Stress time dependent

Thermal power plant components operated at high temperatures (>500°C) and pressures, such as superheater headers, steamline sections and Y-junctions, deserve great attention for both operation safety and plant availability concerns. In particular, during plant operation transients -startups, shutdowns or load transients - the above components may undergo high rates of temperature / pressure variations and, consequently, non-negligible time-dependent stresses which, in turn, may locally destabilize existing cracks and cause the release of acoustic emission. 

Returning to the Maxwell element, suppose we rapidly deform the system to some state of strain and secure it in such a way that it retains the initial deformation. Because the material possesses the capability to flow, some internal relaxation will occur such that less force will be required with the passage of time to sustain the deformation. Our goal with the Maxwell model is to calculate how the stress varies with time, or, expressing the stress relative to the constant strain, to describe the time-dependent modulus. Such an experiment can readily be performed on a polymer sample, the results yielding a time-dependent stress relaxation modulus. In principle, the experiment could be conducted in either a tensile or shear mode measuring E(t) or G(t), respectively. We shall discuss the Maxwell model in terms of shear. 

Schatz, R., Shooman, M. and Shaw, L. 1974 Application of Time Dependent Stress-Strength Models of Non-Electrical and Electrical Systems. In Proceedings Reliability and Maintainability Symposium, 540-547. 

The most characteristic features of viscoelastic materials are that they exhibit a time dependent strain response to a constant stress (creep) and a time dependent stress response to a constant strain (relaxation). In addition when the... 

Relaxation is the time-dependent stress resulting from a constant strain. The stress is a function of the strain level, the application time and the temperature. The results of tests at a defined temperature can be presented as a load versus time curve or a stress retention versus time curve. 

Because of equipment limitations in measuring stress and strain in polymers, the time-temperature superposition principle is used to develop the viscoelastic response curve for real polymers. For example, the time-dependent stress relaxation modulus as a function of time and temperature for a PMMA resin is shown in... 

The properties of a material must dictate the applications in which it will best perform its intended use. All materials made to date with polymerized sulphur show time-dependent stress-strain behaviour. The reversion to the brittle behaviour of orthorhombic sulphur is inevitable as the sulphur transforms from the metastable polymeric forms to the thermodynamically stable crystalline structure. The time-span involved of at most 15 months (to date) would indicate that no such materials should be used in applications dependent on the strain softening behaviour. Design should not be based on the stress-strain relationships observed at an age of a few days. Since the strength of these materials is maintained, however, uses based on strength as the only mechanical criterion would be reasonable. 

D. C. Bogue, An Explicit Constitutive Equation Based on an Integrated Strain History, Ind. Eng. Chem. Fundam., 5, 253-259 (1966) also I. Chen and D. C. Bogue, Time-Dependent Stress in Polymer Melts and Review of Viscoelastic Theory, Trans. Soc. Rheol., 16, 59-78 (1972). 

Time-dependent stress-strain behavior of the neat resins was studied using an Instron (Model 1122) tensile tester. Dog-boneshaped epoxy specimens were prepared in accordance to ASTM D1708-66. Strain-rate used was 5x 10 5 s 1. 

The data are not usually reported as a stress/time plot, but as a modulus/time plot. This time-dependent modulus, called the relaxation modulus, is simply the time-dependent stress divided by the (constant) strain (Equation 13-71) ... 

The scaling, Eq. (9-48), also implies that time-dependent stresses can be rescaled so that data taken at different shear rates collapse onto a single curve. Consider an example in which the sample is sheared at a rate yt until a steady state is reached, and then the shear rate is suddenly increased by a factor of four to y/ — 4yi. After this increase in shear rate, the shear stress undergoes an overshoot and an undershoot, while the first normal stress... 

Substituting the relation between relaxation time and mode wavelength [Eq. (8.109)] into the expression for modulus [Eq. (8.116)] leads to the time-dependent stress relaxation modulus that decays as the - 3/4 power of time ... 

Figure 11.27 Time dependent stress-strain behavior of sand samples grouted with AC-400 acryiate grout. UC tests run to determine creep endurance iimit. (From Technical Report HB-13, Northwestern Univ., Evanston, IL, 1981.)... 

J.P. Koenzen, Time-Dependent Stress-Strain Behavior of Silicate-Grouted Sand, Journal of the Geotechnical Engineering Division, Aug. 1977, pp 903-908, ASCE, Reston, VA. 

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. 

By use of the time-temperature equivalence principle, the viscoelastic response of a given polymeric material over a wide temperature range can be accommodated in a single master curve. By use the superposition principle, this master curve can be used to estimate the time-dependent response to time-dependent stresses in simple tensile or shear specimens or to nonhomogeneous time-dependent stresses arising in stressed objects and structures. 

The boundary conditions shown in Figure 1 were determined from FEBEX in situ stress data (Pahl et al., 1989). An additional boundary condition was used to model the time-dependent stress induced by the alpine miner during excavation of the drift. A pressure value of 25 MPa was applied to the wall in successive sections of the drift when that material was "excavated" numerically in the calculation. 

These equations are often used in terms of complex variables such as the complex dynamic modulus, E = E + E", where E is called the storage modulus and is related to the amount of energy stored by the viscoelastic sample. E" is termed the loss modulus, which is a measure of the energy dissipated because of the internal friction of the polymer chains, commonly as heat due to the sinusoidal stress or strain applied to the material. The ratio between E lE" is called tan 5 and is a measure of the damping of the material. The Maxwell mechanical model provides a useful representation of the expected behavior of a polymer however, because of the large distribution of molecular weights in the polymer chains, it is necessary to combine several Maxwell elements in parallel to obtain a representation that better approximates the true polymer viscoelastic behavior. Thus, the combination of Maxwell elements in parallel at a fixed strain will produce a time-dependent stress that is the sum of all the elements ... 

For experiments performed in shear, there is a rather complicated relation between the time-dependent stress relaxation shear modulus G(t) defined by Equation 3.19 and the time-dependent creep compliance J t) defined by Equation 3.21. But if the slope of log G(r) versus log r is — m, then, to a good approximation. 

Dynamic mechanical and dynamic stress-optical measurements have been performed on side-chain LCEs with different crosslinking densities [8]. It was found that the relaxation strengths depend strongly on the crosslinking density demonstrating that the vicinity of the crosslinking points perturbs the liquid crystalline order. In this experiment the samples were exposed to a time-dependent stress <7(t), and the time-dependent responses, that is the time-dependent strain e(t) and the time-dependent birefringence An (t), were measured. The real part... 

Zhu, J.-G., Yin, J.-H., and Luk, S.-T. 1999. Time-dependent stress-strain behavior of soft Hong Kong Marine Deposits. Geotechnical Testing Journal, 22(2) 112-120. 

---