Modulus apparent

The storage and loss shear modulus behavior of a PS-rich specimen (w = 0.67), shown in Figure 6.13, is also interesting (Erhardt et al, 1970). A Tg for the PS sequences is clearly evident from the maximum in the loss modulus. Apparently the strength of the transition observed depends on the PS content, becoming high when PS forms a continuous phase, even though a PS phase may be observed microscopically at low PS concentrations. It was possible to obtain the melt viscosity as a function of temperature. 

Creep modulus (apparent modulus) Creep mpture strength Creep strength... 

Modulus, apparent The concept of apparent modulus is a convenient method of expressing creep because it takes into account initial strain for an applied stress plus the amount of deformation or strain that occurs with time. 

One of the serious limitations of the earlier creep curves such as the one illustrated in Figure 2-26 was the lack of simplicity of the single-point stress-strain properties such as tensile modulus and flexural strength, especially when one wanted to measure creep as a function of temperature and stress level. Furthermore, the creep data presented in terms of strain were not convenient to use in design or for the purpose of comparing materials. It was obvious that creep curves had to be presented in a more meaningful and convenient way such that they are readily usable. Creep strain curves were easily converted to creep modulus (apparent modulus) by simply dividing the initial applied stress by the creep strain at any time. 

Material properties can be further classified into fundamental properties and derived properties. Fundamental properties are a direct consequence of the molecular structure, such as van der Waals volume, cohesive energy, and heat capacity. Derived properties are not readily identified with a certain aspect of molecular structure. Glass transition temperature, density, solubility, and bulk modulus would be considered derived properties. The way in which fundamental properties are obtained from a simulation is often readily apparent. The way in which derived properties are computed is often an empirically determined combination of fundamental properties. Such empirical methods can give more erratic results, reliable for one class of compounds but not for another. 

For a fiber immersed in water, the ratio of the slopes of the stress—strain curve in these three regions is about 100 1 10. Whereas the apparent modulus of the fiber in the preyield region is both time- and water-dependent, the equiUbrium modulus (1.4 GPa) is independent of water content and corresponds to the modulus of the crystalline phase (32). The time-, temperature-, and water-dependence can be attributed to the viscoelastic properties of the matrix phase. 

In addition to chemical analysis a number of physical and mechanical properties are employed to determine cemented carbide quaUty. Standard test methods employed by the iadustry for abrasive wear resistance, apparent grain size, apparent porosity, coercive force, compressive strength, density, fracture toughness, hardness, linear thermal expansion, magnetic permeabiUty, microstmcture, Poisson s ratio, transverse mpture strength, and Young s modulus are set forth by ASTM/ANSI and the ISO. 

Remember that the modulus E = o/ . will increase during creep at constant o. This will give a lower apparent value of E. Long tests give large creep strains and even lower apparent moduli. 

Creep characteristics temperature range-creep apparent modulus... 

Plastic whose apparent modulus of elasticity is not greater than 10,000 psi at room temperature in accordance with the Standard Method of Test for Stiffness in Flexure of Plastics (ASTM Designation D747). 

Nonrigid plastic Plastic whose apparent modulus of elasticity is not... 

It is apparent therefore that the Superposition Principle is a convenient method of analysing complex stress systems. However, it should not be forgotten that the principle is based on the assumption of linear viscoelasticity which is quite inapplicable at the higher stress levels and the accuracy of the predictions will reflect the accuracy with which the equation for modulus (equation (2.33)) fits the experimental creep data for the material. In Examples (2.13) and (2.14) a simple equation for modulus was selected in order to illustrate the method of solution. More accurate predictions could have been made if the modulus equation for the combined Maxwell/Kelvin model or the Standard Linear Solid had been used. 

Show that the apparent extensional modulus of an orthotropic material as a function of 0 [the first of Equations (2.97)] can be written as... 

That Is, show that an orthotropic material can have an apparent Young s modulus that either exceeds or is less than the Young s moduli in both principal material directions. In doing so, derive the conditions for which each type of behavior exists, i.e., derive the inequalities. Plot E E, for some contrived materials that exemplify these relations. 

The apparent Young s modulus, E2, of the composite material in the direction transverse to the fibers is considered next. In the mechanics of materials approach, the same transverse stress, 02, is assumed to be applied to both the fiber and the matrix as in Figure 3-9. That is, equilibrium of adjacent elements in the composite material (fibers and matrix) must occur (certainly plausible). However, we cannot make any plausible approximation or assumption about the strains in the fiber and in the matrix in the 2-direction. 

Obviously, the assumptions involved in the foregoing derivation are not entirely consistent. A transverse strain mismatch exists at the boundary between the fiber and the matrix by virtue of Equation (3.8). Moreover, the transverse stresses in the fiber and in the matrix are not likely to be the same because v, is not equal to Instead, a complete match of displacements across the boundary between the fiber and the matrix would constitute a rigorous solution for the apparent transverse Young s modulus. Such a solution can be found only by use of the theory of elasticity. The seriousness of such inconsistencies can be determined only by comparison with experimental results. 

Use a mechanics of materials approach to determine the apparent Young s modulus for a composite material with an inclusion of arbitrary shape in a cubic element of equal unit-length sides as In the representative volume element (RVE) of Figure 3-17. Fill in the details to show that the modulus is... 

Paul [3-4] was apparently the first to use the bounding (variational) techniques of linear elasticity to examine the bounds on the moduli of multiphase materials. His work was directed toward-analvsis of the elastic moduli of alloyed metals rath, tha tow5 rdJ ber-reW composite materials. Accordiriglyrthe treatment is for an js 6pjc composite material made of different isotropic constituents. The omposifeTnaterial is isotropic because the alloyed constituents are uniformly dispersed and have no preferred orientation. The modulus of the matrix material is... 

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