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2021 Vol. 42, No. 2 Published: 2021-04-28

	107	Mechanisms of Twinning and Twinning Dislocations in hcp Metals

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2021.017
		For metals with the hexagonal close-packed (hcp) crystal structure, deformation twinning plays an important role in their plastic deformation. Due to the complex lattice structures of hcp metals, the atomic motions in twinning are very complex because not all of the atoms move in the direction of twinning shear. Therefore, the glide-shuffle mechanisms associated with the motion of twinning dislocations (TDs) are responsible for the twinning in hcp metals. In this paper, we focus on the mechanisms of TDs for different types of twinning, such as {101 ̅2}, {101 ̅1},{112 ̅2}, and {102 ̅1}. It is revealed that the lattice shuffles are needed for almost all hcp twinning mechanisms, except for the one-layer TD in {112 ̅2} twinning. This one-layer TD can be achieved by pure shear via the glide of partial dislocations along the twinning plane. Therefore, the twinning mechanisms in hcp metals can be classified as the glide-dominated, shuffle-dominated and glide-shuffle mechanisms. For a twinning with a determined invariant plane k_1 (and the shear direction η_1), different types of TDs with different shears and shuffles can be involved, while the second undistorted plane k_2 and the conjugate shear direction η_2 are altered accordingly, resulting in the corresponding tensile or compressive deformation of twinning. The prediction of possible twinning modes is based on the hypothesis that both the twinning shear and the shuffle magnitudes should be small. The {101 ̅2} twinning is the most easily activated twinning mode in hcp metals due to its small twinning shear and atomic shuffles. Furthermore, the activation of various twinning mechanisms under specific temperature and stress conditions can be responsible for the improvement of plasticity in hcp metals and alloys. The comprehensive understanding of twinning mechanisms will be helpful for further experimental and theoretical exploration on designing alternative and more innovative hcp-type structural materials with superior mechanical properties.
		2021 Vol. 42 (2): 107-120 [Abstract] ( 960 ) HTML (1 KB) PDF (0 KB) ( 199 )

	121	Study on Energy Harvesting Characteristics of the Defect State of Perforated Plates Based on Acoustic Metamaterials

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.051
		An acoustic metamaterial energy harvesting device suitable for working in the low-frequency range is proposed. First, a defect state of local resonance is created by constructing defects in porous acoustic metamaterial structures, the elastic strain energy of incident acoustic waves is concentrated in the defect area, and the energy conversion is realized using piezoelectric chips. Then the finite element method is used to study the properties of power and voltage captured by a cellular porous acoustic metamaterial at resonant frequency. Furthermore, the influence of pore size on the energy harvesting effect is explored by changing the pore size gradually. It is found that compared with those of the device without holes, the energy capture characteristics of the device at low frequency can be significantly improved by drilling holes in the cell. The device proposed in this study has the advantages of easy processing and strong practicability, which further expands its ability to capture energy in low-frequency range and has potential application prospects.
		2021 Vol. 42 (2): 121-128 [Abstract] ( 204 ) HTML (1 KB) PDF (0 KB) ( 154 )

	129	Study of Surface Mobility of Anisotropic Plates

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.036
		The surface mobility of anisotropic plates with different materials, geometric properties and boundary conditions is studied. Surface mobility, which reflects the characteristics of not only the vibration but also the power transmission of structures, is more practical than point mobility in engineering. There are more and more problems about structural vibration and vibration power transmission of anisotropic materials in engineering; however, research on the surface mobility of such structures is insufficient. In this study, according to the theoretical formula, the surface mobility of the orthotropic plate is obtained and compared with the numerical solution of the finite element model. It is found that the two solutions are in good agreement. In this paper, the finite element method is used to study the influence of elastic constants, size of the plate and boundary conditions on the surface mobility and the difference between the point mobility and the surface mobility of the anisotropic plate. It is found that increasing the excitation area and reducing the structural stiffness and the damping coefficient of the structure will make the difference between the point mobility and the surface mobility larger. The influence of shear modulus on the vibration characteristics of the plate is far less than that of elastic modulus. Reducing the model of the anisotropic plate to the model of an orthotropic plate but keeping both shear modulus and elastic modulus unchanged will also make the difference between the point mobility and the surface mobility larger. Increasing the size and the damping coefficient of the plate can reduce the range of mobility fluctuation, and the boundary conditions have little influence on the vibration reduction performance of the plate. These results can be applied to the investigation of the vibration power transmission of anisotropic plate-like structures in civil engineering, aeronautical engineering and mechanical engineering.
		2021 Vol. 42 (2): 129-144 [Abstract] ( 160 ) HTML (1 KB) PDF (0 KB) ( 168 )

	145	Effect of temperature on the phase transition shock wave propagation

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.045
		First-order martensitic transformations usually undergo temperature variations because of release/absorption of latent heat. Such temperature variations, in turn, affect the process of phase transition and the propagation of phase boundary, especially for shock loading. In fact, the phase transition wave front is not only a discontinuity of mechanics and matter, but also a moving temperature interface. This temperature interface is bound to influence the phase transition wave profiles and make the space-time pattern of its propagation more complex. However, it may bring some new wave propagation phenomena, which will have important theoretical value for the extension of stress wave theory. In this paper, the effect of temperature on the propagation of phase transition wave was studied theoretically and numerically. First, we treated the temperature interface as a fixed one to study the basic interaction between the temperature interface and phase transition wave by using the method of one-dimensional characteristic line theory and finite difference numerical calculation. The results showed that such an interaction was related to the temperature gradient of the interface and the applied stress pulse amplitude. Second, the propagation of phase transition wave was given under the conditions of continuous temperature gradient and adiabatic impact, respectively. The results showed that for loading from the austenitic phase to the mixed phase or martensite phase, a shock wave would be generated due to the mixed phase hardening effect; while for unloading, a shock wave was predicated due to a change in the unloading path, which has barely been studied. Through analysis of the thermo-mechanical coupling constitutive equations with phase transition, it was found that the nonlinear hardening characteristics and the change of unloading path are both rooted in the interaction between the self-heating (latent heat and dissipated energy) and the temperature dependence of phase transition stress, reflecting the intrinsic characteristics of materials with strong thermo-mechanical coupling properties. The results are helpful for the design and control of impact resistance for phase transition materials and structures.
		2021 Vol. 42 (2): 145-155 [Abstract] ( 168 ) HTML (1 KB) PDF (0 KB) ( 161 )

	156	Approaches to the Triple-shear Elasto-plastic Constitutive Models with Finite Deformations for Saturated Clays in Normal Consolidation

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.047
		For soils in soft status, with high porosity or under high loading, the finite deformation theory should be used to analyze their deformation characteristics because the calculated results based on the small deformation theory may deviate from their actual practice which is not allowed. Based on the triple-shear unified failure criterion and the methods of equivalent substitution and coordinate translation, the triple-shear failure stress ratios for saturated clays in normal consolidation are derived and combine with the modified Cambridge model to obtain the triple-shear unified yield surface equations. Two triple-shear unified elasto-plastic constitutive models with finite deformations using the methods of equivalent substitution and coordinate translation are established to reflect nonlinear and large deformation characteristics for saturated clays in normal consolidation. In order to verify the applicability of these models, the conventional triaxial CU and CD tests are conducted for Jiangxi red clay samples with three compaction degrees under different confining pressures, and the experimental data are compared with the theoretical results obtained from the two finite deformational models and the corresponding two small deformational models. Conclusions show that the calculated results deduced from the constitutive models with finite deformational theory are closer to the test results compared with the models of infinitesimal deformational theory due to deformation development, so the former can better reflect the large deformation characteristics of the clays with high porosity caused by low initial compaction and low confining pressure in the early compression stage. Although the deformation deviations calculated with the infinitesimal deformation models would decrease with the increase of initial compaction degrees or confining pressures, deformation deviations with the finite deformation models are all relatively small with different initial compaction degrees or confining pressures. The finite deformation model with the equivalent substitution method gives the minimal deviations under conditions of large initial compaction degrees or high confining pressures. True triaxial simulations with the constitutive models proposed in this paper show that the influence coefficient b of the intermediate principal stresses and the initial compaction degrees have certain influences on the strength and deformation characteristics of the clays. Results show that the principal stress differences, the pore water pressures and the volume strains are positively correlated with b; the principal stress differences are positively correlated with the initial compaction degrees, while the pore water pressures and volume strains are negatively correlated with the initial compaction degrees.
		2021 Vol. 42 (2): 156-179 [Abstract] ( 189 ) HTML (1 KB) PDF (0 KB) ( 152 )

	180	A Method for Removing Near Singularity of 3D Weak Singular Boundary Integral Based on (α, β) Transformation and Distance Transformation

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.042
		When the nonlinear transformation is used to evaluate three-dimensional (3D) weakly singular integral, the singularities of integrand can be eliminated by the Jacobian of the transformation. However, if the integration element has poor shape, such as including large angle or large ratio of edge length, the near singularities still exist in the weakly singular boundary integral, which can reduce the computational accuracy of weakly singular integral, and even lead to wrong results. Therefore, a new method for removing near singularity of weak singular boundary integral based on (α, β) transformation and distance transformation is proposed in this paper to accurately compute the 3D weakly singular integral. Firstly, the (α, β) transformation is employed to eliminate the singularity in the α direction. The (α, β) transformation is similar to the polar transformation and the singularity in the α direction can be removed by the Jacobian of the (α, β) transformation. Furthermore, the (α, β) transformation can separate the near singularity in the β direction. Then, the distance transformation is constructed according to the form of integral function in the β direction. The near singularity in the β direction can be eliminated by the Jacobian of the newly constructed distance transformation. Finally, several numerical examples of weakly singular integral with large angle and large ratio of edge length are given. The numerical results show that the relative error obtained by the proposed method can be less than 10-13 even for angle = 1700 or ratio of edge length = 100. These demonstrate that accurate evaluation of weakly singular integral with different shapes can be obtained using the (α, β) transformation combined with the distance transformation in the β direction. The last numerical example shows that the thin-walled structure problem can be analyzed by the presented method with high accuracy and computational efficiency.
		2021 Vol. 42 (2): 180-188 [Abstract] ( 186 ) HTML (1 KB) PDF (0 KB) ( 163 )

	189	Vector Sealing Reliability of Flexible Joint in Solid Rocket Motor

		Flexible joint, a device that provides thrust vector control for some solid rocket motors, is a key component in solid rocket motor. Flexible joint is composed of alternately bonded elastomers and reinforcements. The vector sealing reliability of flexible joint is a pivotal factor affecting the operation of solid rocket motor. In order to investigate the sealing reliability of flexible joint, a cohesive zone model is selected as the constitutive model of interface in flexible joint. By calculating interfacial damage and contact stress, defining the sealing status of nodes, interfaces and flexible joint, and adopting reliability theory, one method is proposed to calculate the vector sealing reliability of flexible joint. Taking one flexible joint as an example, the effects of pressure and vector angle on the sealing reliability of flexible joint are analyzed. Results indicate that the interface bonded to the rear flange is most vulnerable to damage, and shows the minimum sealing reliability, while the middle interfaces have the highest sealing reliability among all the interfaces of flexible joint. The interfaces of flexible joint have the best sealing performance when the vector angle is within 2°. When the vector angle is larger than 2°, the sealing reliability of flexible joint decreases rapidly with the increase of vector angle. With the increase of pressure, the sealing reliability of flexible joint shows a downward tendency first and then increases. When the pressure is around 2 MPa, the sealing reliability of flexible joint reaches the lowest. At the same time, the shear force at the interface is the major factor that affects the sealing reliability of flexible joint. This study can provide a basis for the design, calculation and analysis of flexible joints.
		2021 Vol. 42 (2): 189-199 [Abstract] ( 229 ) HTML (1 KB) PDF (0 KB) ( 177 )

	200	Force Transmissibility of Two-Degree-of-Freedom Quasi-Zero-Stiffness Vibration Isolation System with Nonlinear Springs

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.046
		Based on the anti-resonance characteristics of multi-degree-of-freedom systems, negative-stiffness structures containing nonlinear inclined springs are introduced into both the upper and lower layers of a traditional linear vibration isolation system to form a two-degree-of-freedom quasi-zero-stiffness vibration isolator. First, through the analysis of static characteristics, a set of relations between the parameters of a quasi-zero-stiffness isolation system is derived. The influences of mechanical and structural parameters on stiffness characteristics of the system are studied. Then, the nonlinear dynamic equations of the two-degree-of-freedom vibration isolation system with quasi-zero stiffness are established. Using the averaging method, the frequency-domain analytical solutions and the expression of force transmissibility are derived. The effects of upper damping ratio, lower damping ratio, vertical stiffness ratio and mass ratio on force transmissibility are numerically discussed. The vibration isolation performance of the two-degree-of-freedom quasi-zero-stiffness vibration isolation system with nonlinear inclined springs is compared with that of the single-degree-of-freedom quasi-zero-stiffness vibration isolation system. The results indicate that the smaller the structural parameter (i.e. the ratio of length when the nonlinear inclined springs are at static equilibrium and initial positions) is, or the softer the nonlinear inclined springs are, the smaller stiffness of the system and the larger low-stiffness interval near the equilibrium position can be obtained. Furthermore, by selecting suitable values of the upper damping ratio, lower damping ratio, vertical stiffness ratio and mass ratio, the initial vibration isolation frequency of the system can be reduced, the vibration isolation band width can be further expanded, the attenuation rate of the force transmissibility in a certain frequency region can be obviously accelerated, and the low-frequency vibration isolation performance of the system can be dramatically improved.
		2021 Vol. 42 (2): 200-210 [Abstract] ( 246 ) HTML (1 KB) PDF (0 KB) ( 158 )

	211	Vibration Analysis of Bilayered Circular Plate Considering Surface Effects

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.050
		With the development of the micro-electric-mechanical system (MEMS) technology, MEMS devices, such as micro resonators, sensors and actuators, have been applied more and more extensively. Micro-plate is one of the key components of these MEMS devices. The dynamic characteristics of micro-plate have gained more and more attention from a growing number of scholars. At present, the existing theoretical models including surface effects are mainly developed for the single-layer thin plates. However, the micro-plates are usually bilayered or multilayered structures in practical applications. Therefore, considering the structure of resonators in micro biochemical sensors, the governing equations of the bilayered circular plate including surface effects are developed based on the Kirchhoff plate theory and continuum surface elasticity theory in this paper. The displacement field of the bilayered circular micro-plate with a neutral surface unknown beforehand is given. The Galerkin method is employed to obtain the approximate results. The influences of surface effects and surface residual stress on the natural frequency of the bilayered circular plate are discussed. The comparison shows that the natural frequency of the presented model is obviously different form that of the existed circular plate model. For different thicknesses and thickness ratios, the natural frequencies obtained by the existed model are either larger or smaller than the actual value. For the bilayered circular micro-plate including both stiffened and softened surface effects, the critical value of the thickness ratio is 0.6. Considering the surface residual stress, when the normalized tension parameter k is smaller than 4, the natural frequency of the bilayered micro-plate increases slowly. When k is larger than 4, the natural frequency increases rapidly with the increase of surface residual stress. For the study and design of resonators with bilayered structure, the results of the presented model are more accurate than the existing theoretical models.
		2021 Vol. 42 (2): 211-220 [Abstract] ( 229 ) HTML (1 KB) PDF (0 KB) ( 174 )

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