Ultra-high cycle fatigue experiments can be conducted using traditional testing methods such as electromagnetic vibration (30-3000 Hz) and ultrasonic vibration (20 kHz). Differences in fatigue life for the same material may arise when tested under varying loading frequencies. To fully utilize the ultra-high cycle fatigue life data obtained from different testing systems, the impact of loading frequency on the ultra-high cycle fatigue life of materials needs to be studied imperatively. This paper presents novel prediction models for ultra-high cycle fatigue life, taking into account loading frequency. The models incorporate the crack initiation life prediction model based on Tanaka's dislocation theory and the Paris crack growth life prediction model. The influence of loading frequency is integrated into effective stress and fatigue strength. The proposed models are verified using available very high cycle fatigue test data for titanium alloy TC17 and nickel-based superalloy GH4169 under different loading frequencies. The results show that the models proposed in this work can reasonably characterize the ultra-high cycle fatigue test data of materials under varying loading frequencies, establishing the correlation of fatigue life data under different loading frequencies.

Research on vibration characteristics of functionally graded materials (FGMs) in the aerospace field is a hot topic of current research. In this paper, the vibration characteristics of metal-ceramic functionally graded (FG) stepped cylindrical shells under arbitrary boundary conditions are studied. To conduct this research, a mechanical model of a metal-ceramic FG stepped cylindrical shell based on the axial segmentation concept is developed. First, the properties of metal-ceramic FGMs are obtained using the Voigt model and power function volume fraction. Second, the artificial spring technique is introduced to simulate continuous coupling conditions of shell segments and arbitrary boundary conditions at the ends of the shell. The energy expression for the cylindrical shell is then derived based on the first-order shear deformation theory. Finally, the admissible function is constructed via the Chebyshev polynomial, and the dynamic differential equations of the metal-ceramic FG stepped cylindrical shell under arbitrary boundary conditions are calculated using the Rayleigh-Ritz method. The validity and convergence of the method are verified through comparison with existing literature, and the effects of boundary conditions, volume fraction, geometric parameters, and spring stiffness on modal frequencies are analyzed. It is found that the natural frequency of the FG stepped cylindrical shell initially decreases and then increases with increased number of circumferential waves under classical boundary conditions, and it increases with the number of circumferential waves under both elastic boundary conditions. The natural frequency of the shell increases exponentially with volume fraction. The effects of length-to-radius ratio and thickness-to-radius ratio on the vibration characteristics of the shell differ, with the natural frequency of the shell decreasing with increased length-to-radius ratio and increasing with thickness-to-radius ratio. Additionally, the stiffness of translational springs significantly influences the vibration characteristics of the shell compared to rotational springs.

At a microscopic level, composite materials exhibit intricate structural designs, necessitating detailed finite element mesh discretization for their analysis and design, leading to extensive computational demands. While the in-plane periodic structure, a typical composite structure, can sustain various directional forces at a macroscopic level, defining its performance remains challenging and its design and analysis are complex. This paper introduces a method for optimizing the topology of in-plane periodic structures based on thick plate theory and a multi-resolution meshing strategy. Initially, a coarse mesh is used to distinguish between macro and micro configurations, address the micro boundary value problem, and perform a similar analysis of the mechanical characteristics of the irregular single cell; subsequently, the macroscopic boundary value problems are solved using uniform equivalent properties, and a fine mesh is employed to revise the design variables and chart the density variables. It is found that assuming a thick plate that accounts for out-of-plane shear deformation makes the two-scale topology optimization design closer to real load-bearing scenarios. Employing a multi-resolution meshing strategy circumvents the issue of limited solvable problem size caused by excessive finite element computation, while maintaining the resolution of the optimized configuration.

For some polymers below or near their glass transition temperature, a particular type of non-Fickian solvent diffusion, known as Case Ⅱ diffusion, is typically observed. To describe the coupling effect of Case Ⅱ diffusion and swelling deformation in polymers, theoretical models are established based on continuum mechanics. Here, governing equations for solvent penetration into polymer are derived and specialized in the reference configuration, including the mechanical-chemical equilibrium state equation, the concentration-dependent diffusion equation, and the molecular number conservation equation. Additionally, a visco-hyperelastic constitutive equation taking into account the time-dependent deformation characteristics of the material is integrated to reflect the competition mechanism between relaxation rate of the polymeric network and migration of solvent in Case Ⅱ diffusion. This modeling approach is used to analyze the transient free swelling process for two material systems, so as to investigate the behavior of unidirectional Case Ⅱ diffusion in columnar and tabular polymer specimens without constraint. By applying appropriate boundary and initial conditions, the concentration, stress, and deformation field variables during the unidirectional diffusion are directly obtained. The distribution and evolution of these calculation results are compared with experimental observations, moderately validating the effectiveness and adaptability of the proposed coupling analysis method regarding polymer swelling. This developed theory may provide important guidance for practical applications such as membrane designing or drug delivery systems, where Case Ⅱ diffusion commonly occurs. It also aids in enhancing understanding of the combination of different polymer-solvent diffusion scenarios, from Fickian to non-Fickian circumstances.

In this paper, an asymmetric bristle model based on the combination of bristle model and LuGre model is proposed to explain the direction-dependent friction (i.e., asymmetric friction) phenomenon exhibited by steel brushes. In this model, friction is generated through the horizontal frictionless contact between asymmetric bristles and the contacted substrate. Numerical simulation and expreimental results demonstrate that the asymmetric bristle model can effectively illustrate the direction-dependent friction phenomenon. Furthermore, in a simulation study of a planar biped robot, results show that applying this model can improve the maximum motion speed of the planar biped robot compared to using a symmetric friction model. Additionally, exmprimental resutls indicate that compared to rubber materials, steel brushes possess the advantages of high friction and abrasion resistance. Therefore, due to these propterties, steel brush structures may have great application prospects and potential benefits in the field of legged robotics.

The interaction between a penetrating-type circular-arc crack and a screw dislocation in magnetoelectric composites is studied. Firstly, according to the basic equations of magnetoelastic composites and the theory of complex function, the relationship between the anti-plane shear stress, the normal component of the electric displacement, and the normal component of the magnetic induction along the boundary arc c is derived. Then, based on the conformal mapping technique, the complex form of the generalized stress field is obtained by analyzing the stress conditions of the dislocation. In order to discuss the dislocation, dislocation shielding effect, and crack shielding effect at the crack tip, the force-electric-magnetic field intensity factors and the image forces acting on the dislocation are further deduced. By analyzing the analytical solutions and numerical examples, the results show that the shielding effect of the field strength factor decreases with increasing the distance between the circular-arc crack tip and the dislocation point, and the angle formed by their connecting line and the positive half of the x-axis, indicating that the dislocation has a shielding effect on the crack. Additionally, the effect of dislocation on a circular-arc crack is more prominent than on a straight crack. Besides, the image force on the dislocation is affected by the surface properties of the circular-arc crack. Finally, the screw dislocation can reduce the stress intensity factor of the circular-arc crack tip, and the shielding effect rapidly weakens as the angle increases. The shielding effect of the screw dislocation on the crack tip is strengthened as the ratio between the distance from the dislocation point to the crack tip and the half-chord length of the circular-arc crack increases. These conclusions carry meaningful significance for fracture mechanics research and provide a theoretical basis for improving and evaluating the performance of electromagnetic devices.

Zirconium and its alloys are used as nuclear fuel cladding materials due to their excellent mechanical properties, corrosion resistance, and small thermal neutron absorption cross-sections. When exposed to radiation, a large number of irradiation-induced defects emerge in the zirconium alloy, seriously diminishing its mechanical properties and service life. This study employs molecular dynamics simulations to investigate the interaction between the stacking fault pyramid and point defects (i.e., interstitial atoms and vacancies) in zirconium. It is found that, at 0 K and 300 K, the stacking fault pyramid exclusively absorbs interstitial atoms; while at 600 K, it absorbs both interstitial atoms and vacancies. To explain this phenomenon, the binding energy of interstitial atoms/vacancies and the stacking fault pyramid is calculated. The results indicate that the binding energy is related to the type/position of point defects: the binding energy of interstitial atoms is much greater than that of vacancies, making interstitial atoms more likely to be absorbed. At the same time, the proximity to the stacking fault pyramid amplifies the binding energy, rendering both point defects more susceptible to absorption. These simulation results provide a new insight into understanding the growth mechanism of irradiation-induced defects in zirconium.

The angle of repose in particle systems is a fundamental scientific problem in particle science. A deep understanding of its influencing factors and patterns of variation is of great significance for optimization in fields such as civil and chemical engineering. However, existing research based on experiments is limited by available types of particles and measurement methods, making it difficult to comprehensively reveal the impact regulations of various physical parameters on the angle of repose. This paper conducts a high-precision numerical study on the angle of repose in particle systems using the discrete element method (DEM), uncovering the most important particle property parameters that affect the angle of repose. DEM is a numerical method that directly simulates the motion of complex particle systems. Specifically, this study adopts a rolling friction coefficient to characterize the influence of non-sphericity on the simulation and validates the established model with existing experimental data. In addition, binary images of the heap projection in the vertical plane are utilized to calculate the angle of repose reasonably. Simulation results show that both sliding and rolling friction coefficients are positively correlated with the angle of repose. Increasing the sliding friction coefficient can double the angle of repose, while increasing the angle of repose caused by the rolling friction coefficient will reach an upper threshold. Once reaching this value, the angle of repose cannot be further increased. The particle's Young's modulus and restitution coefficient have a relatively small impact on the angle of repose. At the same time, this study employs the DEM to investigate the heat transfer characteristics of granular heaps. It is observed that during heating, the region with the highest heat flux within granular heaps migrates from the bottom to the top. These results reveal the most important factors affecting the angle of repose and can guide engineering optimization.

Fatigue failure is the most common form of failure in engineering. Under the interaction betweenthe corrosive environment and fatigue load, the fatigue life of a structure is significantly reduced. It often consumes a lot of time and economic costs to evaluate the fatigue properties of materials or structures through corrosion fatigue experiments. Therefore, it is crucial to establish a reliable numerical prediction model for scientific research and engineering design. In this study, we develop a peridynamic corrosion fatigue model, which combines the peridynamic fatigue crack model and the peridynamic stress-corrosion model, according to the superposition model of corrosion fatigue. In this model, corrosion fatigue damage is a linear superposition of corrosion damage and fatigue damage, and the coupling between stress and corrosion is considered. Consequently, the effect of structural deformation on the corrosion rate, the heterogeneity of the products, and the geometry of the corrosion front can be considered simultaneously in the model. The new model is then applied to simulate the corrosion fatigue failure process (including crack initiation and crack growth phases) of stainless steel compact tensile specimens. The simulation results show that the model can accurately describe the complete corrosion fatigue failure process of the compact tensile specimen, with the corrosion fatigue crack initiating randomly but consistently around the expected high-stress region. The decrease in fatigue life due to the interaction between the corrosion environment and fatigue load is captured, and prolonged corrosion time exacerbates the reduction in fatigue life when a lower load is applied. The influence of loading frequency on corrosion fatigue behavior is investigated by calculating the crack initiation life and comparing crack length curves. The model can also capture the significant influence of loading frequency on the fatigue life in corrosion fatigue processes. Reducing the loading frequency extends the corrosion time between each cyclic load, intensifying corrosion damage and ultimately reducing the crack initiation life while accelerating crack growth. The numerical results demonstrate that the introduced mechano-chemical damage model can capture the loading frequency sensitivity.

Ultrasonic resonance technology is the most effective method for studying the ultra-high-cycle fatigue properties of metallic materials. Ultrasonic fatigue specimens typically need a distinctive geometric design to fulfill the resonance requirements. Conventional specimens, such as round rods and dog bones, do not have planar characteristics, making quantitative microscopic characterization difficult. This paper presents an ultra-high-cycle tensile fatigue specimen with a featured plane based on a traditional dog-bone tension-compression specimen design. Different from the traditional specimen design, the dog-bone specimen herein has a flat observation area, readily enabling quantitative microscopic characterization. Using GH4169 nickel-based alloy as an example, the proposed plane-featured dog-bone fatigue specimen design is validated. As expected, the ultrasonic fatigue test results show that the proposed dog-bone plane specimen can resonate at 20 kHz. The measured fatigue life data are basically consistent with available S-N results in the literature. The proposed method provides new ideas for the design of ultrasonic cycle fatigue specimens and helps in the study of micro-deformation mechanisms of ultra-high-cycle fatigue.