The formation of horizontal cracks under environmental loads is closely associated with the development of partial depth distress at early age. Experience from the past decade with the application of Continuous Reinforced Concrete Pavement (CRCP) in Wuhan, China, has shown that partial depth distress is the primary type of early-age deterioration. In this study, a two-dimensional peridynamic model was used to evaluate the effect of various factors on the horizontal cracking of CRCP under environmental loads. The use of preset transverse cracks was adopted to avoid the impact of their random distribution on the analysis results. The results demonstrate the significant effect of temperature and shrinkage loads on horizontal cracking. The enhancement in concrete material properties, the use of two-mat reinforcement and optimised transverse crack distribution can reduce the risk of horizontal cracks. Furthermore, a new method for predicting the risk of horizontal cracks due to environmental loads has been proposed.

Peridynamics (PD) offers unparalleled advantages for modeling discontinuous problems like crack propagation, but suffers from high computational costs, limiting its engineering applications. In this work, a novel model coupling PD with the finite element method (FEM) is proposed to overcome this difficulty. The structure is partitioned into two regions: a localized non-continuous domain around crack simulated with PD, and the remaining bulk region modeled using the FEM. Forces and displacements are transferred across the coupling interface through interpolation. Although the new coupling scheme requires iterative solving, it achieves higher computational efficiency than the pure PD model. The iteration error is deeply investigated to establish its relationship with discretization parameters. Results demonstrate that the coupling model attains comparable accuracy to pure PD while drastically reducing simulation time. The model's efficacy is validated through three numerical examples of fatigue crack growth, confirming its feasibility for simulating crack propagation

This paper develops a peridynamic framework for modeling liquid metal dissolution corrosion in 316L stainless steel/liquid lead-bismuth eutectic (LBE) systems. The proposed model integrates two dominant corrosion mechanisms: interfacial metal dissolution and subsequent diffusion in the liquid phase. A dual-process calibration methodology is established to determine temperature-dependent diffusion coefficients for both cold-drawn (CD) and solution-annealed (SA) 316L stainless steel in the 400–550 °C range. By applying the PD model to simulate the dissolution “pitting” process and comparing it with experimental results, the effectiveness of the model is validated. Moreover, the growth and fusion process of “pitting” under different temperature conditions are simulated, with the final pit morphology being in good agreement with experimental observations. Finally, by combining the oxygen concentration with the probability of oxide layer failure, the influence of oxygen concentration on dissolution corrosion behavior is qualitatively analyzed. This model comprehensively considers the synergistic effects of material processing methods, temperature, and oxygen concentration on corrosion behavior, making it one of the few models capable of simulating the dissolution corrosion of 316L stainless steel in liquid LBE.

The growth of oxide scales on T91 steel in liquid Lead-Bismuth Eutectic (LBE) and the subsequent cracking induced by growth stresses present a key challenge for the structural integrity of leadcooled fast reactors. This study develops a peridynamic (PD) model that couples oxidation kinetics with mechanical damage to simulate the evolution of oxide scales and predict their fracture. Unlike conventional continuum approaches, the model explicitly incorporates the internal oxidation zone (IOZ) as a distinct layer characterized by retarded diffusion. By integrating reaction-diffusion kinetics with a Clarke-based growth strain model and nanoindentation-derived interfacial fracture energies, the simulation captures the simultaneous evolution and failure of the tri-layer oxide structure, composed of the outer oxide layer (OOL), the inner oxide layer (IOL), and the IOZ. Results indicate that cracking is driven primarily by the accumulation of the growth strain, with a predicted spallation window of 4,000-8,000 h consistent with experimental data. The simulations elucidate the mechanisms of interfacial delamination and through-scale cracking, correlating these failure modes directly with local geometric features. Interface roughness is shown to trigger preferential cracking at convex peaks of the IOL/IOZ interface and concave valleys of the OOL/IOL interface, reproducing the "asperity truncation" failure pattern. Moreover, degradation of the OOL or the presence of traction-free defects accelerates failure by reducing mechanical confinement, leading to kinematic incompatibility. This work provides a mechanistic explanation for observed cracking and offers a quantitative estimate of the critical growth strain range, supporting the assessment of T91 steel performance in advanced nuclear systems.

The high-temperature aerodynamic fatigue load test for aeroengine casings evaluates the casing's high-temperature fatigue pressure strength under repeated engine start-stop cycles. This assessment is critical for determining the fatigue life and overall reliability of aeroengines. To enable ground-based high-temperature aerodynamic fatigue testing, a mathematical model simulating the test conditions for a composite aeroengine casing was established. The numerical results show strong agreement with the experimental data. In addition, the sensitivity of the pressurization and heating system's design parameters in the test system was analyzed. The interaction between temperature and pressure during fatigue testing was investigated, and the impact of air leakage on load control during fatigue loading was evaluated. Key findings indicate that pressure variations significantly influence the temperature control, whereas temperature variations have a minimal effect on pressure control. Accurate fatigue load regulation can be attained through optimized thermal/pressure system design and proper selection of control parameters.

Visualizing the corrosion fatigue crack initiation process is crucial for developing accurate life prediction model for corrosion fatigue. In this study, the spatial evolution of damage during corrosion fatigue crack initiation in 7050 aluminum alloy is investigated. An in situ corrosion fatigue testing device, with a chamber storing corrosive solution, is designed and fabricated fully compatible with time-lapse synchrotron radiation X-ray tomography. The corrosion fatigue crack initiation process, including both corrosion pit growth and pit-to-crack transition stages, is successfully observed. Three distinct modes of pit growth are found: (I) pit coalescence with preexisting voids, (II) pit merging with adjacent pits, and (III) detachment of constituent particles from the pit interior. It is found that the Al2CuMg particles initially act as anodes and later transform into cathodes, while the Al7Cu2Fe particles consistently act as cathodes relative to the Al matrix. To simulate these pit growth behaviors, A coupled mechano-chemical peridynamic model is established, allowing for the quantitatively decoupling of the separate roles played by fatigue loading and corrosion during pit growth. Subsequently, the pit-to-crack transition behavior is explored quantitatively, and experiment observations confirms the widely accepted transition criteria. The present full-field visualization of corrosion fatigue crack initiation offers new insight into the underlying mechanisms and provides a foundation for more accurate prediction models of damage evolution in aluminum alloy under corrosion fatigue conditions.

Gradient porous materials (GPMs) exhibit spatial variations in pore structure, resulting in complex fatigue behavior compared to homogeneous materials. In this paper, the fatigue crack growth characteristics of compact tension (CT) alloy specimens with the uniformly porosity gradient distribution are investigated using an intermediately-homogenized peridynamic (IH-PD) fatigue model. The IH-PD framework incorporates a consecutive gradient distribution function of porosity to spatially modulate local material porosity. Stochastic bond breaking, governed by porosity, enables a multiscale porosity representation. Under this framework, pre-damage converges to a target value reflecting local porosity. The PD J-integral is calculated under different gradient parameters and its convergence regarding gradient parameters is investigated. A comparative analysis of the fatigue crack paths and fatigue lives between the IH-PD and fullyhomogenized peridynamic (FH-PD) models is conducted, and the reliability of the IH-PD model is verified through an m-convergence study. We employ the peridynamic fatigue model to simulate fatigue crack propagation in pre-cracked and perforated CT specimens, demonstrating the IH-PD framework's capability to elucidate complex microstructural heterogeneities and their synergistic interactions with cracks and voids.

Gradient-structured (GS) metallic polycrystals exhibit significant potential for integrating strength, ductility, and toughness. Enhancing our understanding of the relationship between their microstructure and mechanical properties of GS polycrystals is essential for optimizing the properties of materials. In this paper, a discrete dislocation dynamics model within the framework of state-based peridynamics (DDD-SBPD) is developed to investigate the elastoplastic deformation and fracture in GS polycrystals. By solving typical boundary value problems and comparing the DDD-SBPD simulation results with those from traditional DDD simulations and theoretical solutions, the DDD-SBPD model is validated. The model is then applied to simulate elastoplastic fracture in GS and homogeneous-structured (HS) polycrystals. By incorporating the intrinsic interaction between grain boundaries and dislocations, the model successfully captures the crack oscillations observed in the experiments. The relationships between the mechanical properties (e.g., strength, ductility, and fracture resistance) of metallic polycrystals and their structure are systematically analyzed. The results demonstrate that GS polycrystals outperform HS polycrystals in achieving a superior balance of mechanical properties, and that gradient orientation has a significant effect on these properties.

To evaluate the impact of tensile pre-deformation on liquid metal embrittlement (LME) susceptibility, slow strain rate tensile tests were performed on pre-deformed T91 steel in static, oxygen-controlled lead-bismuth eutectic (LBE) between 250 degrees C and 540 degrees C. Microstructural characterization via scanning electron microscopy and electron backscatter diffraction demonstrated that the effect of pre-deformation is strongly conditioned by environmental factors. Within the high LME sensitivity domain (low temperatures), pre-deformation exerted minimal influence on fracture elongation or propagation mechanisms. However, in high-temperature environments where LME is generally absent, pre-deformed specimens displayed pronounced premature failure; notably, the ductility loss compared to undeformed specimens expanded with increasing temperature. Analysis of crack propagation demonstrates that pre-existing plastic damage facilitates intergranular oxidation at elevated temperatures, thereby transitioning the failure mechanism from the ductile deformation (observed in undeformed samples) to intergranular fracture.

In this paper, we present a reaction-diffusion peridynamic model for the oxidation of T91 steel in liquid leadbismuth eutectic (LBE). By integrating oxidation kinetics with diffusion dynamics, our model is applicable to a broad range of high-temperature oxidation processes. Validation against experimental data of oxide scale growth for T91 steel in oxygen-saturated LBE at 400-550 degrees C and up to 13,000 h confirms its accuracy. Furthermore, we demonstrate the model's enhanced accuracy relative to traditional formula-based kinetic models. The new framework is utilized to investigate the influence of temperature and oxygen concentration on oxide scale evolution, indicating that elevated oxygen concentrations and temperatures significantly accelerate oxidation. Additionally, we explore the oxidation behavior of T91 steel with a non-uniform surface and oxide scale cracks, revealing that the outer magnetite oxide scale grows more rapidly than the inner Fe-Cr spinel scale in concave regions. Our model captures the transition of the oxide scale from an irregular to a flat, uniform morphology, aligning with experimental observations. This model demonstrates considerable potential for simulating high-temperature oxidation in complex geometries, including irregular surfaces and cracks, across various environmental conditions.

Peridynamics has emerged as a powerful nonlocal framework for modeling material behavior, particularly in the context of damage evolution and fracture mechanics. Building upon Silling's energy minimization criterion for assessing the stability of peridynamic correspondence materials, this work extends Hill's stability criterion to the nonlocal framework, and establishes a generalized energy-based stability criterion for peridynamics. Based on this criterion, we propose a novel and concise method for verifying the material stability of linearized peridynamic models even without requiring material isotropy. For isotropic peridynamic materials, we conduct a rigorous examination of the linearized displacement field under finite deformation. From this analysis, we derive fundamental conditions for linear stability and prove several key theorems revealing : (1) the fundamental role of Poisson's ratio in determining stability; (2) that linear stability is independent of the influence function; and (3) that linear stability depends exclusively on the singular values of the deformation gradient. We demonstrate that the proposed stability criterion is fully characterized by the positive definiteness of a specific tangent modulus tensor, which enables stability analysis via its eigenvalues. By applying the Sylvester criterion, we precisely delineate the stability region in deformation gradient parameter space and systematically investigate its parametric dependence on Poisson's ratio. Our theoretical framework reveals a fundamental dichotomy: materials with low Poisson's ratios are more prone to instability under shear deformations, whereas those with high Poisson's ratios are more susceptible to instability under volumetric compression. These theoretical predictions are systematically validated through computational experiments, demonstrating strong agreement between analytical results and numerical simulations. This work not only deepens the fundamental understanding of stability in peridynamic material models but also delineates the applicability limits of peridynamics under finite deformation, offering valuable insights for the development of robust constitutive models in future peridynamic research.

In peridynamics, the influence function determines the “nonlocality” of the model, which depends on the support of the influence function (the “horizon size”) and its specific shape. In this paper, we introduce a universal scalar parameter - the nonlocality constant - to quantify the strength of nonlocal interactions in bond-based peridynamic models. The nonlocality constant derives rigorously from the nonlocal factor, a key component in analytical solutions of peridynamic equations, and establishes a one-to-one correspondence with the difference between peridynamic and classical solutions. By analyzing eight distinct influence functions, we demonstrate that the nonlocality constant universally governs the deviation of peridynamic responses from their classical counterparts. Using the analytical solution for elastic membrane deflection derived via eigenfunction expansion, we validate that the proposed measure accurately ranks influence functions by their nonlocality strength. This work provides a systematic framework for selecting influence functions in multiscale modeling of materials with microstructural heterogeneities.

This study conducts tensile tests on cylindrical and flat-tapered T91 specimens in liquid lead-bismuth eutectic (LBE) to investigate the effect of long-term pre-exposure (up to 5004 h) on liquid metal embrittlement (LME) behavior and to determine the nominal threshold stress for LME crack initiation. Results show that extended pre-exposure enhances steel surface wetting, increasing the LME effect and leading to more pronounced cleavage characteristics on the fracture surface. Slow strain rate tensile tests using tapered specimens determine the LME threshold stress of T91 under LBE conditions at 350 degrees C and low oxygen content, representing the worst-case scenario, and reveal a clear dependence on strain rate. The threshold stress decreases with lower strain rates due to extended liquid metal-solid interaction. These findings provide practical guidance for defining conservative stress limits for T91 components in oxygen-deficient LBE environments.

This paper introduces a Peridynamic (PD) model for simulating the Advection-Reaction-Diffusion (ARD) processes in a non-uniform flow. The ARD phenomena are influenced by the flow, and the flow is modified by phase-changes (driven by interface reactions) that transform the boundaries of solids in the flow, for example. By coupling the PD governing equations for viscous flow with the PD equations for ARD, the model facilitates the effective simulation of the ARD process in viscous flow within the PD framework. The results demonstrate a high level of agreement with COMSOL simulations for ARD problems in two-dimensional flow, both in the presence and absence of obstacles. Furthermore, the framework demonstrates remarkable versatility in addressing complex scenarios, including ARD processes in heterogeneous media and flow-accelerated solid dissolution dynamics. These capabilities open new avenues for applications in critical areas such as groundwater contaminant transport, karst formation through rock dissolution, targeted drug delivery systems in biological environments, and other types of material degradation through phase-changes under fluid flow conditions, like ice melting and ablation.

The difference between the computational peridynamic results and the corresponding exact classical solutions is contributed by the error induced by numerical discretization and the nonlocality-induced difference. To evaluate and compare these contributions and investigate their dependence on the peridynamic influence functions, in this paper, we apply different peridynamic influence functions and different horizon factors (m, the ratio between the horizon size and the grid spacing) to conduct static (or quasi-static) tensile numerical tests. We calculate the difference between the peridynamic solutions and the corresponding classical solutions for static uniaxial tension of thin plates with or without hole, the J-integral of a single crack under Mode I loading condition, and the quasi-static fracture in a perforated thin plate. For the case of uniaxial tension in a thin, homogeneous plate, we separate the effects of nonlocality and numerical discretization by implementing the boundary conditions in different ways. The numerical results show that both the effects of nonlocality and numerical discretization correspond to the nonlocal constants of the influence functions (with few exceptions). For problems with the presence of the peridynamic surface effect, such as holes, influence function with weaker nonlocality is a better choice to obtain more accurate results.

Lead-bismuth eutectic (LBE) has garnered significant attention as a potential coolant material for nuclear reactors and as a spallation target in accelerator-driven systems. However, LBE experiences volume expansion upon solidification, which may lead to container damage. Thus, understanding the mechanical properties of solid LBE is crucial. This paper analyzes the tensile and compression properties of re-melted and aged LBE at varying temperatures, revealing the underlying reasons for the observed differences. Additionally, we discuss the microstructural instability of solid LBE under heat treatment. The compression constitutive models of solid LBE are developed using Arrhenius equations and a back propagation neural network (BPNN), providing valuable insights into its mechanical response under different conditions.

Pores are a key type of concerns in additive manufacturing technology. They can significantly affect materials' fatigue resistance and fatigue crack growth in the structures. In this paper, an intermediately-homogenized (IH) peridynamic (PD) fatigue crack model is introduced for simulating the fatigue crack growth in porous materials. The effect of micro-scale heterogeneity on fatigue failure is preserved in the IH-PD model, where stochastically-generated pre-damage matches materials' porosity. The PD J-integral, a key parameter used to connect the fatigue simulation and the experimental measurements, is calculated under different porosities, and the independence of PD J-integral on its integration path is verified. Then, the PD fatigue crack model combined with the IH-PD material model is applied to study the dependence of the crack path and growth rate on porosity in compact tension alloy samples. The normalized fatigue life between experimental measurements and numerical results is compared. The normalized fatigue life-porosity relationship calculated from the IH-PD fatigue model matches the average trend of the experimental measurements.

Imposing local boundary conditions and mitigating the surface effect at free surfaces in peridynamic (PD) models are often desired. The fictitious nodes method (FNM) “extends” the domain with a thin fictitious layer of thickness equal to the PD horizon size, and is a commonly used technique for these purposes. The FNM, however, is limited, in general, to domains with simple geometries. Here we introduce an algorithm for the mirror-based FNM that can be applied to arbitrary domain geometries. The algorithm automatically determines mirror nodes (in the given domain) of all fictitious nodes based on approximating, at each fictitious node, the “generalized” (or nonlocal) normal vector to the domain boundary. We tested the new algorithm for a peridynamic model of a classical diffusion problem with a flux singularity on the boundary. We show that other types of FNMs exhibit “pollution” of the solution far from the singularity point, while the mirror-based FNM does not and, in addition, shows a significantly faster rate of convergence to the classical solution in the limit of the horizon going to zero. The new algorithm is then used for mirror-based FNM solutions of diffusion problems in domains with curvilinear boundaries and with intersecting cracks. The proposed algorithm significantly improves the accuracy near boundaries of domains of arbitrary shapes, including those with corners, notches, and crack tips.

Ensuring the continuity and stability of the oxide scale to separate T91 steel from lead-bismuth eutectic (LBE) is an effective method for limiting corrosion in the lead-based fast reactor system. In this study, we specifically investigated the impact of cooling thermal stress on the stability and damage of the oxide scales of T91 steel when exposed to oxygen-saturated liquid lead-bismuth eutectic at high temperatures. A corrosion test was conducted on T91 steels exposed to stagnant oxygen-saturated LBE at 500 degrees C. Experimental results indicated that oxide damage exists without any external force, including interface cracks and through-scale cracks perpendicular to the interface. We developed a three-layer peridynamic model of T91-(Fe,Cr)(3)O-4-Fe3O4 to simulate the deformation and failure of oxides under a cooling process from high temperature to room temperature. The simulation results show that a temperature drop of about 200 degrees C from 500 degrees C can cause through-oxide cracks in the oxide scale, and subsequent cooling can lead to the propagation of interfacial cracks. Additional modifications were introduced in the model to account for the porosity of the oxide scale. Parametric investigations illustrate the effects of oxide scale thickness and porosity on the resulting crack patterns.