加热压电纤维复合材料圆板的横向自由振动

基于经典薄板理论和极正交各向异性材料的本构理论,建立了加热压电纤维复合材料圆板的线性振动控制微分方程。采用打靶法分别获得了加热压电纤维复合材料圆板在周边固支和简支情况下,无量纲固有频率随温度和电场强度变化的关系曲线,并分析了压电纤维体积分数、刚度参数、电场强度和温度变化对压电纤维复合材料圆板无量纲固有频率的影响。结果表明,一定体积分数或者电场强度下,压电纤维复合材料圆板的无量纲固有频率都随温度的升高而单调下降;同一温度下,刚度参数越小,无量纲固有频率越低;电场强度越大,无量纲固有频率越高。     

Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness

In the conventional theory of finite deformations of fibre-reinforced elastic solids it is assumed that the strain-energy is an isotropic invariant function of the deformation and a unit vector A that defines the fibre direction and is convected with the material. This leads to a constitutive equation that involves no natural length. To incorporate fibre bending stiffness into a continuum theory, we make the more general assumption that the strain-energy depends on deformation, fibre direction, and the gradients of the fibre direction in the deformed configuration. The resulting extended theory requires, in general, a non-symmetric stress and the couple-stress. The constitutive equations for stress and couple-stress are formulated in a general way, and specialized to the case in which dependence on the fibre direction gradients is restricted to dependence on their directional derivatives in the fibre direction. This is further specialized to the case of plane strain, and finite pure bending of a thick plate is solved as an example. We also formulate and develop the linearized theory in which the stress and couple-stress are linear functions of the first and second spacial derivatives of the displacement. In this case for the symmetric part of the stress we recover the standard equations of transversely isotropic linear elasticity, with five elastic moduli, and find that, in the most general case, a further seven moduli are required to characterize the couple-stress.     

Optimum material design for functionally gradient material plate

Summary Steady thermal stresses in a plate made of a functionally gradient material (FGM) are analyzed theoretically and calculated numerically. An FGM plate composed of PSZ and Ti-6Al-4V is examined, and the temperature dependence of the material properties is considered. A local safety factor is used for evaluation of the FGM's strength. It is assumed that top and bottom surfaces of the plate are heated and kept at constant thermal boundary conditions. The pairs of the surface temperatures, for which the minimum local safety factor can be of more than one, are obtained as available temperature regions. The temperature dependence of the material properties diminishes, available temperature region as compared with that for an FGM plate without it. The available temperature region of the FGM plate is wider than that of the two-layered plate, especially for the surface temperatures which are high at the ceramic surface and low at the metal side. The influence of different mechanical boundary conditions is examined, and available temperature regions are found to be different, depending on the mechanical boundary conditions. The influence of the intermediate composition on the thermal stress reduction is also investigated in detail for the surface temperatures which are kept at 1300 K at the ceramic surface and 300K at the metal side. Appropriate intermediate composition of the FGM plate can yield the local safety factor of one or more for the four mechanical boundary conditions at once. For the two-layered plate there does not exist, however, any appropriate pair of metal and ceramic thicknesses which would yield the local safety factor of one or more for the four mechanical boundary conditions at once. The influence of the intermediate composition on the maximization of the minimum stress ratio depends on the mechanical boundary conditions. Finally, the optimal FGM plates are determined.     

An adhesive wear model of fractal surfaces in normal contact

A generalized adhesive wear analysis that takes into account the effect of interfacial adhesion on the total load was developed for three-dimensional fractal surfaces in normal contact. A wear criterion based on the critical contact area for fully-plastic deformation of the asperity contacts was used to model the removal of material from the contact interface. The fraction of fully-plastic asperity contacts, wear rate, and wear coefficient are expressed in terms of the total normal load (global interference), fractal (topography) parameters, elastic–plastic material properties, surface energy, material compatibility, and interfacial adhesion characteristics controlled by the environment of the interacting surfaces. Numerical results are presented for representative ceramic–ceramic, ceramic–metallic, and metal–metal contact systems to illustrate the dependence of asperity plastic deformation, wear rate, and wear coefficient on global interference, surface roughness, material properties, and work of adhesion (affected by the material compatibility and the environment of the contacting surfaces). The analysis yields insight into the effects of surface material properties and interfacial adhesion on the adhesive wear of rough surfaces in normal contact.     

Investigation on the Thermoelastic Constant of Carbon Fibre Composites

Orthotropic materials show different thermo-elastic constants depending on their fibre orientation. While most materials undergo a positive elongation with increasing temperature, carbon fibres present a heat-shrink behaviour, which in carbon fibre composites has an important consequence on thermoelastic constants. A decrease in thermoelastic constant with frequency has already been observed in glass fibre composites. Experiments made on uniaxial carbon fibre composites showed that the longitudinal thermoelastic constant increases with the frequency, while the transverse constant decreases. Furthermore, due to the opposite signs of the thermoelastic carbon fibre constant and of the surrounding resin matrix, the absolute values of the longitudinal thermoelastic constant were ten times lower in CFRPs than in GFRPs. An analytical model could successfully reproduce the frequency dependence of the longitudinal thermoelastic constant, thus helping to explain the reason for the observed behaviour. Two calibration samples were used to obtain the thermoelastic constants in the longitudinal and transverse directions. The values of the thermoelastic constants were then applied to a test sample with fibres forming an angle of 10° to the load direction. The expected theoretical results were compared with the results experimentally obtained, showing good agreement. A preliminary calibration of the longitudinal and transverse thermoelastic constants proved to be a useful approach to obtaining the correct value of the thermoelastic constant in a generic direction.     

A parametric-experimental study of void growth in superplastic deformation

Substantial void growth in metals constitutes a problem in many industrial operations that utilize superplastic deformation. This is because of the likelihood of material failure due to such growth. Hence, there is a need to study void growth mechanisms in an effort to understand the parameters governing it. In this work, numerical and experimental studies of void growth, and the parameters that affect it, in a superplastically deforming (SPD) metal have been performed. In the numerical studies, using the finite-element method, a 1×2 sized thin plate (i.e. plane stress conditions) of a viscoplastic material with pre-existing holes has been subjected to a constant extension rate. The experimental studies were performed under similar conditions to the numerical ones and provided for qualitative comparison. The parameters affecting void growth in SPD are: m (the strain-rate sensitivity), void size (i.e. diameter) and the number (density) of existing voids. The results showed that increased m values produced strengthening and decreased the rate of void growth. In addition, larger initial void size (or, equivalently, a larger initial void fraction) had the effect of weakening the specimen through causing accelerated void growth. Finally, multiple holes had the effect of increasing the metal ductility by reducing the extent of necking and its onset. This was realized through diffusing the plastic deformation at the different hole sites and reducing the stress concentration. The numerical results were in good qualitative agreement with the experiment and suggested the need to refine existing phenomenological void growth models to include the dependence on the void fraction.     

Slip, stick, and reverse slip characteristics during dynamic fibre pullout

Inertial effects in the mechanism of fibre pullout (or push-in) are examined, with emphasis on how the rate of propagation of stress waves along the fibre, and thence the pullout dynamics, are governed by friction and the propagation of companion waves excited in the matrix. With a simple shear lag model (assuming zero debond energy at the fibre/matrix interface), the effect of uniform frictional coupling between the fibre and the matrix is accounted for in a straightforward way. Analytical solutions are derived when the pullout load increases linearly in time. The process zone of activated material is generally divided into two or three domains along the axis of the fibre. Within these domains, slip in the sense implied by the load, slip in the opposite sense (reverse slip), and stick may be observed. The attainable combinations define three regimes of behavior, which are realized for different material parameter values. The elastodynamic problem is also solved more accurately using a plane stress finite element method, with friction represented by an interfacial cohesive zone. The predictions of the shear lag theory are broadly confirmed.     

Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet

Various self-consistent polycrystal plasticity models for hexagonal close packed (HCP) polycrystals are evaluated by studying the deformation behavior of magnesium alloy AZ31B sheet under different uniaxial strain paths. In all employed polycrystal plasticity models both slip and twinning contribute to plastic deformation. The material parameters for the various models are fitted to experimental uniaxial tension and compression along the rolling direction (RD) and then used to predict uniaxial tension and compression along the traverse direction (TD) and uniaxial compression in the normal direction (ND). An assessment of the predictive capability of the polycrystal plasticity models is made based on comparisons of the predicted and experimental stress responses and R values. It is found that, among the models examined, the self-consistent models with grain interaction stiffness halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results. Among the available options, the Affine self-consistent scheme results in the best overall performance. Furthermore, it is demonstrated that the R values under uniaxial tension and compression within the sheet plane show a strong dependence on imposed strain. This suggests that developing anisotropic yield functions using measured R values must account for the strain dependence.     

Compressive strength of fibre composites with random fibre waviness

The compressive strength of unidirectional long fibre composites is predicted for plastic microbuckling from a random two-dimensional distribution of fibre waviness. The effect of the physical size of waviness is addressed by using couple stress theory, with the fibre bending resistance scaling with the fibre diameter d. The predicted statistical distribution of compressive strength is found using a Monte Carlo method. An ensemble of fibre waviness profiles is generated from an assumed spectral density of waviness and the compressive strength for each such realisation is calculated directly by the finite element method. The average predicted strength agrees reasonably with practical values, confirming the hypothesis that microbuckles can be initiated by fibre misalignment. It is found that the probability distribution of strength is well matched by a Weibull fit, and the dependence of the Weibull parameters upon the spectral density of waviness is determined. For the practical range of fibre distributions considered, it is concluded that the strength depends mainly upon the root mean square amplitude of fibre misalignment, with the shape of the power spectral density function playing only a minor role. An engineering model for predicting the compressive strength is proposed, akin to weakest link theory for materials containing flaws. A specimen containing randomly distributed waviness is examined to locate regions of high-fibre misalignment. The strength of each of these weak regions is estimated from a look-up table derived from calculations with idealised circular or elliptical patches of waviness. The strength of the composite is given by the failure stress associated with the weakest such patch. For random distributions of waviness, the predictions using this engineering approach are in good agreement with the direct calculations of strength using the finite element method.     

Stress analysis of notched anisotropic finite plates under mechanical and hygrothermal loads

Summary Notch-induced stress concentrations in anisotropic composite materials depend on their directional material properties, especially for uniaxially reinforced composites with high-modulus fibres. The design of notched high-performance composites requires therefore a special proof of their notched strength, which includes the structural parameters of the fibre/matrix combination, fibre orientation and layer arrangement. The assessment of the effects of the finite outer boundary is of practical importance when dimensioning critical notched regions. An anisotropic plate with finite dimensions and a hole in its center will be used here to model stress concentrations. The calculation is based on conformal mappings combined with complex-valued stress functions. The outer boundary is described using point-matching and the least-squares method. The solutions are conducive to the assessment of the essential influencing factors of material properties, geometry and loads. Notched finite plates made of fibre/matrix composites, mainly carbon-fibre reinforced polymers, will be presented as illustrations. Received 29 June 1998; accepted for publication 22 October 1998     

Dynamical analysis of cavitation for a transversely isotropic incompressible hyper-elastic medium: Periodic motion of a pre-existing micro-void

In this paper, the dynamical cavitation behavior is analyzed for a sphere composed of a class of transversely isotropic incompressible hyper-elastic materials, where there is a pre-existing micro-void in the interior of the sphere. A second-order non-linear ordinary differential equation that governs the motion of the initial micro-void is obtained by using the boundary conditions. On analyzing the qualitative properties of the solutions of the differential equation, some interesting conclusions are proposed. It is proved that the number of equilibrium points of the differential equation depends on the values of the material parameters, and that the phase diagrams of the equation are closed, smooth and convex trajectories. For any prescribed surface tensile dead-loads, the motion of the initial micro-void undergoes a non-linear periodic oscillation. The dependence of the periodic motion of the initial micro-void on material parameters and the radius of the initial micro-void is examined, and numerical results are also provided. It is worth pointing out that the conclusions in this paper can be used to describe approximately the physical implications of the dynamical formation of a cavity in the sphere.     

黏弹性层合圆柱壳的临界轴压分析

基于经典屈曲理论,研究了轴向受压黏弹性复合材料层合圆柱壳的临界屈曲载荷. 利用Boltzmann线性积分型本构关系描述铺设单层的各向异性黏弹性行为. 结合解析与数值 方法,由Donnell型屈曲控制方程以及边界条件的Laplace变换导出相空间的特征方程,根 据Laplace逆变换的极值定理,获得层合圆柱壳的瞬时弹性临界载荷与持久临界载荷. 针对 多组铺设方式,通过数值算例重点分析了临界载荷随铺设角的变化特征,两种临界载荷的峰 值点差异程度与铺设方式、几何参数以及材料类型的关系,得到了一些对黏弹性层合圆柱壳 的优化设计有参考价值的结论.     

WAVE PROPAGATION IN ELECTROSTRICTIVE MATERIALS UNDER BIASED FIELDS

I. INTRODUCTION Di?erent from piezoelectricity which is a linear coupling between mechanical and electric ?elds andcan only exist in anisotropic materials[1], electrostriction refers to the quadratic dependence of strainor stress on electric ?elds[2,3] …     

Influence of excitation amplitude on the characteristics of nonlinear butyl rubber isolators

The purpose of this study is to explore the advantages and characteristics of nonlinear butyl rubber (type IIR) isolators in vibratory shear by comparison with linear isolators. It is known that the mechanical properties of viscoelastic materials exhibit significant frequency and temperature dependence, and in some cases, nonlinear dynamic behavior as well. Nonlinear characteristics in shear deformation are reflected in mechanical properties such as stiffness and damping. Furthermore, even when the excitation amplitude is small the response amplitude may often be large enough that nonlinearities cannot be ignored. The treatment involves developing phenomenological models of the effective storage modulus and effective loss factor of a rubber isolator material as a function of excitation amplitude. The transmissibility of a nonlinear viscoelastic isolator is compared with that of a linear isolator using an equivalent linear damping coefficient. Forced resonance vibration and impedance tests are used to characterize nonlinear parameters and to measure the normalized transmissibility. It is found that as the excitation amplitude of the nonlinear viscoelastic isolator increases, the response amplitude decreases and the transmissibility is improved over that of the linear isolator for excitation frequency that exceeds a particular value governed by the temperature and excitation amplitude. The method of multiple scales and numerical simulations are used to predict the response characteristics of the isolator based on the phenomenological modeling under different values of system parameters.     

The onset and progression of damage in isotropic paper sheets

An experimental investigation is performed and analyzed in order to examine the onset and evolution of damage processes in thin isotropic paper sheets made of mechanical pulp. A microscopy technique has been used to estimate the relative fraction of bond and fibre breaks. It has been found that the active damage mechanism is bond failure, hence supporting the assumption of an isotropic scalar valued damage variable.All experiments have been performed by simultaneous with the mechanical loading monitoring the acoustic emission activity. Three different experimental setups have been designed offering the possibility to analyze the influence of stress gradients, as well as different levels of the ratios between the in-plane normal stresses, on the onset of damage. It is concluded that stress gradients in the paper specimens have a large influence on the onset of damage. When stress gradients are present a non-local theory has to be used in the analysis. In this way compliance with an isotropic damage criterion is achieved. The characteristic length, determining the gradient sensitivity, has been found to be of the same order of magnitude as some average fibre length.To study the evolution of the damage processes, wide and short specimens have been loaded in tension resulting in stable damage processes. With the assumptions made regarding the mechanical behavior of the paper material after onset of damage, the damage and the cumulative number of acoustic events curve correlates very well. The experimentally obtained data is used to determine material parameters in a proposed damage evolution law. It is found that the assumed damage evolution law can, for isotropic paper materials with bond rupture as the prevalent failure mechanism, be further simplified as only one specific material dependent damage evolution parameter has to be determined in experiments.     

Dependence of stress intensity factors on elastic constants for cracks in an orthotropic bimaterial with a thin film

An interface crack and a subinterface crack in an orthotropic bimaterial structure consisting of a thin film and a half plane substrate are analyzed. The orthotropic bimaterial structure is subjected to compressive load and bending moment per unit thickness. Complete expressions of stress intensity factors for the two cracks are obtained based on the path independence of the J integral, apart from one dimensionless parameter undetermined each. The dependence of the dimensionless parameters on material constants is examined. A reduction of the number of necessary material parameters for the parameters is made based upon the modified Stroh formalism. The explicit dependence of the dimensionless parameters on one orthotropic parameter for the film is determined by using the orthotropy rescaling technique. Variations of the dimensionless parameters with the other material parameters are also obtained through numerical computations.     

Unsteady mixed convection boundary-layer flow with suction and temperature slip effects near the stagnation point on a vertical permeable surface embedded in a porous medium

The unsteady mixed convection boundary-layer flow near the two-dimensional stagnation point on a vertical permeable surface embedded in a fluid-saturated porous medium with suction and a temperature slip effect is studied numerically. Similarity equations are obtained through the application of a similarity transformation technique. The shooting method is used to solve these similarity equations for different values of the mixed convection, wall mass suction, the unsteadiness and the slip parameters. Results show that multiple solutions exist for certain ranges of these parameters. Some limiting forms are then discussed, namely strong suction, the free convection limit, the situation when there is a large temperature slip and when the time dependence dominates.     

An anisotropic fibre-network model for mechano-sorptive creep in paper

In this paper a simplified network model for mechano-sorptive creep is presented, which is a further development of an earlier paper [Strömbro, J., Gudmundson, P., 2008. Mechano-sorptive creep under compressive loading – a micromechanical model. International Journal of Solids and Structures 45 (9), 2420–2450.]. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys a constitutive law that is non-linear. Fibre kinks are included in order to capture experimental observations of larger mechano-sorptive effects in compression than in tension. Moisture dependent material parameters and anisotropy in the fibre distribution have been introduced. Theoretical predictions based on the model are compared to experimental results for an anisotropic paper both under tensile and compressive loading at varying moisture content and it is found that the important features in the experiments are captured by the model. Different kinds of drying conditions have also been examined.