Showing papers in "Mechanics of Time-dependent Materials in 2007"
TL;DR: A simple if (not) obvious method to extend the range of relaxation data that can be acquired from a single test at a single temperature and draws on new computational developments for inverting ill-conditioned systems of equations which allows the determination of relaxation parameters nearly routinely and trouble-free.
Abstract: Standard methods for deriving relaxation data from measurements invariably involve some form of ramp-type deformation history, the initial portion of which is typically not employed for modulus evaluation. In fact, the “ten-times-rule” or a variant thereof is widely used at the expense of short term data acquisition. This paper suggests a simple if (not) obvious method to extend the range of relaxation data that can be acquired from a single test at a single temperature. The method draws on new computational developments for inverting ill-conditioned systems of equations which allows the determination of relaxation parameters nearly routinely and trouble-free. We demonstrate this process for extraction of relaxation characterization from ramp strain histories through (a) numerical evaluation with a virtual test sequence, as well as through (b) data measured in the laboratory. Limitations regarding the time range over which the relaxation modulus can be extracted from laboratory measurements in terms of equipment resolution and stability are discussed. With these constraints in mind it appears feasible to extend the time range by three to four decades towards shorter times when compared with the application of the “ten-times-rule”. Similar treatments apply to the acquisition of creep compliance data.
84 citations
TL;DR: In this article, the applicability of the Time-Temperature Superposition Principle in the dynamic response of a polyurea polymer at high strain rates and different temperatures is investigated. But the authors focus on the initial deformation part that characterizes linearly viscoelastic behavior.
Abstract: This paper addresses the applicability of the Time–Temperature Superposition Principle in the dynamic response of a polyurea polymer at high strain rates and different temperatures. Careful and extensive measurements in the time domain of the relaxation behavior and subsequent deduction of a master-relaxation curve establish the mechanical behavior for quasistatic deformations over a time range of 16 decades. To examine its validity in a highly dynamic environment, experiments with the aid of a split Hopkinson (Kolsky) pressure bar are carried out. The use of a two-material pulse shaper allows for stress equilibrium across the specimen during the compression process, to concentrate on the initial, small deformation part that characterizes linearly viscoelastic behavior. This behavior of polyurea at high strain rates and different temperatures is then investigated by comparing results from a physically fully three-dimensional (axisymmetric) numerical model, employing the quasistatically obtained properties, with corresponding Hopkinson bar measurements. The experimentally determined wave history entering the specimen is used as input to the model. Experimental and simulation results are compared with each other to demonstrate that the Time–Temperature Superposition Principle can indeed provide the requisite data for high strain rate loading of viscoelastic solids, at least to the extent that linear viscoelasticity applies with respect to the polyurea material.
76 citations
TL;DR: In this paper, a recursive-iterative numerical algorithm is generated for the nonlinearly viscoelastic response of hot mix asphalt (HMA) at different temperatures and strain levels using Schapery's model.
Abstract: This study presents the characterization of the nonlinearly viscoelastic behavior of hot mix asphalt (HMA) at different temperatures and strain levels using Schapery’s model. A recursive-iterative numerical algorithm is generated for the nonlinearly viscoelastic response and implemented in a displacement-based finite element (FE) code. Then, this model is employed to describe experimental frequency sweep measurements of two asphalt mixes with fine and coarse gradations under several combined temperatures and shear strain levels. The frequency sweep measurements are converted to creep responses in the time domain using a phenomenological model (Prony series). The master curve is created for each strain level using the time temperature superposition principle (TTSP) with a reference temperature of 40°C. The linear time-dependent parameters of the Prony series are first determined by fitting a master curve created at the lowest strain level, which in this case is 0.01%. The measurements at strain levels higher than 0.01% are analyzed and used to determine the nonlinear parameters. These parameters are shown to increase with increasing strain levels, while the time–temperature shift function is found to be independent of strain levels. The FE model with the calibrated time-dependent and nonlinear material parameters is used to simulate the creep experimental tests, and reasonable predictions are shown.
68 citations
TL;DR: Lu et al. as mentioned in this paper measured Young's relaxation functions directly using nanoindentation using viscoelastic contact mechanics, extracting Young relaxation modulus using load-displacement data.
Abstract: In a previous paper (Lu et al., Mechanics of Time-Dependent Materials, 7, 2003, 189–207), we described methods to measure the creep compliance of polymers using Berkovich and spherical indenters by nanoindentation. However, the relaxation modulus is often needed in stress and deformation analysis. It has been well known that the interconversion between creep compliance and relaxation function presents an ill-posed problem, so that converting the creep compliance function to the relaxation function cannot always give accurate results, especially considering that the creep data at short times in nanoindentation are often not reliable, and the overall nanoindentation time is short, typically a few hundred seconds. In this paper, we present methods to measure Young’s relaxation functions directly using nanoindentation. A constant-rate displacement loading history is usually used in nanoindentations. Using viscoelastic contact mechanics, Young’s relaxation modulus is extracted using nanoindentation load-displacement data. Three bulk polymers, Polymethyl Methacrylate (PMMA), Polycarbonate (PC) and Polyurethane (PU), are used in this study. The Young’s relaxation functions measured from the nanoindentation are compared with data measured from conventional tensile and shear tests to evaluate the precision of the methods. A reasonably good agreement has been reached for all these materials for indentation depth higher than a certain value, providing reassurance for these methods for measuring relaxation functions.
63 citations
TL;DR: In this paper, the experimental characterization of isothermal physical aging of PEEK and PPS films using a dynamic mechanical analyzer was considered, and the results of creep and stress relaxation testing were compared and shown to be consistent with one another using appropriate interconversion of the viscoelastic material functions.
Abstract: This paper considers the experimental characterization of isothermal physical aging of PEEK and PPS films using a dynamic mechanical analyzer. Using the short-term test method established by Struik, momentary creep and stress relaxation curves were measured at several temperatures within 15–35°C below the glass transition temperature (Tg) at various aging times. Stress and strain levels were such that the materials remained in the linear viscoelastic regime. These curves were then shifted together to determine momentary master curves and shift rates using the PHYAGE program. In order to validate the obtained isothermal physical aging behavior, the results of creep and stress relaxation testing were compared and shown to be consistent with one another using appropriate interconversion of the viscoelastic material functions. Time–temperature superposition of the master curves was also performed. The temperature shift factors and aging shift rates for both PEEK and PPS were consistent for both creep and stress relaxation test results.
50 citations
TL;DR: In this article, the aging viscoelastic behavior of four different cement pastes has been measured and modeled according to both the time-shift approach and the solidification theory, and the results provide evidence that solidification and other intrinsic gel aging mechanisms are concurrently active in the aging process of cementitious materials.
Abstract: Analytical approaches for modeling aging viscoelastic behavior of concrete in- clude the time-shift approach (analogous to time-temperature superposition), the solidifi- cation theory, and the dissolution-precipitation approach. The aging viscoelastic properties of concrete are generally attributed solely to the cement paste phase since the aggregates are typically linear elastic. In this study, the aging viscoelastic behavior of four different cement pastes has been measured and modeled according to both the time-shift approach and the solidification theory. The inability of each individual model to fully characterize the aging viscoelastic response of the materials provides insight into the mechanisms for aging of the viscoelastic properties of cement paste and concrete. A model that considers aging due to solidification in combination with inherent aging of the cement paste gel (modeled using the time-shift approach) more accurately predicted the aging viscoelastic behavior of portland cement paste than either the solidification or time-shift approaches independently. The results provide evidence that solidification and other intrinsic gel aging mechanisms are concurrently active in the aging process of cementitious materials.
48 citations
TL;DR: In this paper, two alternative approaches for estimating linear viscoelastic material functions from a single experiment under random excitation are derived and analyzed, and numerical results are provided to compare and verify the applicability of the presented numerical procedures.
Abstract: Two alternative approaches for estimating linear viscoelastic material functions from a single experiment under random excitation are derived and analyzed. First, Boltzmann’s superposition integral is discretized into a system of linear equations. Due to the ill-posedness of the resulting matrix equation, Tikhonov’s regularization is introduced. Second, the integral is transformed into a recursive formula, using a Prony series representation of viscoelastic material functions, in which gradient-based optimization is applied. Numerical results are provided to compare and verify the applicability of the presented numerical procedures.
47 citations
TL;DR: In this article, two higher-order fractional viscoelastic material models consisting of the fractional Voigt model (FVM) and the FMM were derived due to the models' constructions.
Abstract: Two higher-order fractional viscoelastic material models consisting of the fractional Voigt model (FVM) and the fractional Maxwell model (FMM) are considered Their higher-order fractional constitutive equations are derived due to the models’ constructions We call them the higher-order fractional constitutive equations because they contain three different fractional parameters and the maximum order of equations is more than one The relaxation and creep functions of the higher-order fractional constitutive equations are obtained by Laplace transform method As particular cases, the analytical solutions of standard (integer-order) quadratic constitutive equations are contained The generalized Mittag–Leffler function and H-Fox function play an important role in the solutions of the higher-order fractional constitutive equations Finally, experimental data of human cranial bone are used to fit with the models given by this paper The fitting plots show that the models given in the paper are efficient in describing the property of viscoelastic materials
43 citations
TL;DR: In this paper, the authors compare the simulation results of a unified state variable theory, viscoplasticity theory based on overstress (VBO) and a macro-mechanical constitutive model for elasto-viscoplastic deformation of polymeric materials developed by Boyce et al. (Polymer 41:2183-2201, 2000).
Abstract: The uniaxial tension (loading and unloading), creep and relaxation experiments on high density polyethylene (HDPE) have been carried out at room temperature. The stress–strain behavior of HDPE under different strain rates, creep (relaxation) behavior at different stress (strain) levels have been investigated. These experimental results are used to compare the simulation results of a unified state variable theory, viscoplasticity theory based on overstress (VBO) and a macro-mechanical constitutive model for elasto-viscoplastic deformation of polymeric materials developed by Boyce et al. (Polymer 41:2183–2201, 2000). It is observed that elasto-viscoplasticity model by Boyce et al. (Polymer 41:2183–2201, 2000) is not good enough to simulate stress–strain, creep and relaxation behaviors of HDPE. However, the aforementioned behaviors can be modeled quantitatively by using VBO model.
35 citations
TL;DR: In this paper, different approaches for determination of the limits of linear viscoelastic (LVE) behavior are considered on examples of some thermoplastic and thermosetting polymers.
Abstract: In the present study different approaches for determination of the limits of linear viscoelastic (LVE) behavior are considered on examples of some thermoplastic and thermosetting polymers. Stress or strain level, commonly considered as a limit of LVE behavior, are interrelated time-dependent functions strongly influenced by action of external factors. The concept of energy threshold has an advantage of combining into one physical function the effects of both stress and strain in initiating nonlinear behavior. The value of the stored deviatoric energy is considered as a limit of LVE behavior and is a material characteristic. The experimental data on tension at various constant strain rates and tensile creep at various stresses, temperatures, and moisture conditions are considered. It is proved for some polymers that LVE limits in stress-strain representation fall on a common curve that is an energy curve independent of time. Decrease of the test rate or growth of temperature or moisture content appears only in a shift down along the energy curve to the lower limit stresses and higher limit strains.
34 citations
TL;DR: In this article, a nonlinear viscoelastic orthotropic constitutive equation applied to wood material is presented, which takes into account mechanical and mechanosorptive creep via a 3D stress ratio and moisture change rate for a cylindrical orthotropic material.
Abstract: This paper presents a nonlinear viscoelastic orthotropic constitutive equation applied to wood material. The proposed model takes into account mechanical and mechanosorptive creep via a 3D stress ratio and moisture change rate for a cylindrical orthotropic material. Orthotropic frame is based on the grain direction (L), radial (R) and hoop (T) directions, which are natural wood directions. Particular attention is taken to ensure the model to fulfill the necessary dissipation conditions. It is based on a rheological generalized Maxwell model with two elements in parallel in addition with a single linear spring taking into account the long term response. The proposed model is implemented in the finite element code ABAQUS/Standard® via a user subroutine UMAT and simple example is shown to demonstrate the capability of the proposed model. Future works would deal with damage and fracture prediction for wooden structures submitted to climate variations and mechanical loading.
TL;DR: In this paper, the macroscopic creep and relaxation functions of a heterogeneous viscoelastic porous medium are derived by using Mori-Tanaka homogenization scheme, and analytical and semi-analytical solutions can then be determined with a parametric number of heterogeneous phases embedded in a viscous matrix.
Abstract: In this paper the macroscopic creep and relaxation functions of a heterogeneous viscoelastic porous medium are derived by using Mori-Tanaka homogenization scheme. Analytical and semi-analytical solutions can then be determined with a parametric number of heterogeneous phases embedded in a viscoelastic matrix whose behavior is described with a parametric number of analogical units. Under some simplifying assumptions, a solution strategy is presented in order to make explicit how the microscopic retardation and relaxation times of the viscoelastic matrix control the distribution of the retardation and relaxation times of the homogenized medium.
TL;DR: In this article, a non-linear rheological model was used to predict the viscoelastic behavior of a semi-crystalline polymer under uniaxial monotonous loading and unloading conditions.
Abstract: To predict the behaviour of a semi-crystalline polymer under complex cyclic mechanical loading and unloading conditions, a non-linear rheological model, previously developed to predict the viscoelastic behaviour under uniaxial monotonous loading and unloading conditions, was used as a starting point and generalised in three-dimensions (3D). The initial model was created on the assumption that the amorphous phase of the semi-crystalline polymer follows the particular reversible mechanism of viscoelastic deformations. This assumption allowed to model the mechanical behaviour of the semi-crystalline polymer under loading and unloading conditions without changing the parameters at the point when the loading was reversed. The parameters of the 3D generalised model under tension, torsion (shearing) and compression conditions were identified from the fitting of the respective uniaxial mechanical tests. It was demonstrated that the 3D model agreed with the experimental data obtained under complex proportional and non-proportional mechanical loading. It was also demonstrated that the model is able to reproduce more then one loop of the cyclic loading.
TL;DR: In this article, experiments were performed on hardened cement paste that allowed the simultaneous measurement of both the dilatational and shear compliances, allowing the full three-dimensional characterization of the constitutive response.
Abstract: The majority of the viscoelastic constitutive data for cement paste or concrete found in the literature deal exclusively with uniaxial loading. To predict the isotropic response of concrete or cement paste under multiaxial loading or multiaxial prescribed deformation, it is necessary to have knowledge of at least two viscoelastic constitutive properties. In the past, the typical treatment of three-dimensional modeling of concrete viscoelasticity has involved the assumption of a time-independent viscoelastic Poisson ratio. However, the experimental evidence supporting this simplification is inconclusive. In this study, experiments were performed on hardened cement paste that allowed the simultaneous measurement of both the dilatational and shear compliances, allowing the full three-dimensional characterization of the constitutive response. It was found that the dilatational compliance leveled off after several days for three of four mixtures tested. In these three materials, the Poisson’s ratio was found to be an increasing function of time. Prediction of the measured uniaxial compliance using the measured bulk and shear compliances indicated that the confined compressive test used in this research may cause changes in the material which affect the measured dilatational compliance, and therefore the calculated viscoelastic Poisson ratio.
TL;DR: In this paper, a constitutive model for large strain deformation of semicrystalline polymers has been formulated to predict the complex elasto-viscoelastic-viscoplastic material response.
Abstract: A constitutive model for large strain deformation of semicrystalline polymers has been formulated to predict the complex elasto-viscoelastic-viscoplastic material response. The general form of this model can be represented by three parallel rheological components corresponding to each of the modes of deformation. It will be shown that such a configuration is well suited to the mechanical nature of polymers as observed in recent studies. The constitutive stress-strain-time relationships are drawn from continuum mechanics which are more suitable than simple linear expressions from rheology. The result is a large strain, fully three-dimensional constitutive model, derived from a thermodynamic basis. The proposed model can be fit to macroscopic experimental data and is highly suited to numerical analysis. The paper reviews the literature relevant to constitutive representation of semicrystalline polymers, provides conclusion and validation of the most suitable form of constitutive model and presents the relevant constitutive mathematics.
TL;DR: In this article, the effect of the depth-dependent loading time on pavement temperature was evaluated by means of the concept of pseudo temperature, where the pavement temperature measured from instrumented thermocouples was integrated into one single factor, termed effective temperature.
Abstract: Dynamic response of asphalt concrete (AC) pavements under moving load is a key component for accurate prediction of flexible pavement performance. The time and temperature dependency of AC materials calls for utilizing advanced material characterization and mechanistic theories, such as viscoelasticity and stress/strain analysis. In layered elastic analysis, as implemented in the new Mechanistic-Empirical Pavement Design Guide (MEPDG), the time dependency is accounted for by calculating the loading times at different AC layer depths. In this study, the time effect on pavement response was evaluated by means of the concept of “pseudo temperature.” With the pavement temperature measured from instrumented thermocouples, the time and temperature dependency of AC materials was integrated into one single factor, termed “effective temperature.” Via this effective temperature, pavement responses under a transient load were predicted through finite element analysis. In the finite element model, viscoelastic behavior of AC materials was characterized through relaxation moduli, while the layers with unbound granular material were assumed to be in an elastic mode. The analysis was conducted for two different AC mixtures in a simplified flexible pavement structure at two different seasons. Finite element analysis results reveal that the loading time has a more pronounced impact on pavement response in the summer for both asphalt types. The results indicate that for reasonable prediction of dynamic response in flexible pavements, the effect of the depth-dependent loading time on pavement temperature should be considered.
TL;DR: In this article, the use of a new bitumen modifier, a reactive prepolymer, based on the reaction of 4,4′-diphenylmethane diisocyanate (MDI) and a low molecular weight polyethylene glycol (PEG), was studied.
Abstract: This paper deals with the use of a new bitumen modifier, a reactive prepolymer, based on the reaction of 4,4′-diphenylmethane diisocyanate (MDI) and a low molecular weight polyethylene glycol (PEG). The rheological and thermal behaviours of modified bitumen containing a low MDI–PEG concentration, as well as its morphology, have been studied. A relatively low amount of MDI–PEG (0.5 to 1.5% wt.) yields a significant improvement in the modified bitumen rheological properties, mainly in the high in-service temperature region. In this range of temperature, the rheological properties are clearly affected by curing time at room temperature. These results indicate that chemical changes, due to the reaction of MDI isocyanate groups with the most polar groups (–OH; –NH) of asphaltenes and resins, are produced. Thus, new chemical structures, non-visible by optical microscopy, slowly develop in MDI–PEG modified bitumen when samples are cured at room temperature.
SIDI1
TL;DR: In this paper, an analytical model for the interfacial stresses between RC beam and a thin FRP plate bonded to its soffit is presented, where the influence of creep and shrinkage effect relative to the time of the casting and the loading of the beams is taken into account.
Abstract: External bonding of fibre reinforced polymer (FRP) composites has becomes a popular technique for strengthening concrete structures all over the world. An important failure mode of such strengthened members is the debonding of the FRP plate from the concrete due to high interfacial stresses near the plate ends. For correctly installed FRP plate, failure will occur within the concrete. Accurate predictions of the interfacial stresses are prerequisite for designing against debonding failures. In particular, the interfacial stresses between a beam and soffit plate within the linear elastic range have been addressed by numerous analytical investigations. In this study, the time-dependent behavior of RC beams bonded with thin composite plate was investigated theoretically by including the effect of the adherend shear deformations. The time effects considered here are those that arise from shrinkage and creep deformations of the concrete. This paper presents an analytical model for the interfacial stresses between RC beam and a thin FRP plate bonded to its soffit. The influence of creep and shrinkage effect relative to the time of the casting and the time of the loading of the beams is taken into account. Numerical results from the present analysis are presented to illustrate the significance of time-dependent of adhesive stresses.
TL;DR: In this paper, the effects of physical aging on creep behavior were evaluated quantitatively on pure resin and with various fiber contents without heat treatment, using the grand master curve of creep compliance and shift factors, which was able to estimate the creep deformation of molded materials under varying conditions and fiber contents.
Abstract: Thermoplastic resin and fiber-reinforced thermo-plastics (FRTPs) were used without post-cure treatment as “molded material.” For such materials, creep behavior and physical aging occur simultaneously. This study examined the creep behavior of polycarbonate (PC) and glass-fiber-reinforced polycarbonate (GFRPC) injection moldings, including the effect of physical aging and fiber content, and determined that the time–temperature superposition principle could be applied to the creep behavior for different fiber contents. The effects of physical aging on creep behavior were evaluated quantitatively on pure resin and with various fiber contents without heat treatment. We found that the effect of physical aging could be evaluated with the proposed factor, “aging shift rate.” To discuss the linearity of viscoelasticity in FRTPs, this study used two shift factors: time and modulus shift factors. The fiber content affected creep behavior by both retarding and restraining it through changing the elastic modulus. This was shown by generating a grand master curve of creep compliance, which included the effects of time, temperature, and fiber content. Using the grand master curve of creep compliance and shift factors, it was possible to estimate the creep deformation of molded materials under varying conditions and fiber contents. The estimated creep deformation gave a very good fit to the experimental creep deformation.
TL;DR: In this article, the authors discuss the process of changing and tendency of hysteresis loop and energy dissipation of viscoelastic solid models and show that under certain conditions, the sign of (62) is a sufficient and necessary condition for judging the difference between dissipated energy in the (n+1)th and nth periods.
Abstract: We discuss the process of changing and tendency of hysteresis loop and energy dissipation of viscoelastic solid models. One of our conclusions is that, under certain conditions, the sign of (62) is a sufficient and necessary condition for judging the sign of the difference between dissipated energy in the (n+1)th and nth periods. The citation of the strains’ linear superposition expands the applicable domains. We prove that for the fractional-order Kelvin model and under the condition of quasi-linear theory, the above conclusions also hold. Based on experiments, we divide the strains of this paper into three widely used types and we see the constant domain as experimental error.
TL;DR: In this paper, the authors analyzed the indentation of a rigid indenter into a power-law creep solid for which the relationship between the stress and the strain rate is given by σ = b\dot{\varepsilon}^{n}
Abstract: Based on dimensional analysis, we analysed the indentation of a rigid indenter into a power-law creep solid for which the relationship between the stress and the strain rate is given by \(\sigma=b\dot{\varepsilon}^{n}\) . It is shown that under a described condition the creep exponent n can be determined without invoking the detail knowledge of the indenter profile and the shape of the indented solid. The result reported herein should be useful for interpreting the data of nanoindentation into a power-law creep solid in the case that the indented solid is not a flat half-space and/or the indenter has tip defects. The performance of the simple method to evaluate the creep exponent is examined by using numerical experiments and its limitations also discussed.
TL;DR: In this article, the Laplace integral transform was used to analyze the sensitivity of viscoelastic panel flutter with an arbitrary function of relaxation, and the critical values of free stream velocities and frequencies of vibrations were determined from the condition that the real parts of the poles of integrand must be zero, which correspond to harmonic motion.
Abstract: Using linear model, the parametric sensitivity analysis of viscoelastic panel flutter with an arbitrary function of relaxation, is examined by the Laplace integral transform method. The critical values of free stream velocities and frequencies of vibrations are determined from the condition that the real parts of the poles of integrand must be zero, which correspond to harmonic motion. Approximate and exact values of critical speed and corresponding frequencies for a general isotropic viscoelastic constitutive relations are obtained. The solutions are analyzed for critical, subcritical and supercritical cases. It is shown that the viscoelastic flutter speed is smaller than the corresponding elastic one if elastic moduli of material is equal to the initial value of relaxation function. Influence of aerodynamical damper is studied assuming that the parameter of viscous property of material is small enough in comparison with the parameter of aerodynamical damper and vice versa.
TL;DR: In this article, a spectrum-based model for describing the behavior of time-dependent materials is presented, which is not expressed through the use of series, but instead, certain criteria have been imposed to select a spectrum function that has the potential of describing a wide range of material behavior.
Abstract: A new spectrum-based model for describing the behavior of time-dependent materials is presented. In this paper, unlike most prior modeling techniques, the time-dependent response of viscoelastic materials is not expressed through the use of series. Instead, certain criteria have been imposed to select a spectrum function that has the potential of describing a wide range of material behavior. Another consequence of choosing the spectrum function of the type used in this paper is to have a few closed form analytic solutions in the theory of linear viscoelasticity. The Laplace transform technique is used to obtain the necessary formulae for viscoelastic Lame' functions, relaxation and bulk moduli, creep bulk and shear compliance, as well as Poisson's ratio. By using the Elastic–Viscoelastic Correspondence Principle (EVCP), material constants appearing in the proposed model are obtained by comparing the experimental data with the solution of the integral equation for a simple tensile test. The resulting viscoelastic functions describe the material properties which can then be used to express the behavior of a material in other loading configurations. The model's potential is demonstrated and its limitations are discussed.
TL;DR: In this article, the effect of viscoelasticity on the yield behavior of polycarbonate, PC, was studied and the identification of a yield criterion which takes into account the effects of the mechanical history on the onset of plastic strain, was attempted.
Abstract: In the present work, the effect of viscoelasticity on the yield behaviour of a polycarbonate, PC, was studied and the identification of a yield criterion which takes into account the effects of the mechanical history on the onset of plastic strain, was attempted. The attention was focused on the shear yielding plastic deformation process and different loading histories were performed under uniaxial compression: constant strain rate at different rates, stress relaxation at different applied strain levels, creep under different stress levels. Some tests were also carried out under shear loading, in which the hydrostatic stress component is equal to zero and its effect on the yield onset can be considered. For the definition of a yield criterion, different quantities, some already proposed in an analogous work on a styrene-acrylonitrile copolymer (SAN), were considered and determined at yield onset for each of the applied loading histories. The results obtained in this work show that the relative ratios of the viscoelastic strain over the overall strain and of viscoelastic energy over the deformation work are fairly constant irrespective of both loading history and stress state. The re-elaboration of the data previously obtained on SAN is consistent with these results. Discussing the experimental data, differences between the mechanical behaviour of the two glassy polymers were pointed out and a more difficult activation of the plastic deformation process of PC than SAN was generally observed.
TL;DR: In this article, the effect of the matrix creep on the deformation of microcellular foam and how this effect influences the later deformation characteristics of the material in terms of a Poisson description is investigated.
Abstract: The properties of the Poisson’s ratio of microcellular foams with an internal pressure in the voids and low porosity are investigated. Of prime interest is the effect of the matrix creep on the deformation of the foam and how this effect influences the later deformation characteristics of the material in terms of a Poisson description. First, the definitions of Poisson’s ratio for the microcellular foams under uniaxial stress are reviewed. Second, the deformation of the microvoids under the influence of the internal pressure is analyzed by means of Eshelby’s equivalent inclusion method. Next, the formula of the macroscopic strain of the microcellular foams is derived by using Mori–Tanaka’s scheme, and based on this formula, the expression of the Poisson’s ratio of the material is obtained. Further, the calculation of the Poisson’s ratio of the material is then carried out. Numerical results show that the Poisson’s ratio of the microcellular foams is a time-dependent parameter. It is also discussed that because of the effect of the internal pressure in the voids, the global Poisson’s ratio may be negative. Under the action of remote compressive load, the Poisson’s ratio of the microcellular foams may be unbounded. Finally, the effects of the loading rate, the Poisson’s ratio and the relaxation time of the polymeric matrix material, the porosity, and the pressure in the microvoids on the Poisson’s ratio are discussed with the aid of numerical estimates. These analytical results indicate that the Poisson’s ratio under uniaxial tension is different from that under uniaxial compression.
TL;DR: In this article, a new analytic method for solutions of vibration problems of linear viscoelastisity with arbitrary relaxation kernels is proposed, which is reduced to the solution of a set of ordinary integro-differential equations which are solved using the Laplace integral transform, the method of contour integration and the convolution of functions.
Abstract: A new analytic method for solutions of vibration problems of linear viscoelastisity with arbitrary relaxation kernels is proposed. The problem is reduced to the solution of a set of ordinary integro-differential equations which are solved using the Laplace integral transform, the method of contour integration and the convolution of functions. The branch points of integrand can not be obtained for arbitrary relaxation kernels. For this reason, successive approximation method for calculating the poles and the inverse Laplace transformation of solution is offered. The first approach coincides with the well-known solution obtained by both the averaging method and the method of complex module. It is shown that the limits of these approximations are unique and it is proved that the obtained solution is the exact solution of the considering problem.
TL;DR: In this paper, a generalization of the Kuhn model of linear viscoelasticity is proposed, which has four material parameters and is able to provide a near frequency independent response over a wide range of frequencies.
Abstract: We propose a generalization of the Kuhn model of linear viscoelasticity. This generalization, which has four material parameters, is able to provide a near frequency independent response over a wide range of frequencies. It is useful for highly dissipative materials such as asphalt concrete. It is derived by generalizing Lubliner and Panoskaltsis’s modified Kuhn model, but we also show that it is closely related to fractional derivative models. We show that the model admits a rheological approximation, that is, an approximation by classical springs and dashpots. The model and rheological representation are compared to experimental data.
TL;DR: In this paper, the authors present constitutive modeling of dynamically loaded elastomeric products such as power transmission belts, where the critical angular velocity is proportional to the ratio of the belt length to the common diameters of the pulleys.
Abstract: This paper presents constitutive modeling of dynamically loaded elastomeric products such as power transmission belts. During the normal operation of the belts certain segments of the belt structure are loaded with a tooth-like periodic (cyclic) loading. When the time-dependent properties of the elastomeric material “match” the time-scale of the dynamic loading a strain accumulation process occurs. The critical angular velocity is proportional to the ratio of the belt length to the common diameters of the pulleys. The magnitude of the strain accumulated in each loading cycle decreases with an increase in belt length. For a given belt geometry the critical angular velocity increases with the number of loading cycles. At the same time the magnitude of the accumulated strain decreases non-linearly as the number of loading cycles increases. However if the belt operates at or in the close vicinity of its critical angular velocity it will almost certainly fail! The critical angular velocity depends on the material retardation time (location in the frequency spectrum), while the magnitude of the accumulated strain is dictated by the strength of the corresponding discrete spectrum lines. Thus, the mechanical spectrum of the elastomeric material from which the belt is constructed is the most important material function for predicting the durability of drive belts and similarly dynamically loaded elastomeric products.
TL;DR: In this article, the effect of applied displacement rate on strain distributions and interfacial failure mechanisms in bi-material specimens was investigated under three different loading speeds (0.0254 cm/min, 0.254 cm /min, and 2.54 cm 2 ).
Abstract: Deformation and failure mechanisms in bi-material specimens were investigated under three different loading speeds (0.0254 cm/min, 0.254 cm/min and 2.54 cm/min). Two different viscoelastic materials were used to generate bi-material specimens. The experimental data were analyzed and the effect of applied displacement rate on strain distributions and interfacial failure mechanisms in the bonded specimens are discussed. Close inspection of the specimens showed that at failure initiation widely different deformation rates occurred at roughly the same global strain levels and were concentrated in the interphase regions near the bondlines.