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2020 Vol. 41, No. 3 Published: 2020-06-28

	193	Nonlinear Vibration Characteristics of FG-SMA Micro-beams Based on Size Effect

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.024
		Shape Memory Alloys have excellent characteristics, such as low phase transition temperature, high output stress, low energy consumption, low driving voltage, large recoverable strain, and good bio-compatibility. With the further development of the Shape Memory Alloy technology, some scholars proposed that the functional gradient shape memory alloy material used in the micro-electro-mechanical system and other intelligent micro-structure will make it have better characteristics. Therefore, the study of nonlinear free vibration characteristics of electro-mechanical coupling FG-SMA micro-structures is of importance. Based on the von Karman geometric nonlinear theory, considering the influence of electrostatic force, intermolecular force and the size effect, the functional gradient shape memory alloy micro-beam model fixed at both ends is established. The multi-field coupling nonlinear vibration before and after the phase transformation of the alloy micro-beams is studied in depth. The effects of size effect parameters, geometrical parameters and phase-change parameters on the free vibration characteristics of the functional gradient shape memory alloy micro-beams are analyzed.
		2020 Vol. 41 (3): 193-205 [Abstract] ( 329 ) HTML (1 KB) PDF (0 KB) ( 201 )

	206	Analysis of Multi-field Coupling Responses of Piezomagnetic/Piezoelectric Semiconductor Cylindrical Shell under a Constant Magnetic Field

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.021
		Piezoelectric semiconductors (PSs) simultaneously possess piezoelectricity and semiconducting properties. The polarization electric field resulted from piezoelectricity has a mechanically tuning effect on the transport behavior of charges in PSs. Such a phenomenon is called the piezotronic effect. With the exception of mechanical approach, one may use the magnetic field to control the piezotronic effect in piezoelectric semiconductors. It is a remote-controlled approach. In this paper, we propose a composite piezoelectric semiconductor cylindrical shell consisting of piezomagnetic and piezoelectric semiconductor layers. A polarization electric field is produced in the composite PS cylindrical shell under a magnetic field through the magnetoelectric coupling effect, and thus the magnetic field has a tuning effect on the piezotronic behavior of the composite PS cylindrical shell. We carry out an analysis on an infinite composite PS cylindrical shell under a constant radial magnetic field. The considered problem belongs to a plane strain problem, and all physical fields in the composite shell are only dependent on the radial position. To obtain the analytical solution and make a comparison, we employ the one-way coupled method and the linear fully-coupled method in this paper. The one-way coupled method neglects the effect of free charges on the polarization electric field. For the linear fully-coupled method, we assume that charges in the PS layer have a small perturbation, and thus the nonlinear drift current term can be linearized. We present analytical expressions of the physical fields in the composite PS shell including the displacement, the electric potential, and the carrier concentration. The influences of magnetic field as well as the thickness ratio between the PS layer and the shell on the piezotronic coupling effect in the composite PS shell are studied. The numerical results show that the magnetic field and the thickness ratio play an important role in tuning the piezotronic effect of the piezoelectric semiconductor layer. At the same time, it also provides a theoretical guidance for the design of piezoelectric semiconductor devices.
		2020 Vol. 41 (3): 206-215 [Abstract] ( 224 ) HTML (1 KB) PDF (0 KB) ( 210 )

	216	Modeling the Moisture-Driven Shape-Memory Effect in Polymers

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.048
		Amorphous shape-memory polymers (SMPs) can be programmed to deform by heating above the glass transition temperature (Tg) to a temporary shape, which can then be fixed after cooled down below Tg. In the stress-free state, the shape of polymers can be recovered through increasing the temperature to above Tg. However, some SMPs lose the shape-fixity ability and recover from a temporary shape to a permanent shape in the environment with high relative humility, which is named as the moisture-driven shape-memory effect (SME). On the one hand, this effect is detrimental to the application of thermally-activated SME. On the other hand, this phenomenon can be harnessed to achieve shape recovery in the ambient condition, which can be potentially applied in various areas, since no external heat is needed to activate the shape recovery. In this paper, we develop a chemo-thermo-mechanical model to simulate the moisture-driven shape-memory behaviors of amorphous polymers. The model adopts the concept of free volume to describe the glass transition behaviors. As temperature decreases, the free volume also decreases, resulting in an increase in viscosity and a transition from the rubbery state to the glassy state. The diffusion of moisture into the polymer matrix increases the free volume and decreases the viscosity, and eventually causes the shape recovery. Fick’s law is used to simulate the diffusion of moisture in the polymer matrix. The coupled multi-field model is further implemented into the finite element analysis. The results show that the theory can qualitatively capture the influences of relative humility and recovery temperature on the shape recovery performance, represented as the increases in recovery rate and final recovery ratio with increasing the relative humility and recovery temperature. The model also reveals that the diffusion rate of water molecules significantly affects the recovery behaviors. The model is further demonstrated to be capable of describing the moisture-driven shape-memory effects involving complex finite deformation conditions.
		2020 Vol. 41 (3): 216-222 [Abstract] ( 254 ) HTML (1 KB) PDF (0 KB) ( 206 )

	223	Microstructure Evolution of β-Ti-based SMA in ARB Process and Its Effect on Its Superelasticity

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.013
		β-titanium-based shape memory alloy has broad application prospects in the field of hard tissue material, due to their low elastic modulus, and excellent biocompatibility. However, compared to the traditional NiTi shape memory alloy, Ti-based SMA exhibit low critical stress for the stress-induced martensitic transformation, low super elastic recovery rate and poor super elastic stability, which limit their application in practice. It is well documented that grain refinement is an effective way to improve the mechanical properties of beta Ti-based shape memory alloys. Therefore, in the present thesis, a β-Ti-based shape memory alloy, Ti-7.5Nb-4Mo-2Sn was taken as the research object. The alloy was firstly heavily deformed by using Accumulative Roll-Bonding(ARB) method, and then annealed to produce recrystallization to refine the grain size of alloy. The effects of ARB and subsequent annealing treatment in microstructure and mechanical properties were investigated. In this paper, The Ti-7.5Nb-4Mo-2Sn alloy was prepared by using vacuum are melting method prepared, and the as-cast alloy was rolled at room temperature by Accumulative Roll-Bonding(ARB) process, and then rapid annealed at 973K for 5min. The microstructure evolution of the alloy after the ARB process and annealing was investigated by OM and XRD, and the mechanical property and the superelasticity of the alloy were evaluated. It is found that ultra fine grained(1μm) β phase can be obtained in the alloy after 8th ARB process and annealed at 973K meanwhile for 5min. The alloy exhibits the improved superelasticity and stability due to the ultra fine grain with the recovery strain of 5.9 and the recovery rate of 98% when the pre-strain of 6%.
		2020 Vol. 41 (3): 223-230 [Abstract] ( 171 ) HTML (1 KB) PDF (0 KB) ( 187 )

	231	Molecular Dynamics Simulation of the Formation and Evolution Processes of Shear Bands in Metallic Glass Plate during a Tensile Test

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.014
		In metallic glasses (MGs), shear bands are easy to appear at low temperatures and high stress levels, which lead to the structural damage and greatly limit the structural reliability of MGs. In this paper, the formation and evolution of shear bands and their mechanical properties of three kinds of Cu64Zr36 MG plates (without notch, one notch on one side and two notches on both sides) during tensile test are studied by molecular dynamics (MD) simulations. The results show that the non-notched MG sample spontaneously appears local shear transformation zones (STZs) and shear localization during tensile test. As tensile continues, a shear band forms along approximately 45° with the loading axis in the MG sample. The formation of shear band is related to the distribution and localization of STZs. Strain localization of notched samples occurs earlier than that of the non-notched one, that is, the shear band forms at lower tensile strain, and the tensile strength is also correspondingly lower. Under the same conditions, the tensile strength of sample with one notch on one side is almost the same as that of the sample with two notches on both sides. However, the degree of strain localization of the sample with two notches on both sides is slightly lower, largely because the STZs occur at the both side edges of two notches, leading to the unconcentrated distribution and localization, which is also the main reason for the formations of the main shear band and the secondary shear band. The results provide important information for further understanding the formation and evolution of shear bands in MGs from an atomistic perspective.
		2020 Vol. 41 (3): 231-238 [Abstract] ( 283 ) HTML (1 KB) PDF (0 KB) ( 202 )

	239	Effect of Indentation Depth on Interlayer Friction between Incommensurate Graphene Layers

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.045
		In recent years, the nanoscale friction of layered two-dimensional materials have attracted much attention in both scientific and industrial communities due to their potential applications in various areas. As a typical two-dimensional material, graphene exhibits excellent mechanical properties and may be used as a dry lubricant. Therefore, friction analysis of graphene is essential for its application in engineering fields and has substantially improved our fundamental understanding of nanotribology. Many new nanoscale friction phenomena, laws and mechanisms of graphene have been reported continuously. However, many key issues about the influence of the critical factors on graphene friction behavior remain unclear. For example, the relationship between both the friction force and out-of-plane deformation exhibits complex behavior, which is yet to be understood. In this study, the friction behavior of a graphene flake on a support graphene substrate is investigated, by using molecular dynamics simulations. Based on a “graphene-spring” model, an elastic substrate is constructed to examine the dependence of the friction force on the indentation depth. The present work focuses on the interlayer friction behavior in the incommensurate registry. In the simulations, the friction force at the different normal loads and support stiffnesses are obtained. The results show that the friction force could be closely related to the indentation depth for various load or stiffness conditions, indicating that the indentation depth could be used to modulate the nanoscale friction directly. Particularly, the influence of normal load and substrate stiffness on graphene friction which can be normalized by the indentation depth. The present research has great significance for better understanding the friction law of the surface elasticity of two-dimensional materials.
		2020 Vol. 41 (3): 239-247 [Abstract] ( 410 ) HTML (1 KB) PDF (0 KB) ( 214 )

	248	Analysis of Frequency-Temperature Behavior of SAW Resonator

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.040
		Surface acoustic wave (SAW) devices are widely used in radar, communication and daily consumption due to their excellent performance. However, as operating frequency of the SAW devices grows higher and higher, the influence of temperature variation on frequency stability becomes more serious. Thus it is crucial to study the frequency-temperature behavior of SAW devices and improve frequency stability of SAW devices under variable temperature condition. In this paper, the incremental Lagrange equations are used to analyze the frequency shift of SAW affected by temperature. The temperature coefficient of frequency (TCF) is usually regarded as an evaluation on temperature-frequency behavior. To reduce temperature coefficient of frequency, a two-layer SAW resonator model is proposed with a temperature compensation layer. After optimization, the TCF of the SAW resonator with LiNbO3-AlN structure approaches to 0 ppm/℃ at 25℃ (reference temperature). The resonance frequency of the SAW resonator is 1214.9MHz and the wavelength is 4μm.
		2020 Vol. 41 (3): 248-257 [Abstract] ( 442 ) HTML (1 KB) PDF (0 KB) ( 198 )

	258	Strongly Nonlinear Natural Vibration of the Functionally Graded Rotating Circular Plate in the Thermal Environment

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.044
		In this paper, the nonlinear natural vibration of the functionally graded rotating circular plate composed of metal and ceramic in the thermal environment was analyzed, considering the geometric nonlinearity, the effect of temperature on physical properties of the material, and the continuous variations of material properties in the thickness direction that follow a simple power-law distribution in terms of volume fractions of the constituents of the plate. The nonlinear natural vibration equations of the functionally graded rotating circular plate in a high-temperature environment were derived by using Hamilton’s principle. As for the surrounding clamped boundary conditions, the nonlinear differential equation of transverse natural vibration of the circular plate was obtained through the Galerkin method. Moreover, the static deflection induced by the rotation and functional gradient characteristics was determined. Based on the assumption of strong nonlinearity, an improved method of multiple scales was employed to solve the differential equation of natural vibration, and the nonlinear expression for natural frequency was achieved. Through numerical calculations, the changes of natural frequency of the circular plate with rotational speed, temperature, volume fraction, and plate thickness were discussed, respectively. Furthermore, the degenerated model of the system was introduced to verify the rationality of the dynamic model, where the corresponding numerical solutions obtained by the Runge-Kutta method and the periodic graph method were compared with the analytical ones, and the results were basically consistent. It is found that the nonlinear natural frequency increases with the increase of rotating speed or disk thickness, but decreases with the increase of metal content or temperature of the circular plate surface. Especially, when the surface temperatures of both the metal and the ceramic increase at the same time, the nonlinear natural frequency decreases faster. The given natural frequency and mode shape solutions are of practical importance for various engineering dynamic analyses of functionally graded circular plates.
		2020 Vol. 41 (3): 258-272 [Abstract] ( 270 ) HTML (1 KB) PDF (0 KB) ( 228 )

	273	Vibration Analysis of a Cylindrical Shell of Functionally Graded Piezoelectirc-Magnetic Material

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.003
		In this paper, the symmetric radial vibration of a cylindrical shell of functionally graded piezoelectirc-magnetic material under radial loading is studied on the assumption that the material parameters of a piezoelectric and piezomagnetic cylindrical shell are distributed as a power function along the thickness of the shell without considering volume force, volume current or volume charge. Firstly, in the cylindrical coordinate system, assuming that the material properties are power functions of the radial position, and employing the constitutive, gradient and equilibrium equations of the functionally graded piezoelectirc-magnetic materials and boundary conditions, a non-homogeneous second-order differential equation is obtained. The Bessel function is used to express solutions of the second-order differential equation, and the steady-state solutions of the stress, electric potential and magnetic potential of a cylindrical shell are obtained under the action of external excitation. Furthermore, the theoretical analysis of the dynamic control of functionally graded piezoelectric-magnetic materials is carried out. It can be seen that when the gradient parameter , the results are completely reduced to the symmetric vibration of a transversely isotropic piezoelectric-magnetic cylinder, which are consistent with the results of the literature [20] when the basic equation is under cylindrical coordinate. Finally, numerical examples are given with BaTiO3-CoFeO4 composite materials. The results show that the inhomogeneity index of the material has a significant effect on the physical variables in the radial vibration, and the mechanical-electromagnetic-field coupling performance can be optimized with a specific value of the inhomogeneity parameter , which is of particular importance in modern engineering design.
		2020 Vol. 41 (3): 273-280 [Abstract] ( 246 ) HTML (1 KB) PDF (0 KB) ( 204 )

	281	Type III Fracture Mechanics of a Nanoscale Cracked Hole in One-Dimensional Hexagonal Quasicrystals

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.043
		The type III fracture mechanics problem of a nanoscale cracked elliptical hole in one-dimensional hexagonal quasicrystals is investigated. Based on the complex elastic theory and the surface elasticity theory, analytical s of stress fields, stress intensity factors and energy release rate of an elliptical hole with edge crack considering surface effects are presented, and the degraded results are consistent with the existing literatures. The influences of defect size, crack/hole ratio, coupling coefficient and applied loads on the stress intensity factors and the energy release rate are discussed. The results show that the dimensionless stress intensity factors of the phonon field and the phase field and the dimensionless energy release rate are significantly size-dependent when considering the surface effects of the defects and the size of the defects are at the nanoscale. When the relative size of the crack is very small, the surface effect has little effect on the dimensionless stress intensity factors of the phonon field and the phase field; on the contrary, the effect on above is greater. The dimensionless energy release rate increases with the increase of the coupling coefficient at the nanoscale. When the coupling coefficient is constant, the dimensionless energy release rate is affected by the size of elliptical hole; and the larger the defect size, the higher the dimensionless energy release rate. With the increase of the phonon field loads, the dimensionless energy release rate decreases first, then increases and finally stabilizes. The dimensionless energy release rate monotonously decreases with the increase of the phase field loads, that is, very small and very large phonon field loads (or phase field loads) shield the effects of phase field loads (or phonon field loads). This work shows that the Gurtin-Murdoch surface elasticity theory can be theoretically extended to the quasicrystal material, which is helpful to the development of quasicrystal fracture mechanics.
		2020 Vol. 41 (3): 281-292 [Abstract] ( 226 ) HTML (1 KB) PDF (0 KB) ( 198 )

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