ANALYTICAL SOLUTIONS TO STRESS CONCENTRATION PROBLEM IN PLATES CONTAINING RECTANGULAR HOLE UNDER BIAXIAL TENSIONS

The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions. By using the U-transformation technique and the finite element method, the analytical displacement solutions of the finite element equations are derived in the series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method. The stress concentration factors for various ratios of height to width of the hole are obtained.

Effects of Biaxial Tensile on the Deformation Behavior of DP590 High-strength Steel Sheet under High Strain Rate

The effects of biaxial tensile pre-strain on the forming limit of DP590 high-strength steel under high strain rate were investigated. The stress-strain curves of DP590 steel sheet under the biaxial tensile of different load ratios were obtained. The forming limit diagrams（FLDs） of DP590 steel sheet under biaxial tensile pre-strain and electromagnetic hybrid forming were established. Results showed that the biaxial tensile pre-strain had significant effects on the formability of DP590 steel. The pre-strain in a certain range improved the forming limit of DP590 steel under high rate, and the forming limit increased with the pre-strain. The prestrain in the same direction of high rate increased the forming limit of the final deformation under complex strain paths conditions, but the pre-strain in the vertical direction decreased the minor strain under the high strain rate.

Comparative efficiency analysis of different nonlinear modelling strategies to simulate the biaxial response of RC columns

The performance of different nonlinear modelling strategies to simulate the response of RC columns subjected to axial load combined with cyclic biaxial horizontal loading is compared. The models studied are classified into two categories according to the nonlinearity distribution assumed in the elements： lumped-plasticity and distributed inelasticity. For this study, results of tests on 24 columns subjected to cyclic uniaxial and biaxial lateral displacements were numerically reproduced. The analyses show that the global envelope response is satisfactorily represented with the three modelling strategies, but significant differences were found in the strength degradation for higher drift demands and energy dissipation.

Theory of nine elastic constants of biaxial nematics

In this paper, a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation, nine elastic constants for simple distortion patterns in biaxial nematics are derived in terms of the thermal average （Dmn^（l）） （Dm＇n＇^（l＇））, where Dmn^（l） is the Wigner rotation matrix. In the lowest order terms, the elastic constants depend on coefficients Γ,Γ＇, λ, order parameters Q0 = Q0（D00^（2）） ＋Q2（D02^（2）＋D0-2^（2）） and Q2 = Q0（D20^（2）） ＋ Q2（D22^（2）＋D2-2^（2））. Here Γ and Γ＇ depend on the function form of molecular interaction energy vj′j″j （τ12） and probability function fk′k″k （τ12）, where r12 is the distance between two molecules, and λ is proportional to temperature. Q0 and Q2 are parameters related to multiple moments of molecules. Comparing these results with those obtained from Landau-de Gennes theory, we have obtained relationships between coefficients, order parameters used in both theories. In the special case of uniaxial nematics, both results are reduced to a degenerate case where K11=K33.

Effect of Low-Pressure Nitrogen DC Plasma Treatment on the Surface Properties of Biaxially Oriented Polypropylene, Poly (Methyl Methacrylate) and Polyvinyl Chloride Films

In this study, commercial biaxially oriented polypropylene （BOPP）, polyvinyl chlo- ride （PVC） and poly （methyl methacrylate） （PMMA） films were treated with nitrogen plasma over different exposure times in a Pyrex tube surrounded by a DC variable magnetic field. The chemi- cal changes that appeared on the surface of the samples were investigated using Fourier transform infrared （FT4R） spectroscopy and attenuated total reflectance Fourier transform infrared （ATR- FTIR） spectroscopy after treatment for 2 min, 4 min and 6 rain in a nitrogen plasma chamber. Effects of the plasma treatment on the surface topographies and contact angles of the untreated and plasma treated films were also analyzed by atomic force microscopy （AFM） and a contact angle measuring system. The results show that the plasma treated films become more hydrophilic with an enhanced wettability due to the formation of some new polar groups on the surface of the treated films. Moreover, at higher exposure times, the total surface energy in all treated films increased while a reduction in contact angle occurred. The behavior of surface roughness in each sample was completely different at higher exposure times.

FAILURE MODE AND CONSTITUTIVE MODEL OF PLAIN HIGH-STRENGTH HIGH-PERFORMANCE CONCRETE UNDER BIAXIAL COMPRESSION AFTER EXPOSURE TO HIGH TEMPERATURES

An orthotropic constitutive relationship with temperature parameters for plain highstrength high-performance concrete （HSHPC） under biaxial compression is developed. It is based on the experiments performed for characterizing the strength and deformation behavior at two strength levels of HSHPC at 7 different stress ratios including a=σs ： σ3=0.00：-1,-0.20：-1,-0.30 ： -1,-0.40：-1,-0.50：-1,-0.75：-1,-1.00：-1, after the exposure to normal and high temperatures of 20, 200, 300, 400, 500 and 600℃, and using a large static-dynamic true triaxial machine. The biaxial tests were performed on 100 mm×100 mm×100 mm cubic specimens, and friction-reducing pads were used consisting of three layers of plastic membrane with glycerine in-between for the compressive loading plane. Based on the experimental results, failure modes of HSHPC specimens were described. The principal static compressive strengths, strains at the peak stress and stress-strain curves were measured; and the influence of the temperature and stress ratios on them was also analyzed. The experimental results showed that the uniaxial compressive strength of plain HSHPC after exposure to high temperatures does not decrease dramatically with the increase of temperature. The ratio of the biaxial to its uniaxial compressive strength depends on the stress ratios and brittleness-stiffness of HSHPC after exposure to different temperature levels. Comparison of the stress-strain results obtained from the theoretical model and the experimental data indicates good agreement.

The biaxial compression mechanical properties of crushed rock

Crushed rock subgrade, as one of the roadbed-cooling methods, has been widely used in the Qinghai-Tibet Railway. Much attention has been paid on the cooling effect of crushed rock; however, the mechanical properties of crushed rock are somehow neglected. Based on the discrete element method, biaxial compression test condition for crushed rock is com- piled in FISH language in PFC2D, and the natural shape of crushed rock is simulated with super particle ＂cluster＂. The ef- fect of particle size, crushed rock strength and confining pressure level on overall mechanical properties of the crushed rock aggregate are respectively analyzed. Results show that crushed rock of large particle size plays an essential frame- work role, which is mainly responsible for the deformation of crushed rock aggregate. The strength of gravel has a great influence on overall mechanical properties which means that strength attenuation caused by the freeze thaw cycles cannot be ignored. The stress-strain curves can be divided into two stages including shear contraction and shear expansion at different confining pressures.

Further study of rubber-like elasticity: elastic potentials matching biaxial data

By virtue of the rational interpolation procedure and logarithmic strain, a direct approach is proposed to obtain elastic potentials that exactly match uniaxial data and shear data for elastomers. This approach reduces the determination of multi axial elastic potentials to that of two one-dimensional potentials, thus bypassing usual cumbersome procedures of identifying a number of unknown parameters. Predictions of the suggested potential are derived for a general biaxial stretch test and compared with the classical data given by Rivlin and Saunders （Rivlin, R. S. and Saunders, D. W. Large elastic deformation of isotropic materials. VII： experiments on the deformation of rubber. Phill. Trans. Royal Soc. London A, 243, 251-288 （1951））. Good agreement is achieved with these extensive data.

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.

Stick–slip behavior of Indian gabbro as studied using a NIED large-scale biaxial friction apparatus

This paper reports stick-slip behaviors of Indian gabbro as studied using a new large-scale biaxial friction apparatus, built in the National Research Institute for Earth Science and Disaster Prevention （NIED）, Tsukuba, Japan. The apparatus consists of the existing shaking table as the shear-loading device up to 3,600 kN, the main frame for holding two large rectangular prismatic specimens with a sliding area of 0.75 m^2 and for applying normal stresses an up to 1.33 MPa, and a reaction force unit holding the stationary specimen to the ground. The shaking table can produce loading rates v up to 1.0 m/s, accelerations up to 9.4 m/s^2, and displacements d up to 0.44 m, using four servocontrolled actuators. We report results from eight preliminary experiments conducted with room humidity on the same gabbro specimens at v = 0.1-100 mm/s and an = 0.66-1.33 MPa, and with d of about 0.39 m. The peak and steady-state friction coefficients were about 0.8 and 0.6, respectively, consistent with the Byerlee friction. The axial force drop or shear stress drop during an abrupt slip is linearly proportional to the amount of displacement, and the slope of this rela- tionship determines the stiffness of the apparatus as 1.15 × 10^8 N/m or 153 MPa/m for the specimens we used. This low stiffness makes fault motion very unstable and the overshooting of shear stress to a negative value was recognized in some violent stick-slip events. An abrupt slip occurred in a constant rise time of 16-18 ms despite wide variation of the stress drop, and an average velocity during an abrupt slip is linearly proportional to the stress drop. The use of a large-scale shaking table has a great potential in increasing the slip rate and total displacement in biaxial friction experiments with large specimens.

Effect of Increasing Speed on Stress of Biaxial Bogie Frames

Increasing the trains’ speed has always been one of the goals of any railway industry and train manufacturers. Also, the influence of the train speed on bogie’s dynamics has an immense importance. Therefore, it is important to analyze the effect of train speed on the stress distribution in different parts of train structure. In this study the result of the increasing speed on the applied stresses of a biaxial bogie frame has been examined. For this purpose, a biaxial bogie frame has been modeled using finite element analysis. Static and dynamic forces applied on the bogie with biaxial frame have been obtained for different speeds and rail roughness. The Von Mises stresses are adopted as equivalent stresses in the strength calculation. The results show that maximum stress always has been induced in the bogie bowl also the increase in bogie’s speed has remarkable effect on the increment of applied stresses in the bogie frame.

Temperature dependence of biaxial strain and its influence on phonon and band gap of GaN thin film

Hexagonal GaN epilayer grown on sapphire substrate by metal organic chemical vapour deposition （MOCVD） is studied using Raman scattering and photoluminescence in a temperature range from 100K to 873 K. The model of strain （stress） induced by the different lattice parameters and thermal coefficients of epilayer and substrate as a function of temperature is set up. The frequency and the linewidth of E2^high mode in a GaN layer are modelled by a theory with considering the thermal expansion of the lattice, a symmetric decay of the optical phonons, and the strain （stress） in the layer. The temperature-dependent energy shift of free exeiton A is determined by using Varshni empirical relation, and the effect of strain （stress） is also investigated. We find that the strain in the film leads to a decreasing shift of the phonon frequency and an about 10meV-inereasing shift of the energy in a temperature range from 100 K to 823 K.

FAILURE SURFACE AND CAPACITY OF REINFORCED CONCRETE MEMBERS SUBJECTED TO BIAXIAL TENSION

A computer program is developed for the nonlincar analysis of prestressedconcrete and nonprestressed concrete members subjected to combined biaxial bending andaxial load.The strength-interaction diagrams and failure surface are obtained.Thestrength design formulae are proposed.

Fatigue Behavior of Plain Concrete Under Biaxial Compression: Experiments and Theoretical Model

The effects of different lateral confinement stress on the fatigue behavior of and cumulative damage to plain concrete are investigated experimentally. Eighty 100 mm x 100 mm x 100 mm specimens of ordinary strength concrete are tested under constant- or variable-amplitude fatigue loading and lateral confinement pressure in two orthogonal directions. A fatigue equation is developed by modifying the classical Aas-Jakobsen S-N equation for taking into account the effect of the confined stress on fatigue strength of plain concrete. The results of variable-amplitude fatigue tests indicate that the linear damage theory proposed by Palmgren and Miner is unreasonable in the biaxial stress state. A nonlinear cumulative damage model that could model the effects of the magnitude and sequence of variable-amplitude fatigue loading and lateral confinement pressure is proposed on the basis of the evolution laws of the residual strains in the longitudinal direction during fatigue tests. The residual fatigue. life predicted by this model is found to be in good agreement with the results of the experimental research.

Enhancement of neutron irradiation uniformity for the CFBR-Ⅱ fast burst reactor with a biaxial rotational technique

A biaxial rotational technique is proposed to improve the neutron irradiation uniformity for a large sample,and the theoretical method is established to predict and design the main parameters. The technique used a device to rotate the target sample around two perpendicular axes simultaneously. Numerical calculations found that the lowest common multiple of the two angular speeds should be large enough to improve the uniformity,and the minimal experimental time should be no less than 600 s. For a three-dimensional sample with a size of 20 cm × 12 cm × 14 cm, the maximal non-uniform neutron irradiation factor of the sample is mainly determined by the distance between the center of the sample and of the point neutron source. It was computed to be less than 10% when the distance was no less than 34 cm. Experiments were carried out on the CFBR-II reactor and the experimental results were in good accordance with the theoretical analysis. As a result, the theoretical conclusions given above are reasonable and of reference value for the design of future irradiation experiments.

FATIGUE CRACK PROPAGATION FOR BIAXIAL STRESS CYCLING

Based on the experimental study of complex biaxial mode Ⅰ fatigue crack growth and the discussion on Von Mises'theory,a new approach is proposed for correlating crack propaga- tion rate under both in-phase and out-of-phase biaxial stress cycling.The results emphasize the contribution of plasticity to fatigue crack growth.

Deposition and characterization of YBCO/CeO2/YSZ/CeO2 multilayers on biaxially textured Ni substrates

CeO2/YSZ/CeO2 buffer layers were deposited on biaxially textured Ni substrates by pulsed laser deposition. The influence of the processing parameters on the texture development of the seed layer CeO2 was investigated. Epitaxial films of YBCO were then grown in situ on the CeO2/YSZ （yttria-stabilized ZrO2）/CeO2-buffered Ni substrates. The resulting YBCO conductors exhibited self-fleld critical current density Jc of more than 1 MA/cm^2 at 77K and superconducting transition temperature Tc of about 91K.

Spatial and temporal characteristics of acoustic emission activity during deforma-tion of rock samples with inhomogeneous fault under biaxial compression

The spatial and temporal distributions of acoustic emission （AE） during the deformation of samples containing an inhomogeneous fault have been studied under biaxial compression. The results show that the fault strength and the duration from loading to failure increase and the failure mode changes from abrupt instability to gradual failure with increase of lateral stress σ2. The pre-setting fault and its heterogeneity play an important role in controlling AE spatial distribution during the deformation. The basic pattern of AE spatial distribution is controlled by the pre-setting fault, especially the parts with inhomogeneous strength and the strong segment, and the localization of fracturing starts from the positions with inhomogeneous strength, With increase of σ5, the dense AE distribution area spreads from the positions with inhomogeneous strength to the whole strong segment gradually. AE temporal sequence is significantly affected by σ2. The fault shows abrupt instability in final failure, which occurs on a background of ＂enhancement-quiescence＂ in microfracturing activity at lower σ2. At higher σ5, the fault shows gradual failure, and AE occurrence rate increases continuously and AER increase exponentially before and after the failure, The effect of σ2 on b-value is also remarkable, b-value shows precursory decrease in the weakening stage when fault behavior is abrupt instability, but it shows balanced change when fault behavior is gradual failure,

Monte Carlo simulations of biaxial structure in thin hybrid nematic film based upon spatially anisotropic pair potential

Hybrid nematic films have been studied by Monte Carlo simulations using a lattice spin model, in which the pair potential is spatially anisotropic and dependent on elastic constants of liquid crystals. We confirm in the thin hybrid nematic film the existence of a biaxially nonbent structure and the structure transition from the biaxial to the bent-director structure, which is similar to the result obtained using the Lebwoh-Lasher model. However, the step-like director＇s profile, characteristic for the biaxial structure, is spatially asymmetric in the film because the pair potential leads to K1 ≠ K3. We estimate the upper cell thickness to be 69 spin layers, in which the biaxial structure can be found.

Valence band structure and density of states effective mass model of biaxial tensile strained silicon based on k·p theory

After constructing a stress and strain model, the valence bands of in-plane biaxial tensile strained Si is calculated by k·p method. In the paper we calculate the accurate anisotropy valance bands and the splitting energy between light and heavy hole bands. The results show that the valance bands are highly distorted, and the anisotropy is more obvious. To obtain the density of states （DOS） effective mass, which is a very important parameter for device modeling, a DOS effective mass model of biaxial tensile strained Si is constructed based on the valance band calculation. This model can be directly used in the device model of metal-oxide semiconductor field effect transistor （MOSFET）. It also a provides valuable reference for biaxial tensile strained silicon MOSFET design.