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Some analytical results for the mechanical behavior of elastic composite materials and structures with growing damage are summarized and then extended to viscoelastic media. The effect of strain rate only at crack tips is considered first; it is shown that if the crack speed is a strong function of energy release rate, the overall mechanical response is like that for an aging elastic material. Both stable crack growth and unstable crack growth followed by arrest produce this aging-like behavior. Viscoelastic behavior throughout one or more of the phases is then introduced. A simplification is used in which only one relaxation modulus characterizes the viscoelasticity, apart from that at crack tips. Upon replacing the physical displacements in the response for an elastic material by quantities called pseudo displacements, a simple model for viscoelastic composites with growing damage is obtained.

The rheological properties of rennet-induced skim milk gels were determined by two methods, i.e., via stress relaxation and dynamic tests. The stress relaxation modulusG c (t) was calculated from the dynamic moduliG′ andG″ by using a simple approximation formula and by means of a more complex procedure, via calculation of the relaxation spectrum. Either calculation method gave the same results forG c (t). The magnitude of the relaxation modulus obtained from the stress relaxation experiments was 10% to 20% lower than that calculated from the dynamic tests.

The flow behavior of molten polymers can be described by the theory of linear viscoelasticity only when either the total strain or the maximum strain rate is very small. But there are very few, if any, commercial melt processing operations in which the flow satisfies either of these criteria. Thus, while linear viscoelastic behavior has some application in material characterization, it cannot, in general, be correlated with melt performance in processing machinery.

The Boltzmann model of linear viscoelasticity is an appropriate model for materials that simultaneously exhibit viscous and elastic behaviour, such as synthetic and natural polymers. The nature of the viscoelasticity is encapsulated in terms of the structure of its kernel function (the relaxation modulus) G(t). Husain and Anderssen (2005) proposed a procedure for approximating G(t), based on taking moments of the Boltzmann equation with G(t) the sum of Kohlrausch functions. The shortcoming of this proposal is the need to evaluate the moments on the half-interval [0,?). We propose a method which takes the strain-rates to have a polynomial form and G(t) to be a sum of Kohlrausch functions. It yields methods for the direct estimation of the parameters in Kohlrausch models for G(t).

The incremental relaxation modulus ΔG(t) for a concentrated solution of polyisobutylene has been determined from step-shear experiments in which a small deformation Δγ was superimposed on a large deformation γ1; ΔG(t) was found to decrease with increasing γ1 and to increase with the time te after the imposition of the large deformation. It was also observed that the “apparent relaxation specturm” associated with δG(t) narrows and shifts to shorter times when compared to the spectrum associated with the linear viscoelastic relaxation modulus G(t). The results are well described by the nonlinear constitutive equation of the BKZ elastic fluid theory.

The PB0, P0D, and PI materials were used to show the possibilities of simulating the long-term relaxation processes for a new group of polymer materials using the time analogies in the linear and nonlinear regions of the viscoelastic properties. The results show that the generalized dependences of compliance and relaxation modulus widen the time range of lead of the relaxation processes by approximately six to seven decimal orders. Satisfactory results were obtained in comparing the generalized dependences with the results of the long-term reference experiment carried out in the same basic conditions.

The relaxation modulus and ultimate tensile strength of the soybean seedcoat as a function of drying temperature and moisture content were determined using constant strain rate tensile tests. The master curve for the seedcoat relaxation modulus was derived using the time-temperature and time-moisture shifting technique. Both properties decrease with increasing moisture content and drying temperature. A two-term Maxwell model was derived for describing the relaxation modulus of the seedcoat. The soybean seedcoat can be considered as a thermo-hydro-rheologically simple viscoelastic material..

In the earlier theoretical work of Barnes, Townsend, and Walters on pulsatile flow of viscoelastic fluids, it was found that an Oldroyd model predicted that flow enhancement should decrease with increasing frequency of pulsation, whereas their experimental data showed an increase . Their calculations have been repeated for the Goddard—Miller model using two different expressions for the relaxation modulus; it is found that the Goddard—Miller model leads to the same discrepancy between theory and experiment. It is tentatively concluded that secondary-flow effects are playing an important role. The role of the elastic and inertial effects and the role of the shape of the viscosity vs. shear rate curve are discussed.

The linearized boundary-initial history value problem for simple fluids obeying the Coleman-Noll constitutive equation $$S + p\delta = 2\int\limits_0^\infty {m(s)(E(t - s} ) - E(t))ds$$ is considered. Here S is the stress tensor, δ the Kronecker delta, p the constitutively indeterminate mean normal stress, E the infinitesimal strain tensor, and m(s) a material function. The shear relaxation modulus G is defined as $$G(s) = \int\limits_\infty ^s {m(\xi )d\xi .}$$ (i) In this paper it is shown that if G satisfies the assumptions $$G \in C^2 [0,\infty ),{\text{ }}G(s) \to 0{\text{ as }}s \to \infty,$$ (i) $$( - 1)^k \frac{{d^k G(s)}}{{ds^k }} > 0,{\text{ }}k = 0,1,$$ (ii) $$G''(s) \geqq 0,$$ (iii) then the rest state of the fluid is stable in an appropriate “fading memory” norm. The additional assumption $$ - \int\limits_0^\infty {G'} (s)s^2 ds < \infty$$ (iv) yields asymptotic stability.

Two corn meal extrudates with initial moisture contents of 22% and 31% W.B. were partially dried to moisture contents from 7% to 31% W.B. and stored in hermetically sealed containers to allow redistribution of the water. Compressive strength, compressive relaxation and instrumental texture profile analyses (fracturability, cohesiveness, springiness, gumminess and chewiness) were measured. Compressive strength increased with decrease in moisture content from 31-15%, reached a maximum between 15-10% and then decreased below 10%. Stiffness showed a similar relationship, with the maximum occurring between 10-6%. Relaxation modulus increased with decrease in moisture content over the range studied. Relaxation time was a minimum at 15% moisture content. Fracturability had a similar relationship to moisture content as that of compressive strength. The textural behavior was ductile and chewy at moisture contents above 15% but became crisp or crunchy and collapsed with brittle fractures at lower moisture contents. Both compressive properties and texture profile parameters of the corn meal extrudates changed considerably with changes in moisture content.

A simple procedure is outlined that inverts the specific compliance function for a linear viscoelastic material, similar to concrete, to its specific relaxation modulus by using Laplace transform and age shift function concept.

The rheological properties of concentrated wheat starch gels were measured with shear stress relaxation experiments in cone-plate geometry. The water content of the investigated gels were 80, 60, 50 and 30% (w/w), respectively, and the relaxation modulus (G) and half relaxation time (T1/2) were studied after heating to different temperatures. For the gels with 50% and 60% (w/w) of water, a maximum value of G was obtained when the temperature interval for gelatinization was passed. When these gels were heated to higher temperatures, G decreased, and T1/2 increased, whereas gels with 30 and 80% (w/w) of water behaved differently. The influence of particle size distribution on the rheological properties of concentrated starch gels, was also investigated. It was found that G and T1/2 increased with a greater fraction of small starch granules. Rheologische Eigenschaften von konzentrierten Weizenstarkegelen. Die rheologischen Eigenschaften von konzentrierten Weizenstarkgelen wurden durch Scherkraftentspannungsversuche mit Hilfe des Kegelplattenverfahrens gemessen. Die Wassergehalte der untersuchten Gele betrugen 80, 60, 50 und 30% (w/w), und der Entspannungsmodul (G) sowie die Entspannungs-Halbwertzeit (T1/2) wurden nach Erhitzung auf verschiedene Temperaturen untersucht. Fur die Gele mit 50 und 60% (w/w) Wasser wurde ein maximaler G-Wert erhalten, wenn das Temperaturintervall der Verkleisterung uberschritten war. Wenn diese Gele auf hohere Temperaturen erhitzt wurden, verringerte sich G und erhohte sich T1/2, wogegen sich Gele mit 30 und 80% (w/w) Wasser unterschiedlich verhielten. Der Einflus der Teilchengrosenverteilung auf die rheologischen Eigenschaften konzentrierter Starkegele wurde ebenfalls untersucht. Es wurde gefunden, das G und T1/2 bei groserem Anteil kleiner Starkekorner zunahmen.

An interpretation was attempted of previous results that the method of reduced variables could not be applied to the relaxation curves of mochi cake. Temperature dependence of the apparent specific volume or the apparent density of mochi cake was determined. The correction factor by density Tρ/T0ρ0 was very small and ignored with usual materials. Ineffecti-veness of WLF Eq. to the temperature dependence of relaxation modulus of mochi is attributed to the decrease of viscosity, which might be derived from free space on the mobility of polymer segments. It is suggested that free space corresponds to fine air bubbles mixed in mochi cake during its preparation which causes a decrease in viscosity and relaxation modulus.

Grains of brown rice, paddy variety IR-8, were subjected to two types of uniaxial compressive loading, constant displacement rate and sinusoidally varying stress, to determine behavior over a wide range of time scale. Grains from four different moisture level groups were used. With a time decrease from 120 to 1.6 × 10−4s the relaxation modulus increased 15, 25, 16 and 20 fold at respective moisture contents of 12, 17, 22 and 27%. A master relaxation curve for each moisture content is presented. Understanding the viscoelastic behavior of brown rice as a function at time and moisture content is basic to the solution of stress-strain analysis problems.

The investigations so far available with regard to stress analysis of adhesive joints assume that the adhesive is elastic. In the present analysis the time dependent properties of the adhesive are taken into account by assuming that the adhesive is viscoelastic. The viscoelastic analysis of a tubular joint has been attempted using a prony series fitting for the relaxation modulus of two adhesives. The long term redistribution of the stresses in the adhesive is evaluated using the finite element method. Viscoelastic analysis of an adhesive tubular joint has been performed for the first time, using the finite element method with a prony series fitting for the relaxation modulus of the adhesive. For a typical epoxy it has been found that not only the elastic stresses are different at different levels but also the viscoelastic response shows considerable variation from one level to another. As large a reduction as 57 % is noticed in the normal stress and an even larger reduction of 62% is noticed in ...

The dynamic mechanical properties of a class of plasticized epoxies were investigated over a wide temperature range by means of a Rheovibron Viscoelastometer. Master curves for storage and loss moduli were produced by means of the frequency-temperature superposition principle, as well as for relaxation modulus by a conversion formula. The effect of plasticizer percentage on the said parameters, as well as the loss peaks, corresponding toγ andα relaxations was investigated.

The structure of the shock layers that form in high amplitude acoustic waves in relaxing media is analyzed for a general relaxation modulus. The inner and outer expansions are matched to second order and a closed form expression is obtained for Lighthill's shock displacement due to diffusion. The asymptotic behavior of the shock solution at the edges of the shock layer is also analyzed and conditions obtained for the existence of a fully relaxed shock.

A constitutive equation presented earlier has been generalized to describe the transient shear flow behaviour of polymer liquids. The mathematical structure and properties of such a generalization have been discussed. The practical expressions for the generalized relaxation modulus have been proposed.

The viscoelastic properties of four-armed, star-shaped polystyrenes having narrow molecular weight distributions were studied in a undiluted state by the tensile stress relaxation method. The steady-flow viscosity, the steady-state compliance and other rheological parameters were determined from the relaxation modulus master curves. The molecular weight dependences of these parameters were compared with those of linear and comb-shaped polymers.

Time correlation functions of the dissipative impulse flux have been used as a method to calculate the relaxation modulus of a network in the transition zone. A Gaussian sub-chain model is adopted to describe the micro-Brownian movement of a polymeric chain in the network; in this model, the equilibrium positions of the spheres are assumed to be displaced because of the mutual non-interpenetrability of the chains. The mutual non-interpenetrability of the chains leads to the fact that the relaxation modulus becomes strain-dependent in the low-frequency and of the transition zone. The extent of this dependence decreases as the density of crosslinking increases.

It had been shown previously that the dynamic viscosities measured by superposing in‐line and transverse small‐amplitude oscillations on steady simple shearing were independent of the base rate of shear at ultrasonic frequencies in the BKZ fluid. This result was derived on the assumption that the shear relaxation modulus had a bounded right‐hand derivative at the origin. The present investigation proves this same result without this assumption. A similar conclusion is derived for the derivative of the storage modulus at high frequencies. In addition, it is shown that these ultrasonic measurements cast light on the question of the boundedness of the first two derivatives of the relaxation modulus at the origin.

The temperature dependence of log a of poly(styrene -co- sodium methacrylate) was analyzed by means of the relation based on the free volume and the hole theories of liquids. For the near-Tg region the relation becomes a single parameter equation of T/Tg. The analysis revealed a transition in flow pattein at TT associated with disintegration of the ion multi plets. The Tt-transition was previously detected in other theological functions, viz, relaxation modulus, mechanical and dielectric tan δ plots.

The shear relaxation modulus of melt-crystallized linear polyethylene with and without CCl4 from 5 sec to 30 min after the application of a strain is measured from -185°C to -25°C. The loss modulus at very low frequencies calculated from these data reveals a fine structure in the γ-loss band of this polymer with three component relaxations, A master curve, relaxation spectrum and shift factor are determined by the method of reduced variables for each of the three relaxations designated as γ1, γ2 and γ3 in the order of descending temperature. The activation energies for the γ1-, γ2- and γ3-relaxations are estimated at ca 22 kcal/mol, 11 kcal/mol and, 9 kcal/mol respectively. It is found that the γ1- and the γ2-relaxations are shifted to higher temperatures by the presence of CCl4, but the activation energy and the shape of the spectrum for each of these relaxations are not affected by it.

Both stress relaxation behaviour and time-to-breaktb as a function of stressσ were studied in identical time and temperature intervals using poly(2-hydroxyethyl-methacrylate) gels in the swollen state, prepared both in the homogeneous and in the heterogeneous form. Homogeneous samples were prepared by means of crosslinking polymerization (concentration of ethylene dimethacrylate as a crosslinking agentc=0.21 and 0.65×10−4mol cm−3) in the presence of ethylene glycol (v0=0.6−0.3); heterogeneous samples with various degrees of porosity were prepared in the presence of water (v0=0.8−0.2). Irrespective ofv0, an agreement was found between the temperature shift factors, logaT, obtained from the viscoelastic and ultimate measurements for the systems prepared with a higher concentration of the crosslinking agent; for the lightly crosslinked systems theaT values from the viscoelastic data were less sensitive to temperature. The temperature dependence of logaT was not the same at temperaturesT>30°C and additional horizontal-vertical shifts had to be used; this effect is very similar to that observed previously for the other polymethacrylates byFerry and coworkers.

The stress relaxation behavior of isotropic and oriented cellulose filaments has been studied at 25° and 50°C. and 50% relative humidity at strains between 0.5 and 5%. Log modulus–log time plots were found to be different at different strains, but superposable one upon the other by simple translation along the log time axis. In this manner a master curve for the relaxation modulus may be obtained. This behavior is hypothesized to result from a strain dependence of the relaxation times in which all the relaxation times have the same dependence on strain. The master curves are used to obtain generalized relaxation distribution functions, which are considerably broader for the isotropic filaments than for the oriented filaments.

‘Setting’ was observed in minced hen meat stored with 3.5% wt/wt added NaCl. When gels were made from the ‘set’ sol the breaking energy was greatly increased and the relaxation modulus was characterized by a wide ‘quasi-equilibrium’ region. The effect of added pyrophosphate on the rheological properties of the gel prepared at pH 6.0 from ground ‘set’ sol was very similar to that previously observed for ATP in gels prepared at pH 6.0 from ‘unset’ sols. When pyrophosphate or ATP were added at pH 7.0 to the ‘unset’ minced meat sol, the strain at the breaking point and the ratio of the equilibrium to the instantaneous modulus of the heated gel were increased. A comparison with previous results from a model system suggests that pyrophosphate brings about a change in gel structure by dissociating ‘myosin B’ into myosin A and F-actin.

The tensile relaxation modulus reduced to 25°C in the time scale range from 3×10-2 sec to 1 ×106 sec was determined, and the relaxation spectrum was calculated for kamaboko. A comparison of the relaxation spectra for various kamaboko varying in tensile tough-ness (i.e., the strength of ashi) gives the following information: (1) There is a very good parallelism between the magnitude of tensile toughness and the absolute value of the dif-ferential coefficient of the relaxation spectrum at 1×10-1 sec of relaxation time. (2) There is also good parallelism between the magnitude of tensile toughness and the width of the distribution range of the relaxation times of Maxwell units which are able to relax under applied strain.

The contribution of entanglements to the relaxation modulus of four samples of cis-polyisoprene has been studied in detail. The average number of chain atoms between neighboring entanglements has been calculated according to the theory of Chompff et al. Relaxation spectra and modulus produced by the entanglements were also calculated from the theoretical model. Good agreement was achieved between the modulus measured experimentally and the values predicted theoretically.

To elucidate the dependence of diffusion coefficient of disperse dye in poly(ethyleneterephthalate) (PET) on concentration, p-nitroaniline (PNA) was used as a model penetrant of the dye over the wide range of concentration at 70, 75, 80, 85, 90 and 95°C. Diffusion coefficients were measured by cylindrical film roll method. The dependence of diffusion coefficient on penetrant concentration was clearly observed(Fig.2), and empirically represented by the equation (1), for the lower concentration (up to about 8 X 10-2 mol/kg-1) and (2) for the higher concentration, D=D0Cn(1)D=D0'exp(C)(2)where C is concentration of penetrant and n and 8 are constants. PNA penetrated into an easily diffusible amorphous region at the lower concentration. At the higher concentration of PNA, the penetrant diffused into more closely packed amorphous part without changing the total amounts of amorphous region available for dyeing.It was suggested that the increase of diffusion coefficient was caused by the minute qualitative change of amorphous region of PET, which could not be detected by the IR spectrum (Table 2), small angle X-ray scattering and dichroism of the dyed film. With increasing PNA concentration the decrease of relaxation modulus of the PET film was observed (Fig.6), and this tendency corresponded to the increase of diffusion coefficient mentioned above (Fig.2).

Relaxation moduli and creep compliances for eight two-component blends of polystyrene have been measured in the rubbery region. Relaxation moduli for five two-component blends of polyisobutylene have been evaluated by converting the creep compliance data obtained previously by Leaderman and others. The results for relaxation modulus have been successfully correlated by a relationship proposed previously for polyvinyl acetate. Similar relationships for steady-flow viscosity and steady-state compliance have also been found to be effective.

The viscoelastic properties of a series of graft copolymers of poly(methyl acrylate) with styrene differing in the degree of grafting and, consequently, in the heterogeneous structure, were investigated in terms of the relaxation modulus function in a range from glassy to rubber flow consistencies.

The time-temperature dependence of the cohesive fracture energy is deduced from experiments on a centrally cracked sheet of butadiene-acrylonitrile-acrylic acid viscoelastic terpolymer crosslinked with an epoxy curing agent. Analytic results based upon a cylindrical flaw model of the crack permit the segregation of the fracture energy time dependence from that of the relaxation modulus.

The paper considers isothermal deformations of a linear viscoelastic material in simple tension or compression. The relaxation modulus defining the material is assumed to be a sum of exponential functions, but need not necessarily be a monotonic function. The greatest lower bound on the work required to deform the material from its virgin state in a given time interval (0, T) is determined – independently of the strain-rate history – in terms of T, the strain at the time T, and the constants entering the definition of the relaxation modulus. The optimum strain-rate history, which actually produces the greatest lower bound on the work, is also determined. The results may be extended to the general deformations of a linear anisotropic viscoelastic solid. Der Artikel behandelt isotherme Verformungen eines linear-viskoelastischen Stoffes im einachsigen Spannungszustand. Der den Stoff definierende Relaxationsmodul wird als Summe von Exponentialfunktionen angesetzt, mus aber nicht eine vollmonotone Funktion sein. Die groste untere Schranke fur die am Material wahrend eines gegebenen Zeitabschnitts geleistete mechanische Arbeit wird bestimmt. Diese Schranke ist von der Deformationsgeschichte unabhangig und hangt nur von dem Endpunkt des gegebenen Zeitabschnitts, von der Verzerrung in diesem Zeitpunkt und von dem Relaxationsmodul ab. Die optimale Deformationsgeschichte, die zu dieser grosten unteren Schranke fuhrt, wird ebenso bestimmt. Die Ergebnisse konnen auch auf dreiachsige Verformungen erweitert werden.

In order to clarify the viscoelastic behavior characteristic of FRTP, the stress relaxation measurements of polyethylene films filled with glass fiber fragments were carried out at various strains below 5% at a constant temperature of 23°C.The analysis of the experimental data showed that the correspondence principle, which is a well known formula in the theoretical treatment of linear viscoelasticity, is useful to evaluate the relaxation modulus of FRTP under small strain.

Simultaneous measurements of the longitudinal extension and the lateral contraction strains in tension specimens made from a pure epoxy polymer by using the differential moire method yielded the extension creep compliance and relaxation modulus master curves along the whole viscoelastic spectrum of the material. Moreover, they provided the lateral contraction ratio curves in creep and relaxation. Both pairs of curves determine completely the viscoelastic behavior of the polymeric substances. It was shown that the transient lateral contraction ratio functions are monotonically increasing functions with time and temperature and the creep function is lagging in time with respect to the corresponding relaxation function.

Master curves of log Q(t/K) against log (t/K) were constructed from experimental data on creep compliance, relaxation modulus, stress-optical and strain-optical coefficients of two types of epoxy resins at a series of temperatures in the transition region. The characteristic creep or relaxation time K for each temperature was defined and tabulated. The master curves were fitted to the reduced equation of the Gauss error integral form and the following characteristic parameters were calculated: Q1, the glassy-state parameters (creep compliance, relaxation modulus, stress-optical or strain-optical coefficients); Q2, the rubbery-state parameters; Td, the distinctive temperature; Kd, the characteristic creep or relaxation time at Td; and the parameters ht and hg of the steepness of master curves at the transition and glassy regions, respectively. The investigation was extended to the determination of the distribution functions of mechanical and optical retardation and relaxation times L (log τ) and H (log τ), respectively, representing the differential contribution to instantaneous compliance, stress-optical or strain-optical coefficients associated with retardation times and instantaneous modulus, stress-optical or strain-optical coefficients associated with relaxation times.

The melt rheology of high density polyethylene was investigated. Linear viscoelasticity, capillary flow properties, and molecular weight parameter were measured with a plate relaxometer, capillary rheometer, and gel permeation chromatography, respectively. Intimate correlations among the slope of relaxation modulus curve, non-Newtonian flow behavior, Barus effect, and molecular weight parameter, Mz(Mz+1)/Mw, respectively, were found.

Compressive stress relaxation measurements were performed on specimens of selected dental restorative composites. The relaxation modulus showed a linear dependence on the logarithm of time. The values obtained indicated that stress was dissipated more rapidly in dental composites than in enamel, but less rapidly than in human dentin.

1. Mechanical characteristics of the toad blood vessels under different temperatures were investigated with the use of the universal tensile testing instrument.2. The amplitude of tension generated by cyclic stretches of the aorta at 41% stretched state was constant throughout the temperatures between 3-40°C, while that induced at 100% stretched state increased with decrease of temperature. In both cases, however, the lower tension levels lowered as temperature fell.3. Over 40-50°C, a marked increase of the tension amplitude was observed with distinct elevation of the upper tension level in both cases of 41% and 100% stretched states.4. In the tempreature dependency of mechanical characteristics, the elastin dominant vessel treated with formic acid coincided well with the wall of vessel at 41% stretched state, while the tendon, aponeurosis plantalis, was in accord with the vessel at 100% stretched state. However, the marked increase of tension at temperatures over 50°C was never observed in the digested aorta, supporting a view that it depends on the thermal denature of collagen.5. Hysteresis loops of the aorta and vena abdominalis became small at normal temperature and large at low (2-5°C) and high (40-42°C) temperatures. With the tendon and formic acid treated vessels, the hysteresis loops also tended to enlarge at low temperatures (2-5°C). However, over 50°C merely the tendon showed a great deal of increase in the loop.6. Stress-relaxation curves of the aorta and vena abdominalis declined with a rise of temperature up to 40°C, but no detectable difference between their temperature dependencies of distribution function was observed. The relaxation modulus increased markedly at high temperatures over 50°C, showing distribution function of distinct box-shape.

We simulate viscoelastic phase separation of polymer solutions by solving numerically Langevin equations of a ``viscoelastic model'' that newly includes the bulk relaxation modulus in addition to the shear relaxation modulus. The results reproduce almost all the essential features of viscoelastic phase separation observed experimentally: (i) The existence of a frozen period, the nucleation of the solvent-rich phase, (ii) the volume shrinking of the polymer-rich phase, (iii) the transient formation of a networklike structure, and (iv) the phase inversion in the final stage. Our simulations clearly indicate that the bulk stress is responsible for (i), (ii), and (iv), while the shear stress for (iii).