复合材料粘弹性本构关系与热应力松弛规律研究Ⅱ:数值分析

给出了预测复合材料粘弹性松弛模量、等效热应力松弛系数和等效时变热膨胀系数的均匀化方法的有限元数值实现步骤, 研究了单向纤维复合材料随温度变化的粘弹性本构关系, 以及热应力松弛规律和热膨胀系数的时变特征。单向纤维复合材料的一维热变形分析数据显示了热应变对时间的强烈依赖关系;以数值形式给出的等效热应力松弛模量对时间的依赖关系表明, 等效的热应力松弛模量对时间的依赖性较弱, 其冲击模量和渐近模量只相差0.4 %。     

Viscoplastic response and creep failure time prediction of polymers based on the transient network model

The nonlinear viscoelastic/viscoplastic response of polymeric materials is described by a new model based on previous works in terms of monotonic loading, stress–relaxation, and creep. In the proposed analysis, following a constitutive equation of viscoelasticity, based on the transient network theory, essential modifications are introduced, which account for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. In addition, viscoplastic response is successfully analyzed by a proper kinematic formulation, which is combined with a functional form of the rate of plastic deformation. A three-dimensional constitutive equation is then derived for an isotropic incompressible medium. This analysis is capable of capturing the main aspects of inelastic response and the instability stage taking place at the tertiary creep, related to the creep failure. Model simulations described successfully the experimental data of polypropylene, which were performed elsewhere.     

Micromechanically Established Constitutive Equations for Multiphase Materials with Viscoelastic–Viscoplastic Phases

A model for viscoelastic–viscoplastic solids is incorporated in a micromechanical analysis of composites with periodic microstructures in order to establish closed-form coupled constitutive relations for viscoelastic–viscoplastic multiphase materials. This is achieved by employing the homogenization technique for the establishment of concentration tensors that relate the local elastic and inelastic fields to the externally applied loading. The resulting constitutive equations are sufficiently general such that viscoelastic, viscoplastic and perfectly elastic phases are obtained as special cases by a proper selection of the material parameters the phase. Results show that the viscoelastic and viscoplastic mechanisms have significant effect on the global stress-strain, relaxation and creep behavior of the composite, and that its response is strongly rate-dependent in the reversible and irreversible regimes.     

Isothermal physical aging characterization of Polyether-ether-ketone (PEEK) and Polyphenylene sulfide (PPS) films by creep and stress relaxation

This paper considers the experimental characterization of isothermal physical aging of PEEK and PPS films using a dynamic mechanical analyzer. Using the short-term test method established by Struik, momentary creep and stress relaxation curves were measured at several temperatures within 15–35°C below the glass transition temperature (T _g ) at various aging times. Stress and strain levels were such that the materials remained in the linear viscoelastic regime. These curves were then shifted together to determine momentary master curves and shift rates using the PHYAGE program. In order to validate the obtained isothermal physical aging behavior, the results of creep and stress relaxation testing were compared and shown to be consistent with one another using appropriate interconversion of the viscoelastic material functions. Time–temperature superposition of the master curves was also performed. The temperature shift factors and aging shift rates for both PEEK and PPS were consistent for both creep and stress relaxation test results.     

A semi-analytical integration method for the numerical simulation of nonlinear visco-elasto-plastic materials

A semi-analytic integration method is proposed, which can be used in numerical simulation of the mechanical behavior of nonlinear viscoelastic and viscoplastic materials with arbitrary stress nonlinearity. The method is based upon the formalism of Prony series expansion of the creep response function and accepts arbitrary stress protocols as input data. An iterative inversion technique is presented, which allows for application of the method in routines that provide strain and require stress as output. The advantage with respect to standard numerical integration methods such as the Runge-Kutta method is that it remains numerically stable even for integration over very long time steps during which strain may change considerably due to creep or recovery effects. The method is particularly suited for materials, whose viscoelastic and viscoplastic processes cover a very wide range of retardation times. In the case of simulation protocols with phases of slowly varying stress, computation time is significantly reduced compared to the standard integration methods of commercial finite element codes. An example is given that shows how the method can be used in three dimensional (3D) constitutive equations. Implemented into a Finite Element (FE) code, the method significantly improves convergence of the implicit time integration, allowing longer time increments and reducing drastically computing time. This is shown in the case of a single element exposed to a creep and recovery cycle. Some simulations of non-homogeneous boundary value problems are shown in order to illustrate the applicability of the method in 3D FE modeling.     

复合材料蠕变本构关系及实验测定Ⅰ.本构关系

蠕变是复合材料最重要的力学性能之一,实验表明:复合材料在蠕变条件下的变形可以分为弹性变形、粘弹性变形和粘塑性变形.应用不可逆过程的热力学和广义变量的概念可以分析材料的蠕变变形.本文首先回顾了热力学的基本方程;基于Schapery本构关系的假设和思路推导了蠕变本构关系的一般形式,其中包括弹性变形、粘弹性变形和粘塑性变形;考虑到广义力选取的不唯一性,本文提出了广义力选取的原则以使得到的本构关系尽可能地简单;由此本文给出了复合材料的一维蠕变,各向同性复合材料的二维蠕变和纤维增强复合材料平面内的蠕变的本构关系.     

Viscoelastic incremental formulation using creep and relaxation differential approaches

A new incremental formulation in the time domain for linear, non-ageing viscoelastic materials undergoing mechanical deformation is presented in this work. The formulation is derived from linear differential equations based on a discrete spectrum representation for the creep and relaxation tensors. The incremental constitutive equations are then obtained by finite difference integration. Thus the difficulty of retaining the stress and strain history in computer solutions is avoided. A complete general formulation of linear viscoelastic stress analysis is developed in terms of increments of strains and stresses in order to establish the constitutive stress–strain relationship. The presented method is validated using numerical simulations and reliable results are obtained.     

玻璃态高聚物PMMA的应变软化—强化效应

讨论了玻璃态高聚物PMMA在单轴压缩下的受力变形行为。对加卸载循环的应力-应变曲线,建立了能作理论拟合计算的材料宏观本构理论模型和关系方程。拟合计算表明,理论和实测曲线吻合情况非常良好:相关系数>99.5％,最大应力偏差≯5MPa。着重讨论了屈服后的应变软化和强化效应。对于软化效应,提出了一种新的以粘弹变形的滞后松弛效应为内容的粘弹软化效应。对于强化效应,则讨论了取向强化和粘弹强化两种可能情况。在所研究的应变范围内,认为是粘弹软化和取向强化两种因素的抗衡,决定了屈服后应力-应变曲线的走向特性。     

Creep and recovery of nonlinear viscoelastic materials of the differential type

In this work, the creep and recovery properties of rubberlike viscoelastic materials in simple shear are studied by two special constitutive equations for isotropic, nonlinear incompressible viscoelastic material of the differential type. The creep and recovery processes are of significant importance to both the mechanics analysis and engineering applications. The constitutive equations introduced in this work generalize the Voigt-Kelvin solid and the 3-parameter model of classical linear viscoelasticity. They describe the uncoupled non-Newtonian viscous and nonlinear elastic response of an isotropic, incompressible material. The creep and recovery processes are treated for simple shear deformation superimposed on a longitudinal static stretch. Closed form solutions are provided and both processes are described effectively by the exponential function.     

Creep and relaxation contribution tensors for spheroidal pores in hereditary solids: fraction-exponential operators approach

In this paper, we introduce creep and relaxation contribution tensors that describe the effect ofindividual pores on the overall viscoelastic properties of a porous material. Explicit analytical expressions for these tensors are obtained using the elastic–viscoelastic correspondence principle and the Laplace transform. This becomes possible when viscoelastic properties are expressed in terms of fraction-exponential operators of Rabotnov (J Appl Math Mech (PMM) 12:53–62, 1948). Creep and relaxation contribution tensors can serve as the basic building blocks for the calculation of overall viscoelastic properties of porous hereditary materials.     

The effect of particle shape on the mechanical properties of filled polymers

The existing models for predicting the elastic moduli of polymers dispersed with particles of shape other than spheres and continuous fibres are reviewed. The applicability and limitation of these equations are discussed. The emphasis of the review is to seek a unified understanding and approach to the effect of particle shape at finite concentration on the elastic moduli, thermal expansion coefficient, stress concentration factor, viscoelastic relaxation modulus and creep compliance of filled polymers. The effects of anisotropic particle shape on mechanical properties of polymeric composites are clearly illustrated. Attention is also drawn to the relationship between elastic moduli, thermal expansion, creep elongation and stress relaxation moduli.     

Stress Relaxation of Nonlinear Thermoviscoelastic Materials Predicted from Known Creep

A method to predict the stress relaxation response of nonlinear thermoviscoelastic materials from known creep data is presented. For given nonlinear creep properties, and creep compliance represented by the Prony series, it is shown that the Schapery creep model can be transformed into a set of first order nonlinear differential equations. By solving these equations the nonlinear stress relaxation curves for different strain and temperature levels are established. The strain/temperature-dependent constitutive equation can then be constructed for any nonlinear thermoviscoelastic model, as needed for engineering applications. This revised version was published online in July 2006 with corrections to the Cover Date.     

A model for the Mullins effect during multicyclic equibiaxial loading

In this paper, we derive a model to describe the cyclic stress softening of a carbon-filled rubber vulcanizate through multiple stress–strain cycles with increasing values of the maximum strain, specializing to equibiaxial loading. Since the carbon-filled rubber vulcanizate is initially isotropic, we can show that following initial equibiaxial loading the material becomes transversely isotropic with preferred direction orthogonal to the plane defined by the equibiaxial loading. This is an example of strain-induced anisotropy. Accordingly, we derive nonlinear transversely isotropic models for the elastic response, stress relaxation, residual strain and creep of residual strain in order to model accurately the inelastic features associated with cyclic stress softening. These ideas are then combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation for the cyclic stress softening of a carbon-filled rubber vulcanizate. The model developed includes the effects of hysteresis, stress relaxation, residual strain and creep of residual strain. The model is found to compare extremely well with experimental data.     

A maximum dissipation thermodynamic multi-scale model for the dynamic response of the arterial elastin–water system

The mechanical response of the elastin–water system in an artery wall is viscoelastic. Elastin in vivo must operate in the rubbery region, i.e., above the glass transition, that depends on moisture content. A dynamic multi-scale time-dependent evolution equation is presented for the mechanical response of the elastin–water system that captures the effect of moisture content on the glass transition of the elastin. To define non-equilibrium evolution processes, the construction requires only a hyperelastic strain energy density function describing the long-term behavior and the thermodynamic relaxation modulus that describes the relaxation speed of non-equilibrium processes. The thermodynamic relaxation modulus also relates spatial scales, the molecular scale including moisture bonding to the bulk material scale. The model reproduces published experimental data on the elastin glass transition behavior with respect to load frequency and to ambient relative humidity but is not merely empirical in the sense of being a fit to such data because it predicts dynamic responses such as non-physiological creep and physiological rate-dependent stress–stretch relations. The new viscoelastic model predicts the influence of moisture content and the glass transition of the elastin on the time-dependent response of the circumferential stretch and the change in radius of a hydrated arterial cylindrical elastin lamella under cyclic radial pressure loads in the hemodynamic range. Such an elastin cylinder approximates the behavior of the elastin substructure in an elastic artery wall.     

Calculation of Thermal Stresses in Glass-Ceramic Composites

Opto-electronics make intensive use of composite materialsbased on amorphous materials, which can be considered as smart materialssince they are capable of high performances in their final state.Particularly, glass-ceramic composites involved in welding operationsfor microelectronics applications are subjected to important thermalstresses during their production, which can deteriorate their propertiesat room temperature, until the failure stage is reached. It is thenessential to be able to predict the evolution of the internal stressesgenerated during the cooling. We have performed finite-elementsimulations in order to quantify the stress evolutions for differentcomposite geometries: a ceramic fiber embedded within a glass matrix, aspherical particle located at the center of a spherical glass matrix,and a dispersion of spherical ceramic particles, this last case beingthe most representative of reality. The thermomechanical modeling of theglassy matrix takes into account its viscoelastic behavior, and theglass transition is described by the decrease during cooling of the freevolume as a function of the temperature history. The combined effect ofthe differential thermal strain during the transition and mechanicalrelaxation of glass on stress evolutions is evidenced. It is shown thatthe consideration of a periodical or random distribution of sphericalceramic particles leads to similar stress profiles.     

A nonlinear fractional viscoelastic material model for polymers

In this contribution a test scheme based on tensile tests at different velocities, relaxation experiments and deformation controlled loading and unloading processes with intermediate relaxations has been used to experimentally characterize the nonlinear, inelastic material behavior. Based on the experimental observations a small strain nonlinear fractional viscoelastic material model is derived. In order to use the model within a finite element analysis, the constitutive equations have been generalized for the multiaxial case. The experimental test scheme and the fractional viscoelastic material model are subsequently applied to characterize and compute the mechanical behavior of the thermoplastic Polypropylene. After the identification of the material parameters several uniaxial and multiaxial simulations have been carried out and compared with experimental results.     

INTERACTIONS BETWEEN TIME AND CYCLIC DEFORMATION PROCESSES IN A NIMONIC ALLOY

Interactive creep–fatigue behaviour of a nickel-base superalloy (IN 597) has been examined at 850 °C under various strain-limited, cyclic torsional loading conditions. In one test, forward creep deformation was reversed by creep under equal magnitude stress levels and strain limits. In other tests, forward creep strain was reversed by fast monotonic plasticity with and without a subsequent period of relaxation. These cycles were repeated within each test until fracture. This paper examines empirically the influence of a number of test variables upon cyclic creep curves, and demonstrates the usefulness of predictions based upon continuous low cycle fatigue and simple creep data when used in conjunction with a mechanical equation of state. A cyclic equilibrium condition was not achieved from these tests. Instead, a progressive softening occurred giving reductions to the amount of creep strain, creep time interval and reversed peak stress with each new cycle. Such reductions are expressed from derived formulae that embrace the range of inelastic strain, cycle number, creep dwell stress, reversed peak stress, and times expended in creep and relaxation.
Observations made on accumulated creep strain reveal the contribution to a creep–fatigue fracture from cyclic creep. This has led to a modified form of the linear damage rule which can provide conservative life predictions for components operating in service under similar cyclic conditions.     

Nonlinear Viscoelastic,Viscoplastic Characterization of Unidirectional GF/EP Composite

Viscoplastic strains of unidirectional continuous fiber composite (HEXCEL GF/EPprepreg system) are studied experimentally and theoretically. Creep and strainrecovery tests are used. Schapery's nonlinear viscoelastic viscoplasticconstitutive equations are used and generalized to describe inelastic behavior ofunidirectional composite under isothermal creep and strain recovery conditions. Themethodology to quantify the viscoplastic strains with respect to applied stress isproposed. Viscoplastic strains of composite are described by plastic shear strain inmaterial symmetry axis. Assumptions has been used and validated that the functiondescribing the stress and time dependence of viscoplastic strain can be presented asa product of two, time and correspondingly stress dependent, master curves.     

Memory functions for mechanical relaxation in viscoelastic materials

The roles of memory functions for compliance retardation and modulus relaxation in viscoelastic materials are examined. It is shown that essential features of the mechanical responses are the components which occur instantaneously on the application of either a stress or a strain. Taking these features into consideration it is shown that at non-zero time the cooperative memory function of compliance retardation is the time differential of the modulus relaxation function and the cooperative memory function of modulus relaxation is the time differential of the compliance relaxation function for step up functions of stress and strain, respectively. Zero time singularities in the memory functions have been eliminated in the derivation of the reduced dynamical equations, whose memory functions are limited to non-singular contributions which are always present.