Stress relaxation,creep and set recovery of elastomers

The stress relaxation, creep and recovery behaviour of a cross-linked unfilled natural rubber has been investigated at moderate stresses in tension. The aim being to extend the idea, initially developed by Alan Gent in his seminal 1962 paper on the relaxation behaviour of rubber, in order to understand and examine the time dependent mechanisms that are present in elastomers under strain. A method based upon the Boltzmann superposition principle was used to compare the creep compliance with a measurement of its recovery after release from a range of constant loads held for different times. The creep behaviour was seen to exhibit the usual linear dependence on the logarithm of time. The recovery data was also seen to reduce onto a single recovery curve for any given applied tensile stress for a range of loading times using the Boltzmann superposition principle. The differences between the relative rates of the creep and the recovery behaviour can in part be attributed to the non-linearity in the stress–strain behaviour exhibited in tension of the elastomer.     

Effect of triaxial stress constraint on the deformation and fracture of polymers

One purpose of this paper is to give a brief overview on the research status of deformation, fracture and toughening mechanisms of polymers, including experimental, theoretical and numerical studies. Emphasis is on the more recent progresses of micromechanics of rubber particle cavitation and crazing, and the development of fracture criteria for ductile polymers. The other purpose is to study the effect of triaxial stress constraint on the deformation and fracture behavior of polymers. Polycarbonate (PC), acrylonitrile-butadienestyrene (ABS) and PC/ABS alloy are considered in this investigation. A series of circumferentially blunt-notched bars are used to experimentally generate different triaxial stress fields. The fracture surfaces of specimens with different notch radius are examined by scanning electron microscope (SEM) to study the fracture and toughening mechanisms of polymer alloy. It is shown that the triaxial stress constraint has a significant effect on the deformation, fracture and toughening of PC, ABS and PC/ABS alloy. We will also discuss the extent to which a micromechanics criterion proposed by the first author can serve as a fracture criterion for ductile polymers. A new ductile fracture parameter is emphasized, which can be employed to evaluate the fracture ductility of polymers. Stress state independence of the parameter for the PC, ABS and PC/ABS alloy has been experimentally verified. The project supported by the National Natural Science Foundation of China (10125212), the Trans-Century Training Program Foundation and the Key Research Fund of the Education Ministry of China (01159)     

Investigation of tensile deformation behavior of PC,ABS, and PC/ABS blends from low to high strain rates

This paper experimentally studies the tensile deformation behavior of polycarbonate (PC), acrylonitrile-butadiene-styrene (ABS), and PC/ABS blends (with the blending ratios of PC to ABS being 80:20, 60:40, 50:50, and 40:60) from low to high strain rates. Using the universal MTS-810 machine and the split Hopkinson tension bar (SHTB) testing system, the quasi-static and impact tension tests are carried out at the room temperature. The curves of the true stress and the true strain are obtained. The deformation behaviors of PC, ABS, and PC/ABS blends are characterized in detail. The linear relationship between the strain rate and the yielding stress is given.     

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

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

图像相关法在高分子材料拉伸性能研究中的应用

本文对聚碳酸酯(PC)和丙烯腈丁二烯苯乙烯(ABS)的合金(PC/ABS)高分子材料不同环境温度下的拉伸性能进行了试验研究。根据图像相关分析法编制了图像法位移测量分析软件,并对该分析软件的适用性进行了分析。系统研究了PC/ABS高分子材料拉伸试验时三个方向的位移场和应变场。根据测得的位移场研究了该高分子材料拉伸过程中应变和应变率的变化以及应力应变变化规律,并对试验结果进行了详细分析。结果表明,文中采用的图像法位移测量系统具有较高的测试精度;拉伸过程中,试件厚度方向的收缩变形大于宽度方向的收缩变形;颈缩过程区具有非常高的应变率,颈缩后的平直颈缩区的应变率快速下降到一个很低的应变率继续缓慢变形;尽管载荷位移曲线出现了较大的载荷下降现象,PC/ABS拉伸时的真应力应变曲线没有明显的应力下降现象出现,因此,载荷下降现象主要由颈缩时的截面减小引起;高分子材料PC/ABS的屈服应力随环境温度的升高而降低。     

Prediction of the creep behaviour of polyethylene and molybdenum from stress relaxation experiments

In many applications it is useful to be able to convert observed creep data of a material to corresponding stress relaxation data or vice versa. If the material exhibits non-linear viscoelasticity such a conversion can be rather difficult. In this paper two semi-empirical flow equations, the power law and the exponential law, are used to convert stress relaxation data into corresponding creep behaviour data. These two flow equations are often used to describe non-linear viscoelastic behaviour. The procedure adopted here is based on the assumption that the creep data during the experiment decrease due to an increase in the internal stress level, thus decreasing the effective stress for flow. The conversion method is applied to high density polyethylene and polycrystalline molybdenum at room temperature. In general predictions using the power law are in better agreement with the experimental results than predictions using the exponential formula. The concepts of secondary and ceasing creep are discussed in terms of build-up of internal stress during the creep process.     

Experimental investigation of the low cycle fatigue crack propagation in PC/ABS polymer blends

Low cycle fatigue crack propagation (FCP) behavior of two PC/ABS blends with a weight ratio of PC to ABS being 80/20 and 60/40, respectively, is investigated. Experiments are carried out by using standard compact tension (CT) specimens. The fracture surfaces are examined with a scanning electron microscope (SEM). It is shown that the FCP resistance of PC/ABS blend with 20% ABS particles is higher than that of PC/ABS blend with 40% ABS particles. It is found that proper ABS particle content can result in the toughening of PC/ABS blends through particle cavitation and shear yielding in matrix. Project supported by the Excellent Young Teachers Program and the Research Foundation for Doctoral Project of the Ministry of Education of China.     

Rheological characterization of well-defined tetrafluoroethylene/hexafluoropropylene copolymers

The rheology of tetrafluoroethylene/hexafluoropropylene (TFE/HFP) copolymers, also known as Teflon FEP polymers, having different molecular weight and composition (HFP content) was studied by means of a parallel-plate rheometer. Two groups of polymers having different molecular weights with nearly constant polydispersity (around 2.5) were considered; namely, one group having a relatively low melting temperature (amorphous with a high content of HFP) and a second group having a higher melting point (semi-crystalline with a lower content of HFP). The relaxation time spectrum, H(λ), calculated by use of the BSW model (developed for monodisperse linear polymers) followed a scaling relationship in the terminal zone with scaling exponent of 0.13. However, at higher frequencies the model fails to predict adequately the experimental data. The longest relaxation time calculated from both the BSW model and discrete relaxation spectra (λ _i ,g _i ), which was determined by use of a parsimonious fitting software, depends on the molecular weight in a similar way as the zero-shear viscosity does with the well-established scaling factor of 3.4. The critical molecular weight for the onset of entanglements, M _c , was found to be about 100000, a value much higher than those previously reported in literature for other polymers. The rheology of resins in the second group (higher melting point) was found to exhibit a strong dependence on thermal history during oscillatory-shear measurements. The data obtained in experiments at different temperatures without a preheating to a certain value (330°C) exhibited a violation of the time-temperature superposition principle and no well-defined values of the zero-shear viscosity. This is attributed to residual crystallinity even at temperatures well above their melting point (260°C). However, the same experiments with preheating and subsequent cooling to desired temperature resulted into a very good time-temperature scaling. Received: 13 January 1998 Accepted: 6 April 1998     

Thermal contraction and volume relaxation of amorphous polymers

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

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

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

An intermediate model method for obtaining a discrete relaxation spectrum from creep data

A convenient method is described for obtaining a discrete stress relaxation spectrum from linear viscoelastic creep data by means of a three-stage process. In stage one, a discrete retardation spectrum is fitted to the creep data using a least squares procedure, subject to the constraint that the discrete spectrum must be a specified order of polynomial function of the retardation time. In stage two, the resulting generalised Voigt model is solved numerically for an imposed step in strain, to determine the stress relaxation modulus function of time. In stage three, a discrete relaxation spectrum is fitted to the calculated stress relaxation modulus function. Although three stages are involved instead of the usual two, the procedure has been found to have certain practical advantages. These advantages make it suitable for the generation of relaxation spectra needed in viscoelastic stress analyses of solids, for example by the finite element method. In order to illustrate the proposed procedure it is applied to both artificial data and experimental creep data for poly(methyl methacrylate) at 70°C and at the glass transition.     

Creep phenomena in FRP materials

In this paper the authors present the results of a creep test programme on several glass fibre reinforced polymers (GFRPs) laminates and their constituent phases (matrix and fibre), subject to different stress values under constant environmental conditions. A validation of the mechanical model, recently formulated by the authors, capable of predicting the viscous properties of a FRP laminate starting from those of the single phase is also developed by matching the predicted behaviour with the experimental one recorded in the creep tests.     

A linear viscoelastic model for solid polyethylene

Stress relaxation tests have been carried out on a blue, pipe grade PE 80 medium density polyethylene (BP Chemicals), to provide thermo-viscoelastic rheology for use in calculating thermal stresses in pipe production. Stresses up to 4 MPa were used, with strains up to about 2%, in tests at temperatures from 23° to 90°C. Within this range a linear viscoelastic model was applicable, provided the initial ramp strain rate was less than 7×10^–5 s^–1. The stress relaxation data was fitted directly by a model incorporating an elastic response to volumetric strains, and a generalised linear solid model, consisting of two Maxwell elements and a purely elastic element in parallel, for deviatoric strains. Arrhenius type temperature dependence of relaxation times and shear moduli is found, and within experimental accuracy the temperature dependence of all these model parameters is the same. As a consequence, and provided that the duration of the strain ramp is sufficiently short relative to relaxation times, the model leads to time-temperature superposition of the relaxation moduli, using the same shift factor on both the response magnitude and time axes.     

Phenomenological nonlinear modelling of glassy polymers

Compared with the numerous works into the constitutive equations for the mechanical behaviour of metals, very little attention has been devoted to those of polymers. However, a model is required to describe both the complex shape of the stress–strain curves and strain rate sensitivity of glassy polymers. In this Note, a unified viscoelastic-viscoplastic model is presented in which the nonlinear pre-yield behaviour, the strain softening and the strain hardening are described by internal variables, in analogy with the models developed for metals. In order to check the predictive capability of the model, the numerical results are compared with the experimental data (monotone, creep and relaxation tests) of a typical amorphous glassy polymer. To cite this article: F. Zaïri et al., C. R. Mecanique 333 (2005).     

A molecular network model to describe the nonlinear viscoelastic behavior of polymers

A transient molecular network model is built to describe the nonlinear viscoelasticity of polymers by considering the effect of entanglement loss and regeneration on the relaxation of molecular strands. It is an extension of previous network theories. The experimental data on three thermoplastic polymers (ABS, PVC and PA6) obtained under various loading conditions are used to test the model. Agreement between the theoretical and experimental curves shows that the suggested model can describe successfully the relaxation behavior of the thermoplastic polymers under different loading rates by using relatively few relaxation modes. Thus the micromechanism responsible for strain-rate dependence of relaxation process and the origin of nonlinear viscoelasticity may be disclosed. The project supported by the National Natural Science Foundation of China and Doctorial Fund     

Non-linear Viscoelastic Model for Behaviour Characterization of Temporomandibular Joint Discs

Generally, the complex behaviour of the disc of the temporomandibular joint (TMJ) cannot be adequately represented using linear elastic or linear viscoelastic models. Since the disc is regularly subjected to large strain and stress levels, the study of its non-linear response under compression is of practical interest, especially for analysis of medical dysfunctions. With this aim, relaxation and creep tests were carried out using round specimens of diameters ranging between 4 and 6 mm cut off from the central, anterior, posterior, lateral and medial zones of porcine discs to investigate the regional mechanical properties differences. The experimental data results are fitted using Prony series, based on generalized Maxwell and Kelvin models, allowing the relaxation and creep moduli to be represented, respectively, as a function of the strain and stress. The results show that the non-linear material behaviour of this biological tissue is properly described by the proposed models, to be considered subsequently in numerical calculations.     

Modelling effects of degree of crystallinity on mechanical behavior of semicrystalline polymers

Viscoplasticity theory based on overstress (VBO) which is one of the unified state variable theories is extended to account for crystallinity ratio () on mechanical behavior of semicrystalline polymers. The modifications on VBO are done considering the semicrystalline polymeric materials somewhat as a composite material since it consists of amorphous and crystalline phases. Amorphous and crystalline phase resistances are arranged in two different analog models: amorphous stiffness and flow are in parallel and series with crystalline phase. Apart from many existing work in the literature, not only uniaxial loading are modeled but also creep and relaxation behaviors are simulated for a hypothetical material. It is shown that when amorphous and crystalline phase resistances acting in parallel are considered in the model, creep, relaxation and uniaxial loading and unloading behaviors can be simulated well using the modified VBO. In addition, uniaxial compression loading and unloading behavior of highly crosslinked ultra-high molecular weight polyethylene (UHMWPE) and creep behavior of polytetrafluoroethylene (PTFE) with different crystallinity ratios are simulated using the proposed VBO model where amorphous and crystalline phases are parallel. Simulation results are compared to the experimental data by Kurtz et al. (2002) and Sun et al. (2005) [Kurtz, S.M., Villarragaa, M.L., Herra, M.P., Bergström, J.S., Rimnacc, C.M., Edidin, A.A., 2002. Thermomechanical behavior of virgin and highly crosslinked ultra-high molecular weight polyethylene used in total joint replacements. Biomaterials 23, 3681–3697; Sun, H., Cooke, R. S., Bates, W. D., Wynne, K.J., 2005. Supercritical CO₂ processing and annealing of polytetrafluoroethylene (PTFE) and modified PTFE for enhancement of crystallinity and creep resistance. Polymer 46, 8872–8882] respectively and good match with experimental data is obtained.