An investigation of the yield and postyield behavior and corresponding structure of poly(methyl methacrylate)

The mechanical behavior of glassy polymers is time and temperature dependent as evidenced by their viscoelastic and viscoplastic response to loading. The behavior is also known to depend strongly on the prior history of the material, changing with time and temperature without chemical intervention. In this investigation, we examine the effects of this process of physical aging on the yield and postyield behavior and corresponding evolution in the structural state of glassy polymers. This has been achieved through a systematic program of uniaxial, isothermal, constant strain–rate tests on poly(methyl methacrylate) (PMMA) specimens of different thermal histories and by performing positron annihilation lifetime spectroscopy (PALS) measurements prior to and after mechanical deformation. PALS is an indicator of the free volume content, probing size and density of free volume sites and can be considered to be a measurement of structural state. The results of the mechanical tests show that aging acts to increase both the initial yield stress and the amount of strain softening which occurs subsequent to yield. Moreover, the amount of strain softening was found to be independent of strain rate indicating that softening is related to an evolution in structure as opposed to deformation kinetics. Furthermore, after sufficient inelastic straining, the initial thermal history is completely erased as evidenced by identical values of flow stress following strain softening, for both annealed and quenched polymer. Strong confirmation of the structural state or free volume related nature of the strain softening process is obtained by our companion PALS measurements. PALS detects an increase in the size of free volume sites following inelastic deformation and finds the initially annealed and quenched specimens to posses the same post-deformation distribution. The size of sites is found to evolve steadily with inelastic strain until it attains a steady-state value. This evolution of free volume with strain follows the observed softening of the flow stress to a steady-state value. These results provide experimental evidence that an increase in free volume with inelastic straining accompanies the strain softening phenomenon in glassy polymers and that strain softening is indeed a de-aging process. Based on our experimental results a mechanistically based constitutive model has been formulated to describe the effects of thermal history on the yield and postyield deformation behavior of glassy polymers up to moderate strains. The model is found to successfully capture the effects of physical aging, strain softening, strain rate, and temperature on the inelastic behavior of glassy polymers when compared with experimental results. © 1993 John Wiley & Sons, Inc.     

Modeling of penetrant diffusion in glassy polymers with an integral sorption deborah number

A mathematical model was developed to explain the anomalous penetrant diffusion behavior in glassy polymers. The model equations were derived by using the linear irreversible thermodynamics theory and the kinematic relations in continuum mechanics, showing the coupling between the polymer mechanical behavior and penetrant transport. The Maxwell model was used as the stress–strain constitutive equation, from which the polymer relaxation time was defined. An integral sorption Deborah number was proposed as the ratio of the characteristic relaxation time in the glassy region to the characteristic diffusion time in the swollen region. With this definition, an integral sorption process was characterized by a single Deborah number and the controlling mechanism was identified in terms of the value of the Deborah number. The model equations were two coupled nonlinear differential equations. A finite difference method was developed for solving the model equations. Numerical simulation of integral sorption of penetrants in glassy polymers was performed. The simulation results show that (1) the present model can predict Case II transport behavior as well as the transition from Case II to Fickian diffusion and (2) the integral sorption Deborah number is a major parameter affecting the transition. © 1993 John Wiley & Sons, Inc.     

Dual-mode free volume model for diffusion of gas molecules in glassy polymers

The development of a new model for the diffusion of gas molecules in glassy polymers is presented which utilizes concepts from free volume theory and relies on a dual-mode interpretation of sorptive dilation in glassy polymers. Three assumptions are made in the development of the model. First, the free volume available for molecular transport processes is taken as constant below the glass transition temperature. Second, two populations of gas molecules are assumed to exist—one which contributes to the maintenance of an iso-free volume state upon sorptive dilation and one which does not contribute owing to sorption into regions of unrelaxed volume. Third, the former population is assumed to be mobile while the latter is not. The resulting model predicts, at constant temperature, a diffusion coefficient that is independent of solute volume fraction. This is in contrast to the widely used dual-mode sorption model with partial immobilization for gas transport in glassy polymers which leads to a diffusion coefficient that is dependent on solute mole fraction through the molar gas concentration. The new model is used to interpret gas transport data from permeation experiments for carbon dioxide, methane, and ethylene in three polycarbonates. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1737–1746, 1997     

Plastic deformation of glassy polystyrene: A unified model of yield and the role of chain length

A study was made of yield and plastic flow in glassy polystyrene. A range of 12 linear atactic polystyrenes was studied: monodisperse, bimodal blends, and a polydisperse commercial sample. M_n varied between 66,000 and 490,000 g/mol. These were given standardized thermal treatments and then subjected to uniaxial compression tests in the glassy state over the temperature range 40 to 95 °C and nominal strain-rates 10⁻⁴ to 10⁻³ s⁻¹. Their constitutive responses were interpreted in terms of the physically based three-dimensional constitutive model for small or large deformations in amorphous polymers proposed earlier (Polymer 1995, 36, 3301–3312), including plastic strain-induced structural rejuvenation. In multimode form, the model captured closely both linear viscoelastic response and yield and plastic flow. When the reduction of Vogel temperature caused by chain ends was incorporated in the model, it predicted a fall in yield stress with reducing molecular length. This was also observed in experimental data, with the rate of fall approximately in agreement. The results provide further support for the model as a unifying framework for describing the physical properties of polymer glasses. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2027–2040, 2004     

Visualization of deformation-induced structural rearrangements in amorphous polymers

A technique is proposed for decorating amorphous polymers: Before the deformation (shrinkage) of an amorphous polymer, its surface is decorated with a thin metal coating. The subsequent deformation is accompanied by surface structure formation, which makes the processes that occur in the polymer visible. The proposed technique makes it possible to visualize and describe the mechanism of transfer of the polymer from the surface into the bulk and vice versa and to obtain direct information about the direction of the actual local stress. The technique makes it possible to obtain information about the topological heterogeneity of rubber networks, to reveal the features of structural rearrangements that occur during the cold rolling of amorphous polymers, and to describe the phenomenon of self-elongation during annealing of the oriented PET. These microscopic data explain the following features of the structural and mechanical behavior of glassy polymers from a unified viewpoint: stress relaxation in a polymer in the elastic (Hookean) region of the stress-strain curve, an increase in stress in a deformed glassy polymer during its isometric annealing below T _g, the low-temperature shrinkage of a deformed polymer glass in the strain range below its yield point, the storage of internal energy in a deformed glassy polymer in the strain range below the yield point, some anomalies of thermophysical properties, and some other features.     

Gas sorption and diffusion processes in polymer matrices at high pressures

A theoretical approach has been developed to describe the processes of gases diffusion and sorption in rubbery and glassy polymers. Various models (Flory-Huggins, dual-mode sorption, gas-polymer-matrix) used for interpreting the sorption-diffusion experiments are discussed within this approach framework. Experimental data on carbon dioxide sorption in glassy and rubbery polymers have been considered using the proposed approach. The comparison of the experimental and theoretical data has permitted to make the conclusion on the developed concepts adequacy. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1339–1348, 1997     

Tensile yield-stress behavior of glassy polymers

It is shown that, at the yield stress, glassy polymers exhibit viscous flow which is in agreement with the generalized theory of Eyring. The study of the yield stress over a wide range of temperatures and strain rates provides evidence on the secondary transitions found by other methods. From our measurements we conclude that every secondary transition corresponds to the liberation of one of the degrees of freedom of a segment of the main chain.     

Application of free‐volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review

Theories based on free‐volume concepts have been developed to characterize the self and mutual‐diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer‐solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free‐volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free‐volume based approaches used to evaluate solvent self‐diffusion coefficients in glassy polymer‐solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free‐volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Nonequilibrium statistical theory of damage and fracture for glassy polymers, 1. The statistical distribution and evolution of microcracks in glassy polymers

The purpose of this paper is to construct a unified theoretical framework to link micro to macro-mechanical properties of glassy polymers. Starting from a model of microcrack propagation in craze on a mesoscale, the kinetic process of microcrack propagation resulting from fibril breakdown in the crack tip zone is mathematically formulated by a combination of fracture mechanics and fracture kinetics. A microcrack evolution equation involving both the geometric structure parameters of craze and the meso-mechanical quantities is obtained. After solving this evolution equation, a statistical distribution function of microcrack size which evolves with time and the moment generating function of microcrack size are derived. Any-order averaged damage functions can be therefore deduced. Specifically, the analytical expressions of the first-order averaged damage function and its damage rate are presented, which correspond to a similar definition of damage mechanics.     

苯乙烯基形状记忆聚合物热力学行为的有限元分析

对苯乙烯基形状记忆聚合物进行了拉伸实验研究,测定了该材料在25℃、30℃、40℃和50℃时的弹性模量和屈服极限.根据实验结果,建立了苯乙烯基形状记忆聚合物的材料参数方程,描述了苯乙烯基形状记忆聚合物在玻璃体转化过程中,材料参数和温度的关系.在假设形状记忆聚合物为各向同性材料的基础上,将Tobushi等建立的热力学本构方程从一维扩展到三维.基于有限元分析软件ABAQUS的二次开发功能,针对上述本构方程和材料参数方程,编写了可供ABAQUS调用的UMAT函数,并对苯乙烯基形状记忆聚合物实现形状记忆效应的高温变形、应力冻结和形状恢复等热力学过程,进行了有限元数值模拟分析.     

A constitutive equation derived from the model of doi and edwards for concentrated polymer solutions and polymer melts

In deriving a constitutive equation from a molecular model of polymers in concentrated solutions and melts, Doi and Edwards used a mathematical approximation, the “independent alignment approximation,” which has recently been shown to produce significant error in the particular case of stress relaxation following a double-step strain in opposite direction. In the present paper, in order to examine the approximation in general cases, we derive a new constitutive equation without using the independent alignment approximation. The new equation is a nonlinear integro-differential equation and is solved numerically for several cases, i.e., steady shear and elongational flows, and the transient flows after the start of shear and elongation. It is found that, in the cases examined here, the new constitutive equation gives nearly the same results as the old one: the rheological functions calculated from the two theories differ no more than 30%. This substantiates the expectation that the independent alignment approximation does not produce drastic error as long as the flow direction is not reversed.     

Mechanisms of anelastic deformation in solid polymers: Solidlike and liquidlike processes

Several aspects of anelastic deformation of glassy polymers that cannot be explained in terms of existing theories are considered. Resemblance in the stress-strain response for solids of various natures and structures, including semicrystalline and glassy polymers, organic and inorganic solids, and low-molecular-mass and high-molecular-mass compounds, is analyzed. It was pointed out that the phenomena of the yield peak, strain softening, strain concentration (localization) in narrow shear bands, and transient effects are characteristic of the plastic deformation of any solid. The same is true for differences in the kinetics and mechanism of deformation at low (T _def < 0.7T _g) and high deformation temperatures (T _def > 0.7T _g). The mechanism of plastic deformation is discussed in detail for glassy polymers; at microscopic and nanoscale levels, plastic deformation proceeds via two stages: initial nucleation of small-scale shear transformations and their further coalescence. This coalescence leads to the advance of the shear front in the sample and to the nucleation and displacement of classical shear bands. The heat of plastic deformation is released out at the coalescence of shear transformations. It was assumed that shear transformations are responsible for the development and evolution of the yield peak in glassy polymers, strain softening, and other phenomena. The proposed mechanism of deformation in glasses fully agrees with the results of thermodynamic measurements and other experimental data reported in the literature. Computer simulation makes it possible to visualize the scenario of nucleation and evolution of shear transformations at the atomic level.     

Analysis of thermal reactions of photochromic species in glassy matrices based on the concept of dispersive processes

Thermal decoloration reactions of photochromic spiroindolinonaphthoxazine in glassy polymer matrices have been studied. The non-exponential kinetic behaviour in these systems was analyzed using the phenomenological equation with an exp(-t^α) dependency describing dispersive processes in glassy solids. The dispersive parameter α represents the molecular environmental characteristics of matrix polymers.     

Errors induced in quartz crystal mass uptake measurements by nongravimetric effects: Considerations beyond the EerNisse caution

We report frequency changes in AT‐cut quartz crystals for glassy polymers subsequent to temperature and carbon dioxide pressure changes. Anomalous frequency shifts are observed for the crystal subsequent to such changes. Since, the Sauerbrey equation has been applied routinely for mass uptake measurements in glassy polymers, using the quartz crystal microbalance fitted with AT‐cut quartz crystals, it is important that nongravimetric effects that impact the frequency change be well understood. In the present work, we provide a quantitative analysis of the breakdown of the Sauerbrey equation for viscoelastic materials by using the Johannsmann (Macromol Chem Phys 1999, 200, 501) treatment of the response of AT‐cut crystals. Clearly, there exist significant errors in mass uptake measurements for materials deposited on AT‐cut quartz crystals when precautions pertaining to film thickness and viscoelastic compliance are ignored. We show that while the early caution of EerNisse on stress effects in AT‐cut quartz crystals can be important in mass uptake measurements, for polymers, the major source of error arises from viscoelastic effects in the coating. We conclude that mass uptake measurements for films of compliant materials and polymers above their glass transition cannot be performed with accuracy, using AT‐cut quartz crystals if the results are not corrected for frequency shifts due to viscoelastic effects of the overlayer unless the films are extremely thin, that is, less than 100 nm. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 801–814, 2006     

Application of a nonlinear viscoelastic model to glassy,particulate‐filled polymers

In previous studies, a nonlinear viscoelastic formalism for unfilled glassy polymers was developed, which employed a potential energy material clock. A wide variety of responses ranging from temperature‐dependent mechanical yield to enthalpy relaxation could be predicted accurately with one physical parameter set. The current investigation assessed the applicability of this approach to highly filled polymers (over 50 vol %). The particulate composites were treated as homogeneous continua, and model parameters were extracted directly from characterization tests developed for unfilled polymers. The predictions agreed surprisingly well with experimental data. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3135–3150, 2005