Plastic deformation dependence

A final comparison of low temperature crazes with shear bands reveals that both deformation phenomena are related. The surface morphologies are quite similar because both modes of plastic deformation depend upon the relative displacement of domains of a size of 10 to 100 nm. However, crazing is controlled by a tensile stress and the fibrous matter contains voids. Shear banding, on the other hand, is controlled by a shear stress which encourages lateral movements without voiding. The final breakdown process may then be initiated in both cases by a random rupture at the upper or lower edge of the deformation zone (Fig. 39 a, b). 

Tablet capping and lamination typically create the most difficult problems, due to a variety of causes. Identification of the cause often leads to the solution. The basic concepts to alleviate these problems center on minimizing elastic behavior while promoting plastic deformation. Depending on the exact nature of the problem, this can be achieved from a formulation perspective by modifying the formula to incorporate a plastically deforming matrix, by adding components to enhance bonding, or by increasing the moisture level. Alternatively, from a machine perspective the following guidelines should be followed ...

Particle Diameter Because plastic deformation depends on stress concentration in the whole volume between particles and not directly on the stress at the particles, D is not of primary importance. The only precondition is that for a given particle volume content, the particles must be small enough to ensure that A is less than the critical value according to equation 1. Therefore, the most important function of particles is to produce a dense pattern of microvoids. Recently, an increase of the toughness of modified PA with increasing tendency to form microvoids inside the particles (with decreasing stress to crack the particles or with decreasing cavitation strain) was found (6). The cavitation stress of an elastomer is dependent on its modulus (27). 

Due to the viscoelastic nature of plastics, deformations depend on such factors as the time under load and the temperature. Therefore the classical equations available for the design of structural components, such as springs, beams, plates, and cylinders, and derived under the assumptions that (1) the modulus is constant and (2) the strains are small and independent of loading rate or history and are immediately reversible, cannot be used indiscriminately. For example, classical equations are derived using the relation... 

Plastic deformation depends not only on how easy it is for the dislocations to glide on their slip plane but also the orientation of the slip plane and the slip direction with the applied stress. If we consider a single crystal subject to uniaxial tension as illustrated in Figure 17.6 the shear stress, Tr, acting on the slip plane in the slip direction is... 

If, however, the stress applied to the solid exceeds its elastic limit, the response is plastic deformation. This deformation persists when the stress is removed, and the unstressed solid no longer has its original properties. Plastic deformation is a kind of hysteresis, and is caused by such microscopic behavior as the slipping of crystal planes past one another in a crystal subjected to shear stress, and conformational rearrangements about single bonds in a stretched macromolecular fiber. Properties of a solid under plastic deformation depend on its past history and are not unique functions of a set of independent variables an equation of state does not exist. 

The studies conducted clearly showed that internal stresses developed in the course of the hardening of all studied mineral binders. However, they could show up in both elastic and plastic deformations depending on the crystal hardness and the degree of dispersion. 

The most dramatic consequence of yield is seen in a tensile test when a neck or deformation band occurs, as in Figure 12.1, with the plastic deformation concentrated either entirely or primarily in a small region of the specimen. The precise nature of the plastic deformation depends both on the geometry of the specimen and on the form of the applied stresses, and will be discussed more fiilly later. 

Such a chain orientation in the direction of deformation is accompanied by their plastic deformation depending upon the proportion of entanglements, it occurs by a disentanglement process. The tensile test is the most convenient way to characterize the mechanical strength of a polymer. Before fracture which can be either fragile or ductile, four different scenarios of the stress-strain behavior can be contemplated, depending on the scale considered. 

Enhancement of impact toughness in some semicrystalline polymers is similar to techniques used for some glassy polymers. Usually an elastomeric phase is melt-blended into the host polymer, resulting in a dispersion of spheroidal elastomeric particles or a network. Compatibilization is obtained by copolymerization or chemical reaction at the interface. The toughening mechanisms may include both massive crazing and cavitation-plastic deformation, depending on the... 

The calibration graph for the probe using a strength machine, has been shown in Fig. 7 It can be observed that the dependence of indications of the device of Wirotest type on the loading is linear within the proportionality limit scope. After unloading the indications do not return to zero, but show own stress caused in effect of plastic deformation of the tested sample... 

A number of friction studies have been carried out on organic polymers in recent years. Coefficients of friction are for the most part in the normal range, with values about as expected from Eq. XII-5. The detailed results show some serious complications, however. First, n is very dependent on load, as illustrated in Fig. XlI-5, for a copolymer of hexafluoroethylene and hexafluoropropylene [31], and evidently the area of contact is determined more by elastic than by plastic deformation. The difference between static and kinetic coefficients of friction was attributed to transfer of an oriented film of polymer to the steel rider during sliding and to low adhesion between this film and the polymer surface. Tetrafluoroethylene (Telfon) has a low coefficient of friction, around 0.1, and in a detailed study, this lower coefficient and other differences were attributed to the rather smooth molecular profile of the Teflon molecule [32]. 

Traditionally, production of metallic glasses requites rapid heat removal from the material (Fig. 2) which normally involves a combination of a cooling process that has a high heat-transfer coefficient at the interface of the Hquid and quenching medium, and a thin cross section in at least one-dimension. Besides rapid cooling, a variety of techniques are available to produce metallic glasses. Processes not dependent on rapid solidification include plastic deformation (38), mechanical alloying (7,8), and diffusional transformations (10). 

Forming processes and techniques that are available for a particular alloy depend on its workabiUty, which is the abiUty to be plastically deformed. 

Mechanical properties of mbber-modifted epoxy resins depend on the extent of mbber-phase separation and on the morphological features of the mbber phase. Dissolved mbber causes plastic deformation and necking at low strains, but does not result in impact toughening. The presence of mbber particles is a necessary but not sufficient condition for achieving impact resistance. Optimum properties are obtained with materials comprising both dissolved and phase-separated mbber (305). 

It is important to differentiate between brittie and plastic deformations within materials. With brittie materials, the behavior is predominantiy elastic until the yield point is reached, at which breakage occurs. When fracture occurs as a result of a time-dependent strain, the material behaves in an inelastic manner. Most materials tend to be inelastic. Figure 1 shows a typical stress—strain diagram. The section A—B is the elastic region where the material obeys Hooke s law, and the slope of the line is Young s modulus. C is the yield point, where plastic deformation begins. The difference in strain between the yield point C and the ultimate yield point D gives a measure of the brittieness of the material, ie, the less difference in strain, the more brittie the material. 

Hiestand Tableting Indices Likelihood of failure during decompression depends on the abihty of the material to relieve elastic-stress by plastic deformation without undergoing brittle fracture, and this is time dependent. Those which relieve stress rapidly are less... 

In this case the shear stress (in the plastic deformation region) depends on how much plastic strain y that has accumulated and the current rate of deformation y. For example, in shock compression the shear stress t behind the shock front (where y is nominally zero) is a function of y only, as given by the implicit relationship... 

Steady-propagating plastic waves [20]-[22] also give some useful information on the micromechanics of high-rate plastic deformation. Of particular interest is the universality of the dependence of total strain rate on peak longitudinal stress [21]. This can also be expressed in terms of a relationship between maximum shear stress and average plastic shear strain rate in the plastic wave... 

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