Igor Emri

Poisson's Ratio in Linear Viscoelasticity – A Critical Review

Poissons ratio is an elastic constant defined as the ratio of thelateral contraction to the elongation in the infinitesimal uniaxialextension of a homogeneous isotropic body. In a viscoelastic materialPoissons ratio is a function of time (or frequency) that depends on thetime regime chosen to elicit it. It is important as one of the materialfunctions that characterize bulk behavior.This paper develops the linear theory of the time- orfrequency-dependent Poissons ratio, and it reviews work on itsexperimental determination. The latter poses severe difficulties in viewof the high accuracy required. Thus, reliable information on theviscoelastic Poissons ratio is as yet rather scanty.The paper also reports on attempts to measure the Poissons ratioof a viscoelastic material as a function of temperature. Lateralcontraction in creep and at constant rate of extension receivesattention as well.

NON-LINEAR VISCOELASTICITY BASED ON FREE VOLUME CONSIDERATION

Abstract Many advanced engineering problems suffer from inadequate solution because the appropriate constitutive behavior for the materials involved is not available. This is certainly true where polymers are concerned because in many situations involving failure analysis the non-linear viscoelastic material properties become important. In this paper a non-linear viscoelastic constitutive law is considered. It starts from the assumption that linear viscoelasticity is appropriate under infinitesimal strains and that the material description must revert to this case. The non-linearity of this development is derived from the stress dependent time response in the deformation process. The physical basis for the description derives from the observation that stress induced dilatation effects the mobility of molecular chains through changing the free volume in the polymer. Test data for polyvinyl acetate are compared with computations under conditions of relaxation and constant strain rate deformation. Excellent agreement is obtained between the proposed model and experiments. This agreement would indicate that the free volume model is definitely a possible way of describing non-linear viscoelastic behavior under small to moderate strains.

Generating line spectra from experimental responses. Part I: Relaxation modulus and creep compliance

We describe a recursive computer algorithm which generates line spectra from relaxation modulus or creep compliance data without producing negative spectrum lines. We apply the algorithm here to data read from mathematical models for the relaxation modulus. Since these data were thus free of the usual experimental error, we could use a relatively simple form of the basic algorithm that is applicable also to smoothed data. The spectra faithfully reproduced the input functions and may serve for data storage as well as for predicting other experimental responses.

The Effect of Temperature and Pressure on the Mechanical Properties of Thermo- and/or Piezorheologically Simple Polymeric Materials in Thermodynamic Equilibrium – A Critical Review

The mechanical properties of polymeric materials quite generally dependon time, i.e., on whether they are deformed rapidly or slowly. The timedependence is often remarkably large. The complete description of themechanical properties of a polymeric material commonly requires thatthey be traced through 10, 15, or even 20 decades of time. The class ofpolymeric materials referred to as thermorheologically and/orpiezorheologically simple materials allows use of the superposition ofthe effects of time and temperature and/or time and pressure in suchmaterials as a convenient means for extending the experimental timescale.This paper presents a critical review of models proposed todescribe the effect of temperature and/or pressure on time-dependentthermorheologically and/or piezorheologically simple polymericmaterials. The emphasis here is on the theoretical aspects, althoughexperimental results are used as illustrations wherever appropriate.

Generating line spectra from experimental responses. Part II: Storage and loss functions

A computer algorithm is described which allows the determination of a discrete distribution of relaxation times from simulated or smoothed storage or loss modulus data, or of retardation times from simulated or smoothed storage or loss compliance data. The distributions faithfully reproduce the input data and are suitable for data storage as well as for generating any other response curves.

Generating Line Spectra from Experimental Responses. III. Interconversion between Relaxation and Retardation Behavior

Abstract An algorithm is described which allows relaxation line spectra to be interconverted into retardation line spectra, and vice versa. The first line spectrum is generated from a given experimental response such as the relaxation modulus, the storage modulus, or the loss modulus, or from a response such as the creep compliance, storage compliance, or loss compliance. The interconversion algorithm is here applied to the standard linear solid and liquid models, and to a 32-line spectrum simulating the behavior of an entangled polymer.

Generating line spectra from experimental responses, Part IV : Application to experimental data

The previously reported algorithms for deriving line spectra (respondance time distributions) from synthetic or smoothed experimental responses is here extended to experimental data. The earlier algorithm was modified to improve performance in the presence of experimental errors. The effect of smoothing the data with the aid of the cubic spline function was examined.The performance of the modified algorithm was studied comprehensively. Auto-predictions and cross-predictions of storage and loss compliances from the generated line spectra were in excellent agreement. In equally good agreement were the line spectra obtained from compliance data and from stress relaxation data obtained on the same material.

Generating line spectra from experimental responses

The computer algorithm for determining line spectra from experimental data, described in earlier publications in the form in which it is applicable to data obtained in response to excitations as step functions of time and to sinusoidally oscillating excitations, is modified here to allow line spectra to be obtained from data generated in response to the imposition or the removal of a constant rate of strain.

The determination of creep and relaxation functions from a single experiment

The creep compliance and relaxation functions used in characterizing the mechanical response of linear viscoelastic solids are traditionally found by conducting two separate experiments. Alternatively, one of the functions may be determined from a single experiment while the other is obtained through interconversion. All direct interconversion methods, however, require the solution of an ill-posed problem. The goal of this paper is to present the theoretical framework for developing a new apparatus, based on “spring loading,” which facilitates the determination of both creep and relaxation functions from a single experiment. There is no need for interconversion. Questions of stability with respect to the measured data are discussed and a stable numerical algorithm is presented.

Determination of mechanical spectra from experimental responses

Abstract A recursive computer algorithm was developed which generates line spectra from experimental response functions. The method allows storing information on the mechanical properties of polymeric materials in a convenient way. The algorithm also interconverts between relaxation and retardation spectra. From the spectra, any desired response function can then be recovered. The algorithm essentially utilizes the fact that the kernel functions resemble step functions. Slightly different codes are used for each kernel function. The appearance of negative relaxation or retardation lines is obviated. Mathematically such lines would be acceptable, and they do not seriously affect reconstruction of responses within relaxation or retardation behavior. However, they would seriously interfere with interconversion between the two types of behavior, and they would also pose problems in the interpretation of the spectra.