Elastic modulus isothermal

Near the transition temperature, SMAs also exhibit the curious effect of pseudoelasticity, in which the metal recovers (apparently in the usual manner) from an isothermal bending deformation when the stress is removed. However, the elasticity is not due to the usual elastic modulus of a fixed crystalline form, but instead results from strain-induced solid-solid phase transition to a more deformable crystalline structure, which yields to the stress, then spontaneously returns to the original equilibrium crystal structure (restoring the original macroscopic shape) when the stress is removed. 

The first test is a series of isothermal temperature hold experiments measuring the visco-elastic kinetic cure properties (Figure 1). The temperature values selected bracket every 10 F, the range in which processing is to occur. The four properties measured are the loss modulus (viscous modulus G"), storage modulus (elastic modulus G ), complex viscosity (rf), and tan delta (G"/G ). However, when mainly newtonian liquids or monomers are present (G" G and tan delta >10), viscosity is sufficient to use for the evaluation criteria. 

They may also be suitable for following gelation in near-line or laboratory experiments at a constant temperature. For example, a vibrational viscometer was used to determine the coagulation time of reimeted milk at fixed temperatures (Sharma et al., 1989, 1992). However, in non-isothermal physical gelation, the elastic modulus depends on the temperature dependence of the resonant response so that precise correction for the influence of temperature must be known. 

The sign in the right hand part of this expression should be chosen so that Svp (T) > at r < Ti (adiabatic regime) and the opposite inequality should take place at r > Ti (isothermal regime for the Jahn-Teller system s contribution to the elastic modulus). 

Only for a generalised linear adsorption isotherm the adsorption of the components i are independent and consequently the functions ai. Assuming a generalised Langmuir type adsorption isotherm Eq. (2.47) the following complex elasticity modulus results. 

Fig. 6.13 shows the agreement between the elasticity modulus, derived form the adsorption isotherm and from relaxation experiments with n-dodecyl dimethyl phosphine oxide solutions. 

Fig. 6.13 Dilational elasticity modulus of n-dodecyl dimethyl phosphine oxide determined for oscillating bubble experiments ( ), and calculated from the adsorption isotherm ( ) according to Wantke etal.(1993)...

The above analysis of the viscoelastic behaviour for adsorption layers of a reorientable surfactant leads to important conclusions. It is seen that the most important prerequisite for a realistic prediction of the elastic properties is the adequacy of the theoretical model used to describe the equilibrium adsorption of the surfactant. For example, when we use the von Szyszkowski-Langmuir equation instead of the reorientation model to describe the interfacial tension isotherm, this rather minor difference drastically affects the elasticity modulus of the surface layer. The elasticity modulus, therefore, can be regarded to as a much more sensitive parameter to find the correct equation of state and adsorption isotherm, rather than the surface or interfacial tension. Therefore the study of viscoelastic properties can give much more insight into the nature of subtle phenomena, like reorientation, aggregation etc. 

Figure 11 shows that for the epoxy and urethane acrylates the elastic modulus remains constant during isothermal DMA runs at 150° C. However, the elastic moduli of AM films increase significantly for about 30-40 minutes indicating thermal cure resulting in an... 

The adiabatic and isothermic bulk elasticity modules for water only slightly differ. The adiabatic modulus for water is 2.2-lO Pa. The bulk elasticity modulus for gas can be obtained from the equation of state. For ideal gas the isothermic modulus is approximately equivalent to Pa, and the adiabatic modulus is equivalent to yPA, where Pa is the pressure inside the cell, y = 1.4 the adiabatic constant. The isothermic modulus can be used in the case of infinitely slow processes. In the case of pressure oscillations at sound frequencies the adiabatic modulus should be used. Gas is much more compressible than liquids. The bulk elasticity modulus for gas is four orders of magnitude smaller than for water. Therefore, even small amounts of gas much smaller than the volume of the solution (Voas Va), can mimic small values of the effective cell elasticity modulus Eq. (6), i.e. a strong decrease of the cell resistance to pressure variations. It is extremely important to avoid the presence of any small amounts of gas in the solution because it can lead to uncontrolled changes of the effective cell elasticity modulus. 

In recent years the analysis of Isothermal point contacts has made considerable advances. Procedures have been developed to allow the simultaneous solution of the elasticity and Reynolds equations, and have provided many numerical results from which theoretical film thickness expressions have been derived. These solutions to the elastohydrodynamic problem may be divided Into two types. Firstly, where the lubricant viscosity Is significantly affected by the generation of pressure within the conjunction area the conditions are known as plezovlscous or hard elastohydrodynamic lubrication. Typical situations for this type of lubrication are steel bodies lubricated by a mineral oil, e.g. ball bearings. The second type of elastohydrodynamic lubrication Is that where the fluid experiences very little change In Its viscosity and Is therefore termed Isovlscous or soft elastohydrodynamic lubrication. This type of lubrication would be expected where the contacting materials are of low elastic modulus (e.g. nitrile rubber) lubricated by a mineral oil or a fluid of very low pressure-viscosity coefficient. (These two regimes of lubrication may also be described as... 

Elastic modulus values are classified into two groups one is the static modulus, and the other is the dynamic modulus. The former is called the isothermal modulus and is obtained from the linear relationship between load and displacement of a specimen. The latter is called the adiabatic modulus and is determined from the resonance frequency or the velocity of an ultrasonic wave (USW) in a specimen. The difference between them is caused by thermal expansion, which results from the adiabatic behavior of the specimen during the propagation of an ultrasonic wave pulse in the latter. Some difficulties cannot be avoided in the determination of the isothermal modulus. For example, a relatively large specimen is needed for the static measurement of a small strain. Thus, the elastic modulus is usually determined from the velocity of an ultrasonic wave in a single crystal of a material, for which it is difficult to prepare a large specimen. 

In common with most thermal analysis techniques, DMA analyses can be performed under both ramped and isothermal temperature programmes. The outputs from an experiment are elastic (storage) modulus and viscous (loss) modulus, and tan 8, which is the ratio of viscous modulus over the elastic modulus. 

These Monte Carlo distributions can be used in the standard three-chain model for rubber-like elasticity to generate, for example, stress-strain isotherms [5]. Non-Gaussian effects can cause large increases in modulus at high... 

Liquid Temp T (°C) Density p( kg/nr) Specific gravity S Absolute viscosity m(N s/itt) Kinematic viscosity (m2/s) Surface tension Isothermal bulk modulus of elasticity E N/n ) Coefficient of thermal expansion cT (K-1)... 

The temperature dependences of the isothermal elastic moduli of aluminium are given in Figure 5.2 [10]. Here the dashed lines represent extrapolations for T> 7fus. Tallon and Wolfenden found that the shear modulus of A1 would vanish at T = 1.677fus and interpreted this as the upper limit for the onset of instability of metastable superheated aluminium [10]. Experimental observations of the extent of superheating typically give 1.1 Tfus as the maximum temperature where a crystalline metallic element can be retained as a metastable state [11], This is considerably lower than the instability limits predicted from the thermodynamic arguments above. 

Here, V denotes specific volume, K denotes bulk modulus, subscripts P,V, S and T denote isobaric, isochoric, isentopic and isothermal conditions, respectively s is the second-rank strain tensor, and C is the fourth-rank elastic tensor. 

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