## Poissons Ratio

Poisson's ratio is a required constant in engineering analysis for determining the stress and deflection properdes of materials (plasdcs, metals, etc.). It is a constant for determining the stress and deflection properties of structures such as beams, plates, shells, and rotating discs. With plastics when temperature changes, the magnitude of stresses and strains, and the direction of loading all have their effects on Poisson's rado. However, these factors usually do not alter the typical range of values enough to affect most practical calculations, where this constant is frequently of only secondary importance. The application of Poisson's ratio is frequently required in the design of structures that are markedly 2-D or 3-D, rather than 1-D like a beam. For example, it is needed to calculate the so-called plate constant for flat plates that will be subjected to bending loads in use. The higher Poisson's ratio, the greater the plate constant and the more rigid the plate.

When a material is stretched, it's cross-sectional area changes as well as its length. Poisson's ratio (v) is the constant relating these changes in dimensions. It is defined as the ratio of the change in lateral width per unit width to change in axial length per unit length caused by the axial stretching or stressing of a material. The ratio of transverse strain to the corresponding axial strain below the tensile propordonal limits.

For plasdcs the rado falls within the range of 0 to 0.5. With a 0 ration there is no reduction in diameter or contracdon laterally during the elongation but would undergo a reduction in density. A value of 0.5 would indicate that the specimen's volume would remain constant during elongation or as the diameter decreases such as with elastomeric or rubbery material. Plasdc range is usually from about 0.2 to 0.4; natural rubber is at 0.5 and reinforced TPs at 0.1 to 0.4. In mathematical terms, Poisson's ratio is the diameter of the test specimen before and after elongation divided by the length of the specimen before and after elongation. Poisson's ratio will have more than one value if the material is not isotropic. (Table 3.1)

 Poisson's Shear modulus Shear stress Plastic ratio MPa MPa ABS 0.35 965 51.2 0.36 660 30.0 Acetal homopolymer 0.35 1340 65.5 Acetal copolymer 0.35 1000 53.0 Nylon (0.2 wt°/o) 0.34-0.43 66.4 Polycarbonate 0.37 785 41.5 Polymethyl methacrylate 0.35 Britdeness identifies material easily broken, damaged, disrupted, cracked, and/or snapped. Britdeness can result from different conditions such as from drying, plasticizer migration, etc. Brittle materials exhibit tensile S-S behaviors different from the usual S-S curves. Specimens of such materials fracture without appreciable material yielding. They lack toughness. Their britde point is the highest temperature at which a plastic or elastomer fractures in a prescribed impact test procedure. Plastics that are brittle frequently have lower impact strength and higher stiffness properties. A major exception is reinforced plastics. The tensile S-S curves of brittle materials often show relatively little deviation from the initial linearity, relatively low strain at failure, and no point of zero slope. Different materials may exhibit significantly different tensile S-S behavior when exposed to different factors such as the same temperature and strain rate or at different temperatures. A brittleness temperature value is used. It is the temperature statistically calculated where 50% of the specimens would probably fail 95% of the time when a stated minimum number are tested. The 50% failure temperature may be determined by statistical calculations. There is a Griffith design failure theory. It expresses the strength of a material in terms of crack length and fracture surface energy. Brittie fracture is based on the idea that the presence of cracks determines the britde strength and crack propagadon occurs. It results in fracture rate of decreased elasdcally stored energy that at least equals the rate of formadon of the fracture surface energy due to the creadon of new surfaces.
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