Abstract
In order to gain more information as to the nature of elastic hysteresis phenomena observed in cyclic loading sliver-like fibre system which had been discussed experimentally in previous paper1), the present study was undertaken to determine the theoretical relationships between the amounts of tensile resilience φ, dissipated energy loss H and the variations of sliver constants i. e. fibre length _??_, fibre diameter b, density ρ, Young's modulus ε_??_, Poisson's ratio σ, coefficient of friction f, sliver length L and sliver density _??_. By the application of the law of thermodynamics to the double elastic fibre system, it was possible to obtain a general expression of external work W1 and recovery work W2 done by the applied load on deformed system in a cycle of extension γr.
For the loose sliver having Poisson's ratio ∑0, the following expressions were derived:
Then, according with the definitions of resilience φ(γr)=W2/W1, energy loss H(γr)=W1-W2. it was shown that, in the case of small γr.
Where denote the standard measures of hysteresis.
Where Poisson's ratio of sliver, effective Young's modulus of fibre, frictional factor of inter-fibre and specific length of fibre were determined from the given sliver constants respectively. The quantitative behaviour of standard measures of hysteresis φ0 and η0 shown in Fig. 7.2 as the function of frictional factor α0 and specific fibre length λ0 which varies between zero to unity.
Finally, experiments on the repeated loading for crimped staple sliver and direct roller cutting sliver of viscose rayon fibres have been performed to check the theoretical predictions concerning the precise manner of hysteresis expressed in formulae (2).
