Time-dependent mechanical

Monte Carlo heat flow simulation, 69-70 nonequilibrium statistical mechanics, microstate transitions, 44 46 nonequilibrium thermodynamics, 7 time-dependent mechanical work, 52-53 transition probability, 53-57 Angular momentum, one- vs. three-photon... 

Boltzmann distribution, time-dependent mechanical work, transition probability, 55-57... 

Nonequilibrium molecular dynamics (NEMD) Monte Carlo heat flow simulation, 71-74 theoretical background, 6 Nonequilibrium probability, time-dependent mechanical work, 51-53 Nonequilibrium quantum statistical mechanics, 57-58... 

Yamada-Kawasaki distribution nonequilibrium thermodynamics, 7 time-dependent mechanical work, 52-53... 

Above Tk the time-dependent mechanical properties of a polymer are determined fundamentally by the distribution of relaxation or retardation... 

To help lessen the complications of product testing, a common approach is to separate mechanical and environmental testing. The mechanical properties can be tested on the product, using a relatively simple product test rig, while environmental degradation is studied on samples of the material. For time dependent mechanical properties, the degree of mechanical deterioration of the product is then increased by a factor reflecting the... 

Temperature dependence proton relaxivity 188 relaxation rate 144-5 Temperature-sensitive contrast agents 218-19 Th -" 368 Ti "" 347 Tilt angle 242 Time constant 14 Time correlation functions 76 Time-dependent mechanism 14 Time-dependent perturbation methods 23 Time-dependent perturbation theory 45-8 Titanium(III) 115,134-5,161 TPEN 224 TPPS 219... 

Fatigue is an example of the influence of time on the mechanical properties of a material. Another example of a time-dependent mechanical property is creep. Creep, sometimes called viscoplasticity, is defined as time-dependent deformation nnder constant stress, usually at elevated temperatures. Elevated temperatures are necessary because creep is typically important only above Tmp % where T p is the absolute melting point of the material. 

Because Equation 8.39 is a history-dependent integral, the degree of cure is represented as a function of x and not of the current time, t. Equation 8.39 can be solved by discretizing the time domain into N equal portions At with the initial time /j = 0 and the current time tN — t once the time-dependent mechanical properties in T(a, t) have been determined. 

Dynamic mechanical analysis (DMA) or dynamic mechanical thermal analysis (DMTA) provides a method for determining elastic and loss moduli of polymers as a function of temperature, frequency or time, or both [1-13]. Viscoelasticity describes the time-dependent mechanical properties of polymers, which in limiting cases can behave as either elastic solids or viscous liquids (Fig. 23.2). Knowledge of the viscoelastic behavior of polymers and its relation to molecular structure is essential in the understanding of both processing and end-use properties. 

For this example, using a dynamic policy, as opposed to a static policy, is far more important than using flexible-length management periods instead of fixed-length periods. However, there were no time-dependent fate and transport mechanisms in this problem, such as mass-transfer limitations or biodegradation kinetics. Time-dependent mechanisms may increase the importance of flexibility in the time domain. Thus, the second dynamic example will include mass-transfer limitations. 

T. V. Korsgaard, M. Colding-Jorgensen, Time-dependent mechanisms in beta cell glucose sensing, I. Biol. Phys. 2006, 32 289-306. 

Time-dependent Mechanical Properties of Solid Bodies... 

Bussemer,T., Peppas, N. A., and Bodmeier, R. (2003),Time-dependent mechanical properties of polymers coating used in rupturable pulsatile release dosage forms, Drug Dev. Ind. Pharm., 29, 623-630. 

An example of this effect is illustrated in Figure 10, which shows a series of stress-strain curves as a fiinction of time for a material made with tri-ethoxysilane-end-capped PTMO(2000) (50 wt %) in conjunction with titanium isopropoxide (30 wt %) and TEOS (20 wt %). Over a period of many days, the material clearly stiffens in terms of modulus build-up hence, the time-dependent mechanical characteristics would have to be recognized for any application. However, such materials can be further cured thermally to achieve a more stable mechanical response with time. Therefore, if this aging phenomenon is noted, it can be dealt with accordingly. 

Thus, the Dugdale model has been fitted to the measured craze shapes and time-dependent mechanical parameters have been derived. Figure 3.25 shows and E as a function of crack speed indicating that in the crack speed range... 

Viscoelasticity deals with the dynamic or time-dependent mechanical properties of materials such as polymer solutions. The viscoelasticity of a material in general is described by stresses corresponding to all possible time-dependent strains. Stress and strain are tensorial quantities the problem is of a three dimensional nature (8), but we shall be concerned only with deformations in simple shear. Then the relation between the shear strain y and the stress a is simple for isotropic materials if y is very small so that a may be expressed as a linear function of y,... 

The time-dependent mechanical properties such as creep and subcritical crack growth are dealt with separately in the next chapter. 

All time-dependent mechanical processes, such as a motion of a particle through the space, are still valid on time reversal. This means if we change the sign of time in a physical law, still a possible process will emerge. Maxwell observed that the second law of thermodynamics is not consistent on time reversal [12]. Time reversal plays... 

The object of any degradation test, and also tests of such time-dependent mechanical properties as creep and stress relaxation, is directly or indirectly to predict service life. If time were not important, tests could be made under the expected service conditions and the test continued for the desired lifetime. With expected lifetimes sometimes measured in tens of years, this is clearly not a viable option in most cases, and some form of extrapolation, and usually acceleration, will be needed. 

There are of course many standard methods for carrying out natural or accelerated tests and time dependent mechanical property tests and for measuring the properties used to monitor degradation. These can be found in this volume and in other standard texts [4.5] and their use for weathering tests has been reviewed [6]. 

Time-Dependent Mechanical Properties 4.1 Creep and Stress Relaxation... 

In chapter 5 the use of NMR spectroscopy in studying the various kinds of motion that can take place in solid polymers is described and in the present chapter the way that these motions contribute to the time-dependent mechanical properties of the polymers is considered. In chapter 9 the effects of motion on the dielectric properties and the use of measurements of dielectric relaxation in the study of relaxation mechanisms are considered. 

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