锆基非晶合金的动态弛豫机制和高温流变行为

非晶合金的动态弛豫机制对于理解其塑性变形,玻璃转变行为,扩散机制以及晶化行为都至关重要.非晶合金的力学性能与动态弛豫机制的本征关联是该领域当前重要科学问题之一.本文借助于动态力学分析(DMA),探索了Zr₅₀Cu₄₀Al₁₀块体非晶合金从室温到过冷液相区宽温度范围内的动态力学行为.通过单轴拉伸实验,研究了玻璃转变温度附近的高温流变行为.基于准点缺陷理论(quasi-point defects theory),对两种力学行为的适用性以及宏观力学行为变化过程中微观结构的演化规律进行描述.研究结果表明,准点缺陷理论可以很好地描述非晶合金损耗模量α弛豫的主曲线.基于非晶合金的内耗行为,玻璃转变温度以下原子运动的激活能U_β为0.63 eV.与准点缺陷浓度对应的关联因子χ在玻璃转变温度以下约为0.38,而在玻璃转变温度以上则线性增大.Zr₅₀Cu₄₀Al₁₀块体非晶合金在玻璃转变温度附近,随温度和应变速率的不同而在拉伸实验中显示出均匀的或不均匀的...     

Modelling large deformation behaviour under loading–unloading of semicrystalline polymers: Application to a high density polyethylene

In this work, the large deformation behaviour under monotonic loading and unloading of a high density polyethylene (HDPE) is studied. To analyze the nonlinear time-dependent response of the material, mechanical tests were conducted at room temperature under constant true strain rates and stress relaxation conditions. A physically-based inelastic model written under finite strain formulation is proposed to describe the mechanical behaviour of HDPE. In the model, the inelastic mechanisms involve two parallel elements: a visco-hyperelastic network resistance acting in parallel with a viscoelastic–viscoplastic intermolecular resistance where the amorphous and crystalline phases are explicitly taken into consideration. The semicrystalline polymer is considered as a two-phase composite. The influence of the crystallinity on the loading and unloading behaviour is investigated. Numerical results are compared to experimental data. It is shown that the model is able to accurately reproduce the experimental observations corresponding to monotonic loading, unloading and stress relaxation behaviours at different strain levels. Finally, the model capabilities to capture cyclic loading–unloading behaviour up to large strains are discussed. To demonstrate the improved modelling capabilities, simulations are also performed using the original model of Boyce et al. [Boyce, M.C., Socrate, S., Llana, P.G., 2000. Constitutive model for the finite deformation stress–strain behavior of poly(ethylene terephthalate) above the glass transition. Polymer 41, 2183–2201] modified by Ahzi et al. [Ahzi, S., Makradi, A., Gregory, R.V., Edie, D.D., 2003. Modeling of deformation behavior and strain-induced crystallization in poly(ethylene terephthalate) above the glass transition temperature. Mechanics of Materials 35, 1139–1148].     

Viscosity of Cryoprotective Agents Near Glass Transition: A New Device,Technique, and Data on DMSO,DP6, and VS55

The low strain-rate viscosity of glass-forming cryoprotective agents (CPAs) in the vicinity of the glass transition is studied experimentally. Data on the mechanical behavior in this regime is necessary to the long-term goal of developing planning tools for cryopreservation via vitrification (vitreous means glassy in Latin); such tools will provide guidelines for reducing thermal stress with its devastating effects. While the flow behavior of some glass-forming CPAs is well documented in the literature for the upper part of the cryogenic temperature range (where the CPA has a comparatively low viscosity), it is the flow behavior near the glass transition temperature (where the CPA behaves as nearly a solid with an extremely high viscosity) which is critical to the analysis of stress that develops in the cryopreserved material. If the elevated viscosity limits the material’s ability to flow—in order to accommodate the thermal strain resulting from large temperature gradients, especially at the high cooling rates necessary to form glass—structural damage may follow. Information on the behavior of the CPA in the lower part of the cryogenic temperature range is largely unavailable. A new measurement device is presented in this study, in which a solid rod is pulled from a long narrow cup containing a CPA, producing an essentially one-dimensional and isothermal field of flow. The viscosity and relaxation time of the CPA is inferred from measurements of the resulting load on the rod when extracted at a constant velocity. The current study reports on experimental data near glass transition of 7.05 M DMSO, a reference CPA solution, and the CPA cocktails VS55 and DP6.     

A finite deformation fractional viscoplastic model for the glass transition behavior of amorphous polymers

The stress response of amorphous polymers exhibits tremendous change during the glass transition region, from soft viscoelastic response to stiff viscoplastic response. In order to describe the temperature-dependent and rate-dependent stress response of amorphous polymers, we extend the one-dimensional small strain fractional Zener model to the three-dimensional finite deformation model. The Eyring model is adopted to represent the stress-activated viscous flow. A phenomenological evolution equation of yield strength is used to describe the strain softening behaviors. We demonstrate that the stress response predicted by the three-dimensional model is consistent with that of one-dimensional model under uniaxial deformation, which confirms the validity of the extension. The model is then applied to describe the stress response of an amorphous thermoset at various temperatures and strain rates, which shows good agreement between experiments and simulation. We further perform a parameter study to investigate the influence of the model parameters on the stress response. The results show that a smaller fractional order results in a larger yield strain while has little effect on the yield stress when the temperature is below the glass transition temperature. For the stress relaxation tests, a smaller fractional order leads to a slower relaxation rate.     

Time-temperature dependence in fracture behavior of high impact polystyrene

High Impact Polystyrene (HIPS) is one of the first toughened systems in which the brittle polystyrene becomes more ductile with the addition of an elastomer. However, it exhibits a ductile behavior only above a certain temperature and below a certain loading rate. Fracture in this material, like in most toughened systems, can become brittle when the temperature is lowered or the loading rate is increased. The correlation between temperature and loading rate seems to be controlled by the molecular relaxation according to the Arrhenius equation. The objective of this work is to foster the understanding of the effects of time and temperature on the fracture behavior of HIPS. The time and temperature dependence in fracture performance has been found to be governed by the strain energy density criterion. The theory allows prediction of fracture performance at various loading rates and temperatures. The brittle–ductile transition is controlled by an energy activation process. A peak in fracture energy always occurs at the transition region. This is attributed to the relaxation of the polymer macromolecules. The time and temperature dependence of this relaxation can be predicted by the Arrhenius equation. The rise in fracture energy at high loading speeds is not due to the higher frequency oscillations from dynamic effect but is controlled by the critical strain energy density.     

Thermal contraction and volume relaxation of amorphous polymers

Two experimental techniques are described for the determination of the change of specific volume of polymers with temperature and aging time, which allow measurements between – 160 °C and + 200 °C. Four technical amorphous polymers, PS, PVC, PMMA and PC have been investigated. Volume-temperature curves under constant rate of cooling are presented and interpreted with respect to relaxation processes known from other physical investigations. The rate dependence of dilatometric glass transition temperatures is compared with the time dependence of rheometric glass transition temperatures from shear creep data. Volume relaxation data at constant aging temperature are presented. Aging is found to proceed until very low temperatures in the glassy state for e.g. PMMA.For polystyrene, a comparison is made between the predictions of a very simple theory of volume relaxation due to Kovacs with experimental data, using additional information from volume temperature curves and the time temperature shift of the shear creep transition. The theory predicts a rate of volume relaxation which is much lower than that found by experiment.     

Representation of the glass-transition in mechanical and thermal properties of glass-forming materials: A three-dimensional theory based on thermodynamics with internal state variables

In the vicinity of the glass transition, glass-forming materials exhibit pronounced frequency-dependent changes in the mechanical material properties, the thermal expansion behaviour and the specific heat. The frequency dependence becomes apparent under harmonic stress, strain or temperature excitations. The Prigogine-Defay ratio is a characteristic number which connects the changes in magnitude of these quantities at the glass transition. In order to represent the thermoviscoelastic properties of glass-forming materials in continuum mechanics, a three-dimensional approach which is based on the Gibbs free energy as thermodynamic potential is developed in this article. The Gibbs free energy depends on the stress tensor, the temperature and a set of internal variables which is introduced to take history-dependent phenomena into account. In the vicinity of an equilibrium reference state, the specific Gibbs free energy is approximated up to second order terms. Evaluating the Clausius-Duhem inequality, the constitutive relations for the strain tensor, the entropy and the internal variables are derived. In comparison with other approaches, the entropy, the strain tensor and the internal variables are functionals not only of the stress tensor but also of the temperature. Applying harmonic temperature- or stress-controlled excitations, complex frequency-dependent relations for the specific heat under constant stress, for the thermal expansion coefficients as well as for the dynamic mechanical compliance are obtained. The frequency-dependence of these quantities depicts the experimentally observed behaviour of glass-forming materials as published in literature. Under the assumption of isotropic material behaviour, it is shown that the developed theory is compatible with the Prigogine-Defay inequality for arbitrary values of the material parameters.     

Generalized Maxwell model for the viscoelastic behavior of a soda-lime-silica glass under low frequency shear loading

The linear viscoelastic behavior of a soda-lime-silica glass under low frequency shear loading is investigated in the glass transition range. Using the time-temperature superposition technique, the master curves of the shear dynamic relaxation moduli are obtained at a reference temperature of 566°C. A method to determine the viscoelastic constants from dynamic relaxation moduli is proposed. However, some viscoelastic constants cannot be directly measured from the experimental curves and others cannot be precisely obtained due to non-linearity effects at very low frequencies. The generalized Maxwell model is investigated from the experimental dynamic moduli without fixing the viscoelastic constants. A set of parameters is shown to be in good agreement with the experimental dynamic relaxation moduli, but does not give the correct values of the viscoelastic constants of the investigated glass. The soda-lime-silica glass exhibits a non-linear viscoelastic behavior at very low stress level which is usually observed for organic glasses. This non-linear behavior is questioned.     

Correlation between interfacial interactions and internal stresses in filled high density polyethylene

The stress relaxation and the creep behaviour of high density polyethylene (HDPE) filled with glass fibres, clay (plate-like particles) or CaCO₃ (particles with irregular shape) were measured in uniaxial extension at room temperature. It was observed that the addition of filler increased the internal stress level, as evaluated from stress relaxation data. This increase was larger than the corresponding increase in the (short-term) elastic modulus. This behaviour may be attributed to a reduced macromolecular mobility in the matrix material close to the filler surface, i.e. to formation of an interphase region in the HDPE-matrix. From the internal stress values, the thickness of this interphase region around each filler particle was estimated, assuming a uniform coverage of the particles. It was suggested that the amount of matrix material with reduced mobility (or the thickness of the interphase region) reflected the degree of adhesion between the filler and HDPE. The change in the internal stress level due to the incorporation of different fillers, which were surface treated in some cases, was also consistent with the observed creep behaviour.     

Prediction of nonlinear viscoelastic behavior of polymeric composites using an artificial neural network

Creep tests at constant stress are performed for the carbon-fiber reinforced epoxy composite at various temperatures and initial stresses. A nonlinear viscoelastic constitutive model is developed, and its material parameters are determined by fitting it to creep test data. Model results are found to agree very well with the experimental data at low temperature and low stress conditions. However, the agreement deteriorates at high temperatures, particularly in the vicinity of the glass transition temperature.An alternative model based on an artificial neural network (ANN) is developed to predict the stress relaxation of the polymer matrix composite. The ANN model is trained and validated with 9000 experimental data sets obtained from stress relaxation tests performed at various constant strain (initial stress) and constant temperature conditions. Training of the ANN employs a scaled conjugate gradient method. The optimal brain surgeon algorithm is employed to optimize the topology. The optimal ANN configuration has 88 processing elements (3 in the input layer, 45 in the first hidden layer, 39 in the second hidden layer, and 1 in the output layer) and 410 links. The predictions of the ANN model are found to be more accurate over a wider range of stress and temperature conditions than those of the explicit nonlinear viscoelastic model, in particular near the glass transition temperature.     

Thermodynamics of relaxation processes in the glass transition region

Relaxation processes in the glass transition region, especially the recovery of the volume and the physical ageing of polymers, do not follow the common (linear) theory of relaxation. On the contrary, they show a development which depends on the previous history, may be non-monotonous and requires a relaxation time that may have negative values and a pole. These phenomena can be explained if the single relaxation time is replaced by a spectrum of relaxation times and the relaxation times are supposed to be subjected to a feedback via certain structure- and temperature-parameters (as, for instance, in the KAHR-theory).However, the feedback and a pole of the relaxation time arise already for a single internal degree of freedom by themselves, if, in the non-equilibrium thermodynamics, a dynamic and a static temperature are strictly differentiated. In the case of the relaxation of the diffusive translational motion of the molecules in the glass transition region the dynamic temperature is identical with the socalled fictive temperature introduced by Tool.With regard to the relaxation of the volume three different temperature regions must be distinguished: A fluid region at high temperatures where the relaxation is controlled by the free volume and complies with the linear theory at least approximately; a glass-like region at low temperatures where the relaxation is controlled by the thermal expansivity of the free volume and where, under certain conditions, the statements set up by Davies and Jones are valid; an intermediate region (the glass transition region) where the free volume as well as its coefficient of expansivity are decisive. In that region the effective relaxation time of the volume may have a pole and the dynamic temperature may approach its equilibrium value by discontinuous jumps or in a chaotic manner.Dedicated to Professor Dr. J. Meissner (ETH Zürich) on the occasion of his 60th birthday     

Heat capacities and volumetric changes in the glass transition range: a constitutive approach based on the standard linear solid

A novel approach to represent the glass transition is proposed. It is based on a physically motivated extension of the linear viscoelastic Poynting–Thomson model. In addition to a temperature-dependent damping element and two linear springs, two thermal strain elements are introduced. In order to take the process dependence of the specific heat into account and to model its characteristic behaviour below and above the glass transition, the Helmholtz free energy contains an additional contribution which depends on the temperature history and on the current temperature. The model describes the process-dependent volumetric and caloric behaviour of glass-forming materials, and defines a functional relationship between pressure, volumetric strain, and temperature. If a model for the isochoric part of the material behaviour is already available, for example a model of finite viscoelasticity, the caloric and volumetric behaviour can be represented with the current approach. The proposed model allows computing the isobaric and isochoric heat capacities in closed form. The difference \(c_\mathrm{p} -c_\mathrm{v} \) is process-dependent and tends towards the classical expression in the glassy and equilibrium ranges. Simulations and theoretical studies demonstrate the physical significance of the model.     

Measurement of Temperature-Dependent Young’s Modulus at a Strain Rate for a Molding Compound by Nanoindentation

The mechanical properties of a molding compound on a packaged integrated circuit (IC) were measured by spherical nanoindentation using a 50 μm radius diamond tip. The molding compound is a heterogeneous material, consisting of assorted diameters of glass beads embedded in an epoxy. Statistical analysis was conducted to determine the representative volume element (RVE) size for a nanoindentation grid. Nanoindentation was made on the RVE to determine the effective viscoelastic properties. The relaxation functions were converted to temperature-dependent Young’s modulus at a given strain rate at several elevated temperatures. The Young’s modulus values at a given strain rate from nanoindentation were found to be in a good agreement with the corresponding data obtained from tensile samples at or below 90 °C. However, the values from nanoindentation were significantly lower than the data obtained from tensile samples when the temperature was near or higher than 110 °C, which is near the glass transition. The spatial distribution of the Young’s modulus at a given strain rate was determined using nanoindentation with a Berkovich tip. The spatial variation of the Young’s modulus at a given strain rate is due to the difference in nanoindentation sites (glass beads, epoxy or the interphase region). A graphical map made from an optical micrograph agrees reasonably well with the nanoindentation results.     

Dependence of linear viscoelastic critical strain and stress values on extent of gelation for a thermally activated gelling system

A large body of literature is focused on the accurate determination of a gel point for systems undergoing a sol-gel phase transition. Investigation into the limiting strain and stress for linear viscoelastic behaviour at various stages of a phase transition such as gelation is a subject that is rarely commented on. The small amplitude oscillatory rheological behaviour of a biopolymer cross-linker system through a thermally activated sol-gel transition is presented. Mechanical spectra were interpreted through application of the gelation criteria of Chambon and Winter (Winter and Chambon 1986; Chambon and Winter 1987), where the (so-called gel strength) parameter S, and relaxation exponent, n are obtained. A detailed study of the limit of linear viscoelasticity yields important trends in critical stress (σ°_c) and critical strain (γ°_c) limits highlighting the possible experimental difficulties associated with mechanical measurements obtained in close proximity to the gel point. Received: 17 March 2000 Accepted: 2 October 2000     

Ultrasonic investigation of interpenetrating networks of poly(methyl methacrylate) and polyurethane

Interpenetrating networks are the most recent development in polymeric blend materials. Due to the crosslinking of both the continuous and dispersed phases, a high degree of molecular mixing is achieved in these materials. Notwith-standing that poly(methyl methacrylate)-polyurethane (PMMA-PUR) interpene-trating and semi-interpenetrating networks have been extensively investigated by Meyer et al., ultrasonic relaxation technique has been applied here for the first time. These materials were found to be highly ultrasound absorbing.It is observed that ultrasonic absorption has a peak at a particular composition of PMMA-PUR interpenetrating network. The absorption coefficient increases with frequencyf. The absorption is of relaxational nature and is not due to the scattering of ultrasonic waves by the domains of the dispersed phase. At every composition of the interpenetrating network, the/f ² vs.f curve indicates the presence of a relaxation frequency below 2 MHz and that the absorption increases with the temperature at some compositions which indicates the presence of thermal relaxation. An attempt is made to relate the absorption with the relaxation of pendent groups of polyurethane in the continuous phase.     

Rheology of critical LCST polymer blends: poly(styrene-co-maleic anhydrite)/poly(methyl methacrylate)

The shear rheology of a binary polymer blend exhibiting a lower critical solution temperature (LCST) phase diagram and a small dynamic asymmetry (difference of glass transition temperatures between its constituents) has been investigated in the vicinity of phase separation; it is a mixture of a random copolymer of styrene and maleic anhydrite and poly(methyl methacrylate). In the linear viscoelastic regime, the material functions are sensitive to phase separation, and the effects of critical concentration fluctuations, which dominate the mechanical response, are quantified, yielding both the binodal and spinodal curves. The weak dynamic asymmetry is apparently responsible for the reduced magnitude of the observed effects, compared to blends exhibiting much larger contrast in glass transition; therefore, this property affects to some degree the accuracy of the rheologically determined phase diagram. The steady shear properties are weakly sensitive to phase separation, and suggest that shear-induced demixing may be possible. They also indicate the importance of the amount of strain energy introduced to the blend in controlling the effects of flow on phase behavior.This investigation demonstrates that the universal effects of concentration fluctuations can be detected in LCST binary polymer blends, provided that some dynamic asymmetry exists, and further they can be quantified in order to characterize the interplay between rheology and thermodynamics of these systems.Dedicated to the memory of Professor Tasos C. Papanastasiou     

60Si2Mn螺旋弹簧的压缩应力松弛行为与贮存寿命预测

为评价60Si2Mn螺旋压缩弹簧的室温松弛特性,利用InstronE3000K8953型小吨位电子动静态疲劳试验机,对其在不同温度和初始应力水平条件下进行了高温压缩加速应力松弛试验,研究了环境温度、初始应力水平对松弛行为的影响.基于粘弹性体模型,揭示了应力松弛过程中弹性应变向塑性应变的转化特性与塑性应变随松弛时间的变化规律.在对应力松弛前后弹簧丝材金相和TEM微结构进行对比分析的基础上,探讨了应力松弛的微观机制.结果表明,环境温度与初始应力水平对松弛速率具有显著影响.基于应力松弛过程的热激活特性,建立了60Si2Mn螺旋压缩弹簧的贮存寿命预测方程,并对不同应力水平下弹簧的室温和高温贮存寿命进行了合理预测.     

Evaluation of the extent of the gel particle grafting of impact polystyrene

High Impact Polystyrene (HIPS) consists of a glassy polystyrene matrix and a rubber-like particle phase (gel phase). The extent of grafting of the gel phase is known to be an important parameter in the fracture toughness of the material. [1]. A simple quantitative model is developed in this paper to determine the extent of gel-particle grafting from the observed shifts in the glass transition temperature of the gel phase of three commercial types of HIPS.Although the increase in interfacial [2] and gel-particle grafting accounts for an increase in the energy absorbed before fracture at low strain rates, above a certain amount of grafting the material becomes embrittled at high strain rates. The adhesion factor A of mesophase models [3, 19], considered between the main phases of the material, was found to correlate with the observed impact behaviour.     

Elongational flow and rheology of monodisperse polymers in solution

We describe the utilization of idealized stagnation point extensional flows, produced by opposed jets, for birefringence visualization of induced molecular strain and flow resistance measurements. We identify rheological changes associated with the coil---stretch transition which occurs beyond a critical strain-rate in elongational flow-fields. In dilute solutions of monodisperse atactic polystyrene, increases in extensional viscosity are observed as isolated molecules become stretched. The largest increases in extensional viscosity, however, are found only beyond a critical concentration and strain rate, and are associated with the stretching of transient networks of interacting molecules. These results parallel similar effects seen in porous media flow and capillary entrance experiments. We determine the molecular weight dependence of the critical concentration which scales as M^−0.55 in agreement with pairwise interaction of coils, but is much lower than conventional values of the critical polymer concentration, c^*. We believed that polydispersity may play an important role in the development of such transient networks, and in controlling the degradation behaviour during flow.