Machinery's Handbook, 31st Edition
564 Stress and Strain in Plastics Normal stress ( s ) is illustrated by the simple tension test shown in Fig. 4, where the direct stress is the ratio of applied load to the original cross-sectional area in lb f /in 2 . In the Système International (SI or metric system, see page 2872 and Table 39 on page 2863 ) the stress σ is expressed in newtons/meter 2 (N/m 2 ). (1) If the load is applied as shown in Fig. 4 , the test piece is in tension, and if reversed, it is in compression. Normal strain ( ε ) is also illustrated by the diagram in Fig. 4, where the load or stress applied to the test piece causes it to change its length. If the bar has an original length L and changes its length by D L , the strain, ε , is defined as (2) Strain is the ratio between the amount of deformation of the material and its original length. It is a dimensionless quantity. Extensions of most materials under load are gener ally very small. Strain ( mε or microstrain in most metals) is measured and expressed in microinches (millionths of an inch) per inch, or 10 − 6 in/in (10 − 6 cm/cm). Alternatively, strain is expressed as a percentage. The three methods compare as follows: Modulus of Elasticity E: Most metals and plastics have deformations that are proportional to the imposed loads over a range of loads. Stress is proportional to load, and strain is pro - portional to deformation, so stress is proportional to strain and is expressed by Hooke’s law: (3) The constant E is called by various names: the modulus of elasticity , Young’s modulus , or, in the plastics industry, tensile modulus . Referring to Fig. 4 , tensile modulus is given by the formula: (4) Thus, the modulus is the slope of the initial portion of the stress-strain curve. An elastic material does not necessarily obey Hooke’s law, since it is possible for a material to return to its original shape without the stress being proportional to the strain. If a material does obey Hooke’s law, however, it is elastic. The straight portion of the stress-strain curve for many plastics is difficult to locate, and it is necessary to construct a straight line tangent to the initial portion of the curve to use as a modulus. The shape of a line so obtained is called the initial modulus . In some plastics the initial modulus can be misleading, owing to the nonlinear elasticity of the material. Some suppliers therefore provide the so-called 1 percent secant modulus, which is the ratio of stress to strain at 1 percent strain on the stress-strain curve. In the illustration of typical stress-strain curves in Fig. 5, the secant modulus at the point E is the slope of the line OE . B C E F D F D D C C = Breaking Point D A A A B, C A F or σ = Stress Area Load = or Strain Original Length Change of Length = L L ε D = . . 1000 0 001 0 1 10000 0 010 1 . µε µε = = = = percent strain percent strain E Strain Stress Constant = = E ε = σ = = A L FL ∆ ∆ F ⁄ A L ⁄ L
O H
Strain
Fig. 5. Typical Stress-Strain Curves
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