Comparison of mechanical and molecular measures of mobility during constant strain rate deformation of a PMMA glass

We performed constant strain rate deformation and stress relaxation on a poly(methyl methacrylate) glass at T_g – 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. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1957–1967     

Cyclic nonlinear behavior of a glassy polymer using a contact method

The effects of repeated large strain shear cycles on the dynamics of a glassy acrylate polymer are investigated using an original contact method. It is based on the measurement of the shear properties of thin (about 50 μm) polymer films geometrically confined within contacts between elastic substrates. Under small amplitude (300 nm–10 μm) oscillating lateral displacements, friction at the contact interface can be neglected and the measurement of the contact lateral response thus provides information about the rheology of the sheared polymer film. Using this approach, the complex shear modulus of the polymer film can be measured both in the linear (viscoelastic) and in the nonlinear regimes. The investigations are focused on the changes in mechanical properties induced in a large strain regime where the polymer glass is cyclically sheared up to the yield point. During the application of large strain cycles, the mechanical response of the polymer glass slowly evolves toward a quasi stabilized state which is described from the measurement of an apparent–strain dependent–complex shear modulus. When the applied strain is increased by a tenfold factor, this apparent shear modulus decreases by about one decade. These underlying changes are investigated from a consideration of the time dependent linear viscoelastic properties after the mechanical stimulus. Both mechanical rejuvenation and recovery (ageing) effects are evidenced. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Transient dynamics of cold-rolled and subsequently thermally rejuvenated atactic-polystyrene using broadband dielectric spectroscopy

The effect of plastic deformation on the molecular dynamics of atactic polystyrene (a-PS) was studied by broadband dielectric relaxation spectroscopy (BDRS), Fourier-transform infrared spectroscopy (FTIR) and polarized-light microscopy. Sheets of a-PS have been subjected to cold rolling, that is, mechanical rejuvenation, followed by a quenching step and fast heating above its glass-transition temperature, resulting in thermal rejuvenation. Cold rolling revealed, in addition to the known α- and γ(I)-relaxations, four hitherto unknown relaxation processes (II, III, IV and V). Using the framework of craze formation and multiplicity of the glass transition (E. Donth, G. H. Michler, Colloid Polym. Sci. 1989, 267, 557–567), supported by an activation-enthalpy/entropy analysis (Starkweather, W. Howard, Macromolecules 1981, 14, 1277–1281), the following physical picture emerges: (a) processes I and II represent local conformation transitions γ referring to chains of two different degrees of stretching (T/G-ratio); and (ii) processes III and IV were identified as helix-inversion processes of T₂G₂ helices as reported earlier for syndiotactic-rich PS—an assignment supported by FTIR results. Finally, the relaxation V could be attributed to the onset of the fibrillar glass transition (within crazes), leading to stress release by collapse of the fibrils and hence dying out of process V. Polarized-light microscopy confirmed the creation of oriented structures and internal stresses upon cold rolling, and their removal upon thermal rejuvenation.     

Rejuvenation of PLLA: Effect of plastic deformation and orientation on physical ageing in poly(l‐lactic acid) films

Poly(l ‐lactic acid) (PLLA) is a bio‐degradable polyester which exhibits brittle behaviour due to relatively fast physical ageing of the amorphous phase. This work describes the effects of thermal rejuvenation and molecular orientation of the amorphous phase on this physical ageing process. Uniaxial compression testing showed that physical ageing of the amorphous phase increases the yield stress and the associated strain softening response, both contributing to the observed embrittlement of PLLA in tension. Molecular orientation at constant crystallinity was applied by uniaxial and biaxial plastic deformation just above the glass transition temperature, up to plastic strains of 200% to avoid strain‐induced crystallisation. Using stress‐relaxation experiments combined with tensile testing, both as a function of ageing time, it is shown that both uniaxial and biaxial plastic deformation in excess of 150% plastic strain, decelerates and possibly prohibits the physical ageing process. The oriented monofilaments and films have improved mechanical properties such as stiffness, strength and strain‐to‐break, which were not affected by physical ageing during the whole testing period (40 days). In addition, plastic deformation to higher draw ratios and/or higher temperatures strongly enhanced crystallinity and resulted in PLLA monofilaments and films that also exhibited tough behaviour, not affected by physical ageing. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2233–2244     

Rejuvenation,Aging, and Confinement Effects in Atactic‐Polystyrene Films Subjected to Oscillatory Shear

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.

     

Sheared polymer glass and the question of mechanical rejuvenation

There has been much recent debate as to whether mechanical deformation reverses the aging of a material, and returns it to a structure characteristic of the system at a higher temperature. We use molecular dynamics simulation to address this problem by carrying out shear and temperature increase simulation on atactic glassy polystyrene. Our results show explicitly that the structure (as quantified by the torsion population) changes associated with shear and temperature increase are quantitatively--and in some cases qualitatively--different. This is due to the competition between rejuvenation and physical aging, and we show this by carrying out a relaxation simulation. The conclusion agrees with those from previous experiments and simulations, which were suggestive of mechanical deformation moving the system to structures distinct from those reached during thermal treatment.     

Kinetics of re‐embrittlement of (anti)plasticized glassy polymers after mechanical rejuvenation

Mechanical rejuvenation is known to dramatically alter the deformation behavior of amorphous polymers. Polystyrene (PS)—for example, typically known as a brittle polymer—can be rendered ductile by this treatment, while a ductile polymer like polycarbonate (PC) shows no necking anymore and deforms homogeneously in tensile deformation. The effects are only of temporary nature, as because of physical aging the increasing yield stress, accompanied by intrinsic strain softening, renders PS brittle after a few hours, while for PC necking in tensile testing returns in a few months after the mechanical rejuvenation treatment. In this study, it is found that physical aging upon rejuvenation in both PS and PC can be delayed in two different ways: (1) by reducing the molecular mobility through antiplasticization and (2) by applying toughening agents (rubbery core–shell particles). For the first route, even though progressive aging is found to decrease with increasing amounts of antiplasticizer added, dilution of the entanglement network results in enhanced brittleness. Besides antiplasticization effects, also some typical plasticization effects are observed, like a reduction in matrix T_g. For the second route, traditional rubber toughening using acrylate core–shell modifiers also results in a reduced yield stress recovery, and ductile tensile deformation behavior is observed even 42 months after mechanical rejuvenation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 134–147, 2008     

Fundamental relationship between the nonequilibrium glassy state and yield stress of amorphous polymers

This paper reports the theoretical prediction and experimental verification of the connection between the yield stress of amorphous polymers and the physical aging phenomenon. The analysis reveals the existence of a fundamental relationship between the nonequilibrium glassy state and the thermally activated process controlling viscoelastic and plastic deformation. The results show that the volume relaxation and deformation kinetics share the same relaxation times, and that the activation energy for deformation below T_g is much smaller than previously mentioned in the literature. This indicates that the phenomenon of physical aging plays a very important role in the deformation and processing of polymers at low temperatures. The effect of quenching and annealing on the yield stress is described in terms of the mean energy of hole formation, the departure of volume from its equilibrium state, the distribution of hole energies, and lattice volume. The same set of molecular parameters obtained from the molecular kinetic theory of the glass transition and volume relaxation predicts the yield stress as a function of cooling rate, annealing time, temperature, and strain rate.     

The Nonlinear Viscoelastic Response of Glassy Polymers Subjected to Physical Aging

Constitutive equations are developed for the nonlinear viscoelastic behavior of amorphous glassy polymers in the sub‐yield region. A polymeric glass is treated as an ensemble of cooperatively rearranging regions bridged by links. Stress‐strain relations are derived and verified by comparison with experimental data in static mechanical tests on polycarbonate and poly(methyl methacrylate). We analyze the effects of the straining state (tension, compression and torsion), strain intensity, temperature and time of annealing on stress relaxation. Fair agreement is demonstrated between observations and results of numerical simulation.     

Stress relaxation of PVC below the yield point

Stress relaxation of commercial poly(vinyl chloride) (PVC) is measured at strains below 3% and at different temperatures below the glass transition temperature. First it is shown that below the yield point the material follows a linear viscoelastic behavior. Then the data at a fixed deformation level (0.03) are fitted by considering a lognormal distribution function of relaxation times. Furthermore, from the measured stress-strain curves, the temperature dependence of the elastic tensile modulus is determined. The temperature dependence of the elastic modulus, the relaxation strength, and the parameters of the distribution: mean relaxation time, τ_m, and half-width, β, are given. Moreover, the distribution function and the temperature dependence of its characteristic parameters are discussed in terms of a cooperative model of the mechanisms involved in the mechanical relaxation of glassy polymers. Finally, the relationship proposed between the tensile modulus and the free volume helps explain the temperature dependence of the relaxation strength. © 1996 John Wiley & Sons, Inc.     

Viscoelastic properties of UHMW-PE fibers in simple elongation

Stress relaxation after a simple elongational step strain, creep under a constant simple elongational stress, and stress build-up under a constant Hencky strain rate have been measured for ultrahigh-molecular-weight polyethylene (UHMW-PE) fibers. The data from the various experiments are consistent with the Boltzman superposition principle in the experimental region of small strains or short times. This leads to a simple constitutive equation in which temperature can be incorporated via time-temperature superposition. The measured power-law relaxation of the UHMW-PE fiber leads to analytical expressions for the dynamic quantities in simple elongation. The constitutive equation is the one-dimensional equivalent of the gel equation derived for cross-linking gels at the gel point. The similarity between the rheological behavior of fibers and cross-linking gels at the transition point might lead to an enhanced understanding of the molecular processes occurring during deformation.     

Athermal simulation of plastic deformation in amorphous solids at constant pressure

An algorithm is introduced for the molecular simulation of constant-pressure plastic deformation in amorphous solids at zero temperature. This allows to directly study the volume changes associated with plastic deformation (dilatancy) in glassy solids. In particular, the dilatancy of polymer glasses is an important aspect of their mechanical behavior. The new method is closely related to Berendsen's barostat, which is widely used for molecular dynamics simulations at constant pressure. The new algorithm is applied to plane strain compression of a binary Lennard-Jones glass. Conditions of constant volume lead to an increase of pressure with strain, and to a concommitant increase in shear stress. At constant (zero) pressure, by contrast, the shear stress remains constant up to the largest strains investigated (ε = 1), while the system density decreases linearly with strain. The linearity of this decrease suggests that each elementary shear relaxation event brings about an increase in volume which is proportional to the amount of shear. In contrast to the stress–strain behavior, the strain-induced structural relaxation, as measured by the self-part of the intermediate structure factor, was found to be the same in both cases. This suggests that the energy barriers that must be overcome for their nucleation continually grow in the case of constant-volume deformation, but remain the same if the deformation is carried out at constant pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2057–2065, 2004     

On the use of a four-cameras stereovision system to characterize large 3D deformation in elastomers

The mechanical behavior and volume change of filled elastomers were studied thanks to a four-cameras stereovision system. The device allows measuring simultaneously the displacement field on two faces of the sample using 3D Digital Image Correlation (3D DIC). Subset size, step size and filter size, associated with DIC calculations, are carefully calibrated to ensure efficient analysis of the displacement fields. The smoothing parameter (i.e. filter size times step size) appears to be a discriminating criterion with an upper limit below which the strain field can be appreciably estimated. Within the appropriate choice of analysis parameters, volume changes under large deformation can be evaluated. For sufficiently large deformation, volume change exhibits an upturn during stretching which could be the sign of a significant increase of void fraction. Volume change appears to be reversible during unloading phase when maximum stretch ratio is low enough. So cavities that could have been open under tension are closed when elastic deformation is released. Conversely, for high stretching ratio, volume change exhibits a hysteresis loop-like evolution indicating that either some plastic cavities remained or closure kinetics is slower.     

Two nearly equivalent approaches for describing the non-linear creep behavior of glassy polymers

Two approaches are proposed to account for the creep curve of glassy polymers under high applied stress; one is analytical, the other is in the form of a ladder mechanical model. Both approaches consider that creep deformation induces the rejuvenation of the sample, giving rise to faster kinetics, and they predict an inflection in the creep curve. The related responses were found to fit experimental data better than the stretched exponential law, especially at high strain. The mechanical model must be preferred because it is hierarchical, which is useful for visualization and allows memory effects to be taken into account.     

Physical aging of an amorphous polyimide: Enthalpy relaxation and mechanical property changes

The physical aging behavior of an isotropic amorphous polyimide possessing a glass transition temperature of approximately 239°C was investigated for aging temperatures ranging from 174 to 224°C. Enthalpy recovery was evaluated as a function of aging time following sub‐T_g annealing in order to assess enthalpy relaxation rates, and time‐aging time superposition was employed in order to quantify mechanical aging rates from creep compliance measurements. With the exception of aging rates obtained for aging temperatures close to T_g, the enthalpy relaxation rates exhibited a significant decline with decreasing aging temperature while the creep compliance aging rates remained relatively unchanged with respect to aging temperature. Evidence suggests distinctly different relaxation time responses for enthalpy relaxation and mechanical creep changes during aging. The frequency dependence of dynamic mechanical response was probed as a function of time during isothermal aging, and failure of time‐aging time superposition was evident from the resulting data. Compared to the creep compliance testing, the dynamic mechanical analysis probed the shorter time portion of the relaxation response which involved the additional contribution of a secondary relaxation, thus leading to failure of superposition. Room temperature stress‐strain behavior was also monitored after aging at 204°C, with the result that no discernible embrittlement due to physical aging was detected despite aging‐induced increases in yield stress and modulus. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1931–1946, 1999     

A structural interpretation of the two components governing the kinetic fragility from the example of interpenetrated polymer networks

Kinetic fragility and cooperativity length, two major characteristics of the relaxation dynamics at the glass transition, are, respectively, investigated by dynamic mechanical analysis and modulated temperature differential scanning calorimetry in a series of interpenetrated polymer networks based on acrylate and epoxy systems. The relaxation dynamics are impacted by two variables: the rigidity of the network, and the structural heterogeneity resulting from blending. However, the fragility and the cooperativity do not vary similarly. The glass transition progressively broadens as the mass fractions of acrylate and epoxy become equivalent, leading to a strong decrease in cooperativity. On the other hand, under the same conditions, the fragility transitions between the lower value of pure acrylate and the higher value of pure epoxy. This divergence helps concluding that the variations in the temperature dependence of the relaxation time are not purely related to the more or less cooperative nature of the glass transition. By splitting the fragility index in a volume contribution and an energetic contribution, it is shown that the contribution of cooperativity to the variations of the relaxation time with temperature is increased under two structural conditions: low backbone rigidity and high intermolecular interactions. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1393–1403     

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.     

Molecular mobility of poly(methyl methacrylate) glass during uniaxial tensile creep deformation

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 T_g ? 9 K and T_g ? 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     

Effects of the strain rate and temperature in stress–strain tests: study of the glass transition of a polyamide-6

In this work new insights are presented on the measurement of the tangent and secant moduli from stress–strain curves in polymeric systems. Expressions for the strain-rate and strain dependence of both moduli are derived for systems characterised by a distribution of relaxation times. The equivalent frequency of the stress–strain experiments is shown to be dependent on the strain rate and on the strain at which the measurements are carried out. Such considerations enable using quasi-static tensile stress–strain tests to study relaxational processes in polymeric materials. The tensile behaviour of a 30% glass fibre reinforced polyamide 6 was characterised at different strain rates and temperatures, covering the glass transition region. A master curve of the tangent modulus as a function of strain rate was successfully constructed by simple horizontal shifting of the isothermal data. The temperature dependence of the shift factors was well described by the WLF equation. It was also possible to fit the master curve considering a polymeric system with a distribution of relaxation times, relevant parameters such as the KWW β parameter being extracted. The results were found to be consistent with dynamic mechanical analysis results.     

Mechanical Properties and Failure Mechanisms of Graphene under a Central Load

By employing molecular dynamics simulations, the evolution of deformation of a monolayer graphene sheet under a central transverse loading are investigated. Dependence of mechanical responses on the symmetry (shape) of the loading domain, on the size of the graphene sheet, and on temperature, is determined. It is found that the symmetry of the loading domain plays a central role in fracture strength and strain. By increasing the size of the graphene sheet or increasing temperature, the tensile strength and fracture strain decrease. The results have demonstrated that the breaking force and breaking displacement are sensitive to both temperature and the symmetry of the loading domain. In addition, we find that the intrinsic strength of graphene under a central load is much smaller than that of graphene under a uniaxial load. By examining the deformation processes, two failure mechanisms are identified namely, brittle bond breaking and plastic relaxation. In the second mechanism, the Stone–Wales transformation occurs.