Dynamic constitutive equation of GFRP obtained by Lagrange experiment

The note presents a method of constructing dynamic constitutive equations of material by means of Lagrange experiment and analysis. Tests were carried out by a light gas gun and the stress history profiles were recorded on multiple Lagrange positions. The dynamic constitutive equations were deduced from the regression of a series of data which was obtained by Lagrange analysis based upon recorded multiple stress histories. Here constitutive equations of glass fibre reinforced phenolic resin composite(GFRP) in uniaxil strain state under dynamic loading are given. The proposed equations of the material agree well with experimental results.

On dilatational plastic constitutive equation of ductile materials and plastic loading paths at bifurcation

The dilatational plastic constitutive equation presented in this paper is proved to be in a form of generality. Based on this equation, the constitutive behaviour of materials at the moment of bifurcation is demonstrated to follow a loading path with the response as "soft" as possible.

A meso elastoplastic constitutive model for polycrystalline metals based on equivalent slip systems with latent hardening

A meso material model for polycrystalline metals is proposed, in which the tiny slip systems distributing randomly between crystal slices in micro-grains or on grain boundaries are replaced by macro equivalent slip systems determined by the work-conjugate principle. The elastoplastic constitutive equation of this model is formulated for the active hardening, latent hardening and Bauschinger effect to predict macro elastoplastic stress-strain responses of polycrystalline metals under complex loading conditions. The influence of the material property parameters on size and shape of the subsequent yield surfaces is numerically investigated to demonstrate the fundamental features of the proposed material model. The derived constitutive equation is proved accurate and efficient in numerical analysis. Compared with the self-consistent theories with crystal grains as their basic components, the present theory is much simpler in mathematical treatment.

Nonlinear Constitutive Behavior Of Ferroelectric Materials

The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism, a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated, the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material, one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Meanwhile, the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation, the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The interaction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results.

Stress Wave Propagation in a Gradient Elastic Medium

The gradient elastic constitutive equation incorporating the second gradient of the strains is used to determine the monochromatic elastic plane wave propagation in a gradient infinite medium and thin rod. The equation of motion, together with the internal material length, has been derived. Various dispersion relations have been determined. We present explicit expressions for the relationship between various wave speeds, wavenumber and internal material length.

Strain Gradient Effects on Deformation Strengthening Behavior of Particle Reinforced Metal Matrix Composites

Dislocation models with considering the mismatch of elastic modulus between matrix and reinforcing particles are used to determine the effective strain gradient \ita for particle reinforced metal matrix composites (MMCp) in the present research. Based on Taylor relation and the kinetics of dislocation multiplication, glide and annihilation, a strain gradient dependent constitutive equation is developed. By using this strain gradient-dependent constitutive equation, size-dependent deformation strengthening behavior is characterized. The results demonstrate that the smaller the particle size, the more excellent in the reinforcing effect. Some comparisons with the available experimental results demonstrate that the present approach is satisfactory.

Analysis of a Rubber Cone Tensioned by a Concentrated Force

Using the constitutive equation of a rubber-like materials given by Gao (1997), this paper investigates the problem of a cone under tension of a concentrated force at its apex. Under consideration is the axial-symmetry case and the large strain is taken into account. The stress strain fields near the apex are obtained by both asymptotic analysis and finite element calculation. The two results are consistent well. When the cone angle is 180 degrees, the solution becomes that of non-linear Boussinesq's problem for tension case.

Onset of Adiabatic Shear Instability in Strain Gradient Dependent Metal Matrix Composites

In this paper, effect of strain gradient on adiabatic shear instability in particle reinforced metal matrix composites is investigated by making use of the strain gradient dependent constitutive equation developed by Dai et al. [9] and the linear perturbation analysis presented by Bai [10]. The results have shown that the onset of adiabatic shear instability in metal matrix composites reinforced with small particles is more prone to occur than in the composites reinforced with large particles. This means that the strain gradient provides a strong deriving force for onset of adiabatic shear instability in metal matrix composites.

Creep characterization of a fiber reinforced plastic material

Creep behavior of [±45°]_s composite material is characterized by using uniaxial creep and recovery tests. The well-known Schapery nonlinear viscoelastic consti tutive relation was modified to make it suitable for characterizing the creep behavior of this material. Then, using this modified Schapery constitutive equation, by which the vis coplastic and creep damage can be taken into consideration, the creep behavior of [±45°]. glass fiber reinforced epoxy laminate was studied. The constitutive parameters of the material were determined experimentally, and the procedure and method of determination of the material parameters are proved to be valid.

Small-dynamic-angle measurement using tangent relationship and phase-modulating technique

A method using two prisms for measurement of small dynamic angles is proposed in which the measurement is based on a simple tangent equation and a phase-modulating interferometer with a laser diode to measure dynamic optical path differences with higher accuracy. Owing to the simple tangent equation, the symmetry requirement on the two prisms in the optical configuration is eliminated, and easy measurement of the separations between two parallel beams with a position-sensitive detector is achieved. Small-dynamic-angle measurements are experimentally demonstrated with high accuracy. (C) 2007 Society of Photo-Optical Instrumentation Engineers.

Small-dynamic-angle measurement using tangent relationship and phase-modulating technique

A method using two prisms for measurement of small dynamic angles is proposed in which the measurement is based on a simple tangent equation and a phase-modulating interferometer with a laser diode to measure dynamic optical path differences with higher accuracy. Owing to the simple tangent equation, the symmetry requirement on the two prisms in the optical configuration is eliminated, and easy measurement of the separations between two parallel beams with a position-sensitive detector is achieved. Small-dynamic-angle measurements are experimentally demonstrated with high accuracy. (C) 2007 Society of Photo-Optical Instrumentation Engineers.

Verification of EL2 electronic absorption effect on charge transfer in semi-insulating GaAs

The electronic absorption of EL2 centers has been clarified to be related to the electron acid hole photoionizations, and the transition from its ground state to metastable state, respectively. Under an illumination with a selected photon energy in the near infrared region, these three processes with different optical cross sections will show different kinetics against the illumination time. It has recently been shown that the photosensitivity (measured under 1.25 eV illumination) of the local vibrational mode absorption induced by some deep defect centers in SI-GaAs is a consequence of the electron and hole photoionizations of EL2. This paper directly measures the kinetics of the electronic transition associated with EL2 under 1.25 eV illumination, which implies the expected charge transfer among different charge states of the EL2 center. A calculation based on a simple rate equation model is in good agreement with the experimental results.

A Study of Composite Beam with Shape Memory Alloy Arbitrarily Embedded under Thermal and Mechanical Loadings

The constitutive relations and kinematic assumptions on the composite beam with shape memory alloy (SMA) arbitrarily embedded are discussed and the results related to the different kinematic assumptions are compared. As the approach of mechanics of materials is to study the composite beam with the SMA layer embedded, the kinematic assumption is vital. In this paper, we systematically study the kinematic assumptions influence on the composite beam deflection and vibration characteristics. Based on the different kinematic assumptions, the equations of equilibrium/motion are different. Here three widely used kinematic assumptions are presented and the equations of equilibrium/motion are derived accordingly. As the three kinematic assumptions change from the simple to the complex one, the governing equations evolve from the linear to the nonlinear ones. For the nonlinear equations of equilibrium, the numerical solution is obtained by using Galerkin discretization method and Newton-Rhapson iteration method. The analysis on the numerical difficulty of using Galerkin method on the post-buckling analysis is presented. For the post-buckling analysis, finite element method is applied to avoid the difficulty due to the singularity occurred in Galerkin method. The natural frequencies of the composite beam with the nonlinear governing equation, which are obtained by directly linearizing the equations and locally linearizing the equations around each equilibrium, are compared. The influences of the SMA layer thickness and the shift from neutral axis on the deflection, buckling and post-buckling are also investigated. This paper presents a very general way to treat thermo-mechanical properties of the composite beam with SMA arbitrarily embedded. The governing equations for each kinematic assumption consist of a third order and a fourth order differential equation with a total of seven boundary conditions. Some previous studies on the SMA layer either ignore the thermal constraint effect or implicitly assume that the SMA is symmetrically embedded. The composite beam with the SMA layer asymmetrically embedded is studied here, in which symmetric embedding is a special case. Based on the different kinematic assumptions, the results are different depending on the deflection magnitude because of the nonlinear hardening effect due to the (large) deflection. And this difference is systematically compared for both the deflection and the natural frequencies. For simple kinematic assumption, the governing equations are linear and analytical solution is available. But as the deflection increases to the large magnitude, the simple kinematic assumption does not really reflect the structural deflection and the complex one must be used. During the systematic comparison of computational results due to the different kinematic assumptions, the application range of the simple kinematic assumption is also evaluated. Besides the equilibrium study of the composite laminate with SMA embedded, the buckling, post-buckling, free and forced vibrations of the composite beam with the different configurations are also studied and compared.

Thermal stress wave and spallation induced by an electron beam

Thermal stress wave and spallation in aluminium alloy exposed to a high fluency and low energy electron beams are studied theoretically. A simple model for the study of energy deposition of electrons in materials is presented on the basis of some empirical formulae. Under the stress wave induced by energy deposition, microcracks and/or microvoids may appear in target materials, and in this case, the inelastic volume deformation should not vanish. The viscoplastic model proposed by Bodner and Partom with corresponding Gurson's yield function requires modification for this situation. The new constitutive model contains a scalar field variable description of the material damage which is taken as the void volume fraction of the polycrystalline material. Incorporation of the damage parameter permits description of rate-dependent, compressible, inelastic deformation and ductile fracture. The melting phenomenon has been observed in the experiment, therefore one needs to take into account the melting process in the intermediate energy deposition range. A three-phase equation of state used in the paper provides a more detailed and thermodynamical description of metals, particularly, in the melting region. The computational results based on the suggested model are compared with the experimental test for aluminium alloy, which is subjected to a pulsed electron beam with high fluency and low energy. (C) 1997 Elsevier Science Ltd.

Experiments about Simple Liquid Flows in Microtubes

The behavior of micro-scale flow is significant for the performance of Micro-Electro-Mechanical- Systems (MEMS) devices. Some experiments about liquid flow through microtubes with diameters about 3similar to20mum are presented here. The liquids used in our experiments include some simple liquids with small molecules, such as non-ion water and several kinds of organic liquids (CCL4, C6H5C2H5 and Isopropanol etc.). The flow rate and the normalized friction cocfficients were measured in micro-flow experimental apparatus. The results show that when the driven pressure varies from 0 to 1Mpa, the flow behaviors in 20mum microtube for both polar and non-polar liquids are in agreement with Hagen-Poiseuille law of the classical theory. It means that N-S equation based on continuous medium still acts well in this case. For higher pressure drop from 1 to 30Mpa, in the microtubes with diameter of 3similar to10mum, the normalized friction coefficients of organic liquids can't keep constant with pressure increases. However the non-ion water reveals different trends.