation creep rupture life when compared with the one under thermal creep. The proposed model could provide an efficient theoretical tool for material creep life assessment under extreme environments.

The porous irregular functional gradient material (FGM) coupled plates, composed of two arbitrary quadrilateral plates coupled at any angle, are widely used in aerospace applications and equipment such as hypersonic vehicles. This paper investigates the stochastic response mechanisms of the porous irregular FGM coupled plate under aerothermal environments and base acceleration excitations. Three typical geometric models are established to validate the universality of the present method. The equations derived from supersonic piston theory and Mindlin plate theory incorporate temperature-dependent material properties. Subplate displacements are approximated using the first-kind Chebyshev polynomials, with irregular domain integrals resolved through coordinate transformations. Sufficient comparisons with the finite element method (FEM) and published literature confirm the accuracy and computational efficiency of this approach. The resulting systematic framework enables stochastic response analysis in analogous complex structures. Numerical discussions are conducted to analyze the effects of FGM gradient p, porosity zeta, coupling angle theta, boundary conditions, and temperature variations Delta T on the stochastic response, establishing practical tools for optimizing and conducting rapid integrity assessment of such structures.

Nanocrystals have been well known for their high strength, but the comparatively poor creep properties have limited the application as engineering structural materials. Recently, it has been noticed that adding nanoclusters of alloying elements can effectively inhibit the creep behavior of nanocrystals. In order to fundamentally comprehend the creep inhibition mechanism, a theoretical model is proposed in this work that combines the crystal plasticity theory and viscoplastic self-consistent method. At the grain level, creep strain rate dominated by the grain boundary and grain interior is characterized, respectively. Nanoclusters result in the suppression of grain boundary creep from three aspects, including the influence on diffusion coefficient, dislocation glide area and movement resistance. For the grain interior, the average distance between dislocations is reduced by nanoclusters, thereby affecting the evolution of dislocation density. At the polycrystalline level, viscoplastic self-consistent method is applied to predict the creep behaviors of nanocluster-contained nanocrystals. To validate the developed creep model, experimental data of both nanocrystalline pure Cu and Cu-Ta alloys has been considered. A good agreement of the creep curves is achieved between the theoretical results and experimental data, which provides a basis for further analyzing the creep inhibition mechanisms from the perspective of microstructure evolution.

3-power law creep of high entropy alloys (HEAs) is different from that of conventional alloys. In order to help comprehend the relation between microstructure evolution and macroscopic creep response, three dominant mechanisms related to dislocation movements are considered in this work, i.e. dislocation climb, thermally activated dislocation glide and viscous glide. Thereinto, the influence of dislocation viscous glide on the evolution of dislocation density and velocity is systematically analyzed. For the former, the time effect of viscous glide is taken into account in the derivation of the static recovery term for dislocation density evolution. For the latter, dislocation viscous glide can lead to the reduction for dislocation climb velocity due to the drag effect of solute atmosphere, and the dislocation glide velocity is controlled by the competition between the preparation stage for dislocation climb or thermally activated dislocation glide and viscous glide. To validate the developed creep model, experimental data of CoCrFeMnNi HEAs for both the high stress region (n approximate to 5) and low stress region (n approximate to 3) has been considered. A good agreement is achieved between the theoretical results and experimental data, which offers a solid basis to further analyze the effect of dislocation viscous glide from the aspect of microstructure evolution for HEAs.

The classic Hall-Petch model effectively captures the relationship between strength and layer thickness for thicknesses above 100 nm, while the constrained layer slip (CLS) model provides a better prediction for thicknesses below 100 nm. Nonetheless, the precision of the current CLS model is insufficient, especially for structures with FCC/HCP interfaces, which limits the development of lightweight composites such as Al/Mg. To address this gap, this study uses molecular dynamics (MD) simulations to explore the CLS mechanism under compression in Al/Mg composites. We propose a novel dual-mode CLS model aimed at enhancing the accuracy of stress predictions across a wide range of layer thicknesses and various slip angles. Our findings indicate that with decreasing layer thickness and the loss of lattice structure, the FCC/HCP interface becomes unstable and exhibits reduced strength when the layer thickness falls below 26.7 nm. Moreover, as the slip angle rises from 0 degrees to 75 degrees, the improved interface compatibility aids in the initiation of basal slip in the Mg layer. This triggers a migration of dislocations from the Al side to the Mg side, thereby altering the dominant CLS mechanism. This work is expected to accelerate the development of Al/Mg composites and other similar FCC/HCP composite systems.

Interpenetrating phase composites (IPCs) have demonstrated tremendous potential across various fields, particularly those based on triply periodic minimal surface (TPMS) structures, whose uniquely interwoven lattice architectures have attracted widespread attention. However, current research on the dynamic mechanical properties of such IPC remains limited, and their impact resistance and damage mechanisms are yet to be thoroughly understood. In this study, a novel design of two volume fractions of IPCs based on the TPMS IWP configuration is developed using Python-based parametric modeling, with the Ti6Al4V alloy TPMS scaffolds fabricated via selective laser melting (SLM) and the AlSi12 reinforcing phase through infiltration casting. The influence of Ti alloy volume fraction and strain rate on the dynamic mechanical behavior of the Ti/Al IPC is systematically investigated using a split Hopkinson pressure bar (SHPB) experimental setup. Microscopic characterization validates the effectiveness and reliability of the proposed IPC fabrication method. Results show that the increasing Ti alloy volume fraction significantly affects the dynamic mechanical properties of the IPC, and IPCs with different Ti alloy volume fractions exhibit contrasting mechanical behaviors under increasing strain rates, attributed to the dominance of different constituent phases. This study enhances the understanding of the dynamic behavior of TPMS-based IPCs and offers a promising route for the development of high-performance energy-absorbing materials.

In this work, a mechanistic steady-state creep model is developed to characterize the macroscopic strain rate of metallic materials affected by irradiation flux, testing temperature and applied stress. Thereinto, the steady-state strain rate is obtained by considering the density evolution of mobile dislocations, which involve the mechanisms of dislocation multiplication, dynamic annihilation and time-dependent dislocation annihilation. In order to effectively analyze the irradiation creep behavior in the low and high stress region, main attentions are focused on the influence of dislocation mobility on the process of time-dependent dislocation annihilation. At low stress, dislocation mobility is affected by dislocation climb and thermally activated glide. For the former, the absorption of irradiation-induced point defects can promote dislocation climb; whereas, thermally activated dislocation glide might be inhibited by the existing defect clusters. At high stress, the dominant deformation mechanism changes from dislocation climb to displacement cascade unpinning. For the latter, an explicit formula for dislocation mobility is deduced to address the influence of dislocation unpinning from the barriers on irradiation creep. To further verify the established model, thermal creep and irradiation creep data of zirconium alloys are considered to compare with the theoretical results. A good agreement is achieved over a wide range of temperature and stress indicating that the model can well describe the deformation behavior of steady-state creep. In addition, contribution of the dominant dislocation mobility components and dislocation density evolution components is compared under both thermal and irradiation creep, which can facilitate the comprehension of fundamental creep mechanisms of metallic materials.

To theoretically analyse how void swelling and spatial heterogeneity impact the fracture behaviour of metallic materials, a coupled porous crystal plasticity framework has been developed. The proposed framework is then applied to analyse the fracture behaviour of metallic materials under different swelling conditions and types of spatial heterogeneity. It is revealed that at low porosity, the spatial heterogeneity of voids will have limited influence on the fracture behaviour of the material. However, at high porosity, owing to void swelling, a concentrated distribution of voids near grain boundaries can lead to a strong deformation localization, which can be seen as an indicator of possible quasi-brittle fracture. It is further discovered that the inner pressure of the voids tends to reduce the yield stress of the material and promote localized plastic deformation. As a result, such pressure will enhance the impact of concentrated distribution of voids, which can lead to further embrittlement of the material. The present study reveals the key role of void swelling and spatial heterogeneity in regulating the fracture behaviour of metallic materials, a step towards a better understanding over the failure mechanisms of metallic materials under extreme conditions.

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 order to help comprehend the underlying deformation mechanisms related to irradiation creep of metallic polycrystalline materials, the crystal plasticity theory and viscoplastic self-consistent method are combined in this work. In the developed constitutive laws for single crystals, the influence of irradiation-induced defects on the creep strain rate has been effectively addressed by considering dislocation climb and glide. For the former, dislocation climb with irradiation effect can be enhanced through the absorption of point defects by dislocations, where the steady-state concentration of point defects is affected by the defect sinks including dislocations and defect clusters. As a comparison, dislocation glide may be retarded through the impediment of mobile dislocations by irradiation-induced defects. More importantly, the effect of dislocation static recovery has been incorporated into the dislocation evolution law, which is noticed to play a deterministic role for the annihilation of dislocations during the long-term creep process. In addition, the viscoplastic self-consistent method is taken as a cross-scale way to predict the irradiation creep properties of polycrystals. To validate the developed creep model, experimental data of both single crystalline and polycrystalline nickel has been considered under both thermal and irradiation creep. A good agreement between the theoretical results and experimental data is achieved, which offers a solid basis to further analyze the macroscopic irradiation creep deformation from the aspect of microstructure evolution.

Microplasticity, a behavior lies between elasticity and macroplasticity, is not only closely related to the origin of plasticity in crystalline materials, but also profoundly affects the service life of materials under small deformation, e.g., high cycle fatigue. Here a constitutive framework considering the micro- and macroplasticity is established for modeling the elastic–plastic transition of metallic materials. It reveals the origin of macro-yielding as the instability of microplasticity and demonstrates the intrinsic characteristics of the macro-yield point, including its dependence on dislocation density and offset strain. This model formulates the microplastic strain based on short-range dislocation motion, which stems from the dislocation network reconfiguration or dislocation pile-up against grain boundaries, depending on the characteristic length scales. By incorporating the grain anisotropy, a new crystal plasticity framework is developed and applied to examine the mechanical behaviors of lath martensitic steels under various loading modes, temperatures, and irradiation effects. The analysis of microplasticity encompasses aspects such as microstructural sensitivity, links to macro-yielding, and active slip systems involved. The significance of microplasticity is exemplified by its role in cyclic softening behavior, particularly in the irradiated case, which successfully captures the transition from nearly perfect elastic to elastoplastic cycling. This framework provides a quantitative understanding of microplasticity in crystalline materials, sheds light on the mechanisms underlying elastic–plastic transitions, and has potential to inform predictions of material damage and lifetime.

Void nucleation and growth under dynamic loading are essential for damage initiation and evolution in ductile metals. In the past few decades, the development of experimental techniques and simulation methods has helped to reveal a wealth of information about the nucleation and growth process from its microscopic aspects to macroscopic ones. Powerful and effective theoretical approaches have been developed based on this information and have helped in the analysis of the damage states of structures, thereby making an important contribution to the design of damage-resistant materials. This Review presents a brief overview of theoretical models related to the mechanisms of void nucleation and growth under dynamic loading. Classical work and recent research progress are summarized, together with discussion of some aspects deserving further study.

In this work, a mechanistic steady-state creep model is proposed for pure metallic materials to characterize the evolution of macroscopic creep strain rate as a function of the testing temperature and applied stress. Dislocation-dominated and diffusion-dominated creep are both addressed in the developed creep model, which is able to effectively characterize the phenomena of "first-power-law" creep, "five-power-law" creep and "power-law-breakdown" creep. Thereinto, the dislocation-dominated creep behavior is systematically analyzed by considering the evolution of dislocations, which includes dislocation multiplication, strain-rate dependent dynamic recovery and time-related static recovery. Main attentions are focused on the description of dislocation static recovery that covers the annihilation of dislocations induced by the creep mechanisms of dislocation climb and thermally related dislocation glide during the long term plastic deformation. A novel form of the dislocation mobility is deduced that not only considers the effect of dislocation climb and glide, but also takes into account the contribution of mechanical work on atomic diffusion. Moreover, the latter is noticed to be the dominant reason resulting in the transition from "five-power-law" creep to "power-law-breakdown" creep. In order to verify the developed model, creep data of six metallic materials with different crystalline structures is considered to compare with the theoretical results. Good agreement is achieved for all these data over a wide range of temperature and stress, which indicates that the model can well characterize the deformation behavior during the steady-state creep stage. In addition, the contribution of dislocation multiplication, dynamic recovery and static recovery to the evolution of dislocation density is further discussed at different temperatures and stresses, which can facilitate the comprehension of the fundamental creep mechanisms of metallic materials.

Micromechanical tests are performed to investigate the sample size effects on creep behavior of single crystalline Cu micropillars at room temperature. We report a transition from size-dependent to size-independent creep, where the transition size decreases with increasing holding stress. Furthermore, we find that the stress-related transition from size-dependent to size-independent creep can be explained by the competition between thermally-activated dislocation generation from sources and thermally-activated dislocation motion. Based on this competition mechanism, a quantitative model is established to further formulate the transition, where the model predictions agree well with the experimental results.

Void nucleation on grain boundary (GB) has been regarded as an important mechanism of damage initiation in ductile polycrystalline materials under dynamic loading. The high tensile stress induced by this loading mode enables interface incompatibility (i.e. the incompatibility of mechanical properties across the GB) to significantly affect intergranular spall damage initiation. In the present work, the concept of compatibility energy release rate is proposed to quantify the influence of interface incompatibility on interfacial failure. A tensor-formed criterion incorporating the compatibility energy release rate is established for modeling GB void nucleation in dynamic failure of ductile metals. We show that considering interface incompatibility enables the model to accurately describe the dependence of GB void nucleation on multiple factors reported by experiments and simulations, including the loading state and the GB characteristics. A statistical model on the basis of the criterion, aimed at further analyzing statistical features of GB void nucleation, provides a valid reference for quantitatively assessing the GB damage resistance and gives a physical explanation for the widely-adopted Weibull-form distribution of the nucleation stress.

A novel dislocation mechanism to interpret the Bauschinger effect in polycrystalline metals is proposed namely dislocation pile-up polarization. We show that the variability of GB resistance to dislocation transmission, an inherent characteristic in polycrystalline metals, can break the symmetry of double dislocation pile-ups during plastic deformation, resulting in the polarization of dislocation pile-ups. This polarization mechanism strengthens the material in forward loading but softens it in reverse loading, thus being a source of back stress, which is verified by the dislocation dynamic simulations. Further, an analytical model based on the polarization mechanism is proposed and coupled with the crystal plasticity constitutive framework to analyze the stress–strain behavior of materials during loading and reverse loading. It is found that the Bauschinger effect and the strain-dependent Hall–Petch effect naturally appear as the intrinsic properties of polycrystalline metals in this theoretical framework, and the associated microstructural sensitivity is well captured. Our theoretical studies demonstrate the key role of GB resistance variability in regulating mechanical properties of polycrystalline metals and shed light on the physical mechanism of the Bauschinger effect. Moreover, this study indicates that the back stress hardening can be enhanced by the polarization mechanism, which might reveal new routes for design of high-performance metallic materials.

As a common feature observed in irradiated metallic materials, the formation of dislocation channels has been extensively studied and is considered to play a key role in irradiation embrittlement. However, modeling dislocation channels with the conventional crystal plasticity theory has been a theoretical challenge due to the difficulty of capturing microstructural inhomogeneities. Here a continuum crystal plasticity framework incorporating a stochastic distribution model of critical resolved shear stress (CRSS) is developed to describe the formation of dislocation channels and further plastic flow localization in irradiated materials. We show that the stochastic model is capable of capturing the heterogeneity of microscale plastic strain, which is an inherent feature of metallic materials during plastic deformation. It acts as an important microscale perturbation to trigger the dislocation channel nucleation in irradiated metals, especially for single crystals that lack mesoscale perturbations such as intergranular incompatibility and grain anisotropy. Without predetermining the potential nucleation position of dislocation channels, the stochastic irradiation crystal plasticity framework successfully simulates the dislocation channel formation and plasticity localization in both irradiated single- and polycrystalline copper (Cu), and further indicates the irradiation defect density threshold for the dislocation channel formation. This stochastic model broadens the application of the conventional crystal plasticity framework, and might provide new insights for other studies on plasticity localization, including shear bands formation of metals, mechanical behaviors with heterogeneous deformation and so on.

Softening behavior of lath martensitic steels is related to the coarsening of laths and dislocation evolution during cyclic deformation. Involving the physical mechanism, we developed a dislocation-based model to study the cyclic plastic response for lath martensitic steels. For a block, we proposed an interfacial dislocation evolution model to physically present the interaction between mobile dislocations in the block and interfacial dislocations by considering the coarsening mechanism of the laths. Moreover, the evolution behavior of backstress caused by dislocation pile up at the block boundary has been considered. Then, a hierarchical model based on the elastic-viscoplastic self-consistent (EVPSC) theory is developed, which can realize the scale transition among representative volume element (RVE), prior austenite grains (PAGs) and blocks. According to the proposed model, the effective mechanical responses including the cyclic hysteretic loop and peak stress at different cycles for lath martensitic steel have been theoretically predicted and investigated.