Creep Dynamic modulus

Distributions of relaxation or retardation times are useful and important both theoretically and practicably, because // can be calculated from /.. (and vice versa) and because from such distributions other types of viscoelastic properties can be calculated. For example, dynamic modulus data can be calculated from experimentally measured stress relaxation data via the resulting // spectrum, or H can be inverted to L, from which creep can be calculated. Alternatively, rather than going from one measured property function to the spectrum to a desired property function [e.g., Eft) — // In Schwarzl has presented a series of easy-to-use approximate equations, including estimated error limits, for converting from one property function to another (11). 

Janmey, P. A., Amis, E. J., and Ferry, J. D. (1983). Rheology of fibrin clots. VI. Stress relaxation, creep, and differential dynamic modulus of fine clots in large shearing deformations. / Rheol. 27, 135-153. 

In addition to creep and stress relaxation experiments, another type of measurement is quite common. Here the stress or strain, instead of being a step function, is an oscillatory function with an angular frequency a. The standard unit of a is radians per second (rad/s).++ Dynamic modulus values measured using such perturbations are functions of a> rather than time. The problem of putting dynamic experiments on a quantitative level is only slightly more difficult than is the case with step-deformation experiments. 

Concrete has a viscous behaviour when it is loaded with a constant stress it shows a strain that increases with time. Conventionally an elastic deformation is considered when it occurs during application of the load, while subsequent deformation is attributed to creep. It is possible to define a modulus of elasticity for concrete that can be evaluated with short-term tests [9]. Similarly as for the tensile strength, empirical formulae are available that give an approximate correlation of the modulus of elasticity with the compressive strength [1,9]. A dynamic modulus can also be estimated with non-destructive tests that measure the rate of propagation of ultrasonic vibrations through concrete [1],... 

Parameter Dynamic modulus Glass transition temperature Melting temperature Cross-link density Relaxation behaviour CrystaUinity, cure Dynamic modulus Glass transition temperature Creep, cure, compliance Relaxation behaviour Viscosity Gelation... 

For a single lot of material, just the cost of generating single-point data alone is reported to exceed 2600 (Table 11.24), while the cost of generating a multipoint data package comprising tensile stress-strain curves at five temperatures (23°C and four additional temperatures), dynamic modulus versus temperature at 1-Hz frequency, and tensile creep curves at four stress levels at each of the three temperatures (23° C and two elevated temperatures) amount to nearly 9000, as shown in Table 11.25. 

The Yerseley Mechanical Oscillograph supplied by ATS FAAR measures, according to ASTM D945 [142], the mechanical properties of rubber vulcanisations in the small range of deformation that characterises many technical applications. These properties include resilience, dynamic modulus, static modulus, kinetic energy, creep, and set under a given force. 

Ccmipared to many thermoplastics, PVDF has excellent resistance to creep and fatigue. Yet in thin sections such as films, filament and tubing PVDF components are flexible and transparent. The dynamic mechanical spectrum of KYHAR PVDF in Figure 3 shows that its dynamic modulus of elasticity (E ) is high and decays only gradually as the temperature is increasing. 

Fig. 2.28. A plot of tan 3 as a function of actual frequencies at several temperatures for NBS-PIB. The data were obtained by using several instruments spanning the frequency range as shown in the abscissa. The high-frequency data at -35.8 °C (open circles) are from Fitzgerald et al, J. Appl. Phys. 24 (1953), 640. The rest of the data were obtained by a combination of creep-compliance and dynamic-modulus measurements [209]. From Plazek et al. by permission [209].

Therefore, with the exception of the Giesekus model, the parameters for all of these constitutive equations can be deduced from the relaxation time spectrum of the material which can be obtained from the small strain linear viscoelasticity measurements alone. There are various numerical methods in the literature which allow the determination of this spectrum from measured viscoelastic master curves, such as dynamic modulus, relaxation modulus, and creep compliance. 

Although time-temperature superposition is applicable to any viscoelastic response test (creep, dynamic, etc.), here, we will focus on its application to stress relaxation. Figure 16.12 shows tensile stress relaxation data at various temperatures for polyisobutylene, plotted in the form of a time-dependent tensile (Young s) modulus E t) versus, time on a log-log scale ... 

Another resonant frequency instmment is the TA Instmments dynamic mechanical analy2er (DMA). A bar-like specimen is clamped between two pivoted arms and sinusoidally oscillated at its resonant frequency with an ampHtude selected by the operator. An amount of energy equal to that dissipated by the specimen is added on each cycle to maintain a constant ampHtude. The flexural modulus, E is calculated from the resonant frequency, and the makeup energy represents a damping function, which can be related to the loss modulus, E". A newer version of this instmment, the TA Instmments 983 DMA, can also make measurements at fixed frequencies as weU as creep and stress—relaxation measurements. 

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

Tackifying resins enhance the adhesion of non-polar elastomers by improving wettability, increasing polarity and altering the viscoelastic properties. Dahlquist [31 ] established the first evidence of the modification of the viscoelastic properties of an elastomer by adding resins, and demonstrated that the performance of pressure-sensitive adhesives was related to the creep compliance. Later, Aubrey and Sherriff [32] demonstrated that a relationship between peel strength and viscoelasticity in natural rubber-low molecular resins blends existed. Class and Chu [33] used the dynamic mechanical measurements to demonstrate that compatible resins with an elastomer produced a decrease in the elastic modulus at room temperature and an increase in the tan <5 peak (which indicated the glass transition temperature of the resin-elastomer blend). Resins which are incompatible with an elastomer caused an increase in the elastic modulus at room temperature and showed two distinct maxima in the tan <5 curve. 

Some viscoelasticity results have been reported for bimodal PDMS [120], using a Rheovibron (an instrument for measuring the dynamic tensile moduli of polymers). Also, measurements have been made on permanent set for PDMS networks in compressive cyclic deformations [121]. There appeared to be less permanent set or "creep" in the case of the bimodal elastomers. This is consistent in a general way with some early results for polyurethane elastomers [122], Specifically, cyclic elongation measurements on unimodal and bimodal networks indicated that the bimodal ones survived many more cycles before the occurrence of fatigue failure. The number of cycles to failure was found to be approximately an order of magnitude higher for the bimodal networks, at the same modulus at 10% deformation [5] ... 

An instrument for measuring the mechanical properties of rubbers in relation to their use as materials for the absorption and isolation of vibration. These properties are resilience, modulus (static and dynamic), kinetic energy, creep and set. The introduction of an improved version has recently been announced. 

The dynamic viscoelastic properties of acetylated wood have been determined and compared with other wood treatments in a number of studies. Both the specific dynamic Young s modulus (E /j) and tan S are lower in acetylated wood compared with unmodified wood (Akitsu etal., 1991, 1992, 1993a,b Korai and Suzuki, 1995 Chang etal., 2000). Acetylation also reduces mechanosorptive creep deformation of the modified wood (Norimoto etal., 1992 Yano etal, 1993). In a study of the dynamic mechanical properties of acetylated wood under conditions of varying humidity, it was concluded that the rate of diffusion of moisture into the wood samples was not affected by acetylation (Ebrahimzadeh, 1998). 

Figure 4.121. Polyimides examples of creep modulus (GPa) versus time (h) at 100°C and 300°C 4.26.5 Ageing Dynamic fatigue...

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