Characterization of high-loss viscoelastic elastomers

The behaviour of a variety of high-loss viscoelastic elastomers is described. Measurements were conducted using a novel micromechanics apparatus which is capable of creep, constant load rate, subresonant dynamic and resonant dynamic experiments in bending and torsion upon a single specimen. The range of equivalent frequency is from 10^–6 Hz to several kilohertz under isothermal conditions.     

非线性黏弹复合材料有效性质

提出了一个细观力学模型 , 用于预测非线性黏弹聚合物基复合材料的有效性质。该方法利用广义割线模量方法对单积分型热力学本构进行线性化 , 并运用 Laplace变换技术将黏性问题转化为弹性问题。利用热力学本构拟合高密度聚乙烯的实验数据 , 得到基体的材料参数。 利用该模型计算了玻璃微珠填充高密度聚乙烯复合材料(GB/HDPE)在恒应变率下的应力应变关系 , 计算结果与文献实验结果吻合较好。数值计算结果表明 GB/HDPE复合材料表现出明显的非线性力学行为。 该细观力学模型可以很好地预测复合材料非线性黏弹性性质。      

Deformation of extreme viscoelastic metals and composites

The figure of merit for structural damping and damping layer applications is the product of stiffness E and damping tan δ. For most materials, even practical polymer damping layers, E tan δ is less than 0.6 GPa. We consider several methods to achieve high values of this figure of merit: high damping metals, metal matrix composites and composites containing constituents of negative stiffness. As for high damping metals, damping of polycrystalline zinc was determined and compared with InSn studied earlier. Damping of Zn is less dependent on frequency than that of InSn, so Zn is superior at high frequency. High damping and large stiffness anomalies are possible in viscoelastic composites with inclusions of negative stiffness. Negative stiffness entails a reversal of the usual directional relationship between force and displacement in deformed objects. An isolated object with negative stiffness is unstable, but an inclusion embedded in a composite matrix can be stabilized under some circumstances. Ferroelastic domains in the vicinity of a phase transition can exhibit a region of negative stiffness. Metal matrix composites containing vanadium dioxide were prepared and studied. The concentration of embedded particles was sensitive to the processing method.     

An adaptive MsFEM for nonperiodic viscoelastic composites

We present a modification of the multiscale finite element method (MsFEM) for modeling of heterogeneous viscoelastic materials and an enhancement of this method by the adaptive generation of both meshes, ie, a macroscale coarse one and a microscale fine one. The fine mesh refinements are performed independently within coarse elements adjusting the microscale discretization to the microstructure, whereas the coarse mesh adaptation optimizes the macroscale approximation. Besides the coupling of the hp‐adaptive finite element method with the MsFEM we propose a modification of the MsFEM to accommodate for the analysis of transient nonlinear problems. We illustrate the efficiency and accuracy of the new approach for a number of benchmark examples, including the modeling of functionally graded material, and demonstrate the potential of our improvement for upscaling nonperiodic and nonlinear composites.     

Micromechanics of local viscoelastic buckling in thick composites

The time-dependent, local microbuckling of multilayered viscoelastic media is modeled with emphasis on bifurcation and imperfection sensitivity. The instability or ‘growth-of-waviness’-type analysis is carried out for initially straight fibers (bifurcation), as well as for initially wavy fibers (imperfection-sensitivity), assuming a perfect-slip condition at the fiber-matrix interface. The concept of dominant wavelength (i.e. the fastest growing wavelength within the Fourier spectrum), previously defined for viscoelastic bifurcation (Biot, M. A. ‘Mechanics of Incremental Deformations’, John Wiley and Sons, Inc., New York, 1965), is extended from the single fiber analysis (Bhalerao, M. and Moon, T., On the growth-of-waviness in fiber-reinforced polymer composites: viscoelastic bifurcation and imperfection sensitivity, ASME J. Appl. Mechanics, in press, 1995) to multiple fiber analysis for a multilayered medium. A parametric study is presented which covers a wide range of physically relevant values. The results for the multiple fiber analysis are found to be analogous to those for single fiber analysis. The bifurcation dominant wavelength depends negligibly on matrix properties, yet highly on the applied load. On the other hand, the imperfection-sensitive dominant wavelength is predicted to depend strongly on matrix properties, while negligibly on load. The imperfection-sensitive wavelength is the one important in composites processing and in-service behavior.     

复合材料固化相关黏弹性性能演化及残余应力分析

通过对复合材料固化度和温度相关黏弹性本构方程的分析,定义一个能综合反映固化度和温度等对复合材料黏弹性性能影响的无量纲参数De_m。当参数De_m都大于10~2时,复合材料基体处于流动状态;当参数De_m都小于10~(-2)时,复合材料为弹性状态;仅当部分参数De_m小于10~2而大于10~(-2)时,复合材料处于黏弹性状态。以AS4纤维/3501-6树脂复合材料为例,基于对其参数De_m在典型固化工艺过程中的演化,研究该复合材料黏弹性性能的发展过程,发现基于参数De_m分析得到的凝胶点时间与实验结果一致。根据复合材料黏弹性性能对残余应力发展的影响,将复合材料残余应力计算分为流动阶段和黏弹性阶段,并建立了相应的状态相关黏弹性本构模型。最后通过与原始模型预测结果的比较验证了提出的本构模型,表明本文提出的计算方法与原始黏弹性本构模型计算结果一致,但大大降低了计算所需的时间和存储空间。     

A model for anisotropic viscoelastic damage in composites

A model for continuous damage combined with viscoelasticity is proposed. The starting point is the formulation connecting the elastic properties to the tensor of damage variables. A hardening law associated with the damage process is identified from available experimental information and the rate-type constitutive equations are derived. This elastic damage formulation is used to formulate an internal variable approximation to viscoelastic damage in the form of a non-linear Kelvin chain. Elastic and viscoelastic equations are implemented into a finite element procedure. The code is verified by comparison with closed-form solutions in simplified configurations, and validated by fitting results of experimental creep tests.     

Micromechanics-based viscoelastic damage model for particle-reinforced polymeric composites

The objective of this study is to develop a micromechanics-based viscoelastic damage model that can predict the overall viscoelastic behavior of particle-reinforced polymeric composites undergoing damage. The emphasis here is that the present model successfully combines a rate-dependent viscoelastic constitutive model and a damage model. The Laplace transform based on the Boltzmann superposition principle and the ensemble-volume averaged method suggested by Ju and Chen (Acta Mech 103:103–121, 1994a; Acta Mech 103:123–144, 1994b) are extended toward effective viscoelastic properties. Further, the probability of the distribution function of Weibull (J Appl Mech 18:293–297, 1951) is adopted to describe a damage model that is dependent on damage parameters. A series of numerical simulations including parametric studies, and experimental comparisons are carried out to give insight into the potential capacity of the present micromechanics-based viscoelastic damage framework.     

Homogenization of viscoelastic composites with fibres of diamond-shaped cross-section

The present paper provides details on the application of asymptotic homogenization techniques to the analysis of viscoelastic composite materials with fibres of diamond-shaped cross-section. The Correspondence principle allows transforming the governing boundary value problems to quasistatic ones. Then, we apply the homogenization approach. For solving the cell problem for small volume fractions, the boundary shape perturbation procedure and the composite cylinder assemblage model are used. For a volume fraction equal to 1/2, we use the Dykhne–Keller–Mendelson formula. Matching of limit solutions by two-point Padé approximants gives a formula for the effective properties valid for any volume fraction from the interval [0, 0.5].     

Thermal-stress concentration near inclusions in viscoelastic random composites

The determination of thermal-stress concentrations near inclusions in viscoelastic random composites is concerned with the prediction of the overall response of random nonlinear viscoelastic multi-component media. The continuum considered here is assumed to be subjected to a finite deformation. First Piola’s stress tensor and deformation gradient are used as conjugate field variables in a fixed reference state. A nonlinear problem is investigated in a second-order approximation theory when the gradient deformation terms higher than second order are neglected. A convex potential function in a thermo-elastic problem and time functionals in a viscoelastic one are used to construct overall constitutive relations. The technique of surface operators developed by R. Hill and others is used to determine stress concentrations near inclusions for nonlinear matrix creep.     

Computational optimization of characteristics for composites of viscoelastic components

The problem of describing of the viscoelastic properties of composite materials that consist of more than one viscoelastic component is studied. It is supposed that the viscoelastic properties of the components are known. The difficulty in the application of the mixture theory arises in the cases when the properties are described by integral operators with different integral kernels. This difficulty is avoided by the approximations of the viscoelastic operators in the stress–strain relations. A method is proposed to obtain appropriate approximations that reduce all the viscoelastic operators to a general kernel using rational approximations of their Laplace transforms. The proposed method allows for the reduction of the approximation error for related operators. Examples are given for the adjustment of viscoelastic functions in the cases of increase and decrease of functions parameter.     

Determination of effective damping characteristics of fiber-reinforced viscoelastic composites

A numerical method for the determination of effective complex moduli and vibration decrements of fiber-reinforced viscoelastic composites is proposed, which is based on the finite element modeling of representative volume element and equation of the elastic and viscous parts of the strain energy of composite and quasi-homogeneous material volumes. Translated from Problemy Prochnosti, No. 4, pp. 124–132, July–August, 2009.     

Problems of identification of mechanical characteristics of viscoelastic composites

Summary The problem of modelling and identification of viscoelastic properties of composites as asphalt concrete, based on experimental investigations is the subject of this paper. Only viscoelastic properties of such materials are taken into consideration and usefulness of linear constitutive relations in differential form is examined. The identification problem is formulated in terms of sensitivity analysis and optimization theory. An approach to select the best from the considered class of material models is proposed and the values of associated material parameters are determined by minimization of objective function representing a measure of a difference between theoretically calculated and experimentally obtained response of a sample to sinusoidal loading. Obtained this way, results are compared with those calculated using the method based on the approach proposed by Bland and Lee [1] for calculation material parameters of Burgers model. It has been shown that differential constitutive relations with constant coefficients have very restricted application in the considered case because they are in force in narrow domains of excitation frequency. The application of models with frequency-dependent coefficients is one of the possible solutions of this problem [2]. Another approach can also be proposed based on the application of fractional calculus in viscoelasticity, see Bagley and Torvik [3].     

Dynamic mechanical analysis of some randomly-oriented viscoelastic short-fiber composites

The mechanical properties of two series of composites consisting of tanned leather fibers in an ethylene-vinyl acetate copolymer matrix were studied by means of tensile and dynamic mechanical tests. The effect of fiber content on Young's modulus and the viscoelastic properties was studied by using five distinct fiber concentrations. Dynamic measurements were carried out at a frequency of 11 Hz and temperatures from - 70 to 80°C. The applicability of the Hashin correspondence principle was tested in order to provide a better understanding of the fiber content effect on the viscoelastic properties of these composites.     

Glass transition and viscoelastic behaviour of partially cured composites

For this study, two tests were conducted in order to investigate the cure monitoring of composite parts utilizing XMTM-49 (carbon/epoxy composite) as the specimen. The first test involved the use of a dynamic mechanical thermal analyzer to investigate the nature of the loss modulus while the second test incorporated a differential scanning calorimeter to evaluate the degree of cure of the composite.

From the results of the research, it was found that the loss modulus is an extremely sensitive cure monitoring indicator for composites beyond 70% cured. This is a significant finding since traditional ultrasonic procedures could only be effective in monitoring the cure of composite structures when the degree of cure reaches approximately 70% but decreases when the cure reaches 80% or more. Therefore, it is recommended that future developments should focus attention on a non-contact technique for measuring loss modulus for cure monitoring.     

Deformation in viscoelastic sandwich composites subject to moisture diffusion

This study analyzes the effect of moisture diffusion on the deformation of viscoelastic sandwich composites, which are composed of orthotropic fiber-reinforced laminated skins and viscoelastic polymeric foam core. It is assumed that the elastic and time-dependent (transient) moduli at any particular location in the foam core depend on the moisture concentration at that location. Sequentially coupled analyses of moisture diffusion and deformation are performed to predict overall performance of the studied viscoelastic sandwich systems. Time and moisture dependent constitutive model is used for the polymer foam core, while skins are assumed linear elastic. The overall time-dependent responses of the sandwich composites subject to moisture diffusion are analyzed using finite element (FE) method. Experimental data available in the literature and analytical solutions are used to support convergence studies in the FE analyses. Contributions of moisture dependent elastic and the time-dependent moduli to the overall stress, strain and displacement field are studied. FE analyses of the delamination between skins and core in sandwich composite under combined moisture diffusion and mechanical loading are also performed.     

On attenuation and measurement of Lamb waves in viscoelastic composites

In this work, the influence of viscoelastic material properties, as featured by fibre reinforced plastics, on the measurement of Lamb waves with the aid of surface-applied piezoelectric sensors is examined. The focus points are frequency dependent material dampening and dispersion on the one hand and the impact of sensor size, wave excitation and measurement method on the other hand. The dependence of the measured wave propagation characteristics and the deviation from the actual characteristics is investigated to assess the relevance for Lamb wave based nondestructive testing and structural health monitoring methods. The sensor responses of piezoelectric sensors bonded to the surface of a viscoelastic composite are predicted by a comprehensive model including these influencing factors. The modelling approach is compared with experimentally measured values to evaluate both the methods and the relevance of the influencing factors.     

Effective thermal properties of viscoelastic composites having field-dependent constituent properties

This study introduces a micromechanical model for predicting effective thermal properties (linear coefficient of thermal expansion and thermal conductivity) of viscoelastic composites having solid spherical particle reinforcements. A representative volume element (RVE) of the composites is modeled by a single particle embedded in the cubic matrix. Periodic boundary conditions are imposed to the RVE. The micromechanical model consists of four particle and matrix subcells. Micromechanical relations are formulated in terms of incremental average field quantities, i.e., stress, strain, heat flux and temperature gradient, in the subcells. Perfect bonds are assumed along the subcell’s interfaces. Stress and temperature-dependent viscoelastic constitutive models are used for the isotropic constituents in the micromechanical model. Thermal properties of the particle and matrix constituents are temperature dependent. The effective coefficient of thermal expansion is derived by satisfying displacement and traction continuity at the interfaces during thermo-viscoelastic deformations. This formulation leads to an effective time–temperature–stress-dependent coefficient of thermal expansion. The effective thermal conductivity is formulated by imposing heat flux and temperature continuity at the subcells’ interfaces. The effective thermal properties obtained from the micromechanical model are compared with analytical solutions and experimental data available in the literature. Finally, parametric studies are also performed to investigate the effects of nonlinear thermal and mechanical properties of each constituent on the overall thermal properties of the composite.     

On attenuation and measurement of Lamb waves in viscoelastic composites

In this work, the influence of viscoelastic material properties, as featured by fibre reinforced plastics, on the measurement of Lamb waves with the aid of surface-applied piezoelectric sensors is examined. The focus points are frequency dependent material dampening and dispersion on the one hand and the impact of sensor size, wave excitation and measurement method on the other hand. The dependence of the measured wave propagation characteristics and the deviation from the actual characteristics is investigated to assess the relevance for Lamb wave based nondestructive testing and structural health monitoring methods. The sensor responses of piezoelectric sensors bonded to the surface of a viscoelastic composite are predicted by a comprehensive model including these influencing factors. The modelling approach is compared with experimentally measured values to evaluate both the methods and the relevance of the influencing factors.