Creep compliance extracted

Experiments have been made in which uncross-linkable polymer rubbers have been added to a similar rubber that is subsequently cross-linked (199). As an example, polyisobutylene was added to butyl rubber before it was cross-linked. The polyisobutylene molecules were not attached to the network structure, so they could be extracted by a solvent. As expected, the polyisobutylene greatly increased the creep compliance over that of the pure butyl rubber. 

The four commonly used techniques to extract information on the viscoelastic behavior of suspensions are creep-compliance measurements, stress-relaxation measurement, shear-wave velocity measurements, and sinusoidal oscillatory testing (25-27). In general, transient measurements are aimed at two types of measurements, namely, stress relaxation, which is to measure the time dependence of the shear stress for a constant small strain, and creep measurement, which is to measure the time dependence of the strain for a constant stress. 

Table 14.1 Characteristics M, M /Mn and Tg (based on DSC and defined at ts = 1,000sec) and parameters A, / and Z extracted by analyzing the creep-compliance J(t) curves or viscoelastic spectra G (ta) of the polystyrene samples, whose structural-relaxation times TS, structural-growth parameters s and frictional factors K are displayed, respectively, in Figs. 14.13, 14.14 and 14.15. Also shown are the K values at 127.5°C of samples A, B, C and F2 along with the average value of K shown in Table 10.1 and the Mw, MwjMn, and Tg (DCS) of F2. The reference theory used in each analysis is indicated. 

Special specimen preparation as with tensile testing. However, the extraction of intrinsic mechanical parameters from creep indentation data is analytically complex [3, 4]. Confined compression or unconfined compression tests require preparation of cylindrical cored specimens of tissue and underlying bone. With unconfined compression, the free draining tissue edges and low aspect ratio, layered nature of the test specimen may introduce error. Compression of a laterally confined specimen by a porous plunger produces uniaxial deformation and fluid flow. Confined compression creep data has been analyzed to yield an aggregate equilibrium compressive modulus and permeability coefficient [5] and uniaxial creep compliance [6]. 

A and D indicate the two parameters most commonly extracted from a creep curve. A represents the instantaneous elastic compliance and can be used to calculate an elastic modulus. D represents the limiting viscosity, which is related to the reciprocal of the slope. In some cases, parameters from creep testing have been related to molecular mechanisms (Shama and Sherman, 1970 Davis, 1973 deMan et al., 1985). The parameters have also been correlated with hardness and spreadability (Scott-Blair, 1938). 

Creep, Swelling, and Extraction Studies. Additional indications of component interaction were found in the results of creep experiments with the xl series shown in Tables VI and VII. Creep in the xl series is fully recoverable, i. e. there is no permanent set, consistent with a PUx continuous phase. The increase in recoverable compliance, however, indicates a reduction in apparent crosslink density with increasing delay time before irradiation. This result is reinforced by the data in Table VII Ci and Cg are the material constants in the Mooney-Rivlin equation. The rubbery plateau modulus and the crosslink density of PUx prepared in BHA, which mimics xl formation, is less than that of PU prepared neat. 

An analogous procedure based on (18.25) can be used to extract the and Ji = 1/Gj in a generalized Voigt-Kelvin model from creep data, (t). It requires a knowledge of the equilibrium elastic compliance, (oo). Its development will be left as an end-of-chapter exerdse. 

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