Modulus constants

Viscoelastic creep data can be presented by plotting the creep modulus (constant applied stress divided by total strain at a particular time) as a function of time [23-26], Below its critical stress, the viscoelastic creep modulus is independent of stress applied. A family of curves describing strain versus time response to various applied stress may be represented by a single viscoelastic creep modulus versus time curve if the applied stresses are below the material s critical stress value. 

Shear Modulus (Constant) Modulus Function of y or "c Viscosity Function of y or "c Vicosity (Constant) ... 

The modal of numerical calculation is same with elasticity modulus. Constant face load <7 was applied at the age 3d, 7d, 14d, 28d and 90d. After measuring the average displacement of the top node Ah(t, z), strain and Creep can be calculated by formula ... 

Several functions are used to characterize tire response of a material to an applied strain or stress [4T]. The tensile relaxation modulus E(t) describes tire response to tire application of a constant tensile strain l/e -. 

One can define a phase that is given as an integral over the log of the amplitude modulus and is therefore an observable and is gauge invariant. This phase [which is unique, at least in the cases for which Eq. (9) holds] differs from other phases, those that are, for example, a constant, the dynamic phase or a gauge-transformation induced phase, by its satisfying the analyticity requirements laid out in Section I.C.3. 

Dielectric strength, kV mm Electrical Volume (dc) resistivity, ohm-cm Dielectric constant (60 Hz) Dielectric constant (10 Hz) Dissipation (power) factor (60 Hz) Dissipation factor (10 Hz) Mechanical Compressive modulus, 10Mb in-2 9.8-12 24-31 16-24 1014-1016 4.5-6.0 19 335-600 14 ... 

This result is the shear equivalent to Eq. (3.42) for tensile deformation. Note the modulus is a constant independent of strain for shear, while this is only true for a = 1 in the case of tension as shown by Eq. (3.43). 

As long as the moduli are constants, it makes no difference in either a tensile or shear experiment which variable, stress or strain, is independent and which is dependent that is, we could apply a constant force and measure the strain or induce a constant strain and measure the force responsible. The modulus is the ratio of the stress to the strain. If the ratio were calculated as the ratio of the strain to the stress, the reciprocal of the modulus would result. The latter is called the compliance and is given the symbols D and J for tensile and shear conditions, respectively. When they are independent of time, the moduli and compliances for a particular deformation are simply reciprocals. 

The situation is not so simple when these various parameters are time dependent. In the latter case, the moduli, designated by E(t)and G(t), are evaluated by examining the (time dependent) value of o needed to maintain a constant strain 7o- By constrast, the time-dependent compliances D(t) and J(t)are determined by measuring the time-dependent strain associated with a constant stress Oq. Thus whether the deformation mode is tension or shear, the modulus is a measure of the stress required to produce a unit strain. Likewise, the compliance is a measure of the strain associated with a unit stress. As required by these definitions, the units of compliance are the reciprocals of the units of the moduli m in the SI system. 

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. 

Equation (3.58) can be written in terms of the shear modulus by dividing both sides of the equation by the constant strain ... 

Equations (3.77) and (3.81) both have the same general form dy/dt + Py = Q, so the general solution-given in Example 3.5—is the same for both, although the values of the constants are different. When the constants are evaluated, the storage and loss components of the modulus are found to be... 

The coefficient Tj is termed the modulus of rigidity. The viscosities of thixotropic fluids fall with time when subjected to a constant rate of strain, but recover upon standing. This behavior is associated with the reversible breakdown of stmctures within the fluid which are gradually reestabflshed upon cessation of shear. The smooth sprea ding of paint following the intense shear of a bmsh or spray is an example of thixotropic behavior. When viscosity rises with time at constant rate of strain, the fluid is termed rheopectic. This behavior is much less common but is found in some clay suspensions, gypsum suspensions, and certain sols. 

Elasticity. Glasses, like other britde materials, deform elastically until they break in direct proportion to the appHed stress. The Young s modulus E is the constant of proportionaUty between the appHed stress and the resulting strain. It is about 70 GPa (10 psi) [(0.07 MPa stress per )Tm/m strain = (0.07 MPa-m) / Tm)] for a typical glass. 

Ultrasonic Microhardness. A new microhardness test using ultrasonic vibrations has been developed and offers some advantages over conventional microhardness tests that rely on physical measurement of the remaining indentation size (6). The ultrasonic method uses the DPH diamond indenter under a constant load of 7.8 N (800 gf) or less. The hardness number is derived from a comparison of the natural frequency of the diamond indenter when free or loaded. Knowledge of the modulus of elasticity of the material under test and a smooth surface finish is required. The technique is fast and direct-reading, making it useful for production testing of similarly shaped parts. 

Another anomalous property of some nickel—iron aHoys, which are caHed constant-modulus aHoys, is a positive thermoelastic coefficient which occurs in aHoys having 27—43 wt % nickel. The elastic moduH in these aHoys increase with temperature. UsuaHy, and with additions of chromium, molybdenum, titanium, or aluminum, the constant-modulus aHoys are used in precision weighing machines, measuring devices, and osciHating mechanisms (see Weighing AND proportioning). 

Laminate T °C GTE below ppm/°C Water uptake, MIL-P-13949F, mg Dielectric constant at IMH2 Dissipation factor at 1 MH2 Tensde strength, MPa " Modulus of elasticity, GPa Thermal conductivity, W/(m-K)... 

The critical property for conformal coatings is resistance to chemicals, moisture, and abrasion. Other properties, such as the coefficient of thermal expansion, thermal conductivity, flexibiHty, and modulus of elasticity, are significant only in particular appHcations. The dielectric constant and loss tangent of the conformal coating are important for high speed appHcations. 

Fig. 7. Relations between elastic constants and ultrasonic wave velocities, (a) Young s modulus (b) shear modulus (c) Poisson s ratio and (d) bulk...

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