Creep contraction ratios

The modulus term in this equation can be obtained in the same way as in the previous example. However, the difference in this case is the term V. For elastic materials this is called Poissons Ratio and is the ratio of the transverse strain to the axial strain (See Appendix C). For any particular metal this is a constant, generally in the range 0.28 to 0.35. For plastics V is not a constant. It is dependent on time, temperature, stress, etc and so it is often given the alternative names of Creep Contraction Ratio or Lateral Strain Ratio. There is very little published information on the creep contraction ratio for plastics but generally it varies from about 0.33 for hard plastics (such as acrylic) to almost 0.5 for elastomers. Some typical values are given in Table 2.1 but do remember that these may change in specific loading situations. 

In a small mechanism, a polypropylene spring is subjected to a fixed extension of 10 mm. What is the initial force in the spring and what pull will it exert after one week. The length of the spring is 30 mm, its diameter is 10 mm and there are 10 coils. The design strain and creep contraction ratio for the polypropylene may be taken as 2% and 0.4 respectively. 

Creep contraction ratios, which are time dependent functions analogous to the Poisson s ratios of elastic theory can be defined. 

If the spring is subjected to a 50% overload for 1 day, estimate the percentage increase in the extension over the normal 1 day extension. The shear stress in the material is given by 16 WR/d. Use the creep curves supplied and assume a value of 0.4 for the lateral contraction ratio. 

So far the parameters defined, compliances, moduli and contraction ratios, are in forms which can be rigorously interpreted for infinitesimal time dependent deformation under constant stress, thus creep moduli E 9, r) are functions of angle and time. Extension to accommodate nonlinear behaviour at finite strain is obtained by allowing the quantities to become also functions of stress or strain. Thus modulus has the form E 6,t,%) and compliance functions Si/t.t). Such an extension is not rigorous but is useful. 

Creep lateral contraction ratio The ratio of lateral strain to longitudinal strain measured simultaneously in a creep experiment (also known as Poisson s ratio). 

Figure 8.6 Photograph of the extensometry system of Clayton, Darlington and Hall (1) upper arm of tensile extensometer (2) specimen (3) brass contact pieces on lateral extensometer arms (4) lower arm of tensile extensometer and (5) glass plates with shoulders resting on ends of lateral extensometer arms. (Redrawn from Clayton, D., Darlington, M.W. and Hall, M.M. (1973) Tensile creep modulus, creep lateral contraction ratio, and torsional creep measurements on small nonrigid specimens. J. Phys. E., 6, 218. Copyright (1973).)...

Clayton, D., Darlington, M.W. and Hall, M.M. (1973) Tensile creep modulus, creep lateral contraction ratio, and torsional creep measurements on small nonrigid specimens. J. Phys. E., 6,218. 

The Poisson ratio, like the bulk, tensile, and shear creep compliance, is an increasing function of time because the lateral contraction cannot develop instantaneously in uniaxial tension but takes an infinite time to reach its ultimate value. In response to a sinusoidal uniaxial stretch, the complete Poison ratio is obtained ... 

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