Modulus Subject

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. 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

Free- Vibration Methods. Free-vibration instmments subject a specimen to a displacement and allow it to vibrate freely. The oscillations are monitored for frequency and damping characteristics as they disappear. The displacement is repeated again and again as the specimen is heated or cooled. The results are used to calculate storage and loss modulus data. The torsional pendulum and torsional braid analy2er (TBA) are examples of free-vibration instmments. 

Automated soldering operations can subject the mol ding to considerable heating, and adequate heat deflection characteristics ate an important property of the plastics that ate used. Flame retardants (qv) also ate often incorporated as additives. When service is to be in a humid environment, it is important that plastics having low moisture absorbance be used. Mol ding precision and dimensional stabiUty, which requites low linear coefficients of thermal expansion and high modulus values, ate key parameters in high density fine-pitch interconnect devices. 

At the present time it is generally accepted that the toughening effect is associated with the crazing behaviour.Because of the presence of the low-modulus rubber particles most of the loading caused when a polyblend is subject to mechanical stress is taken up by the rigid phase (at least up to the moment of... 

Figure 3.9. Rubber particle straddling craze perpendicular to stress is subjected to triaxial stresses and because of its high bulk modulus becomes load bearing. (After Bucknall )...

We examined the role of vector percolation in the fracture of model nets at constant strain and subjected to random bond scission, as shown in Fig. 11 [1,2]. In this experiment, a metal net of modulus Eo containing No = 10" bonds was stressed and held at constant strain (ca. 2%) on a tensile tester. A computer randomly selected a bond, which was manually cut, and the relaxation of the net modulus was measured. The initial relaxation process as a function of the number of bonds cut N, could be well described by the effective medium theory (EMT) via... 

The friction and wear of plastics are extremely complex subjects which depend markedly on the nature of the application and the properties of the material. The frictional properties of plastics differ considerably from those of metals. Even reinforced plastics have modulus values which are much lower than metals. Hence metal/thermoplastic friction is characterised by adhesion and deformation which results in frictional forces that are not proportional to load but rather to speed. Table 1.7 gives some typical coefficients of friction for plastics. 

Example 2.1 A ball-point pen made from polypropylene has the clip design shown in Fig. 2.11. When the pen is inserted into a pocket, the clip is subjected to a deflection of 2 mm at point A. If the limiting strain in the material is to be 0.5% calculate (i) a suitable thickness, d, for the clip (ii) the initial stress in the clip when it is first inserted into the pocket and (iii) the stress in the clip when it has been in the pocket for 1 week. The creep curves in Fig. 2.5 may be used and the short-term modulus of polypropylene is 1.6 GN/m. ... 

The bulk modulus is appropriate for situations where the material is subjected to hydrostatic stresses. TTie proof of equations (2.15) and (2.16) is given by Benham et al. 

A plastic beam is to be subjected to load for a period of 1500 hours. Use the 1500 hour modulus values given below and the data in Table 1.5 to decide which of the materials listed would provide the most cost effective design (on a stiffness basis). 

J7 In a tensile test on a plastic, the material is subjected to a constant strain rate of 10 s. If this material may have its behaviour modelled by a Maxwell element with the elastic component f = 20 GN/m and the viscous element t) = 1000 GNs/m, then derive an expression for the stress in the material at any instant. Plot the stress-strain curve which would be predicted by this equation for strains up to 0.1% and calculate the initial tangent modulus and 0.1% secant modulus from this graph. 

The transverse modulus, Ect, may be determined in a matmer similar to that described earlier for the longitudinal modulus. Consider a unidirectional fibre composite subjected to a transverse force, Fct, in the direction perpendicular to the fibre axis. 

The in-plane stiffness behaviour of symmetric laminates may be analysed as follows. The plies in a laminate are all securely bonded together so that when the laminate is subjected to a force in the plane of the laminate, all the plies deform by the same amount. Hence, the strain is the same in every ply but because the modulus of each ply is different, the stresses are not the same. This is illustrated in Fig. 3.19. 

A sheet of chopped strand mat-reinforced polyester is 5 mm thick and 10 mm wide. If its modulus is 8 GN/m calculate its flexural stiffness when subjected to a point load of 200 N midway along a simply supported span of 300 mm. Compare this with the stiffness of a composite beam made up of two 2.5 mm thick layers of this reinforced material separated by a 10 mm thick core of foamed plastic with a modulus of 40 MN/m. ... 

To find an upper bound on the apparent Young s modulus, E, subject the basic uniaxial test specimen to an elongation eL where e is the average strain and L is the specimen length. TRelntemal strain field that corresponds to the average strain at the boundaries of the specimen is... 

Use the bounding techniques of elasticity to determine upper and lower bounds on the shear modulus, G, of a dispersion-stiffened composite materietl. Express the results In terms of the shear moduli of the constituents (G for the matrix and G for the dispersed particles) and their respective volume fractions (V and V,j). The representative volume element of the composite material should be subjected to a macroscopically uniform shear stress t which results in a macroscopically uniform shear strain y. 

Three different commercial formulations of silicone sealants from Dow Corning was used in the NSF sponsored studies. They were DC-790, DC-995, and DC-983, in the order of increasing modulus. Dumbbell test coupons (samples) were prepared as per the ASTM standards. Some test coupons were maintained at ambient conditions as control and the rest were subjected to simulated weathering. The weathered coupons were removed from the test layout at regular intervals of time and were tested for any changes in crosslink density due to exposure. 

Contrary to widespread opinion, the value of Ea is not a constant quantity. As was proved previously [52], the value of E is variable, since it depends on the ordering of macromolecules in the amorphous material of the fiber. At the same time, one can suppose that this ordering will be affected by the specificity of the fine structure of the fiber, and particularly by the type of substructure of the fiber. The relationship determining the modulus Ea appropriate for a definite type of fiber substructure can be derived from Eq. (11) when appropriate values of A are assumed. In the case of the microfibrillar substructure, i.e., for A < I, typical of PET fibers stretched, but not subjected to annealing, this equation has the form [52] ... 

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