Amorphous stress distribution

Figure 2.1 illustrates the stress distribution on an amorphous PET sample at an indentation depth, h = 2 mi (Rikards et al, 1998). It can be seen that the depth of the plastic zone shown is here about five times the penetration distance of the Vickers indenter. 

Figure 2.1. Stress distribution, in MPa, for amorphous PET at an indentation depth h = 2 um (c is the depth of the plastic zone and a is one-half the projected length of the indentation diagonal). Stresses larger than 78 MPa are elastic. (After Rikards et ah, 1998.)...

Aoba T, Moriwaki Y, Doi Y, Okazaki M, Takahashi J, Yagi T (1980) Diffuse X-ray scattering from apatite crystals audits relation to amorphous bone mineral. J Osaka Univ Dental School 20 81-90 Aoba T, Yagi T, Okazaki M, Takahashi J, Doi Y, Moriwaki Y (1981) Crystalhnity of enamel apatite an X-ray diffraction study of human and bovine-fetus teeth. J Osaka Univ Dental School 21 87-98 Bacon GE, Bacon PJ, Griffiths RK (1979) Stress distribution in the scapula studied by neutron diffraction. Proc Roy Soc London B204 355-362... 

Example of internal stress due to cooling Parabolic temperature profiles form across the thickness of a warm, cooling sheet of amorphous plastic. Fig. 71. If the initial temperature is above the glass transition temperature and cooling is rapid (quenching), the internal stress distribution across the cross-section of the material is nearly parabolic as well. 

Nevertheless, further careful investigations did not discern a rigid correlation between polymer strength and the stress distribution on amorphous regions [109] ... 

What is the nature of brittleness The chains of amorphous polymers are entangled. At low temperatures most degrees of freedom are frozen the chains, therefore, become stiff. This is the situation where steric hindrance prevents chain movement relative to one another. When an external load is applied, stress concentration occurs at some points. If no plastic flow is possible to equalize the stress distribution within the material, crack initiation and brittle fracture may occur. 

The possibility of a nonsymmetrical stress tensor is discussed by Dahler and Scriven (1961, 1963). Asymmetry has not been observed experimentally for amorphous liquids. Body torques do exist on suspension particles, but these can treated by calculating the stress distribution over the particle surface for each orientation (see Chapter 10). 

The photoelasticity method can only apply to amorphous materials which have very good birefringent properties, such as polycarbonate. Experiment is used to observe the stress distribution, judge the high stress area and determine the value of residual stress [9]. 

Since at temperatures below the Tg the chains of an amorphous polymer are randomly distributed and immobile, the polymers are typically transparent. These glassy polymers behave like a spring and when subjected to stress, can store energy in a reversible process. However, when the polymers are at temperatures slightly above the Tg, i.e., in the leathery region, unless crosslinks are present, stress produces an irreversible deformation. 

An early example of Raman mapping by Breitenbach et al. [52] showed that when crystalline ibuprofen is formulated in a hot melt extrudate the API changes to the amorphous form. Ibuprofen is a sparingly water-soluble compound, so this formulation provides a route to better bioavailability via the more soluble amorphous form. Using confocal Raman mapping the form of the API was determined at the time of manufacture and under stress conditions and was used to assess the stability of the amorphous form. These studies also showed that the API was homogeneously distributed throughout the formulation based on the relative band intensities of the amorphous API and a formulation excipient, polyvinylpyrrolidone (PVP). 

The answers to these questions can be gleaned from Table 13-2, which compares approximate values of the tensile modulus for various polymers. Rubbers or elastomer are also amorphous, of course, but they respond to a stress in an entirely different manner to all other types of materials. Because they have low Ts, at ordinary temperatures, they respond to a load by changing their distribution of chain conformations, the chains becoming more extended as the material is stretched. A rubber has to be extended many limes its original dimensions before the covalent bonds take the load. We will consider rubber elasticity as a separate topic later. 

III. The third step of direct longitudinal transmission of strain onto connected crystalline blocks leads to a perfect stretching of these fibrils. Because of the alignment of the molecules the fibers in this condition should possess a strength about 1 to 2 orders of magnitude higher than the yield stress of randomly distributed folded polycrystals. As the fibrils are able to stabilize the enhanced micro-void volume between them, a lateral coalescence of these voids finally provides a local deformation zone in the shape of a craze as known from amorphous polymers. 

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