Stress relaxation characteristics

Creep and stress relaxation characteristics for viscoelastic materials... 

The mathematical behavior suffers from several defects, including the description of creep as da/t = 0, which projects viscous flow (del dt = a/ t Max). In reality, the stress relaxation characteristics do not go to zero over long time periods, and they are often more complicated than a single exponential decay. 

These effects have the potential to influence the important time dependent stress relaxation characteristics of foamed components, possibly accelerating compression set. Clearly evident from this work is the need to minimise residual catalyst and cure associated acid levels within the rubber so as to maximise material reliability over extended timescales. 

As known, the macroscopic load-deformation or stress-strain and stress relaxation characteristics of any polymeric material, during and following deformation, are a consequence of the mean molecular motions of its chains ( ). These properties are additionally affected In the case of cartilage by the following (1) many of the tissue s macromolecules are associated In a variety of fibrous and other arrays (7 ) (2) the tissue Is both... 

Tobolsky and his coworkers made extensive efforts to characterize the stress relaxation characteristics of elastomers, notably polyisobutylene. The stress would decay over time to zero at a rate dependent on temperature and molecular weight (Fig. 2). They expressed the relaxation through a series of exponentials or a spectrum of relaxation times. Consider the shear stress decay a t) following an shear imposed strain yo- This may be used to define a shear relaxation modulus G i) through... 

Figure 3-63. Stress-relaxation characteristics at 23°C (73T). a) Rigid PVC, pressure relaxation b) rigid PVC, tension relaxation c) PE, pressure relaxation d) PE, tension relaxation e) nylon, tension relaxation f) FIFE, tension relaxation.

These bonds readfly participate in interchange reactions with polysulphide groups and result in products with poor stress relaxation characteristics. (See later.) The inclusion of sulphur in the system reduces the number of lead mercaptide links by the formation of lead sulphide ... 

Figure 5.5 The stress relaxation characteristic modulus C(t) as a function of time, t is the characteristic time (the retardation time).

Pig. 4 Compression stress relaxation characteristics of different polymeric materials at 100°C and 100% relative humidity... 

Recently Maxwell and Cook presented data on die observation of Tn for six different molecular weight polystyrenes by five different theological measurements (1) an abrupt decrease in the shear modulus vs. temperature (2) an abrupt change in the recoverable strain characteristics as a function of temperature (3) a change in the recoverable strain as a fimction of time (4) an abrupt change of yield stress as a function of temperature and (5) a change in the stress relaxation characteristics. This data was obtained by several different researchers using two different rheometers. 

Figure 7.11 Stress relaxation curve for vulcanized natural rubber showing characteristic upswing at higher stresses...

Unlike other aqueous dental cements, the zinc polycarboxylate retains plastic characteristics even when aged and shows significant stress relaxation after four weeks (Paddon Wilson, 1976). It creeps under static load. Wilson Lewis (1980) found that the 24-hour creep value for one cement, under a load of 4-6 MPa, was 0-7 % in 24 hours, which was more than that of a zinc phosphate cement (0-13 %) and a glass-ionomer cement (0-32%), but far less than that of the zinc oxide eugenol cement (2-2%). 

The longest relaxation time. t,. corresponds to p = 1. The important characteristics of the polymer are its steady-state viscosity > at zero rate of shear, molecular weight A/, and its density p at temperature 7" R is the gas constant, and N is the number of statistical segments in the polymer chain. For vinyl polymers N contains about 10 to 20 monomer units. This equation holds only for the longer relaxation times (i.e., in the terminal zone). In this region the stress-relaxation curve is now given by a sum of exponential terms just as in equation (10), but the number of terms in the sum and the relationship between the T S of each term is specified completely. Thus... 

The data has been superimposed by dividing the relaxation function G(t) by G(t = 0), the limiting short time value, and the time has been divided by the characteristic relaxation time Tr. The first feature to notice is that the stress relaxation function overshoots and shows a peak. This is an example of non-linear behaviour. It is related to both the material and the instrumental response (Section 4.5.1). The general shape of the curves (excluding the stress overshoot) can be described using two approaches. 

The observations above can be rapidly turned into a semi-quantitative theory for star-polymer stress-relaxation [24] which is amenable to more quantitative refinement [25]. The key observation is that the diffusion equation for stress-re-lease, which arises in linear polymers via the passage of free ends out of deformed tube segment, is now modified in star polymers by the potential of Eq. (16). Apart from small displacements of the end, the diffusion to any position s along the arm will now need to be activated and so is exponentially suppressed. Each position along the arm, s, will possess its own characteristic stress relaxation time T(s) given approximately by... 

ISO 6914 2004 Rubber, vulcanized or thermoplastic - Determination of ageing characteristics by measurement of stress relaxation... 

ASTM D1646, 2004. Viscosity, stress relaxation and pre-vulcanisation characteristics (Mooney viscometer). 

The broadened transition response is a general characteristic of power feed polymers as evidenced by the results of stiffness-temperature, stress relaxation and dynamic mechanical measurements. 

Equations 3.4-3 and 3.4-4 form the molecular theory origins of the Lodge rubberlike liquid constitutive Eq. 3.3-15 (23). For large strains, characteristic of processing flows, the nonlinear relaxation spectrum is used in the memory function, which is the product of the linear spectrum and the damping function h(y), obtained from the stress relaxation melt behavior after a series of strains applied in stepwise fashion (53)... 

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