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Comparison of mechanical and molecular measures of mobility during constant strain rate deformation of a PMMA glass
Abstract
We performed constant strain rate deformation and stress relaxation on a poly(methyl methacrylate) glass at Tg - 19 K, utilizing three strain rates and initiating the stress relaxation over a large range of strain values. Following previous workers, we interpret the initial rate of decay of the stress during the relaxation experiment as a purely mechanical measure of mobility for the system. In our experiments, the mechanical mobility obtained in this manner changes by less than a factor of 3 prior to yield. During these mechanical experiments, we also performed an optical measurement of segmental mobility based on the reorientation of a molecular probe; we observe that the probe mobility increases up to a factor of 100 prior to yield. In the post-yield regime, in contrast, the mobilities determined mechanically and by probe reorientation are quite similar and show a similar dependence on the strain rate. Dynamic heterogeneity is found to initially decrease during constant strain rate deformation and then remain constant in the post-yield regime. These combined observations of mechanical mobility, probe mobility, and dynamic heterogeneity present a challenge for theoretical modeling of polymer glass deformation.
... τ (ǫ) decreases rapidly with increasing strain as stress-activated plasticity becomes increasingly important, passes through a minimum at ǫ ≃ ǫ y , increases again for ǫ > ǫ y , and then decreases again for ǫ > ǫ pysm . All trends are consistent with experimental observations [39][40][41] showing that relaxation in real glasses often speeds up by orders of magnitude near yielding, and can then slow down again upon strain softening. Panel (c) shows the dynamical heterogeneity ...
... Experiments typically show [39][40][41] that heterogeneity decreases during yielding and remains relatively low during plastic flow. The different trends shown in panel (c) may arise because currently available SGR theories lack any "facilitation" mechanism. ...
... cannot force-balance such large stresses), and zones that carry very low stresses may similarly yield faster when σ is large. The net effect is homogenization of the yielding dynamics and of systems' relaxation in the postyield, plastic-flow regime [39][40][41][42]. It would be interesting in future work to add mean-field facilitation (or a comparable stress-diffusion mechanism [43]) to SGR theory. ...
We present a version of soft glassy rheology that includes thermalized strain degrees of freedom. It fully specifies systems' strain-history-dependent positions on their energy landscapes and therefore allows for quantitative analysis of their heterogeneous yielding dynamics and nonequilibrium deformation thermodynamics. As a demonstration of the method, we illustrate the very different characteristics of fully-thermal and nearly-athermal plasticity by comparing results for thermalized and nonthermalized plastic flow.
... The fact that yield stress and plastic flow result from a stress-induced acceleration of the dynamics at the molecular level has been demonstrated by recent experiments in which the microscopic dynamics were probed under stress [5][6][7][8][9][10][11][12]. Molecular dynamics simulations also support the fact that the dynamics is enhanced during plastic deformation [13,14]. ...
... It is experimentally known that relaxation is accelerated with respect to the equilibrium rate τ −1 α when a large enough stress is applied on a glassy material [3,[6][7][8][9][10][11][12]. This implies that the local relaxation time is not a function of the local density only, but must also depend on the local stress. ...
Applying a stress to a glassy polymer accelerates its dynamics as one goes from low stress up to plastic regime. For decades, the phenomenological Eyring's model has been used to describe plastic flow in polymers. This model, however, raises fundamental issues which makes its use deleterious in glassy polymers. We propose an alternative model in which the elastic energy stored at the length scale of dynamical heterogeneities ξ≈3–5 nm reduces the free energy barrier for relaxation. Contrary to the Eyring's activation volume, which has no clear interpretation, this length scale is derived from physical arguments, based on a detailed account of relaxation mechanisms at the molecular scale. Recent creep experiments in glassy polymers by Ediger and coworkers allow for discriminating the two pictures. It is shown that the whole evolution of the τα relaxation time under stress can be reproduced quantitatively, using as the only adjustable parameter the scale ξ. The obtained value of ξ is the same as the value previously determined by considering the whole set of properties of glassy polymers. This confirms the coherence and completeness of the theory of relaxation processes in nonpolar glassy polymers that we proposed in previous works.
... τ (ǫ) decreases rapidly with increasing strain as stressactivated plasticity becomes increasingly important, passes through a minimum at ǫ ≃ ǫ y , increases again for ǫ > ǫ y , and then decreases again for ǫ > ǫ pysm . All trends are consistent with experimental observations [32][33][34] showing that relaxation in real glasses typically speeds up by orders of magnitude near yielding, and can then slow down again upon strain softening. Panel (c) shows the dynamical heterogeneity ∆ log 10 (τ ) log 10 (τ ) = log 10 (τ ) 2 − log 10 (τ ) 2 log 10 (τ ) (15) of this relaxation. ...
... Panel (c) shows the dynamical heterogeneity ∆ log 10 (τ ) log 10 (τ ) = log 10 (τ ) 2 − log 10 (τ ) 2 log 10 (τ ) (15) of this relaxation. Heterogeneity increases markedly with increasing strain for ǫ < ǫ y , then decreases again for ǫ > ǫ y , in a fashion qualitatively similar to that observed in experiments [32][33][34]. While log 10 (τ ) decreases sharply with ǫ, ∆ log 10 (τ ) increases slightly, and the net effect is that heterogeneity increases sharply. ...
We develop a continuous formulation of soft glassy rheology that corresponds to the infinite-system-size limit and includes thermalized strain degrees of freedom. The continuous formulation provides multiple novel results that cannot be straightforwardly obtained via the standard discrete-zone formulation. In particular, since it fully specifies systems' strain-history-dependent positions on their energy landscapes, it allows for quantitative analysis of their heterogeneous yielding dynamics and nonequilibrium deformation thermodynamics. As a demonstration of the method, we illustrate the very different characters of fully-thermal and nearly-athermal plasticity by comparing results for thermalized vs. nonthermalized strain degrees of freedom and plastic flow rules.
... In their pioneering work, Ediger and colleagues measured changes in molecular mobility during the deformation of a glassy polymer, and have shown that under stress, segmental mobility may increase by up to a factor of 1000. [13][14][15][16][17][18][19][20][21] . Using photobleaching techniques, they have also shown that in the early stage of deformation, polymer glass presents strong dynamic heterogeneity and becomes more homogeneous after the onset of the flow 8 . ...
We investigate the local viscosity of a polymer glass around its glass transition temperature using environment-sensitive fluorescent molecular rotors embedded in the polymer matrix. The rotors' fluorescence depends on the local viscosity, and measuring the fluorescence intensity and lifetime of the probe therefore allows to measure the local free volume in the polymer glass when going through the glass transition. This also allows us to study the local viscosity and free volume when the polymer film is put under an external stress. We find that the film does not flow homogeneously, but undergoes shear banding that is visible as a spatially varying free volume and viscosity.
... Dai et al. (2020) employed the effective temperature theory (Xiao and Nguyen, 2015), the Adam-Gibbs model (Adam and Gibbs, 1965) and Eyring' viscoplastic law to reproduce the thermo-mechanical response of amorphous polymers, which shows good prediction for the stress relaxation behavior. The stress relaxation behavior of amorphous polymers has also been explored by Liu et al. (2015), Kim et al. (2013), Kropka and Long (2018), Lee et al. (2010), Ayoub et al. (2010), Bending and Ediger (2016). It was found that the stress relaxation response was indistinguishable amongst strain levels in the post-yield region and the relaxation rate increased with increasing of deformation rate or temperature. ...
The deformation behavior of amorphous polymers in the post-yield region is viscoelastic-viscoplastic (VE-VP) as it exhibits both viscoelastic and viscoplastic characteristics. However, a systematic experimental and modeling study for it is lacking. In this paper, the VE-VP deformation behavior of an amorphous polymer was experimentally investigated over a wide temperature range. It was found that some of the observed deformation behaviors cannot be reasonably explained by the common assumptions of the thermally-activated segmental motions and the formation of a topologically-entangled rubbery network. With the assumption that there is a glassy network formed from weak linkages in the polymer, the observed deformation behaviors over a wide temperature range can be well explained by considering the stretch and relaxation of the glassy network. The glassy network assumption was first proposed by one of our coauthors and employed for modeling the VE-VP deformation behavior of amorphous polymers at room temperature. In this paper, the glassy network assumption was further examined at different temperatures and employed to establish a constitutive model for simulating the VE-VP deformation behavior of amorphous polymers over a wide temperature range. The model was validated by corroboration with experiments. It was demonstrated that a constitutive model based on the glassy network assumption is capable of representing the loading, strain recovery, and stress relaxation behaviors simultaneously, in contrast to most of the existing constitutive models. Hence, this work not only proposes a reasonable physical picture for understanding but also provides a robust constitutive model for simulating the VE-VP deformation behavior of amorphous polymers and its temperature dependence.
... However, it is also found the absolute value of yield strength for predeformed polymers is around 5 MPa lower than that of undeformed polymers in the same aging condition, which suggests the mechanical deformation influences the microstructure of PETG. Applying mechanical deformation on amorphous polymers can induce an opposite effect of physical aging, known as mechanical rejuvenation [25][26][27][28][29]. With physical aging, the nonequilibrium structure of amorphous solids evolves towards the equilibrium state, which leads to a decrease in energy, entropy and molecular mobility. ...
Amorphous glassy polymers are widely used as structural materials. However, their mechanical properties continuously evolve with physical aging, which significantly influences their applications. In this work, we investigate the effects of aging on stress response of poly(ethylene terephthalate)-glycol (PETG). The PETG specimens are either quenched or annealed around or below the glass transition temperature (Tg) for a period of time. The uniaxial compression tests are then performed at Tg-40 °C and strain rate 0.001/s. The quenched polymers exhibit the smallest yield strength and strain softening, indicating that negligible structural relaxation occurs for the quenched condition. For annealed polymers, the yield strength increases with aging time. The results also show that there exists an optimal temperature to achieve the highest structural relaxation rate, which is around Tg-20 °C. Compared with annealing at a single temperature, annealing at multiple temperatures in discrete steps is a more efficient method for structural relaxation. The same experiments are also performed on specimens with 30% predeformation. The optimal aging temperature does not change with predeformation. However, at the same annealing condition the yield strength of specimens with 30% predeformation is around 5 MPa less than that of undeformed specimens.
... The main Fig. 7 (c) has the data at 0.02 min À1 shifted by a factor of ten. recently, the same method has been applied to measure molecular mobility during stress relaxation not far from T g for three strain rates and to show that the stress relaxation from the pre-yield regime is hardly accelerated although the photobleaching measurements reveal improved molecular mobility by a factor of a hundred [97]. ...
Understanding the evolution of local structure and mobility of disordered glassy materials induced by external stress is critical in modeling their mechanical deformation in the nonlinear regime. Several techniques have shown acceleration of molecular mobility of various amorphous glasses under macroscopic tensile deformation, but it remains a major challenge to visualize such a relationship at the nanoscale. Here, we employ a new approach based on atomic force microscopy in nanorheology mode for quantifying the local dynamic responses of a polymer glass induced by nanoscale compression. By increasing the compression level from linear elastic to plastic deformation, we observe an increase in the mechanical loss tangent (tan δ), evidencing the enhancement of polymer mobility induced by large stress. Notably, tan δ images directly reveal the preferential effect of the large compression on the dynamic acceleration of nanoscale heterogeneities with initially slow mobility, which is clearly different from that induced by increasing temperature.
We investigate the local viscosity of a polymer glass around its glass transition temperature using environment-sensitive fluorescent molecular rotors embedded in the polymer matrix. The rotors' fluorescence depends on the local viscosity, and measuring the fluorescence intensity and lifetime of the probe therefore allows to measure the local free volume in the polymer glass when going through the glass transition. This also allows us to study the local viscosity and free volume when the polymer film is put under an external stress. We find that the film does not flow homogeneously, but undergoes shear banding that is visible as a spatially varying free volume and viscosity.
The acceleration of structural relaxation or physical aging by deformation, known as overaging, has been reported in experiments and simulations of polymer and colloid glasses, and correct accounting for overaging is important for the prediction of the long-term behavior of polymer glasses in engineering applications. Here, the effects of cyclic loading/unloading on the segmental dynamics and mechanical properties of poly(methyl methacrylate) glasses are investigated using a probe reorientation technique and time-aging time superposition of the mechanical response, respectively. Sets of 5000 tensile loading/unloading cycles were performed at temperatures between Tg - 10 K and Tg - 25 K with cycle extension strains ranging from 0.003 to 0.007. After cycling, the segmental dynamics measured with the probe reorientation technique either remained unchanged or were faster relative to an undeformed sample. The relaxation times of cycled glasses recovered with a common time scale on the order of their aging time, indicating that they retain a memory of their original age, as opposed to a full erasure of their thermal and mechanical history. Surprisingly, changes as a result of cycling were more obvious in probe reorientation measurements than in the mechanical properties, suggesting that the probe reorientation technique can sensitively detect nonlinear effects of deformation. No evidence of overaging was observed in the optical or mechanical measurements as a result of these cyclic loading/unloading experiments.
Our experiments show for both uniaxial extension and compression that the post-yield stress relaxation can be slower than the pre-yield stress relaxation on all time scales. Such phenomena reveal that high stresses may result from chain tension due to large deformation of the chain networking in glassy polymers. In combination with molecular dynamics (MD) simulation, we demonstrate that even in the case of compression the stress buildup stems from the mechanical resistance against the lateral expansion of the chain network, which produces bond distortion such as bond stretching. As further evidence of how chain network dictates the mechanical responses, it is shown that significant network deformation produced by large deformation can suppress segmental relaxation in compression. Thus, the present study has made a first combination of experiment and MD simulation to elucidate (a) the remarkable effects that the chain network has in response to large post-yield deformation and (b) the direct (indirect) chain-network contributions to the macroscopic stress in extension (compression).
Physical aging widely exists in amorphous polymers, which refers to the nonequilibrium structure of amorphous polymers evolving towards the equilibrium state. Aging can significantly influence the thermomechanical properties and subsequently the macroscopic response of polymers. In our recent work, we performed a series of uniaxial compression tests on amorphous thermoplastic poly(ethyleneterephthalate)-glycol (PETG) subject to different annealing temperature and time. The results showed that both annealing time and temperature have a significant influence on the yield strength. Here we apply a two-temperature continuum model to simulate the stress response of PETG with different thermal treatments. The model employs the effective temperature as a variable to characterize the nonequilibrium state. The physical aging is characterized by the evolution of the effective temperature. The effective temperature is also coupled with the viscoplastic deformation to describe strain softening induced by mechanical rejuvenation. The simulation results can reasonably reproduce the main experimental observations with some discrepancies. The possible reasons for the discrepancies between experiments and simulations are also critically analyzed. The theory is also used to simulate the response of amorphous glassy polymers in the creep and strain-rate-switching tests. The model successfully captures the important features of experimental observations in the literature.
Graft block copolymers (BCPs) with poly(4-methyl caprolactone)-block-poly(±-lactide) (P4MCL-PLA) side chains containing 80–100% PLA content were synthesized with the aim of producing tough and sustainable plastics. These graft BCPs experience physical aging and become brittle over time. For short aging times, ta, the samples are ductile and shear yielding is the primary deformation mechanism. A double-yield phenomenon emerges at intermediate ta where the materials deform by stress whitening followed by shear yielding. At long ta, the samples become brittle and fail after crazing. PLA content strongly governs the time to brittle failure, where a 100% PLA graft polymer embrittles in 1 day, an 86% PLA graft BCP embrittles in 35 days, and at 80% PLA, the material remains ductile after 210 days. Molecular architecture is also a factor in increasing the persistence of ductility with time; a linear triblock ages three times faster than a graft BCP with the same PLA content. Small-angle X-ray scattering and transmission electron microscopy analysis suggest that the rubbery P4MCL domains play a role in initiating crazing by cavitation. Prestraining the graft BCPs also significantly toughens these glassy materials. Physical aging-induced embrittlement is eliminated in all of the prestrained polymers, which remain ductile after aging 60 days. The prestrained graft BCPs also demonstrate shape memory properties. When heated above the glass-transition temperature (Tg), the stretched polymer within seconds returns to its original shape and recovers the original mechanical properties of the unstrained material. These results demonstrate that graft BCPs can be used to make tough, durable, and sustainable plastics and highlight the importance of understanding the mechanical performance of sustainable plastics over extended periods of time following processing.
Mechanochromic functionality realized through force-responsive molecules (i.e., mechanophores) has great potential for spatially localized damage warning in polymers. However, in structural plastics, for which damage warning is most critical, this approach has had minimal success because brittle failure typically precedes detectable color change. Herein, we report on the room-temperature mechanochromic activation of spiropyran in high Tg bisphenol A polycarbonate. The mechanochromic functionality was introduced by polymerization of dihydroxyspiropyran as a comonomer while retaining the excellent thermomechanical properties of the polycarbonate. The mechanochromic behavior is thoroughly evaluated in response to changes in stress, deformation, and time, providing new insights regarding how loading history controls stress accumulation in polymer chains. In addition, a new method to incorporate mechanochromic functionality in structures without dispersing costly mechanophores in the bulk is demonstrated by using a mechanochromic laminate. The room-temperature mechanochromic activation in a structural polymer combined with the new and efficient preparation and processing methods bring us closer to the application of mechanochromic smart materials.
Optical probe reorientation experiments and mechanical stress relaxation measurements in the linear response regime were performed on a polymer glass. Segmental dynamics of lightly cross-linked poly(methyl methacrylate) (PMMA) were monitored via both methods at temperatures between 9 and 24 K below the glass transition temperature (Tg) and over the course of 8 h of aging. Relaxation times from the two methods cover a range of ∼1.7 decades. Similar results were obtained from the two experiments other than a slight difference in the aging rate. A difference of ∼0.3 decades (a factor of ∼2) is observed between the optically and mechanically obtained relaxation times, related primarily to the size of the probe. Both experiments give a value near 0.3 for the Kohlrausch–Williams–Watts (KWW) β parameter. These results provide an important baseline for the interpretation of optical probe reorientation experiments during nonlinear deformation.
The ability to relax a macroscopically applied stress is often associated with molecular mobility, or the possibility for a molecule to move outside the confines of its current position, within the material of which the stress is applied. Here, a viscoelastic constitutive analysis is used to investigate the counter-intuitive experimental observation of “mobility decrease with increased deformation through yield” [1] for a glass forming polymer during stress relaxation while under compressive and tensile loading conditions. The behavior of an epoxy thermoset is examined using an extensively validated, thermorheologically simple, material “clock” model, the Simplified Potential Energy Clock (SPEC) model.[2] This methodology allows for a comparison between the linear viscoelastic (LVE) limit and the true non-linear viscoelastic (NLVE) representation and enables exploration of a wide range of conditions that are not practical to investigate experimentally. The model predicts the behavior previously described as “mobility decrease with increased deformation” in the LVE limit and at low strain rates for NLVE. Only when loading rates are sufficient to decrease the material shift factor by multiple orders of magnitude is the anticipated deformation induced mobility or “mobility increase with increased deformation” observed. While the model has not been “trained” for these behaviors, it also predicts that the normalized stress relaxation response is indistinguishable amongst strain levels in the “post-yield” region, as has been experimentally reported. At long time, which has not been examined experimentally, the model predicts that even the normalized relaxation curves that exhibit “mobility increase with increased deformation” “cross back over” and return to the LVE ordering. These findings demonstrate the ability of rheologically simple models to represent the counter-intuitive experimentally measured material response and present predictions at long time scales that could be tested experimentally.
Literature data on structural rearrangements taking place in amorphous glassy polymers upon their plastic deformation are analyzed. This deformation is shown to be primarily accompanied by polymer self-dispersion into fibrillar aggregates composed of oriented macromolecules with a diameter of 1—10 nm. The above structural rearrangements proceed independently of the deformation mode of polymers (cold drawing, crazing, or shear banding of polymers under the conditions of uniaxial drawing or uniaxial compression). Principal characteristics of the formed fibrils and the conditions providing their development are considered. Information on the properties of the fibrillated glassy polymers is presented, and the pathways of their possible practical application are highlighted.
Strain rate dependency is an important issue for the mechanical response of materials in impact events. Dynamic mechanical properties of a high-strength poly(methyl methacrylate) (PMMA) were studied by using split Hopkinson pressure bar technology. The maximum stress is enhanced with the increase of strain rate, and then keeps a constant with the further increase of strain rate, which is accompanied with a linear increase of fracture energy density. The critical data of strain rate and maximum stress were determined. Eyring's equation was applied for analyzing the influence factors, which relate to the hardening induced by strain rate and softening caused by adiabatic temperature rise. Inherent physical mechanisms were clarified and the strategies for designing advanced impact-resistant polymers were proposed. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018, 135, 46189.
A coarse-grained model has been proposed recently in order to describe plastic properties of glassy polymers with space resolution the scale ξ of dynamical heterogeneities. This model allows for describing plastic flow by assuming that the elastic energy stored at the scale of dynamical heterogeneities reduces by a similar amount the free energy barriers for α-relaxation. The aim of this article is to consider in more details the evolution of the distribution of relaxation times under plastic deformation. This is achieved by taking explicitly into account the so-called facilitation mechanism during plastic flow introduced by Merabia and Long [ Eur. Phys. J. E2002, 9, 195; J. Chem. Phys.2006, 125, 234901]. This mechanism, which allows for calculating the scale of dynamical heterogeneities, is key for explaining temporal asymmetry regarding the dynamical evolution of a glassy polymer upon cooling or upon heating, as observed experimentally by Kovacs. Upon heating, fast regions appear first and melt the slowest ones. We propose that this same process is at work upon stretching a polymer material. Some subunits get accelerated due to deformation, and their growing number allows for melting the slowest subunits. We show that this facilitation mechanism is responsible for the narrowing of the relaxation time spectrum observed e.g. during plastic strain by using optical probe dynamics measurements by Ediger and co-workers. The physical model is solved numerically in 3D by a method similar to dissipative particle dynamics, in which the strain and stress fields, as well as the local relaxation times, are calculated with a resolution the size of dynamical heterogeneities.
Optical probe reorientation measurements were performed to monitor changes in segmental dynamics resulting from the nonlinear deformation of a polymer glass. Segmental dynamics were monitored in a poly(methyl methacrylate) glass near Tg before and after a series of reversing deformations in which the sample was extended at constant strain rate and then allowed to retract back to zero stress at constant strain rate. Evidence of a rejuvenation mechanism, as quantified by a departure of the segmental dynamics from the quiescent aging dynamics after the reversing deformation, is observed for deformations which reach 60% of the yield strain or greater. By this measure, a saturation of the rejuvenation mechanism is not observed until at least 5 times the yield strain. For comparison, purely mechanical measurements of rejuvenation, based upon the reduction of the yield stress in a subsequent deformation, were also performed. These purely mechanical experiments show broad qualitative agreement with the probe reorientation experiments but quantitatively differ in the pre-yield regime. The results are discussed in the context of recent theoretical approaches and simulations which provide a molecular-level description of polymer glass deformation.
A direct relation between molecular characteristics and macroscopic mechanical properties of polymeric materials was subject of a vast number academic and industrial research studies in the past. Motivation was that an answer to this question could, in the end, result in guidelines how to construct tailored materials, either on the molecular level or, in heterogeneous materials, on the micro-scale, that could serve our needs of improved materials without the need of extensive trial and error work. Despite all attempts, no real universally applicable success was reported, and it was only after the introduction of the concept of the polymer's intrinsic deformation behavior that some remarkable progress could be recognized. Thus, it is first important to understand where intrinsic deformation behavior of polymeric materials stands for. Second, it is interesting to understand why this intermediate step is relevant and how it relates to the molecular structure of polymers. Third and, in the end, the most computational-modeling-based question to be answered is how intrinsic behavior relates to the macroscopic response of polymeric materials. This is a multi-scale problem like encountered in many of our present research problems.
A specially designed solid-state deuterium nuclear magnetic resonance probe was used to examine the effect of uniaxial elongation on the chain mobility in the amorphous region of semicrystalline nylon 6. In measurements conducted near the glass transition temperature, there was measurable deformation-induced enhancement of the mobility of the amorphous chains up to the yield point. This enhanced mobility decayed once deformation was stopped. Enhanced mobility was not observed in deformation at room temperature. The mechanics of deformation can be explained by the Robertson model for glassy polymers near the glass transition temperature, which states that applied stress induces liquid-like behavior in the polymer chains.
Using fast confocal microscopy we image the three-dimensional dynamics of particles in a yielded hard-sphere colloidal glass under steady shear. The structural relaxation, observed in regions with uniform shear, is nearly isotropic but is distinctly different from that of quiescent metastable colloidal fluids. The inverse relaxation time tau(alpha)(-1) and diffusion constant D, as functions of the local shear rate gamma*, show marked shear thinning with tau(alpha)(-1) proportional to D proportional to gamma*(0.8) over more than two decades in gamma*. In contrast, the global rheology of the system displays Herschel-Bulkley behavior. We discuss the possible role of large scale shear localization and other mechanisms in generating this difference.
We study the dielectric relaxation of polycarbonate (PC) at room temperature under imposed strain rate γ, above the yield stress, and up to 13% strain. We find that the dielectric response of stretched PC behaves as if it was heated up at a temperature just below its glass transition temperature, Tg ∼ 423 K for PC. Indeed, in the frequency range of our experiment (10-2 and 103 Hz), the dielectric response of the stretched PC at room temperature superimposes to the dielectric response of PC at a temperature Ta(γ) < Tg, which is a function of strain rate. Specifically we observe that at Ta the dominant relaxation time τα(Ta) of PC at rest is related to γ in such a way that τα(Ta) 1/γ at and beyond the yield point. In our experiment, 10-5 s-1 < γ < 10-3 s-1, the temperature shifts Tg - Ta are of a few kelvin. The mechanical rejuvenation modifies the dielectric response at frequencies smaller than 10 Hz, whereas for higher frequencies the spectrum is only slightly modified.
Optical probe reorientation measurements were utilized to investigate the effect of temperature on the segmental dynamics of a glassy polymer during deformation. Constant strain rate deformations were performed on poly(methyl methacrylate) glasses at temperatures from Tg – 27 K to Tg – 11 K and engineering strain rates from 3 × 10–6 to 3 × 10–5 s–1. Deformation enhances segmental mobility by up to a factor of 100 in these experiments. In the postyield flow state at a given strain rate, the effect of temperature on dynamics is reduced, relative to the undeformed polymer glass. However, we still observe a significant effect of temperature on segmental dynamics during flow, with calculated free energy barriers of ∼39 kTg. The Kohlrausch–Williams–Watts parameter βKWW, a measure of spatially heterogeneous dynamics, is observed to increase in the postyield regime with increasing strain rate and decreasing temperature, indicating more homogeneous dynamics. βKWW is correlated with the enhancement of segmental dynamics relative to the undeformed polymer, independent of temperature.
Nonlinear creep is one of the generic features of deformation response of glassy polymers, where a rich set of strain vs time responses is observed that depend upon the applied stress and the thermal history used to form the glass. Although existing constitutive models may be able to describe some aspects of nonlinear creep, these models are unable to provide a unified description of the diverse nonlinear creep behaviors exhibited by glassy polymers, where predicting the effects of thermal history has proved especially challenging. In this paper the ability of a recently developed Stochastic Constitutive Model (SCM) to describe nonlinear creep is critically examined, where it is demonstrated that the SCM qualitatively captures all of the major features of nonlinear creep of glassy polymers, including the tertiary creep. In particular the SCM predicts how the duration of the secondary creep and the range of the tertiary creep depend on the aging time prior to deformation. The SCM predicts the existence of Stage IV creep, which comes after the tertiary creep - where examination of nonlinear creep data clearly indicate the presence of Stage IV creep, although heretofore not recognized, in the experimental data. The SCM unifies the description of nonlinear creep, and provides a detailed mesoscopic picture of the processes that underlie both strain controlled and stress controlled experiments.
Kim, et al. (Polymer, 54(15), 3949, 2013) recently reported on the unexpected relaxation behavior of an amorphous polymer in the Tg-region, where the rate of stress relaxation increased with deformation at a strain rate of 1.5 × 10−4 s−1 but decreased at a strain rate of 1.2 × 10−5 s−1. This inversion in the ordering with strain rate challenges the underlying structure of the existing nonlinear viscoelastic and viscoplastic constitutive models, where the key nonlinearity is a deformation dependent material clock. The nonlinear stress relaxation predictions of a recently developed stochastic constitutive model, SCM, (Medvedev, et al., J. Rheology, 57(3), 949, 2013) that acknowledge dynamic heterogeneity of the glass have been investigated. The SCM predicts the inversion in the ordering of the mobility with the loading strain rate as reported by the stress relaxation response. The change in perspective on the nonlinear viscoelastic behavior of glassy polymers engendered by the SCM is discussed.
We present a quantitative analysis of the correlation between quasi-localized, low energy vibrational modes and structural relaxation events in computer simulations of a quiescent, thermal polymer glass. Our results extend previous studies on glass forming binary mixtures in 2D, and show that the soft modes identify regions that undergo irreversible rearrangements with up to 7 times the average probability. We study systems in the supercooled- and aging-regimes and discuss temperature- as well as age-dependence of the correlation. In addition to the location of rearrangements, we find that soft modes also predict their direction on the molecular level. The soft regions are long lived structural features, and the observed correlations vanish only after > 50% of the system has undergone rearrangements.
Molecular‐dynamics simulations of 5 nm‐thick atactic‐polystyrene films have been used to study the influence of cyclic‐shear deformation on the stress–strain behavior and local segmental mobility. Upon cyclic yield the stress–strain behavior of the films slowly evolves towards a steady state which is characterized by a decrease of the maximum stress and by an enhanced dissipative process. Immediately after plastic deformation the storage modulus is decreased and the loss modulus is increased as compared with their initial values. Such changes in the viscoelastic moduli reflect the mechanical rejuvenation of a polymer glass. This mechanical rejuvenation of polymers is connected to the increase in the simulated segmental mobility, which is calculated for the entire film as well as in different layers.
In this study a phenomenological constitutive model is proposed to describe the finite, nonlinear, viscoelastic behavior of glassy polymers up to the yield point. It is assumed that the deformation behavior of a glassy polymer up to the yield point is completely determined by the linear relaxation time spectrum and that the nonlinear effect of stress is to alter the intrinsic time scale of the material. A quantitative three-dimensional constitutive equation for polycarbonate as a model polymer was obtained by approximating the linear relaxation time spectrum by eighteen Leonov modes, all exhibiting the same stress dependence. A single Leonov mode is a Maxwell model employing a relaxation time that is dependent on an equivalent stress proportional to the Von Mises stress. Furthermore, a Leonov mode separates the (elastic) hydrostatic and (viscoelastic) deviatoric stress response and accounts for the geometrical complexities associated with simultaneous elastic and plastic deformation. Using a single set of parameters, the multi-mode Leonov model is capable of describing realistic constant strain rate experiments, including the strain rate dependent yield behavior. It is also capable of giving a quantitative description of nonlinear stress-relaxation experiments. (C) 1996 Society of Rheology.
A stochastic constitutive model has been developed that explicitly acknowledges the nanometer size dynamic heterogeneity of glassy materials, where the distribution of the viscoelastic relaxation times emerges naturally as a result of the dynamic heterogeneity. A set of stochastic differential equations for local stresses and entropy describing behavior of a mesoscopic domain are developed, and the observed macroscopic response of the material is obtained as an average of an ensemble of domains. The stochastic constitutive model naturally predicts and provides a mechanism for the postyield stress softening and its dependence on physical aging that is observed during constant strain rate uniaxial deformations.
Recent experiments show that deformation of a polymer glass can lead to
orders-of-magnitude enhancement in the atomic level dynamics. To
determine why this change in dynamics occurs, we carry out molecular
dynamics simulations and energy landscape analyses. The simulations
address the coarse-grained polystyrene model of Kremer and co-workers,
and the dynamics, as quantified by the van Hove function, are examined
as the glass undergoes shear deformation. In agreement with experiment,
the simulations find that deformation enhances the atomic mobility. The
enhanced mobility is shown to arise from two mechanisms: First, active
deformation continually reduces barriers for hopping events, and the
importance of this mechanism is modulated by the rate of thermally
activated transitions between adjacent energy minima. Second,
deformation moves the system to higher-energy regions of the energy
landscape, characterized by lower barriers. Both mechanisms enhance the
dynamics during deformation, and the second mechanism is also relevant
after deformation has ceased.
An advanced broadband dielectric relaxation spectroscopy technique was developed to measure dipolar reorientation dynamics in an actively deforming amorphous polymer below the glass transition temperature. The application of a weak oscillating electric field during deformation allows for direct probing chain segment mobility. Results show that the application of a monotonically increasing strain on a glassy poly(vinyl chloride) induces a significant increase of the out-of-phase dielectric permittivity, thereby reflecting enhancement of the transition activity of chain segments. Moreover, the strain-dependent relaxation spectra suggest that the bifurcation of the relaxation processes decreases together with an overall increase in molecular mobility upon active deformation. The dielectric results also display a highly pronounced sensitivity to the apparent strain rate used for the mechanical excitation and isothermal aging prior to the deformation.
We describe an apparatus for performing constant strain rate deformations of
polymer glasses while simultaneously measuring the segmental mobility with an
optical probe reorientation method. Poly(methyl methacrylate) glasses were
deformed at Tg - 19 K, for local strain rates between 3.7x10-5/s and
1.2x10-4/s. In these experiments, the mobility initially increases in the
pre-yield regime, by a factor of 40 to 160, as compared to the undeformed PMMA
glass. The mobility then remains constant after yield, even as the stress is
decreasing due to strain softening. This is consistent with the view that the
sample is being pulled higher on the potential energy landscape in this regime.
Higher strain rates lead to higher mobility in the post-yield regime and, for
the range of strain rates investigated, mobility and strain rate are linearly
correlated. We observe that thermal history has no influence on mobility after
yield and that deformation leads to a narrowing of the distribution of
segmental relaxation times. These last three observations are consistent with
previously reported constant stress experiments on PMMA glasses. The
experimental features reported here are compared to computer simulations and
theoretical models.
The mobility evolution in an epoxy glass during constant strain rate uniaxial deformation was examined via the stress relaxation response observed at various locations along the stress–strain curve, including the pre-yield, yield, and post-yield regions. Experiments were performed in the temperature range from Tg-30 °C to Tg-5 °C in both uniaxial extension and compression. At the faster loading strain rates the initial rate of stress relaxation is the slowest in the pre-yield region and the fastest in the post-yield region. However, at the slower loading strain rate the ordering is unexpectedly reversed so that the initial rate of stress relaxation is the fastest in the pre-yield region and the slowest in the post-yield region. These findings challenge the key assumption made in most existing constitutive models for glassy polymers that yield is the straightforward consequence of deformation induced increase in the mobility.
Yield in amorphous glassy polymers has been studied in shear and uniaxial tension/compression, where the volume change is relatively small and the deviatoric components of the strain/stress tensor are dominate. In order to study volumetrically driven yield in a different geometry, a specially designed experimental set-up was developed to create a longitudinal deformation that is dilatationally dominated. The longitudinal stress response of an epoxy resin was measured at temperatures just below Tg, where for the first time yield of a glassy polymer is observed in a nearly triaxial extension deformation. The yield behavior in uniaxial tension and compression was also determined, where all the yield data can be described with pressure-modified von Mises yield criterion but now for much wider pressure range than has been previously accessible.
The origins of molecular mobility in polymer glasses, particularly under deformation, are not well understood. A concerted experimental and computational approach is adopted to examine the segmental motion of a polymeric glass undergoing creep and constant strain rate deformations. Through a combination of molecular dynamics simulations and optical photobleaching experiments we are able to directly probe how dynamic heterogeneity evolves during deformation. Two distinct regimes emerge from our analysis; early in the deformation, the dynamics of the glass are strongly heterogeneous, as evidenced by the spectrum of relaxation times measured experimentally and the participation ratio of the atomic non-affine displacements measured computationally. After the onset of flow, the dynamics become significantly more homogeneous, and the participation ratio increases considerably.
The material response after the application of a constant strain rate ramp, followed, at time t1, by a constant strain differs from the response to an ideal (instantaneous) step of strain at short test times. Due to experimental limitations, the ideal step-strain cannot be achieved. As a result, short time stress relaxation data have to be corrected in order to obtain reliable estimates of, for example, the modulus G(t) at times shorter than approximately ten times the ramp time. Here we compare two methods of correction to the stress relaxation data obtained after a linear ramp, assuming a relaxation modulus of the form G(t) =G0 e-(t/t)ß. The Lee and Knauss correction uses an iterative scheme based on Boltzmann superposition. We compare this method with the Zapas–Craft approach in which the `true' relaxation time becomes t-t1/2 (t is the experimental time and t1 is the finite time to apply the step in strain). Our numerical computations show that when the relaxation time is short, there is a substantial error in the Lee–Knauss correction. Although the Zapas–Craft approach provides a better correction for times just slightly greater than t1/2, it is limited in that it cannot be used for times shorter than t1/2. We also investigate the case for which the ramp-step is replaced with a more realistic nonlinear function of time. Finally, it is often desirable to have a similar correction for large deformation responses. The Lee–Knauss method is valid only for linear viscoelastic systems whereas the Zapas–Craft approach has not been rigorously evaluated for large deformations. We evaluate the use of the latter for large deformations within the context of the Bernstein, Kearsley and Zapas single integral model.
Dramatic enhancement of diluent conductance in glassy polymers actively undergoing plastic flow has long been suspected. We report observations of this phenomenon in a glassy poly(ether imide) (Ultem)™ in the presence of resorcinol bis(diphenyl phosphate) (RDP) by means of the limited-supply diffusion experiment developed earlier by Nealey et al. In this experiment it is demonstrated that RDP uptake in plastically deforming Ultem is nearly identical at 113°C, ie. 102°C below Tg, as it is at 215°C, at Tg, without concurrent plastic flow. While the characteristic profiles of penetrating Case-II fronts are present in experiments at 130°C without plastic flow, they are absent in experiments above Tg without plastic flow and in those at 113°C undergoing concurrent plastic flow. This demonstrates that in the plastically deforming polymer, well below Tg, a steady dilated flow state exists, which resembles in its molecular level conformational rearrangements that at Tg without deformation, where in both the resistance to diluent penetration has been radically reduced. Based on the measured diffusion constant of RDP in Ultem, the structural correspondence of the thermally dilated state at Tg and the flow dilated state at 113°C is equivalent to an increase of the diffusion constant by a factor of 1.9×104 in the latter.
Glassy polymers show "strain hardening": at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes then to re-vitrify. Here, we present new results for the corresponding behavior under step-stress shear loading, to which very similar physics applies. To explain the unloading behavior in the extensional case requires introduction of a "crinkle factor" describing a rapid loss of segmental ordering. We discuss in more detail here the physics of this, which we argue involves non-entropic contributions to the polymer stress, and which might lead to some important differences between shear and elongation. We also discuss some fundamental and possibly testable issues concerning the physical meaning of entropic elasticity in vitrified polymers. Finally, we present new results for the startup of steady shear flow, addressing the possible role of transient shear banding.
Since to form a hole the size of a molecule in a liquid requires almost the same increase in free energy as to vaporize a molecule, the concentration of vapor above the liquid is a measure of such ``molecular'' holes in the liquid. This provides an explanation of the law of rectilinear diameters of Cailletet and Mathias. The theory of reaction rates yields an equation for absolute viscosity applicable to cases involving activation energies where the usual theory of energy transfer does not apply. This equation reduces to a number of the successful empirical equations under the appropriate limiting conditions. The increase of viscosity with shearing stress is explained. The same theory yields an equation for the diffusion coefficient which when combined with the viscosity and applied to the results of Orr and Butler for the diffusion of heavy into light water gives a satisfactory and suggestive interpretation. The usual theories for diffusion coefficients and absolute electrical conductance should be replaced by those developed here when ion and solvent molecule are of about the same size.
We have used a holographic fluorescence recovery after photobleaching (FRAP) techanique to measure translational diffusion coefficients of tracer levels of 9,10-bis(phenylethynyl)anthracene (BPEA) in polystyrene. Values for the diffusion coefficient DT ranged from 10-8 to 10-14 cm^2/sec over the temperature range T_g+90K to Tg (Tg = 373K). DT has a considerably weaker temperature dependence than matrix viscosity eta. In contrast, the rotational correlation time tau c for BPEA has the same temperature dependence as eta. At T_g, translational diffusion of BPEA is enhanced over rotation by 2.4 decades. These results support the idea that spatially heterogeneous dynamics are responsible for enhanced translation and are an important feature of dynamics at T_g.
Optical photobleaching experiments and molecular dynamics computer simulations were used to investigate changes in segmental mobility during tensile creep deformation of polymer glasses. Experiments were performed on lightly cross-linked PMMA, and the simulations utilized a coarse-grained model. For both single-step and multistep creep deformations, the experiments and simulations show remarkably similar trends, with changes of mobility during deformation exceeding a factor of 100. Both experiment and simulation show a strong correlation between strain rate and mobility in single-step creep. However, in multistep creep, the correlation between strain rate and mobility is broken in both experiment and simulation; this emphasizes that no simple mechanical variable is likely to exhibit a simple relationship with molecular mobility universally. Both simulations and experiments show many features that are inconsistent with the Eyring model.
We have examined the response of a polymer and a polymer nanocomposite glass to creep and constant strain rate deformations using Monte Carlo and molecular dynamics simulations. We find that nanoparticles stiffen the polymer glass, as evidenced by an increase in the initial slope of the stress−strain curve and a suppression of the creep response. In contrast to previous reports, we also find that, during deformation, the effective relaxation time or mobility of the material is only qualitatively characterized by the instantaneous strain rate. Constant strain rate and constant stress deformations have different effects on the material’s position on its energy landscape, and neither a mechanical variable, such as the stress or strain rate, nor a thermodynamic variable, such as the material’s position on its energy lanscape, is uniquely indicative of the relaxation times in the material.
The nonlinear Langevin equation theory of segmental relaxation, elasticity, and nonlinear mechanical response of deformed polymer glasses with aging and mechanical rejuvenation processes taken into account is applied to study material response under a constant strain rate deformation. In the postyield softening regime, the amplitude of the stress overshoot feature, and its breadth in strain, are predicted to be positively correlated with the mechanically induced disordering process. The key physics is the increase of the density fluctuation amplitude due to mechanically generated disorder (rejuvenation) which reduces the elastic modulus and speeds up relaxation beyond the effects of the landscape tilting mechanism. Detailed numerical calculations reveal that the emergence of strain softening is not directly tied to a difference between the initial and steady plastic flow states, but rather on whether there exists a rejuvenation-dominated process during deformation. Calculations suggest a roughly linear relation between the strain softening amplitude (SSA) and the amount of rejuvenation as quantified by variation of the density fluctuation amplitude. The dependences of the yield stress and strain, steady state flow stress, and SSA on deformation rate, temperature, preaging time, and also two distinct thermal history protocols are investigated in detail for PMMA glass. Overall, good agreement between theory and experiment is found.
Rotational correlation times tau(c) for rubrene and tetracene are reported near and below T-g in three polymers: polyisobutylene, polystyrene, and Bisphenol A polysulfone. A photobleaching method was used to obtain tau(c) values from 10(-1) to 10(3) s. In each polymer matrix, the orientation autocorrelation function for tetracene (the smaller probe) decays more rapidly and less exponentially than the correlation function for rubrene. tau(c) for a given probe at the T(g)s of the matrices varies more than 3 decades. For the three polymers studied, probe rotation times at T-g showed a systematic decrease with increasing matrix T-g. Viscoelastic relaxation times characteristic of the Rouse modes of the matrix polymers are closely related to probe rotation times and also not constant at T-g. Thus T-g is not an isolocal mobility state for molecular motions on a fixed length scale. On the other hand, the viscoelastic relaxation time associated with the glassy modulus is almost constant at T-g. These results suggest that the characteristic length scale for motions associated with the relaxation of the glassy modulus varies significantly for the three polymers studied. Trends in the KWW beta values which describe probe reorientation support this interpretation.
Glassy polymers show strain hardening: at constant extensional load, their
flow first accelerates, then arrests. Recent experiments have found this to be
accompanied by a striking and unexplained dip in the segmental relaxation time.
Here we explain such behavior by combining a minimal model of flow-induced
liquefaction of a glass, with a description of the stress carried by strained
polymers, creating a non-factorable interplay between aging and strain-induced
rejuvenation. Under constant load, liquefaction of segmental motion permits
strong flow that creates polymer-borne stress. This slows the deformation
enough for the segmental modes to re-vitrify, causing strain hardening.
Tensile experiments in polystyrene (PS) and poly(methyl methacrylate) (PMMA) conducted at constant strain rate over a wide range of pressure and temperature have shown that a brittle-to-ductile transition is induced in these amorphous polymers by the superposition of hydrostatic pressure as well as by the raise of the experimental temperature. A detailed stress–strain analysis permits explanation of the mechanism for the brittle-to-ductile transition in terms of interaction between two competing processes of plastic yielding—crazing and shear banding phenomena. The crazing and shear banding processes respond quite differently to changes of pressure or temperature, causing shifting of the brittle-to-ductile transition point to where the craze initiation stress and shear band initiation stress again become equal. The evidence that the brittle-to-ductile transition pressure becomes lower with increasing temperature refutes a previously suggested concept that the transition relates primarily to mechanical relaxation phenomena.
The stress relaxation response in the glassy state just below Tg was measured for poly(methylmethacrylate) following application of constant strain rate uniaxial tensile deformation at various locations on the stress–strain curve, including the yield and post-yield region. The macroscopic mobility was determined from analysis of the relaxation response. Up to a factor of 3 decrease in relaxation time was observed with the fastest relaxation occurring in the post-yield softening region. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010
Translational diffusion of tetracene and rubrene in bisphenol A polysulfone (Tg = 460 K) was measured using a holographic fluorescence recovery after photobleaching (FRAP) technique. In the temperature range from 493 to 462 K, probe translation was diffusive and the translational diffusion coefficients varied from 10−8 to 10−13 cm2/s. Surprisingly, the observed translational diffusion coefficients showed a weaker temperature dependence than the rotational correlation times of the same probes. Rotational correlation times have the same temperature dependence as the viscoelastic relaxation times characteristic of the rubberlike modulus, while translational relaxation times decouple from the viscoelastic relaxation times. On average, probe molecules are translating larger and larger distances per probe rotation time as the temperature is lowered to Tg. These results can be explained qualitatively in terms of spatially heterogeneous segmental dynamics in the polysulfone matrix. © 1996 John Wiley & Sons, Inc.
The incremental response ΔG(t) obtained by superposing a deformation, Δ, on a large deformation, 1, has been determined in step shear experiments for a polyisobutylene solution and for a poly(methylmethacrylate) glass in torsion. For both systems ΔG(t) at 1 was found to be smaller than the linear viscoelastic modulus, G(t), at zero prestrain. ΔG(t) was found to increase with increasing time, te, after imposition of the large deformation. It was also observed that the “apparent relaxation spectrum” associated with ΔG(t) narrows and shifts to shorter times when compared to the spectrum associated with the linear viscoelastic modulus, ΔG(t). The results for the solution art-well described by the nonlinear constitutive equation of the BKZ elastic fluid theory. It is found that ΔG(t) for the glass falls between the behavior predicted by the BKZ theory and the linear viscoelastic behavior.
The strain hardening modulus, defined as the slope of the increasing stress with strain during large strain uniaxial plastic deformation, was extracted from a recently proposed constitutive model for the finite nonlinear viscoelastic deformation of polymer glasses, and compared to previously published experimental compressive true stress versus true strain data of glassy crosslinked poly(methyl methacrylate) (PMMA). The model, which treats strain hardening predominantly as a viscous process, with only a minor elastic contribution, agrees well with the experimentally observed dependence of the strain hardening modulus on strain rate and crosslink density in PMMA, and, in addition, predicts the well-known decrease of the strain hardening modulus in polymer glasses with temperature. General scaling aspects of continuum modeling of strain hardening behavior in polymer materials are also presented. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1464–1472, 2010
A study done to find out the physics of deformation and the properties of polymer glasses was discussed. Polymer glasses have appealing properties for a number of optical and other applications and their high resistance to plastic deformation, expressed as the ratio of low temperature yield stress to elastic modulus of order 0.05, is an additional bonus. Physical aging of the polymer glass increases the shear yield stress, the stress required to continue shear deformation at moderately larger strains. The results show that simulations, that treat the aging and rejuvenation of polymeric glasses at constant pressure rather than constant density at a finite temperature, can play a major role to arrive at a possible understanding of the phenomena.
In this paper the authors describe in detail the experimental techniques for the simultaneous measurement of the dynamic Young's modulus and the dynamic Poisson's ratio, from which the dynamic bulk and shear moduli can be calculated. Experimental results are presented on the effects of temperature, frequency, and tensile strain on these properties of poly(methyl methacrylate) (PMMA). The temperature and frequency effects indicate that the β relaxation in PMMA is not a purely internal motion but is coupled to the bulk.
Polymeric materials subjected to large strains undergo an evolution in molecular orientation. The developing orientation and corresponding strengthening are highly dependent on the state of strain. In this paper, we examine and compare the very different stress-strain results of polycarbonate produced from four types of mechanical testing: uniaxial compression, plane strain compression, uniaxial tension, and simple shear. These tests produce different states of orientation within the material and, in the case of simple shear, the principle axes of orientation rotate during the deformation. The ability of the recent constitutive model of Arruda and Boyce (1992) to predict the to predict the observed behavior is evaluated. The model has been incoporated into a finite element code in order to properly simulate the material behavior during the inhomogenous deformations of tension (cold drawing) and simple shear. The material properties of the model are obtained from the uniaxial compression test and the model is then found to be truly predictive of the other states of deformation demonstrating its fully three dimensional capability. The disadvantages of the tensile and simple shear tests for obtaining the data needed to accurately quantify the large strain material behavior of polymers are shown and discussed.
The continuous development of constitutive equations for the finite strain deformation of glassy polymers has resulted in a number of sophisticated models that can accurately capture the materials' intrinsic behavior. Numerical simulations using these models revealed that the thermal history plays a crucial role in the macroscopic deformation. Generally, macroscopic behavior is assumed not to change during a test, however, for certain test conditions this does not hold and a relevant change in mechanical properties, known as physical aging, can be observed. To investigate the consequences of this change in material structure, the existing models are modified and enhanced by incorporating an aging term, and its parameters are determined. The result is a validated constitutive relation that is able to describe the deformation behavior of, in our case, polycarbonate over a large range of molecular weights and thermal histories, with one parameter set only.
An optical photobleaching method has been used to measure the segmental dynamics of a poly(methyl methacrylate) (PMMA) glass during uniaxial creep deformation at temperatures between Tg − 9 K and Tg − 20 K. Up to 1000-fold increases in mobility are observed during deformation, supporting the view that enhanced segmental mobility allows flow in polymer glasses. Although the Eyring model describes this mobility enhancement well at low stress, it fails to capture the dramatic mobility enhancement after flow onset, where in addition the shape of the relaxation time distribution narrows significantly. Regions of lower mobility accelerate their dynamics more in response to an external stress than do regions of high mobility. Thus, local environments in the sample become more dynamically homogeneous during flow. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1713–1727, 2009
Many advanced engineering problems suffer from inadequate solution because the appropriate constitutive behavior for the materials involved is not available. This is certainly true where polymers are concerned because in many situations involving failure analysis the non-linear viscoelastic material properties become important.In this paper a non-linear viscoelastic constitutive law is considered. It starts from the assumption that linear viscoelasticity is appropriate under infinitesimal strains and that the material description must revert to this case. The non-linearity of this development is derived from the stress dependent time response in the deformation process. The physical basis for the description derives from the observation that stress induced dilatation effects the mobility of molecular chains through changing the free volume in the polymer. Test data for polyvinyl acetate are compared with computations under conditions of relaxation and constant strain rate deformation. Excellent agreement is obtained between the proposed model and experiments. This agreement would indicate that the free volume model is definitely a possible way of describing non-linear viscoelastic behavior under small to moderate strains.
A thermodynamically consistent nonlinear viscoelastic constitutive theory is derived to capture the wide range of behavior observed in glassy polymers, including such phenomena as yield, stress/volume/enthalpy relaxation, nonlinear stress–strain behavior in complex loading histories, and physical aging. The Helmholtz free energy for an isotropic, thermorheologically simple, viscoelastic material is constructed, and quantities such as the stress and entropy are determined from the Helmholtz potential using Rational Mechanics. The constitutive theory employs a generalized strain measure and a material clock, where the rate of relaxation is controlled by the internal energy that is likewise determined consistently from the viscoelastic Helmholtz potential. This is perhaps the simplest model consistent with the basic requirements of continuum physics, where the rate of relaxation depends upon the thermodynamic state of the polymer. The predictions of the model are compared with extensive experimental data in the following companion paper.
A molecular level analysis of segmental trajectories obtained from molecular
dynamics simulations is used to obtain the full relaxation time spectrum in
aging polymer glasses subject to three different deformation protocols. As in
experiments, dynamics can be accelerated by several orders of magnitude, and a
narrowing of the distribution of relaxation times during creep is directly
observed. Additionally, the acceleration factor describing the transformation
of the relaxation time distributions is computed and found to obey a universal
dependence on the global strain, independent of age and deformation protocol.
This paper gives a brief review of recent results of rheo-dielectric studies for oligo-styrene (OS) and cis-polyisoprene (PI). OS has type-B dipoles perpendicular to the backbone, and its dielectric α relaxation (glassy mode relaxation) is accelerated under the shear flow even at rates much smaller than the equilibrium relaxation frequency. This acceleration, resulting in the decrease of the viscosity (thinning) observed at those rates, is related to flow-induced reduction of the cooperativity of the segmental motion. For PI chains, having type-A dipoles parallel to the backbone, the dielectric relaxation detects the global chain motion. For well entangled PI chains, this relaxation is only moderately accelerated and its intensity is only mildly reduced even under fast flow in the non-Newtonian thinning regime. This result is related to a flow-induced orientational cross-correlation of entanglement segments. Within the context of the tube model for entangled chains, this cross-correlation can be related to the dynamic tube dilation induced by the convective constraint release.
The nonlinear viscoelastic behavior of glassy polymers and its relationship to ductile yielding is studied by single- and double-step stress relaxation experiments. In the latter case a small stress relaxation step is superimposed on a specimen at an elevated state of temperature or strain. The results show that the changes in the relaxation behaviors in the two cases closely parallel each other. The relaxation behavior at strains near yield closely approximates that at low strain but near Tg. The small strain relaxation response can be described well by a Kohlrausch-Williams-Watts (KWW) type function. The interpretation of these data in terms of a coupling model which includes the KWW form is discussed. Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/38856/1/090261206_ftp.pdf
When sufficient force is applied to a glassy polymer, it begins to deform through movement of the polymer chains. We used
an optical photobleaching technique to quantitatively measure changes in molecular mobility during the active deformation
of a polymer glass [poly(methyl methacrylate)]. Segmental mobility increases by up to a factor of 1000 during uniaxial tensile
creep. Although the Eyring model can describe the increase in mobility at low stress, it fails to describe mobility after
flow onset. In this regime, mobility is strongly accelerated and the distribution of relaxation times narrows substantially,
indicating a more homogeneous ensemble of local environments. At even larger stresses, in the strain-hardening regime, mobility
decreases with increasing stress. Consistent with the view that stress-induced mobility allows plastic flow in polymer glasses,
we observed a strong correlation between strain rate and segmental mobility during creep.
Although it has long been recognized that dynamics in supercooled liquids might be spatially heterogeneous, only in the past few years has clear evidence emerged to support this view. As a liquid is cooled far below its melting point, dynamics in some regions of the sample can be orders of magnitude faster than dynamics in other regions only a few nanometers away. In this review, the experimental work that characterizes this heterogeneity is described. In particular, the following questions are addressed: How large are the heterogeneities? How long do they last? How much do dynamics vary between the fastest and slowest regions? Why do these heterogeneities arise? The answers to these questions influence practical applications of glass-forming materials, including polymers, metallic glasses, and pharmaceuticals.
The reorientation of dye molecules can be used to monitor the segmental dynamics of a polymer melt. We utilize this technique to measure stress-induced mobility in a lightly cross-linked poly(methyl methacrylate) (PMMA) glass during tensile creep deformation. At 377 K (18 K below the glass transition temperature Tg), the mobility increased by a factor of 100 during deformation with a stress of 20 MPa. Generally, the mobility increased as the stress, strain, and strain rate increased. After removing the stress, we observed that the enhanced mobility slowly disappeared during strain recovery. At 377 K, when the stress is lower than 11 MPa, almost no mobility enhancement was observed. Once the stress crossed this threshold value, the mobility dramatically increased.