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2021 Vol. 42, No. 4
Published: 2021-08-28
345
A Review of Shape Memory Alloys: Mechanical Behavior and Application
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2021.028
The mechanical characteristics, constitutive models of Shape Memory Alloys (SMAs) and their applications in different fields are reviewed. Firstly, the material and mechanical properties and the application of SMAs in smart structures are analyzed, and the methods and characteristics of current micro/meso/macroscopic constitutive models to describe the thermodynamic behavior of SMAs are introduced. Secondly, the application status of SMAs in different fields is described in detail, and the application of structure optimization technology in improving the properties of smart structures is particularly summarized, and the problems existing in current research of SMAs are analyzed. Finally, the key technologies and in the future development of SMAs based smart structures are discussed.
2021 Vol. 42 (4): 345-367 [
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376
Characterization of Mechanical Properties of Bulk Metallic Glasses Based on Knoop Hardness
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2021.002
A variety of loads were applied to test Knoop hardness of 14 kinds of bulk metallic glasses. The results showed that Knoop hardness decreased with the increase of load, and finally tended to be stable. Indentation size effect was analyzed using Meyer's law, the elastic-plastic deformation model, Hays-Kendall model and deformation resistance model, a positive indentation size effect was found. Under large loads when there was no crack on the indentation surface, hardness approached to a contant, which was used to calculate Young's elastic modulus E and Yield strength σy. For most experimental materials, Young's elastic modulus values obtained by Marshall model and Conway model are too large. The parameter α in Marshall model linearly decreased with the increase of the indentation diagonal ratio b′/d, and the correction factor β in Conway model linearly increased with the square of the indentation short diagonal ratio (b′/b)2. We proposed modified models with α and β being expressed linearly as b′/d and (b′/b)2 respectively. Meanwhile, it was found that the Knoop hardness of metallic glass was proportional to its Young's elastic modulus, and the proportionality coefficient was 0.0445. When the Yield strength was calculated using Tabor, Lockett, Yu, Marsh, Johnson and Vandeperre models respectively, the calculated results were low except for that of Johnson model giving results close to the actual values. The scaling relationship between Knoop hardness HK and nominal hardness H should be modified in order to obtain the correct yield strength by differrent models. The Notch toughness KQ of bulk metallic glass increased linearly with Knoop hardness HK and glass transition temperature Tg respectively when Knoop hardness is smaller than 6 GPa and glass transition temperature is smaller than 800 K.
2021 Vol. 42 (4): 376-392 [
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393
Research on Modeling of Normal Contact Stiffness of Joint Surface of Fixed Machinery interface Based on Three-dimensional Anisotropic Fractal Theory
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.054
Abstract: In this article, the asperity of joint surface is equivalent to the micro ellipsoid. According to the KE finite element model and the elastic Hertz contact theory of ellipsoid, the relationship between normal load, contact area and deformation was obtained by analogy with the elastoplastic contact deformation mechanism of the spherical asperity. Combined with the theory of three-dimensional anisotropic fractal geometry, the strict effective interval of the eccentricity of the contact point of the joint surface is [0,0.7374]. Assuming that the eccentricity of the contact point of the joint surface obeys the exponential distribution in the effective range, and is independent with the area distribution, Using probability theory and the area size distribution function of the contact point, the two-dimensional joint distribution density function of the area of the contact point and the eccentricity of the joint surface was obtained. Furthermore, the fractal model of the normal contact stiffness of the joint surface including the complete elasticity, elastoplasticity and complete plasticity of the ellipsoidal asperities was established. The comparison between the theoretical stiffness of the model and the experimental data shows that: the model can better predict the normal contact stiffness of the joint surface. Especially under light load conditions, the model has a higher prediction accuracy.
2021 Vol. 42 (4): 393-406 [
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407
COUPLED DISCRETE-FINITE ELEMENT METHOD FOR BALLASTED RAILWAY TRACK CONSIDERING INTERLAYER CREATION
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.056
Considering the interpenetration phenomena between ballast layer and subgrade surface, the soil resistance using hyperbolic function is applied to ballast located at interlayer. Based on proposed transfer algorithm of contact force between discrete sphere and hexahedron element, a coupled discrete-finite element model of ballasted railway track is established considering interlayer creation. The ballast granule with irregular shapes is constructed using the clump model in DEM. Meanwhile, the subgrade is modeled using 20-node hexahedron solid elements in FEM. The effect of the traffic load and the subgrade stiffness on the overall settlement of the ballast bed was analyzed. The stress and displacement contours in the cross section of model are drawn. It is found that the proposed coupling model can not only present the elastic and cumulative plastic deformation of the ballast layer itself, but also reflect the penetration settlement caused by the penetration of the ballast into the soft subgrade surface. The study can provide an important insight for understanding the settlement and degradation mechanism of ballasted rail track under high speeds and heavy loads.
2021 Vol. 42 (4): 407-419 [
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420
Research on 3D Scattering and Dynamic Stress Concentration of SV Waves in Spherical Shells With Spherical Inclusions
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2021.007
Due to the influence factors in the material processing, manufacturing and other links, inclusions (cavity) are inevitable in the large structures, which will destroy the continuity of metal matrix and it will lead to stress concentration in the structures, which is an important factor to reduce the strength of the structure. Especially in the case of dynamic load, the diffraction and superposition of elastic waves will aggravate the stress concentration. Plate and shell structures are widely used in petrochemical, electric power, aerospace and other industrial fields. The inclusion in plate and shell structures is an important factor affecting the structural strength and fatigue life. The stress concentration of plate and shell structures has always been a hot spot in academic and industrial research. The establishment and solution of elastic wave diffraction equation is very complex. At present, the main research object is focused on two-dimensional model. Dynamic stress concentration caused by inclusions in three-dimensional finite domain is common in large-scale structures. The boundary of bounded domain is not only as boundary conditions, but scattering wave sources as well, which improves the difficulty of solution. Generally, the three-dimensional model is simplified to two-dimensional by approximate method, which often leads to the conservative solution results and can not explain the actual problems. In this paper, according to the general situation of inclusion in three-dimensional spherical shell, spherical coordinates are established with the center of spherical shell and inclusion respectively to describe the scattering wave potential function of the inner, outer wall and inclusion surface of the spherical shell, and a type of addition formula for spherical wave function is introduced to conduct the potential function transformation under different coordinates, through the boundary conditions of the inner and outer walls of the spherical shell and the continuity condition of the inclusion interface, the dynamic stress concentration could be solved. This study provides theoretical support for the strength analysis of spherical shells with inclusions in general.
2021 Vol. 42 (4): 420-433 [
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434
Thermoelastic-Structural Dynamics Analysis of Rigid-Flexible Coupling System for the Hub with a Thin-Walled Beam
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.057
Thermally induced vibrations of flexible structures of spacecraft appendages are a typical one of the spacecraft failure causes. The flexible structures are usually subjected to the thermal shock from solar flux due to night-day transition in the orbit. Therefore during the satellite design, it is a basis for making an accurate prediction of responses and stability of thermally induced dynamics. A new analysis model for thermally induced vibrations of a spacecraft structure composed of a rigid cabin and a flexible thin-walled tube was proposed. In this model, the effect of rigid-flexible coupling, the coupled thermoelastic effect, and the coupled thermal-structural effect were considered simultaneously. The rigid-flexible coupling includes the attitude angle of cabin, the rotation of tip mass, and the rigid motion and elastic deformation of thin-walled tube. The coupled thermo-elasticity that assumes the strain rate coupling term exists in the heat conduction equation due to the fact that the work done by external forces should be included in the energy conservation equation. The coupled thermal-structural analysis model that takes into account of the effects of rigid rotation and elastic deformation on the absorbed solar flux by the outside surface of thin-walled tube. First, the heat conduction equation with the above three coupling effects were given by applying the principle of conservation of energy and based on thermo-elasticity theory. The governing equations of motion with thermal effect were derived by using the Lagrange equation and the assumptions of small rigid body motion and small elastic deformation. Then, these equations were solved analytically by means of the approximating temperature and displacement fields, and the equation of stability boundary was obtained by the Routh-Hurwitz criterion. The results of numerical examples indicate that the analysis model presented in this article can give more accurate predictions for dynamical responses and stability criterion of thermally induced vibrations of spacecraft structures.
2021 Vol. 42 (4): 434-442 [
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443
Effect of Hydrogen Bond on Interlayer Shear Behaviors of Graphene Oxides
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2021.004
According to the optimization design of graphene oxide (GO) layered composites and their high sensitivity to environmental humidity, the interlayer shear behaviors of GO in humid environment have been studied. Firstly, expressions of interlayer cohesive energy, interlayer hydrogen bond (HBond) interaction and shear stress have been obtained by employing theoretical models. Good agreements can be achieved for the results obtained by theoretical models and molecular dynamics simulations. Different numbers of water molecules have been further introduced into the interlayer of GO structures. Then, interfacial properties of GO composites can be improved by adjusting oxidation concentrations and contents of interlayer water molecules, which determine the interlayer HBonds networks. The results show that increasing the oxidation concentration can effectively increase the density of the interlayer HBonds networks, thus improving the interlayer shear strength of GO structures. However, an optimal oxidation concentration can be obtained for GO structures with limited sizes, where enhancement of shear stress of GO will reach saturation. In this situation, introducing water molecules into interlayers of GO structures can further enhance their shear strength, and an optimal content of water molecules has also been observed. The research put forward a simple numerical method to evaluate HBond energy and propose two ways to improve the mechanical properties of GO layered composites. During these processes, the effect of HBonds networks on interlayer shear properties of GO composites has been highlighted. This study should be of great importance to providing a significant theoretical support for designing GO-based composites.
2021 Vol. 42 (4): 443-454 [
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455
Scattering of Flexural Waves in an Infinite Piezoelectric Thin Plate with a Non-circular Hole
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2021.015
The scattering and dynamic stress concentration of flexural waves in an infinite piezoelectric thin plate with a non-circular hole are studied. First, according to Kirchhoff's thin plate hypothesis, the displacement and strain are assumed to be linearly distributed along the thickness direction of the infinite piezoelectric thin plate. Then, the linear piezoelectric dynamics theory, wave function expansion method, complex function and conformal mapping are used and based on the relationship between the internal force and deflection of the thin plate bending, the expressions of the stress, moment and other fields of the infinite piezoelectric thin plate are derived, and the analytical expressions of the dynamic moment concentration factor(DMCF) are obtained. Finally, to illustrate the problem, takes PZT-4 as an example, the effects of the applied electric field, the ratio of two semi-axes' length of the elliptical hole, the inclination angle of the elliptical hole and the frequency of the incident wave on the elastic wave scattering of the infinite piezoelectric thin plate with a circular hole and an elliptical hole are discussed, and the numerical results of the dynamic moment concentration factors of infinite piezoelectric thin plate with a circular hole and an elliptical hole are given, respectively. The numerical results show that the greater the applied electric field, the greater the dynamic moment concentration factor near the defect is, and it is obviously larger than that of ordinary elastic materials, but with the increase of incident wave frequency, the influence of the change of the applied electric field on DMCF gradually decreases. For different incident wave frequencies, the peak value of the dynamic moment concentration factor mainly occur atand. With the increase of incident wave frequency, the value of dynamic moment concentration factor decreases. When the inclination angle of the elliptical hole is larger or the elliptical hole is flatter, the value of the dynamic moment concentration factor is correspondingly larger. Therefore, in contrast, the dynamic moment concentration factor of the circular hole is the smallest. In this paper, the scattering of flexural waves in an infinite piezoelectric thin plate with a hole is studied. The research results can provide some reference for theoretical application and engineering practice.
2021 Vol. 42 (4): 455-466 [
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Vibration Analysis Method of beam Structure in Peridynamics
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2021.008
Peridynamics (PD) is a new continuum mechanics formulation, which is in the form of integro-differential equations. Moreover, PD has a length scale parameter which allows to analyze nonlocal phenomenon and problems that cannot be represented by classical continuum mechanics. Since its introduction, many research interests have been received especially in recent years. However, it is quite computational expensive for PD to model and analyze engineering structures in three dimensional. Hence, it is important to develop simplified PD formulations for beam like structures. In this study, vibration analysis of beam structure in PD is carried out. First, based on the Euler beam theory, a two-degree ordinary state based PD model is derived for beam structure, the method for assembling density matrix and micromodulus matrix is also explained, and then the approach to apply boundary condition is given based on Taylor series expansion and local boundary conditions. The vibration characteristic of beam with three different boundary conditions is studied and compared with the finite element results of local beam to verify the accuracy of the model and method, the influence of the PD length scale parameter on the natural frequencies is analyzed. It is found that when the density of material points is small, the non-locality of PD beam model is weak, and the PD results are closed to the finite element results. As the density of material points gradually increases, the non-locality of PD beam increases and the natural frequency decreases. When length scale parameter approaches zero, the frequency of PD beam converges to the finite element solution of local beam. Results show that the PD beam model and free boundary conditions proposed in this paper can effectively analyze the vibration characteristics of the beam, and provide means to analyze the dynamic characteristics of beam structures in PD.
2021 Vol. 42 (4): 467-475 [
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476
A structural reliability analysis method based on BP Neural Network and Laplace progressive integration method
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2021.005
In traditional reliability theory based on surrogate model, sampling methods are often used to obtain failure probability, the correlation of random variables and the influence of the uncertainty of the surrogate model are often not considered. This paper proposes a reliability analysis method combining (Back propagation) BP neural network and Laplace progressive integration method, which is called BP-Lap method. Latin hypercube sampling method and a learning function are adopted to generate sample points. Based on function approximation theory, the limit state function and its first and second partial derivatives are all approximated by the BP network. The trained BP network is used to solve the failure probability by the Laplace progressive integration method, and ten-fold cross-validation method is used get the failure probability interval. Four numerical examples are used to verify the effectiveness of the BP-Lap method under correlated and uncorrelated random variables respectively. The research shows that BP-Lap method can measure the influence of the uncertainty of the surrogate model on the failure probability, and obtain the the upper and lower bounds of failure probability. BP-Lap method is suitable for both explicit and implicit limit state functions, and has higher accuracy for reliability problems with correlated random variables.
2021 Vol. 42 (4): 476-489 [
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490
Calculation of equivalent elastic constants of Voronoi element with interface phase
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2021.006
The equivalent elastic constant is one of the important indicators to characterize the mechanical properties of materials. To study the influence of the interface on the overall mechanical properties of the particle-reinforced composites, the Voronoi element finite element method containing the interface phase is used in this paper. According to the generalized Hooke’s law, we calculated the equivalent elastic constant of particle-reinforced composites under certain boundary conditions. In order to ensure the validity of the results, the VCFEM model and the ordinary finite element model containing multiple randomly distributed elliptical inclusions and interfacial phases were established. Then, the impact of several factors on the equivalent elastic constant of particle reinforced composites,including the ratio of inclusions, the thickness of the interfacial phase and the elastic modulus of the interfacial phase were analyzed. It is found that the thickness and elastic modulus of the interface phase have a greater influence on the equivalent elastic modulus of the material,but have a smaller influence on the equivalent Poisson's ratio. Meanwhile, the results show that, when the elastic modulus of the interface phase is smaller than that of the matrix and inclusions, the equivalent elastic modulus of the material will be inversely proportional to the thickness of the interface phase and inversely proportional to the proportion of the inclusions.Furthermore, if the interface is too thin, the equivalent of the material The elastic modulus is proportional to the ratio of inclusions; When the elastic modulus of the interface phase is greater than that of the matrix or inclusions, the equivalent elastic modulus of the material is proportional to the ratio of the inclusions and the thickness of the interface phase.
2021 Vol. 42 (4): 490-500 [
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