Mechanical behaviour of isotactic polypropylene subjected to various strain histories in uniaxial extension

The mechanical behaviour of a slowly quenched isotactic polypropylene has been studied for various strain histories in extension. Creep, constant rate of strain, and constant rate of loading experiments were carried out at deformations up to and beyond the point where necking occurs. A creep diagram, which includes the failure envelope, is presented. From the available data we have also obtained an extrapolated surface of the single step stress-relaxation behaviour. From this surface we can calculate, using the Bernstein and Zapas theory on the instability of viscoelastic bars, the deformation at which necking occurs for various strain histories.     

Compressive large deformation viscoelastic behaviour of a polycarbonate

The effect of deformation level and loading rate on compression creep and stress-relaxation behaviour of a polycarbonate has been studied. The possibility of obtaining master curves has been examined throughout. Satisfactory results were obtained for the stress-relaxation data by considering only the relaxable part of stress and by using a time shift factor proportional to both the inverse of deformation rate just prior to the test and the strain. The same shift factor allowed us to obtain a single master curve for the creep data.     

Resistive viscoelasticity of silicone rubber/carbon black composite

Electrical conductive polymer composites are shown as prospective flexible pressure and stretch sensors for detecting the dangerous deformations and for sensing the pressure with minimal intrusion. To better understand the piezoresistive mechanism and improve the performance of this type of sensor, a series of experiments were conducted to investigate the resistive viscoelasticity of silicone rubber/carbon black composite film. First, the flexible conductive composite film was composed with liquid silicone rubber as the matrix and conductive carbon black as the filler. The filler loading was fixed at 5 phr in mass ratio. Then, the resistive viscoelasticity of the composite film was studied as a function of frequency in the range from DC to 1 MHz, including resistive creep, resistive relaxation, and resistive recovery, although in a standard experiment, one‐step stress or one‐step strain was loaded in transient time and the resistance responses were measured. Result from the experiment shows that the creep of resistance is composed of two distinct segments. One is coincident with the strain creep of a typical viscoelastic material, while the other is quite different. Both the relaxation and the recovery of resistance exhibit strong frequency dependence. The relaxation speed becomes slower with the increase of exciting frequency except DC, and the relaxation speed is marginal when excited by DC electrical field. The recovery time becomes shorter with the increase of the exciting frequency. POLYM. COMPOS., 32:29–35, 2011. © 2010 Society of Plastics Engineers     

Prediction of stress–relaxation and creep of linear aromatic polyesters related to poly(ethylene terephthalate) in the nonlinear range

A study of the nonlinear viscoelastic properties of polymers was made using the Halsey-Eyring model with one- and three-dimensional mathematical analyses. Various parameters to calculate stress–relaxation and creep could be calculated from a single stress–strain curve of the same polymer. The parameters so calculated reconstituted the stress-strain curves, the one-dimensional equations yielding the better fit. The same constants were applied to predict stress-relaxation and creep. The fit using the three-dimensional equations is much better for stress-relaxation and creep than the one-dimensional equations.     

On‐line opto‐viscoelastic analysis of polypropylene fibres using multiple‐beam Fizeau fringes in transmission and a modified creep device

A creep device attached to an automated multiple‐beam Fizeau system in transmission was modified with a designed digital ruler. This device allows on‐line measurements of fibre length during creep experiments in terms of an analogue voltage value. The influence of sustained stress values on creep deformation and optical properties (n^||, n^? and Δn) for polypropylene (PP) fibres was studied interferometrically. The opto‐viscoelastic properties of PP fibres were determined for three different values of constant applied stress of 11.536, 18.717 and 25.905 MPa, at room temperature. Also, the variations of the cross‐sectional area and Poisson's ratio were studied during creep extensions. The compliance curves were obtained as a function of both time and applied stresses. Empirical formulae are suggested to describe the creep compliance curves for PP fibres, and the constants of these formulae were determined and described at each applied stress. A Kelvin chain was used to model the mechanical behaviour of the PP fibres under study. The effect of strain on the mean refractive indices, orientation function density and crystallinity was investigated as a result of the recorded data. Microinterferograms are given for illustration. The modified creep device with the designed digital ruler enables one to obtain instantaneous automatic accurate recording of fibre length values during creep experiments. Calculation of refractive indices, orientation function and crystallinity shows a difference in material behaviour at small stresses from that at higher stresses which may be attributed to different strain rates caused by different stresses. Copyright © 2010 Society of Chemical Industry     

Nonlinear viscoelasticity of a vulcanized elastomer

The material nonlinearities in the viscoelastic behavior of rubbers at modest-to-large deformations have been studied. A vulcanized network based on the styrene–butadiene elastomer has been tested in stress-relaxation experiments at room temperature for a wide range of deformations. After time–strain separabality was confirmed, the damping function could be calculated and introduced into the Boltzmann superposition integral. The equilibrium stress–strain behavior of the system could then be described, while comparison with other theoretical equations has also been made. © 1994 John Wiley & Sons, Inc.     

Application of time–stress superposition to viscoelastic behavior of polyamide 6,6 fiber and its “true” elastic modulus

The viscoelastic behavior of semi‐crystalline polyamide 6,6 fiber is exploited in viscoelastically prestressed polymeric matrix composites. To understand better the underlying prestress mechanisms, strain–time performance of the fiber material is investigated in this work, under high creep stress values (330–665 MPa). A latch‐based Weibull model enables prediction of the “true” elastic modulus through instantaneous deformation from the creep‐recovery data, giving 4.6 ± 0.4 GPa. The fiber shows approximate linear viscoelastic characteristics, so that the time–stress superposition principle (TSSP) can be implemented, with a linear relationship between the stress shift factor and applied stress. The resulting master creep curve enables creep behavior at 330 MPa to be predicted over a large timescale, thus creep at 590 MPa for 24 h would be equivalent to a 330 MPa creep stress for ～5200 years. Similarly, the TSSP is applied to the resulting recovery data, to obtain a master recovery curve. This is equivalent to load removal in the master creep curve, in which the yarns would have been subjected to 330 MPa creep stress for ～4.56 × 10⁷ h. Since our work involves high stress values, the findings may be of interest to those involved with long‐term load‐bearing applications using polyamide materials. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44971.     

Modelling of biaxial ratcheting behaviour of ultrahigh‐molecular‐weight polyethylene with viscoplasticity theory based on overstress for polymers

Biaxial ratcheting behaviour of ultrahigh‐molecular‐weight polyethylene (UHMWPE) has been modelled using the viscoplasticity theory based on overstress for polymers (VBOP) with the modified Chaboche kinematic hardening rule. Investigated loading condition is: axial strain‐controlled cyclic loading of thin‐walled tubular specimen in the presence of constant pressure. To improve the circumferential strain ratcheting response of UHMWPE, changes designed to account for kinematic hardening and tangent modulus effects are proposed. Numerical results are compared with previously obtained experimental data. It is shown that modified tangent modulus improves the model responses. The biaxial ratcheting behaviour of UHMWPE is modelled quantitatively with VBOP. © 2015 Society of Chemical Industry     

Characterization and modeling of creep behavior of a thermoset nanocomposite

In this article, we report creep and recovery behavior of nanocomposites based on a high‐temperature‐resistant thermosetting matrix. Nanocomposites with up to 2 wt% of organically modified clay were prepared. The creep and recovery behavior was investigated under various stress levels and at various temperatures. Creep behavior was modeled by a modified Burgers model by introducing a stretched exponential function. This stretched Burgers model satisfactorily describes the creep behavior of the matrix and nanocomposites. The role of filler on the system dynamics has been also discussed and an interesting finding discovered from the stretched Burgers model results. The model results suggest that the dynamics of the filled system is independent of the filler, which is scientifically quite interesting in the field of nanocomposites. The multiple cycle creep and recovery behavior of the matrix were also investigated and the Boltzmann superposition principle was applied to describe the multistep loading creep response. POLYM. COMPOS., 36:322–329, 2015. © 2014 Society of Plastics Engineers     

The viscoelastic extension of polymer fibres: complex loadings

The response of oriented polymer fibres to complex loading patterns is investigated. It is shown that the creep and stress relaxation is non-linear with the applied stress. The ratio of the creep rate and the stress-relaxation rate is given by the local slope of the tensile curve and not by the elastic modulus as predicted by linear viscoelastic theory. A consequence of this observation is that viscoelastic and yield deformations are coupled. By analysing the results of the step-creep and the strain-relaxation-strain experiments performed on poly(p-phenylene terephthalamide) fibres, it is shown that the linear superposition principle does not apply to the tensile deformation of polymer fibres above the yield point. Finally the various components of the tensile deformation that should be covered by a constitutive equation for polymer fibres are discussed.     

Some aspects of the mechanical response of BMI 5250‐4 neat resin at 191°C: Experiment and modeling

The inelastic deformation behavior of BMI‐5250‐4 neat resin, a high‐temperature polymer, was investigated at 191°C. The effects of loading rate on monotonic stress–strain behavior as well as the effect of prior stress rate on creep behavior were explored. Positive nonlinear rate sensitivity was observed in monotonic loading. Creep response was found to be significantly influenced by prior stress rate. Effect of loading history on creep was studied in stepwise creep tests, where specimens were subjected to a constant stress rate loading followed by unloading to zero stress with intermittent creep periods during both loading and unloading. The strain‐time behavior was strongly influenced by prior deformation history. Negative creep was observed on the unloading path. In addition, the behavior of the material was characterized in terms of a nonlinear viscoelastic model by means of creep and recovery tests at 191°C. The model was employed to predict the response of the material under monotonic loading/unloading and multi‐step load histories. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Using creep and recovery to study flow behavior of fresh cement paste

A controlled stress rheometer has been used to determine the creep and recovery behavior of flocculated cement pastes. The behavior was found to depend on the level of applied stress. At a lower applied stress, the creep curve of each paste was characteristics of a nonlinear viscoelastic solid, with an instantaneous strain superimposed on an elastic strain; the recovery, on the other hand, was characteristics of a viscoelastic liquid, with little or no instantaneous strain, but some retarded strain and a substantial unrecovered strain. At a higher applied stress the behavior was strikingly different. In this case, the behavior was characteristics of a viscous liquid, with a nearly linear increase in strain throughout the duration of the stress and no recovery when the stress was released. This transition from solid-like behavior to liquid-like behavior occurred over a very narrow stress increment, and the transition stress corresponded to the yield stress estimated from flow curves and from oscillatory shear measurements.     

Development of a simplified relationship between uniaxial creep,stress relaxation,and constant strain-rate results for viscoelastic polymeric materials

This publication introduces a new mathematical model to describe a definitive relationship between constant strain-rate, creep, and stress-relaxation analysis for viscoelastic polymeric compounds. This new concept is especially significant since it adequately describes all the important characteristics of both creep and stress relaxation in the same model. In particular, all three phases of creep (i.e., primary, secondary, and tertiary) can be described adequately using this model. This new model for polymeric materials also indicates that yielding for constant strain-rate measurements and the inception of tertiary creep appear to be directly related and may, in fact, be manifestations of the same phenomena. The initial buildup of stress followed by the drop off in stress as a function of time for stress relaxation is also adequately described. This new formulation approach also offers a reasonably simple process in which to shift from a constant strain-rate configuration to a creep calculation or stress-relaxation configuration without changing formulation considerations. Most importantly, this model can be used to make a transition from one of these stress-configuration modes to another without stress or strain discontinuities. It is hoped that this analysis approach will open new doors for the design of plastic products for both short-term and long-term applications. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 527–540, 2001     

Behaviour of concrete under thermal steady state and non-steady state conditions

Stress–strain behaviour of concrete at elevated temperatures is extremely complex and is not completely understood up to now. The creep properties of concrete at temperatures up to 300°C thus need to be determined, as well as the thermal stability of concrete during repeated cycles of heating and cooling. In this report the results of recent high temperature experiments with normal concrete specimens are presented. The main objectives of the tests were to investigate the dependence of strength and elasticity on temperature and to study the creep and deformation characteristics of concrete at temperatures up to 450°C. Transient creep data, i.e. data derived under transient temperature conditions, are compared with creep data which were measured at constant elevanted temperatures. The results suggest that transient creep values and steady state creep values in some cases may be of the same magnitude. The creep measurements appear to be in good agreement with data presented by other workers. However, the scatter in all data increases significantly with increasing temperature and differences of more than 100% can be observed. When loaded concrete specimens were cooled down to ambient temperature exptraordinarily large compressive strains can be observed. The experiments indicate clearly the considerable strain capacity of normal structural concrete can be used at temperatures higher than 100°C. In areas of high stress concentrations a tures. On the other hand, with respect to the whole structure it is necessary to limit the deformations. For a constant maximum temperature this can only be done by limiting the admissible stresses. The test results permit an initial estimation of maximum permissible stress and temperature values.     

Stress Relaxation of Polycrystalline Ceramics with Grain-Boundary Sliding and Grain Interlocking

The stress relaxation of two-phase polycrystalline ceramics has been examined. A two-dimensional array of elastic hexagonal grains embedded in a contiguous fluid has been used as a model for grain-boundary sliding and grain interlocking. The viscoelastic constitutive equation, in a phenomenological sense, is of a nonlinear Maxwell type; the model is composed of a strain-dependent dashpot and an elastic spring connected in series. The squeezing-in/out processes and mechanisms of grain-boundary fluid essentially result in the rheological nonlinearity. The experimental results in stress-relaxation tests of a β-spodumene glass-ceramic under simple shear are characterized from the standpoint of the nonlinear constitutive equation. It is emphasized that the stress-relaxation test is one of the important test techniques that enables one to study quantitatively the rheological behavior of polycrystalline ceramics with grain-boundary sliding and grain interlocking without any of the difficulties and ambiguities that are accompanied by stress-induced grain-boundary cavities, which so often appear in conventional creep tests.     

Non-linear creep of polymers under superimposed static and dynamic stress

The non-linear creep of polymeric materials under super-imposed static and dynamic stress is considered theoretically. The equation of state due to Green, Rivlin, and Spencer to-gether with the power law of time dependence for the kernel functions as suggested by Nakada is assumed to characterize the non-linear materials. Expressions for creep strain under constant static, oscillatory dynamic and superimposed static and dynamic stress are obtained in terms of the material constants and time dependent functions, called dynamic creep functions. It is shown that the creep strain due to dynamic stressing is damped as the number of stress cycles is increased. Damping is faster if the power law of time dependence is high. Expressions for the cumulative creep strain after multiple stress cycles are also obtained in terms of cumulative strain functions. All these functions are evaluated numerically at one thousand stress cycles. Finally, a special case of stress history is considered where the stress periodically reaches zero. It is shown that the ratio of the strains due to dynamic and static stressing can be characterized by the power law parameter when the mean stress is either very high or very low. Due to the slow damping when the power law parameter is small, the decrease of the strain ratio with number of cycles is slow compared to higher power law parameters.     

Dimensional recovery of cold-rolled polycarbonate

The dimensional recovery of cold-rolled polycarbonate was measured between 100 and 147°C, and compared to stress-relaxation data. The strain-recovery isotherms were superimposed to produce a master curve which could be represented by a distribution function, U(τ), termed the strain recovery spectrum. U(τ) is found to be nearly identical to the relaxation spectrum, H(τ), calculated from the stress-relaxation master curve; and the shift in U(τ) as a function of temperature, WLF shift factor, is similar to that obtained from other viscoelastic measurements on polycarbonate. For the deformations studied, 25 and 50% reduction in thickness, the recovery behavior is found to be independent of strain (linear), suggesting that nonlinearity in a polymer glass results from large stresses, and not from large strains.