This paper focuses on analyzing the circumferential free vibration of the functionally graded joined conical-cylindrical shell to enhance the vibration performance and stability of the structure, particularly in the aerospace field. First, the properties of the functionally graded materials (FGMs) are described using the Voigt model and the four-parameter power function volume fraction. The energy expressions for the conical shell and cylindrical shell are derived based on the previously obtained displacement-strain relationships formulated utilizing the Donnell thin shell theory. Then, artificial springs are introduced to simulate the continuity conditions and boundary conditions. The displacement function is constructed using Chebyshev polynomials to enable a more accurate analysis of the structural response and performance. The modal frequencies of the functionally graded joined conical-cylindrical shell are calculated employing the Rayleigh-Ritz method with this displacement function. Hence, the influence of gradient exponent, boundary conditions, and geometric parameters on the modal frequencies is analyzed to reveal the vibration characteristics of the structure. The main results indicate that increasing the volume fraction of ceramics effectively enhances the modal frequencies of the structure, while higher gradient exponents lead to a decrease in the modal frequencies. Stronger boundary constraints result in higher modal frequencies for the functionally graded joined conical-cylindrical shell. With an increase in the circumferential wave number, the influence of boundary conditions on the structural modal frequencies diminishes. The effect of boundary constraints is more pronounced on the cylindrical shell compared to the conical shell. Additionally, the axial spring stiffness has a more significant impact on the modal frequencies of the structure compared to the circumferential and radial spring stiffnesses. When the circumferential wave number is greater than 3, the modal frequency of the structure exhibits a linear increase with increasing shell thickness, whereas increasing the conical and cylindrical shell length ratio leads to a decrease in modal frequency. Finally, when the length ratio of the conical and cylindrical shell is fixed, increasing the cone angle initially results in an increase in the modal frequencies of the structure until it reaches a peak value, after which it starts to decrease.

To study the problem of a semi-infinite plane with an embedded deflected crack and a microcrack at any position under tensile loading, the integral equation for the corresponding dislocation density is established based on the method of continuous distributions of dislocations, and its mechanical parameters are obtained using the Gauss-Chebyshev numerical integration method. The theoretical results are verified using the finite element method. Compared with the case without microcracks, microcracks in certain directions (i. e., the azimuth angle of the microcrack is between -90° and 45°) promote the growth of the main crack, while microcracks in other directions (i. e., the azimuth angle of the microcrack is between 45° and 90°) inhibit its growth. The stress intensity factor at the main crack tip decreases with the increase of the embedded depth of the crack and the distance from the center of the microcrack to the tip of the deflected main crack. When the azimuth angle of the microcrack is between -90° and -65°, or between -25° and 10°, the propagation direction of the main crack deflects clockwise from the original propagation direction. When the azimuth angle of the microcrack is between -65° and -25°, or between 10° and 90°, the propagation direction of the main crack deflects counterclockwise from the original propagation direction. Horizontal microcracks have a greater influence on the propagation direction of the main crack and the equivalent stress intensity factor compared with inclined microcracks.

With the development of engineering technology and materials science, pure elastic materials can no longer meet the application needs of materials in industrial manufacturing. Magneto-electro-elastic (MEE) materials have more complex internal structures compared to classical elastic materials, and the methods for solving mechanical and physical performance are more difficult compared to classical elastic materials. Therefore, the mode III fracture behavior of MEE materials with nano-defects (pores and cracks) is investigated in this study. Based on the Gurtin-Murdoch surface theory and conformal mapping theory, the mode III fracture properties of MEE materials containing an arbitrary-location through crack emanating from a nano-hole under anti-plane mechanical loading, in-plane electrical loading, and in-plane magnetic loading are studied. The accurate solution of the MEE field in the matrix is obtained using the MEE theory and the far-field loading conditions. Analytical expressions for the MEE field intensity factors of the tips at both ends of the through crack, assuming that the surface of nano-defects is magneto-electric impermeable, are given. The proposed method is validated through a comparison with existing research. The effects of crack location, crack interaction, and the application of multiple physical loads on the dimensionless MEE field strength factors are discussed. The results show that the dimensionless MEE field intensity factors exhibit a significant size effect. The surface effect of nano-defects on the MEE tip fields of the cracks is constrained by the crack location. The dimensionless MEE field intensity factors are significantly affected by the ratio of the through crack length to the applied MEE loads. The results obtained in this study provide a theoretical basis for the experiments and numerical simulations of the mode III fracture behavior of an arbitrary-location through crack emanating from a nano-hole in MEE materials.

Defects play a crucial role in understanding the physical and mechanical behavior of materials. In this study, the fracture problem of an infinite one-dimensional hexagonal piezoelectric quasicrystal material matrix containing secondary asymmetric straight cracks with lip-shaped pores is investigated. A defect mechanics model of secondary asymmetric cracks with lip-shaped pores is constructed for the first time. Utilizing conformal transformation technology, a conformal transformation formula from an infinite region containing secondary asymmetric cracks at the lip on the physical plane to the outer region of the unit circle is built. Using the complex variable method, analytical expressions for the field intensity factor and energy release rate at the crack tip are obtained. Under given conditions, these analytical results can be simplified into solutions for other defect models, such as secondary single cracks at the lip and secondary symmetric cracks at the lip. At the same time, they can also degenerate into the solutions of classical Griffith cracks and lip cracks without secondary cracks. Numerical examples reveal the effects of defect size, particularly the lip height and crack length, on the field intensity factor and energy release rate. The results show that increasing the length of both sides of the crack promotes crack propagation, while increasing the height of the lip inhibits crack propagation. These findings are consistent with the conclusions drawn from theoretical analysis. When the length of the secondary crack on one side of the lip is zero, as the height of the lip increases, the stress intensity factor and energy release rate at the crack tip on the other side first increase to a peak and then gradually decrease, eventually stabilizing at a constant level. The research results presented in this paper can contribute to the development of a theoretical framework for material fracture mechanics and provide technical assistance for nondestructive testing, reliability design, and optimization of piezoelectric quasicrystal material equipment and components.

In hypervelocity impact problems, it is difficult to accurately obtain the crater morphology under certain conditions. Studying the damage zone can compensate for this limitation and serve as an important basis for understanding the impact mechanism and validating numerical simulations. However, there has been limited research on numerical simulation of the damage zone due to the lack of experimentally validated criteria. This paper presents a summary of the existing quantitative measurement results for the damage zone. The findings reveal that, for the same target, the depths of the damage zone obtained through multiple microscopic testing methods are relatively consistent, which facilitates the analysis of the damage zone. Based on the iSALE code, the applicability of total plastic strain (TPS), damage factor (D), and peak pressure as criteria for assessing the damage zone is analyzed. The results indicate that, TPS=0.1 is appropriate as a damage criterion, D=1 could be used as a damage criterion with caution, while peak pressure is not a suitable damage criterion. Through parametric analysis, it is found that the damage zone gradually decreases with increasing porosity and target strength.

To investigate the influence of adhesive layer thickness and adhesion strength on the scratch damage of polymethylmethacrylate (PMMA) coating, scratch experiments were systematically conducted on PMMA coatings with different adhesive layer thicknesses and adhesion strengths. A constitutive model considering the competition between shear yielding and brittle fracture was employed to describe the mechanical behavior of PMMA coating. The scratch behavior of PMMA coating was simulated using the finite element method. The physical mechanisms behind the complex scratch damage modes were revealed. The results show that, different from the coating structures with a zero-thickness adhesive layer, the deformation of the finite-thickness adhesive layer leads to local bending of the PMMA coating, resulting in the formation of internal cracks in the bottom region of the coating beneath the scratch tip. An adhesive layer with strong adhesion strength restricts the deformation of the coating during scratching, preventing severe buckling of the coating in front of the scratch tip and avoiding the formation of longitudinal cracks that penetrate through the coating along the thickness direction. Increasing the coating thickness can enhance the resistance of the coating to bending and buckling during scratching, thereby delaying the formation of the internal and longitudinal cracks. These findings contribute to the understanding of the scratch mechanism and further improvement of the scratch resistance and functional integrity of PMMA coatings.

Due to progress in micro and nano technologies, nanoscale piezoelectric bimorphs have gained extensive popularity in various fields such as nanosensors, nanoactuators, nanoscale energy recovery devices, and nanoresonators. With a decrease in size, the influence of scale effect becomes more prominent. The aim of this research was to investigate the scale effect on the frequency characteristics of nanoscale piezoelectric bimorphs according to scale-dependent theory. This work may broaden our understanding of the wave characteristics of piezoelectric nanostructures. On the basis of nonlocal strain gradient theory, the wave dispersion properties in nanoscale piezoelectric bimorphs were studied, taking into account surface elasticity and residual stress. The upper and lower piezoelectric layers of the bimorphs were subjected to an electric field and deposited on a viscoelastic substrate. The control equation was derived based on Hamilton's principle and sinusoidal shear theory. The equation of motion was derived according to the scale-dependent constitutive equation with nonlocal and length scale parameters, and the corresponding characteristic equation was solved by incorporating harmonic solutions. The obtained numerical results revealed the effects of surface elasticity, residual stress, scale parameters, wave number, and viscoelastic substrate on piezoelectric bimorphs. The research showed that the dispersion properties of piezoelectric bimorphs were influenced by a combination of surface residual stress and surface elastic coefficient. The existence of surface effects was found to be essential for the investigation of the frequency properties of piezoelectric bimorphs. Scale parameters and wave number also had a combined effect on dispersion characteristics, and the influences of elastic coefficient, damping coefficient, and piezoelectric layer thickness on frequency exhibited regional characteristics. Therefore, it is possible to use appropriate substrate materials to regulate the center frequency of piezoelectric bimorphs. This work contributes to the theoretical research on the dispersion mechanism of piezoelectric nanoresonators and provides useful reference for the design and manufacturing of piezoelectric nanofilters.

Electrical connectors widely used in electrical and electronic devices suffer from severe contact failure problems which determine the reliable service of these devices or even cause their destruction. The insertion and withdrawal forces are significant factors to evaluate the performance and quality of electrical connectors. The wear behavior due to the repeated insertion and withdrawal processes has a non-negligible influence on the forces. Therefore, the forces and wear behavior are investigated in this paper. A simulation model is developed to study and evaluate the performance of electrical connectors. The finite element method (FEM) is used to simulate the insertion and withdrawal processes and the wear profile of an electrical connector in the application. According to the development of the FEM model of the electrical connector, the equivalent insertion and withdrawal forces with and without the consideration of wear behavior are calculated. Frictional behavior is used to study the insertion and withdrawal forces without considering wear. In cooperation with the adaptive mesh technique of the commercial FEM software ABAQUS, the wear model based on frictional dissipation energy is applied to predict the wear morphology. The characteristics of the insertion and withdrawal procedure are analyzed using the forces vs. time curves. Furthermore, the wear profiles of the contact surface are obtained at different times of the insertion and withdrawal processes, and the effect of wear on the insertion and withdrawal forces of the electrical connector is discussed. The critical number of insertions and withdrawals leading to a larger wear depth is found. The size parameter of the contact component is modified to validate the conclusion of wear influence. It is worth emphasizing that this study is significant to the failure problem of electrical connectors and provides a guideline for the production and application of electrical connectors.