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2015 Vol. 36, No. 5
Published: 2015-10-28
369
Interlayer Friction in Incommensurate Double Walled Carbon Nanotubes
Owing to the coupling effect between interlayer spacing and stacking angle, the interlayer friction in incommensurate double walled carbon nanotubes (DWCNTs) exhibits complex behavior and remains to be understood. Molecular dynamics simulation (MD) was applied in this paper to study the interlayer friction in incommensurate DWCNTs. In the calculations, the chiral angle of the outer tube was kept as 0° or 30°, while the chiral angle of the inner tube varied from 0°~30°. The results show that the interlayer friction is larger for smaller interlayer spacing or smaller difference in interlayer chiral angles. When the chiral angle difference is larger than 10° and the interlayer spacing is round 0.34 nm, the interlayer friction is linearly dependent on the interlayer spacing. The results show also that the friction force on edge atoms is significantly higher than that on inner atoms, indicating the edge effect is a general effect in nanoscale friction.
2015 Vol. 36 (5): 369-375 [
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429
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376
The numerical simulation of tensile plate with circular hole using peridynamic theory
basic equation of non-ordinary state-based peridynamic theory is deduced at first,then damage theory is introduced, Its numerical program is compiled after the basic equation of non-ordinary state-based peridynamic theory is discretized. The rupture and non-rupture problem of a tensile plate with circular hole is modeled using non-ordinary state-based peridynamic theory. The numerical results show that it can not only model rupture problem but also non-rupture problem by using non-ordinary state-based peridynamic theory. In comparison with the other numerical methods, the propagation and coalescence of cracks can be simulated using non-ordinary state-based peridynamic theory without any outer fracture criterion. Therefore, it has great advantages over other numerical methods. And it also offers a new method and thought to simulate the rupture problem of materials.
2015 Vol. 36 (5): 376-383 [
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400
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384
Free Vibration of Axially Functionally Graded Beams with Non-uniform Cross-section
Abstract: A new and simple approximate method is introduced to solve natural frequencies of free vibration of beams with axially inhomogeneity in this paper. The governing differential equation is transformed to a system of linear algebraic equations by changing the form of the expression of displacement with the Chebyshev polynomials expansion. Under the non-zero solution of existence conditions, the characteristic equations are numerically obtained to get the natural frequency. The effectiveness and accuracy of present method are confirmed by comparing numerical results with the exact solution of some specific gradient. Furthermore, the influences of gradient parameter and support conditions on natural frequency are studied.
2015 Vol. 36 (5): 384-391 [
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404
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392
STUDY OF EVOLUTION OF ADIABATIC SHEAR FAILURE IN HAT-SHAPED SPECIMEN UNDER DYNAMIC LOADING
Combined with digital image correlation method (DIC) and microscopic metallurgical observation of " freezing" samples, this paper experimentally discuses about the initiation and propagation of adiabatic shear localization of Ta2 titanium alloy in a closed flat hat-shaped specimen struck by Split Hopkinson Pressure Bars. The results show that the width of shear zone in hat-shaped specimen is continually narrow-down until the formation of adiabatic shear band, and the crack will propagate along this band from the end to the center of shear zone. It is also shown that the critical shear strain of initiation sensitivity increase with an increasing loading rate. Furthermore, the results of DIC show that the initiation of adiabatic shear localization can be taken as the time when the elastic strain of element located near the plastic shear zone begins to rebound according to the stress unloading theory, and the adiabatic shear band initial in that localization area and cracks propagation along the band. The evolution of heat in shear zone converted by plastic work shows that the temperature of initiation is only 86℃, this result means that the heat softening of material may not the key condition of initiation of adiabatic shear localization, however, the sharp increase of temperature is the result of high-plastic-strain in adiabatic shear band.
2015 Vol. 36 (5): 392-400 [
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361
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401
SIZE EFFECT AND MECHANICAL PROPERTIES FOR COPPER ALLOY?MICRO PLASTIC FORMING
Different grain sizes, different feature sizes of H62 brass foil was studied by micro tensile test, the effects of grain size and specimen size on the deformation behavior of material?characteristics was analyzed.With the decrease of the grain size, tensile yield stress increases, grain size effects on the yield stress satisfy Hall-Petch fine grain strengthening relations.Yield strength first decreases and then increase with the thickness decreases, and enhanced with the decrease of the width.Crystal plasticity theory, the surface layer model can the phenomenon of explain the elongation rate, tensile strength increases with the increase of specific surface area.Based on the experimental data of a micro plastic forming establishing micro-plasticity constitutive model by correcting bilinear models.
2015 Vol. 36 (5): 401-409 [
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295
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410
EXPERIMENTAL INVESTIGATION ON TENSION-COMPRESSION LOW CYCLE FATIGUE OF Q235 STEEL NOTCHED SPECIMENS
Q235 steel U-shape notched plate specimens are taken as subject investigated. The low-cycle fatigue experiments under tension-compression loading are conducted by controlling the elongations of specimen’s gauge section, which are calculated by finite element method (FEM) prior experiments. Then the local stress-strain method is adopted to analyze the fatigue lives by test. According to the results, it is found that: whether FEM or modified Neuber method is taken to calculate stress and strain of notch root region, for fatigue life assessment the local stress-strain method is applicable only to the specimens with larger notch radius; the estimated lives obviously lower than test data for those specimens with smaller notch radius, and more serious in life estimation for the strain in notch root evaluated by FEM than by modified Neuber equation. On this basis, the effect of strain gradient for notched specimen is investigated. The famous Taylor’s model is applied to estimate the raise of yield stress and flow stress due to the high strain gradient in notch root region, by which the strain distribution of specimen is recalculated. The fatigue life estimation taken the influence of strain gradient into account is found improved for all notched specimens.
2015 Vol. 36 (5): 410-420 [
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489
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421
Modified 3-chain model and Mullins constitutive model of carbon black filled rubber materials
The constitutive model of carbon black filled rubber materials is investigated in this paper. Taking into account the interaction between a single chain with the surrounding molecules network and carbon black particles of rubber reinforcement, a modified 3-chain model is proposed. The interactions and constraints between molecular chains are described by Edward’s tube model and the effects of carbon black content are considered by strain amplification factor. Based on this model, using the theory of network alteration, a new constitutive model for the Mullins effect is presented. Comparing with experimental data, the modified 3-chain model is more suitable for characterization of the mechanical properties of unfilled rubber with different deformation modes and the uniaxial tension mechanical behavior of Carbon black particles filled rubber material, moreover, the proposed model of Mullins has a good description of Mullins effect.
2015 Vol. 36 (5): 421-428 [
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432
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429
Experimental Research on Jumping Course of Inclined Cable in Nonlinear Vibration
Jump phenomenon is a representative nonlinear behavior of inclined cable. Although it has been discovered both in theory and experiment, jumping course is yet to be observed. An experiment was carried out to directly observe the jumping course and to ascertain nonlinear behaviors in this course. An automatic jump was directly observed by continuously repeat the sweep testing to make one of the excitation frequencies just right equal to the threshold frequency. Attributes of spatial motion during the jumping course were investigated. It is found that the spatial motion goes through three stages in the course, no merely sharp changes of the response amplitude as traditionally believed. These stages are: sharp changes of the response amplitude, dominative motion alternate between the out-of-plane and in-plane vibrations, and balloon motion alternate between the clockwise and anticlockwise directions.
2015 Vol. 36 (5): 429-435 [
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309
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436
Later Load Displacement Approximate Solution Under Initial Loads for Four Non-orthogonal Boundary Plates
Based on general static equilibrium differential equation of plate considered initial load effect, the polar form static equilibrium differential equation was presented for circular plate considered initial load effect under axisymmetric condition. The approximate solutions of later load displacement considered initial load effect for the simply supported equilateral triangular plate, the clamped ellipse plate, the clamped circular plate and the simply supported circular plate, were derived by the Galerkin method. These approximate solutions of displacement were verified using the finite element method presented in related literature. Initial load effect on later load displacement of the above 4 plates was analyzed with these solutions, which clearly illustrated the initial load effect and corresponding factors that influence the static performance of plates. Due to initial loads effect, the bending stiffness of plate increased, the displacements of later loads decreased. The key physical factors governing the effect of initial loads on plates are the initial load, the ration of span to thickness and boundary condition etc.
2015 Vol. 36 (5): 436-443 [
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195
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444
Coupled Vibration Analysis of Tower-Cable-Deck of Long-Span Cable-Stayed Bridge
In order to analyze coupled vibration of tower-cable-deck under end excitation. Considering sag, angle, damping and gravity of the tangential component of cable, the high precision parabola was introduced. The refined coupled model of tower-cable-deck was established. The nonlinear vibration differential equation of tower-cable-deck under end excitation was deduced. The vibration characteristic of cable was compared with two different modes. The effect of frequency ratio of cable and deck, deck excitation amplitude, cable force, damping and angle on structure were analyzed. The results show that the frequency ratio of cable and deck have larger influence on cable vibration. The cable strongly vibrate under the frequency ratio of 2:1 and 1:2, but the amplitude of cable under 2:1 vibration mode is larger, and longer resonance time. With the increase of the deck excitation amplitude, the amplitude growth rate under 2:1 vibration mode is faster. The cable amplitude decreases with cable force increasing. When the cable damping is over 2%, the vibration amplitude of cable cannot be effectively reduced, and the vibration of the cable can be suppressed by setting additional damping.
2015 Vol. 36 (5): 444-452 [
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274
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453
Barycentric rational interpolation iteration collocation method to analyse nonlinear MEMS microbeam
The nonlinear governing equation of micro beams is transfered into the linear differential equation by assuming the initial function. Barycentric rational interpolation collocation method is applied to solve linear differential equation .Barycentric rational interpolation iteration collocation method (BRIICM) as a numerical analysis method is presented to solve nonlinear bending problem of MEMS micro beams. The direct linearization formulations and the Newton linearization formulatons of nonlinear differential equation are given. The calculation method and formulation of nonlinear integral item are discussed in detail. The matrix-vector calculation formula of barycentric rational interpolation iteration collocation method is constructed by using barycentric rational interpolation differentiation matrix. Numerical examples demonstrate that the presented method for solving nonlinear bending problem of MEMS micro beams has merits of simple calculation formulations, convenient program and high calculation precision.
2015 Vol. 36 (5): 453-459 [
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460
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