A new constitutive equation for the long-term creep of polymers based on physical aging

Based on the observation that during long-term creep the viscosity of polymers will continue to increase due to physical aging, a new constitutive equation is derived to describe the long-term creep behavior of polymers that are chrono-rheologically simple. The theory is developed using the concept of effective time for such materials whose long-term creep compliances with various aging times are characterized by a horizontal shift on the log(t)-scale. The derivation makes use of the basic mathematical structure for such a horizontal shift, with a result that is both sufficient and necessary. A linear viscosity function is found to be required for such a material, and the corresponding shift rate for both the long-term creep and the short-time creep is found to increase with aging time t_e, reaching an asymptotic value of unity. This theory improves Struik's (1978) classic theory for the special class of chrono-rheologically simple materials, in that, when the aging time is sufficiently long, both theories are identical, but when it is short, the present one can account for the transition to the asymptotic state. The developed effective-time theory is then extended to a polymer–matrix composite to predict the effect of physical aging on the long-term creep of a fiber-reinforced composite material.     

Numerical-graphical method for determining characteristics of damaged viscoelastic materials

A method for determining the material functions of nonlinear endochronic theory of aging viscoelastic materials (NETAVEM) with preliminary mechanical damage was developed. The proposed method is based on an analysis of the differences between two graphs of the stress dependence on time obtained in tension with the same constant speed of two specimens made of the same filled polymer material. One of the specimens was not preloaded, and the other was preloaded. The reduced time [1] contained in the NETAVEM constitutive relations and its dependence on the actual time are determined by the distances from the stress axis to two points corresponding to the same stress value and lying on the graphs for the damaged and undamaged specimens. The relaxation kernel is determined in the experiment with the undamaged specimen. These two material functions and the curve obtained for the damaged specimen are used to obtain the NETAVEM aging function, and then the function of viscosity can be calculated. As a result, all characteristics of the damaged material become known, and the strength of structures made of this material can be calculated.     

第三型应变时效的提出与研究进展

第三型应变时效现象的发现使得传统的对于金属塑性流动行为的认识、位错的热激活理论以及常见的金属热粘塑性本构模型均需要进一步完善。为了系统地认识第三型应变时效,首先介绍了第三型应变时效现象区别于静态应变时效和Portevin-Le Chatelie动态应变时效的宏观特征,其次,对第三型应变时效的微观机理以及第三型应变时效与Portevin-Le Chatelier动态应变时效、蓝脆现象以及机械波谱的关联性进行了系统总结。最后,介绍了包含第三型应变时效的金属热黏塑性本构模型的发展。     

基于频率二阶摄动的结构损伤识别方法

结构损伤的定位和定量是结构健康监测的关键技术之一。本文将矩阵摄动理论、结构振动理论和有限元理论相结合推导出结构固有频率变化的二阶摄动公式,由此公式可以反演结构的损伤位置与损伤程度。该方法仅需要在役结构的固有频率测量值就能识别出结构的损伤位置和损伤程度,而且还可以识别出结构的老化程度。通过数值仿真算例证明了该方法的有效性和实用性。该方法可用于大型结构的损伤识别和健康监测。     

The dynamics of structural and functional complexity across the lifespan

The paper addresses the process of human physiological development and aging from the perspective complexity at the structural level and functional levels. The goal is to present a view of the human lifespan as a continuous increase in structural complexity of the human system, resulting in increased independence of the physiological subsystems. This brings about an increase in functional complexity early in the lifespan and an eventual loss of complexity during human aging (Lipsitz & Goldberger, 1995). Different nonlinear dynamics concepts are presented as a means of providing support for this theory of human aging and development.     

新型高分子固化材料耐老化性能的试验研究

因一般高分子材料容易老化 ,尤其是在沙漠环境下 ,强烈的热光辐射、氧化更加速其老化过程。SH为新型高分子固化材料。本文通过SH固化沙体的室内老化试验 ,初步研究了SH的耐老化特征。结果表明 ,在间断或连续紫外线辐照下 ,SH耐老化性能优于同类其他固沙剂 ,可用于沙漠地区固沙     

物理老化对玻璃态高聚物非线性蠕变行为的影响

在不同应力水平下对经历不同老化时间的有机玻璃(PMMA)进行常温蠕变测试,分析物理老化和应力对材料蠕变柔量函数的影响.分析表明,老化时间对PMMA蠕变行为的影响满足流变简单性规律,即不同老化时间的蠕变柔量曲线可以沿对数时间轴平移而叠加到参考曲线上.取最长的老化时间为参考状态,依时间-老化时间等效原理,得到了各应力水平下的蠕变柔量主曲线.老化移位因子与老化时间在双对数坐标图上呈现线性关系,其负斜率就是老化移位率.结果表明,老化移位率随应力的增高而减小.     

One method of solution of problems in the linear theory of viscoelasticity for aging anisotropic materials

A method of solution of problems in the linear theory of viscoclasticity for aging anisotropic materials is discussed. The method is based on evaluation of irrational functions of nondiffcrence viscoelasticity operators using the theory of continued fractions. It is shown that operator-valued continuedS-fractions converge for a wide class of integral Voltcrra operators. Application of the method is illustrated by the evaluation of an irrational function of a linear combination of nondiffcrence-type resolvent operators obtained in the solution of a concrete problem of failure of an aging anisotropic viscoclastic body. Translated from Prikladnaya Mekhanika, Vol. 34, No. 11, pp. 60–65, November, 1998.     

Designing with scattered-light photoelasticity

Scattered-light photoelasticity can be utilized in locating ‘critical’ stress points in a structural component and can be further utilized in experimentally reshaping the structural component's surface to minimize stress in critical regions. The theory and techniques to accomplish this experimental design are noted in the paper.     

Long-term crack resistance of aging viscoelastic composite in static loading

The safe load and crack aging period are determined for an aging orthotropic plate on the basis of the theory of subcritical crack growth, which was proposed by A. A. Kaminskii. As an example, the safe load and crack incubation period are plotted for a ferroconcrete plate. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 85–89, February, 1999.     

Delayed Fracture of an Aging Viscoelastic Composite under Plane Strain

The theory of delayed fracture of cracked viscoelastic bodies and the method of continued fractions are used to study the problem on the delayed fracture of an unidirectional fibrous composite subjected to uniaxial tension under plane-strain conditions. The aging viscoelastic binder contains a mode I macrocrack, which is parallel to the fibers. The results of a numerical crack-resistance analysis of a composite whose aging properties are described by the Volterra operator with the Maslov–Arutyunyan kernel are presented. A convergence analysis is made of the expansion of an irrational function of the resolvent Volterra operator into a continued fraction.     

多自由度参激系统稳定性的数值分析

提出多自由度周期参激系统稳定性的数值直接法。通过将扰动方程表示成状态方程形式,再根据Flo-quet理论将扰动解表示成指数特征分量与周期分量之积,并将其周期分量与系统周期系数展成Fourier级数,导出一系列代数方程,建立矩阵特征值问题,从而由数值求解特征值可直接确定参激系统的稳定性。该方法可用于一般周期参激阻尼系统,特征值矩阵不含逆子阵。应用于斜拉索在支座周期运动激励下的参激振动不稳定性分析,数值结果表明该方法的有效性。     

Plane nonaxisymmetric deformation of a viscoelastic cylinder with consideration of its physical and geometric nonlinearity

The nonaxisymmetric plane problem of the nonlinear theory of viscoelasticity is solved for a cylinder reinforced by an elastic circular shell. The cylinder has an internal cut resembling a Maltese cross in shape. The identification of the nonlinear endochronous theory of aging viscoelastic materials is conducted by a genetic algorithm method on the basis a nonmonotonic experimental stress-strain dependence. Some numerical results obtained for the stress-strain state of this cylinder under the action of internal pressure are discussed with consideration of the above physical nonlinearity and the finite logarithmic strains.     

Flow stability in a channel with porous walls

We study the stability of the flow which forms in a plane channel with influx of an incompressible viscous fluid through its porous parallel walls. Under certain assumptions the study of the stability reduces to the solution of modified Orr-Sommerfeld equation accounting for the transverse component of the main-flow velocity. As a result of numerical integration of this equation we find the dependence of the local critical Reynolds number on the blowing Reynolds number R₀, which may be defined by two factors: the variation of the longitudinal velocity profile with R₀ and the presence of the transverse velocity component. A qualitative comparison is made of the computational results with experimental data on transition from laminar to turbulent flow regimes in channels with porous walls, which confirms that it is necessary to take into account the effect of the transverse component of the main-flow velocity on the main-flow stability in the problem in question.Flows in channels with porous walls are of interest for hydrodynamic stability theory in view of the fact that they can be described by the exact solutions of the Navier-Stokes equations by analogy with the known Poiseuille and Couette flows. However, in contrast with the latter, the flows in channels with porous walls (studies in [1], for example) will be nonparallel.The theory of hydrodynamic stability of parallel flows has frequently been applied to nonparallel flows (in the boundary layer, for example). In so doing the nonparallel nature of the flow has been taken into account only by varying the longitudinal velocity component profiles. A study was made in [2, 3] of the effect of the transverse component of the main flow on its stability. In the case of the boundary layer in a compressible gas, a considerable influence of the transverse velocity component on the critical Reynolds number was found in [2] and confirmed experimentally. A strong influence of the transverse velocity component on the instability region was also found in [3] in a study of the flow stability in a boundary layer with suction for an incompressible fluid.     

A micropolar mixture theory of multi-component porous media

A mixture theory is developed for multi-component micropolar porous media with a combination of the hybrid mixture theory and the micropolar continuum theory. The system is modeled as multi-component micropolar elastic solids saturated with multi- component micropolar viscous fluids. Balance equations are given through the mixture theory. Constitutive equations are developed based on the second law of thermodynamics and constitutive assumptions. Taking account of compressibility of solid phases, the volume fraction of fluid as an independent state variable is introduced in the free energy function, and the dynamic compatibility condition is obtained to restrict the change of pressure difference on the solid-fluid interface. The constructed constitutive equations are used to close the field equations. The linear field equations are obtained using a linearization procedure, and the micropolar thermo-hydro-mechanical component transport model is established. This model can be applied to practical problems, such as contaminant, drug, and pesticide transport. When the proposed model is supposed to be porous media, and both fluid and solid are single-component, it will almost agree with Eringen＇s model.     

高龄混凝土表面碳化与应力腐蚀关系的研究

对多栋在役80年的混凝土建筑进行调查,检测了不同受力状态下的高龄混凝土构件的表面回弹值,并设计了一组混凝土构件老化室内模拟实验,用以分析高龄混凝土结构表面碳化发展机理。研究结果表明:普通混凝土的表面碳化速度与结构应力状态密切关联,处于拉应力状态的区域,其碳化深度明显大于压应力或无应力区域,表面碳化成为微观裂纹形成的基础,而微观裂纹的扩展将导致钢筋的锈蚀,最终导致结构承载力下降。只有处于低应力状态的混凝土才有可能达到理想的在役年限。该结论对于正确评估混凝土结构的寿命提供了实验依据。     

Homogenization-based constitutive models for magnetorheological elastomers at finite strain

This paper proposes a new homogenization framework for magnetoelastic composites accounting for the effect of magnetic dipole interactions, as well as finite strains. In addition, it provides an application for magnetorheological elastomers via a “partial decoupling” approximation splitting the magnetoelastic energy into a purely mechanical component, together with a magnetostatic component evaluated in the deformed configuration of the composite, as estimated by means of the purely mechanical solution of the problem. It is argued that the resulting constitutive model for the material, which can account for the initial volume fraction, average shape, orientation and distribution of the magnetically anisotropic, non-spherical particles, should be quite accurate at least for perfectly aligned magnetic and mechanical loadings. The theory predicts the existence of certain “extra” stresses—arising in the composite beyond the purely mechanical and magnetic (Maxwell) stresses—which can be directly linked to deformation-induced changes in the microstructure. For the special case of isotropic distributions of magnetically isotropic, spherical particles, the extra stresses are due to changes in the particle two-point distribution function with the deformation, and are of order volume fraction squared, while the corresponding extra stresses for the case of aligned, ellipsoidal particles can be of order volume fraction, when changes are induced by the deformation in the orientation of the particles. The theory is capable of handling the strongly nonlinear effects associated with finite strains and magnetic saturation of the particles at sufficiently high deformations and magnetic fields, respectively.     

The determination of plough draught—Part I. prediction from soil and meteorological data with cone index as the soil strength parameter

Using cone index as an indication of soil strength, empirical equations are developed in accordance with soil mechanics theory to relate soil moisture content to plough draught. The plough draught equation comprises a quasi-static component dependent on cone index and a dynamic component which is a function of the soil specific weight, plough speed and mouldbard tail angle. It is further argued that the cohesive and frictional components of the cone penetration resistance can be predicted by means of a simple equation comprising a reciprocal function of the square of the soil moisture content and a linear function of the soil specific weight. The cone index equation explained 98% of the experimental data for threthree soils over a wide range of moisture contents. These empirical equations, together with a soil moisture model, provide a method of predicting plough draught directly from soil and meteorological data.     

Measurement of residual stress using interferometric moiré: A new insight

The use of interferometric moiré and hole drilling to determine residual stress has been well reported and accepted for stress fields whose principal directions can be predicted well enough to permit the moiré grids to be aligned with the principal strain axes. When the principal strains do not align themselves with the grid axes, a third strain component can be obtained by working with the diagonal pitch of the moiré grid, but this requires resetting the optical bench to the lower frequency. Diffraction efficiency is lost, with an additional loss in sensitivity. In this paper, the authors determine the shear strain component by observing the rotation of the moiré fringes in close proximity to the hole. The results of experiments on a specimen containing a model residual stress distribution are presented and compared with the theoretical prediction. Finally, the isothetic contours, based on elastic theory, were computed and plotted for several cases to verify this proposition. These results and the expected residual stress distribution are also compared to the experimentally obtained moiré fringes.     

Elastic recovery of immiscible blends 1. Analysis after steady state shear flow

Due to the interfacial tension, immiscible blends can show an elastic recovery that is substantially larger than that of their pure components. Here it is attempted to relate the elastic recovery after steady shear flow to the underlying morphology. On the one hand, the predictions of the Palierne and the Doi-Ohta models are calculated for the flow conditions during recoil. On the other hand, systematic recoil experiments after steady state shearing have been performed on a model blend. As the component polymers hardly show any recoil under the stresses applied in these tests, the measured recovery can be attributed completely to the action of the interface. Comparison of the model predictions with the experimental results shows that the recoverable strain can be derived quantitatively from the linear Palierne theory. Although the droplet deformation remained limited during the preshear, the retardation time predicted by this model has to be multiplied by the aspect ratio of the droplet phase to the power 2/3 to describe the experiments. For conditions in which the material does not show an intrinsic length scale, particular scaling relations as derived from the Doi-Ohta theory are found to apply also to recoil. Received: 5 August 1998 Accepted: 17 November 1998