Semi-analytical solution for electro-thermo-mechanical non-stationary creep behaviour of rotating disk made of nonlinear piezoelectric polymer

Electro-thermo-mechanical non-stationary creep response of a rotating disk made of nonlinear polymeric piezoelectric material has been investigated. The viscoelastic properties of the material are time, stress and temperature dependent which vary along radius. The long-term creep constitutive equation is the Burgers viscoelastic model. A non-homogeneous differential equation with variable coefficients is derived using stress-displacement relations, equilibrium equation, charge equation of electrostatics and the Maxwell equation. Time-dependent creep strains are involved in the non-homogeneous term of the differential equation. A semi-analytical solution has been developed to obtain displacement, stresses, strains and electric potential in terms of creep strains. Then, Prandtl–Reuss relations and the creep constitutive model are employed in a novel numerical procedure based on the Mendelson method to obtain history of displacement, stresses, electric potential and strains. It has been concluded that the displacement is increasing with time while effective stresses are decreasing. The results are validated by finite element methods modelling using ABAQUS software. A very good agreements between the results can be observed.     

A novel methodology to model the creep behavior of polymers at different temperatures

A new methodology for modeling the creep behavior of polymers at different temperatures, by using phenomenological constitutive models, is presented in this paper. The viscoelastic model is given by a combination of springs and dashpots and is used to describe the nonlinear response of polymers, and the viscoplastic formulation is given by a power-law equation. The approach proposed in this work is based on building master curves for different stress levels, and finding the dependency of the constitutive parameters with the temperature. After fitting the equations to the tensile creep tests at different temperatures, the final constitutive formulation is capable of modeling the behavior of polymers at any stress level and temperatures. Poly methyl metacrytale (PMMA) was used to investigate the accuracy of this proposal, and the results showed good agreement with the experimental data.     

A micromechanical approach to elastic and viscoelastic properties of fiber reinforced concrete

Some aspects of the constitutive behavior of fiber reinforced concrete (FRC) are investigated within a micromechanical framework. Special emphasis is put on the prediction of creep of such materials. The linear elastic behavior is first examined by implementation of a Mori-Tanaka homogenization scheme. The micromechanical predictions for the overall stiffness prove to be very close to finite element solutions obtained from the numerical analysis of a representative elementary volume of FRC modeled as a randomly heterogeneous medium.The validation of the micromechanical concepts based on comparison with a set of experiments, shows remarkable predictive capabilities of the micromechanical representation.The second part of the paper is devoted to non-ageing viscoelasticity of FRC. Adopting a Zener model for the behavior of the concrete matrix and making use of the correspondence principle, the homogenized relaxation moduli are derived analytically. The validity of the model is established by mean of comparison with available experiment measurements of creep strain of steel fiber reinforced concrete under compressive load. Finally, the model predictions are compared to those derived from analytical models formulated within a one-dimensional setting.     

Creep resistance of linear low density polyethylene/carbonaceous hybrid nanocomposites: Experiments and modeling

In the present work, the creep response of nanocomposites based on metallocene linear low density polyethylene (mLLDPE), reinforced with three types of carbonaceous nanofillers, namely carbon nanotubes (CNTs), graphene oxide (GO) platelets, and carbon nanofibers (CNFs) was experimentally studied. The effect of the nanofiller loading and the hybrid character of nanocomposites on the creep resistance of the nanocompsites was analyzed. In all cases, the creep resistance of the nanocomposites examined has been postulated. To support these results, creep has been modeled by a power creep law, while the creep- recovery modeling was achieved by a viscoelastic model. The implementation of the viscoelastic model has been made by assuming that the nanocomposite's structure can be represented by a physical network, with the dispersed nanofillers participating in the molecular rearrangements, which take place upon the imposition of stress. The time dependent constitutive equation involves a relaxation function, based on a Gaussian type distribution function, associated with the energy barriers that molecular segments need to overcome, for transitions to occur. It was found that creep-recovery strain could be accurately captured with the same set of parameters, whereas the number of required model parameters was quite lower than that in the widely known viscoelastic models.     

Tensile creep of a long‐fibre glass mat thermoplastic (GMT) composite. II. Viscoelastic‐viscoplastic constitutive modeling

In Part I of this article, the short‐term tensile creep of a 3‐mm‐thick continuous long‐fibre glass mat thermoplastic composite was characterized and found to be linear viscoelastic up to 20 MPa. Subsequently, a nonlinear viscoelastic model has been developed for stresses up to 60 MPa for relatively short creep durations. The creep response was also compared with the same composite material having twice the thickness for a lower stress range. Here in Part II, the work has been extended to characterize and model longer term creep and recovery in the 3‐mm composite for stresses up to near failure. Long‐term creep tests consisting of 1‐day loading followed by recovery were carried out in the nonlinear viscoelastic stress range of the material, i.e., 20–80 MPa in increments of 10 MPa. The material exhibited tertiary creep at 80 MPa and hence data up‐to 70 MPa has been used for model development. It was found that viscoplastic strains of about 10% of the instantaneous strains were developed under load. Hence, a non‐linear viscoelastic–viscoplastic constitutive model has been developed to represent the considerable plastic strains for the long‐term tests. Findley's model which is the reduced form of the Schapery non‐linear viscoelastic model was found to be sufficient to model the viscoelastic behavior. The viscoplastic strains were modeled using the Zapas and Crissman viscoplastic model. A parameter estimation method which isolates the viscoelastic component from the viscoplastic part of the nonlinear model has been developed. The model predictions were found to be in good agreement with the average experimental curves. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

Accelerated characterization of a chopped fiber composite using a strain energy failure criterion

The creep and creep rupture response of a chopped fiber composite material (SMC-R50) were investigated experimentally and analytically. The goal of this research was to use the short time laboratory data to predict long time creep and creep rupture behavior. The creep response data up to 200 min duration were obtained at various constant temperature and stress levels. The short time creep data were then modeled using a modified power law equation. The modified power law equation contains the parameters of the so-called accelerated characterization procedure. Using this power law equation, the short time creep response at the elevated temperatures were able to successfully predict the long time creep response at a lower temperature and stress level. To predict the creep rupture behavior, the modified power law equation was then coupled with a strain energy based failure criterion. It was found that the same parameters that were used in the prediction of the long-time creep response can also be used to predict the creep rupture. At a given temperature level, the strain energy density related to creep rupture was found to be a constant. Furthermore, this strain energy density was found to increase with an increase in temperature. With a limited amount of data, it was found that the strain energy based failure criterion coupled with the modified power law equation can be used to predict long time creep rupture behavior.     

Micromechanical model of time-dependent damage and deformation behavior for an orthogonal 3D-woven SiC/SiC composite at elevated temperature in vacuum

This paper presents a micromechanical model to predict the time-dependent damage and deformation behavior of an orthogonal 3-D woven SiC fiber/BN interface/SiC matrix composite under constant tensile loading at elevated temperature in vacuum. In-situ observation under monotonic tensile loading at room temperature, load–unload tensile testing at 1200 °C in argon, and constant load tensile testing at 1200 °C in vacuum were conducted to investigate the effects of microscopic damage on deformation behavior. The experimentally obtained results led to production of a time-dependent nonlinear stress–strain response model for the orthogonal 3-D woven SiC/SiC. It was established using the linear viscoelastic model, micro-damage propagation model, and a shear-lag model. The predicted creep deformation was found to agree well with the experimentally obtained results.     

Rheological study on the adhesion properties of the blends of ethylene vinyl acetate/terpene phenol adhesives

Measurements of the shear, tensile, peel, and creep strength of ethylene vinyl acetate (EVA)/CaCO₃/terpene phenol adhesive system at three different ratios [100/60/0 (EVA-O), 80/48/20 (EVA-20), and 60/36/40 (EVA-40) by weight, using wood and aluminum as adherends] were conducted. Over a wide range of temperatures and rates of deformation, adhesion shear, tensile, and peel strength results, as well as the creep response over a broad range of temperature and stresses, were found to yield a single master curve by means of the reduced-variable technique. It was observed that the peak of E′ representing Tg, shifted toward higher temperatures as the amount of terpene phenol in the blend was increased. The most obvious effect of increasing the tackifier resin was the shifting of the adhesion strength master curves to the direction of lower rates. The shift was associated with the rise in Tg as the blend ratio was increased. The influence of the tackifier resin in modifying the viscoelastic properties of the adhesive was further described in a comparison of the adhesion strength master curves with corresponding dynamic viscoelastic curves of the adhesive films. The master curves for the creep response of the adhesives showed that the stress-breaking time relationship shifts toward longer time for EVA-40 with high Tg. Thus, it was found that the strength of adhesion is due mainly to dynamic effects in the adhesive of a viscous nature in the same way to the cohesive strength of the viscoelastic materials. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 409–418, 1998     

Viscoelastic behavior of Cytec FM73 adhesive during cure

In this work, the viscoelastic properties of Cytec FM73 structural film adhesive were characterized. Several resin plates were cured using various process cycles to achieve a range of final cure states. Specimens cut from these plates were tested using a dynamic mechanical analyzer (DMA) and the glass‐transition temperature at each degree of cure was determined. Stress relaxation tests at different temperatures were then performed using DMA in stress relaxation mode and time‐temperature superposition was used to generate master stress relaxation curves and associated shift functions for each degree of cure. Several different constitutive models were examined for their ability to describe relaxation modulus development during cure. A simple three‐parameter model consisting of a stretched exponential with cure‐dependent terms was found to provide the best results. The results indicate that of the parameters used in the model, relaxation time strongly depends on cure state. The empirical DiBenedetto equation was used to obtain an expression for glass‐transition temperature as a function of degree of cure. This expression was in turn used to derive a new relation to describe stress relaxation time as a function of degree of cure. The shift function was modeled using a simplified form of the Vogel equation with cure‐dependent coefficients. Good correlation between measured relaxation modulus and model predictions was observed. © 2003 Wiley Periodicals, J Appl Polym Sci 91: 2548–2557, 2004     

Time–temperature superposition principle applied to a kenaf‐fiber/high‐density polyethylene composite

The time–temperature superposition principle was applied to the viscoelastic properties of a kenaf‐fiber/high‐density polyethylene (HDPE) composite, and its validity was tested. With a composite of 50% kenaf fibers, 48% HDPE, and 2% compatibilizer, frequency scans from a dynamic mechanical analyzer were performed in the range of 0.1–10 Hz at five different temperatures. Twelve‐minute creep tests were also performed at the same temperatures. Creep data were modeled with a simple two‐parameter power‐law model. Frequency isotherms were shifted horizontally and vertically along the frequency axis, and master curves were constructed. The resulting master curves were compared with an extrapolated creep model and a 24‐h creep test. The results indicated that the composite material was thermorheologically complex, and a single horizontal shift was not adequate to predict the long‐term performance of the material. This information will be useful for the eventual development of an engineering methodology for creep necessary for the design of structural building products from these composites. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1995–2004, 2005     

An experimental investigation of normal and shear stress interaction of an epoxy resin and model predictions

The axial‐torsional interaction of an epoxy resin was investigated by subjecting thin‐walled tubular specimens to combined normal and shear stress components. It is shown that a superimposed normal stress (tensile or compressive) or hydrostatic pressure will influence shear creep behavior. Similarly, a superposed shear stress affects the normal stress response of the resin. The axial‐torsional stress interaction is also observed in transient stress responses under different strain paths, and in the creep deformation with non‐proportional stress histories. Urear viscoelastic constitutive models are unable to predict the aforementioned behaviors. Two typical nonlinear viscoelastic constitutive models are examined with respect to their capabilities to predict the observed response. It Is shown that the predictions of these two models agree only qualitatively but not quantitatively with the experimental results.     

Modeling of creep and shrinkage behavior of polymeric films used in magnetic tapes

For ever increasing high recording densities of magnetic tape drives, improved dimensional stability of the polymeric films used as magnetic tape substrates is required. During storage and use, creep and shrinkage occur simultaneously and it needs to be minimized. To obtain constitutive relationships for creep and shrinkage, these contributions need to be separated and modeled. A mathematical model based on Kelvin–Voigt models has been developed to characterize simultaneous creep and shrinkage behavior to obtain the constitutive relationships for creep and shrinkage. Experiments have been performed to separate out creep and shrinkage effects and this model has been used to compensate the effect of shrinkage on creep data and to get true creep data. The experimental creep and shrinkage data of various films have been modeled to obtain viscoelastic parameters. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 78–88, 2004     

Stress relaxation behavior of 3501-6 epoxy resin during cure

Epoxy resins and other thermosetting polymers change from liquids to solids during cure. A precise process model of these materials requires a constitutive model that is able to describe this transformation in its entirety. In this study the viscoelastic properties of a commercial epoxy resin were characterized using a dynamic mechanical analyzer (DMA). Specimens were tested at several different cure states to develop master curves of stress relaxation behavior during cure. Using this experimental data, the relaxation modulus was then modeled in a thermorheologically complex manner. A Prony (exponential) series was used to describe the relaxation modulus. An original model was developed for the stress relaxation times based on similar work by Scherer (16) on the relaxation of glass. Shift functions used to obtain reduced times are empirically derived based on curve fits to the data. The data show that the cure state has a profound effect on the stress relaxation of epoxy. More important, the relaxation behavior above gelation is shown to be quite sensitive to degree of cure.     

Interphasial viscoelastic behavior of CNT reinforced nanocomposites studied by means of the concept of the hybrid viscoelastic interphase

In this study the effect of carbon nanotubes content as well as of the tensile stress level applied upon the linear viscoelastic creep response of carbon nanotube polymer nanocomposites was investigated. Experimental findings were modeled by means of the newly developed hybrid viscoelastic interphase model, which constitutes an extension of the previously developed hybrid interphase model. According to this model, the viscoelastic interphase thickness has not of constant value but is dependent upon the property considered at the time as well as on the creep time. In addition, the parameter of imperfect bonding is introduced through the degree of adhesion. Experimental findings combined with analytical results gave a better understanding of the viscoelastic response of epoxy resin carbon nanotubes nanocomposites. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Creep and stress relaxation modeling of vinyl ester nanocomposites reinforced by nanoclay and graphite platelets

This article discusses the viscoelastic behavior of a vinyl ester (Derakane 411‐350) reinforced with 1.25 and 2.5 wt % nanoclay and exfoliated graphite nanoplatelets during short‐term creep and relaxation tests with a dynamic mechanical analyzer. Linear viscoelastic models are generally composed of one or more elements such as dashpots and springs that represent the viscous and elastic properties. Stress relaxation data from the dynamic mechanical analyzer have been used to obtain the elastic parameters based on model constitutive equations. The standard linear solid model, which is a physical model, has been used for predicting the creep deformation behavior of the vinyl ester nanocomposites over a wide temperature range. Some correlations have been made with the mechanical model, such as the effect of temperature on the deformation behavior, which is well explained by the dashpot mechanism. At lower temperatures, higher creep compliance has been observed for the vinyl ester versus the nanocomposites, whereas at temperatures near the glass‐transition temperature of the vinyl ester, creep compliance in the nanocomposites is closer in magnitude to that for the vinyl ester. The creep response of the pure vinyl ester and its nanocomposites appears to be modeled reasonably well at temperatures lower than their glass‐transition temperatures. A comparison of the predictions and experimental data from the creep tests has demonstrated that this model can represent the long‐term deformation behavior of these nanoreinforced materials reasonably well. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

The draw ratio–Deborah number diagram: A useful tool for coating applications

The understanding of the basic physical effects of viscoelasticity on drawing performances in the coating process leads to a useful approach to link the rupture of the polymer melt to critical processing conditions. In particular, we show that when solving the drawing problem in the air gap with a simple constitutive equation—like the upper convected Maxwell model—a mathematical inconsistency appears for some drawing parameters. This mathematical instability may be experimentally correlated to the occurrence of melt‐rupture, giving rise to a discussion on the effect of viscoelastic properties on drawing performances. Results are given in terms of a diagram representing the maximum drawing ratio Dr with respect to the Deborah number De. A master curve, obtained form experimental results, accounts for the temperature, melt‐index, air‐gap height, and extrusion output dependences. The limitations of the “universality” of the concept are discussed later. POLYM. ENG. SCI. 46:372–380, 2006. © 2006 Society of Plastics Engineers     

A method for determination of time‐ and temperature‐dependences of stress threshold of linear–nonlinear viscoelastic transition: Energy‐Based Approach

A methodology for determination of time‐ and temperature‐dependences of stress threshold of linear–nonlinear viscoelastic transition is proposed and validated by example of uniaxial creep of epoxy resin. Energy approach is applied for characterization of the region of linear viscoelasticity (LVE) and the threshold of LVE is given in the stress–strain representation as the master curve independent of time and temperature. Time‐ and temperature‐dependences of the stress threshold are calculated by extending LVE theory and time–temperature superposition principles (TTSP) to the energy relations. Reasonable agreement between experimental data and calculations is obtained. It is shown that number of tests required for characterization of LVE region in a wide range of test time and temperatures can be considerably reduced by applying the proposed methodology. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

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.     

A model for the thermoviscoelastic behavior of physically aged polymers

A constitutive model is derived for the viscoelastic behavior of physically aged amorphous polymers under non-isothermal loading. The model is based on the concept of transient reversible networks, where a polymeric material is treated as a network of active chains (adaptive links) that break and reform because of micro-Brownian motion. The breakage and reformation rates for active chains in an aged medium are assumed to depend on the current temperature and the time after cooling below the glass transition temperature. To validate the model, the long-term viscoelastic response is predicted on the basis of data obtained in the standard short-term creep tests and compared with data from long-term experiments. Fair agreement is demonstrated between numerical results and observations. The model is used to calculate residual stresses in a polymeric spherical pressure vessel cooled down (after curing) to the room temperature. It is shown that physical aging of the polymer significantly affects stresses and displacements in the vessel.