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 γ_r.
For the loose sliver having Poisson's ratio ∑₀, the following expressions were derived:
Then, according with the definitions of resilience φ(γ_r)=W₂/W₁, energy loss H(γ_r)=W₁-W₂. it was shown that, in the case of small γ_r.
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).

抄録全体を表示

In this paper, the load-elongation curves P (γ) and lateral contraction-elongation curves β(γ) due to tensile extension of direct draft cutting sliver of viscose rayon filaments are discussed. On the assumption of λ_??_1, x_??_1 in the model of double elasticity of fibre system, the following theoretiral formulae are derived;
On the other hand, the experimental results of load-elongation, lateral contraction relations for samples of sliver having variation of length L₀ linear density k₀, and bulk density _??_₀ are expressed respectively by the formulae of second power of elongation γ. By the procedure of comparing observed values of coefficients of power of γ with above theoretical expression, the effects of fibre properties into Poison's ratio ∑₀, Young's modules E₀, breaking strength and breaking elongation of direct draft cutting sliver have been determined.

抄録全体を表示

The purpose of this research is to estimate the influence of elementary fibre properties on _??_ torsional elastic behaviour of sliver-like fibre system for the analysis of spinning mechanisms and for the prediction of yarn quality.
In this paper, using the principle of double elasticity theory which was previously discussed by the author, the shear modulus G of sliver-like fibre bundle (length L, radius R, sectional area A and density _??_) is derived as a function of fibre dimensions (length l, diameter b, density ρ and direction to sliver axis θ) and fibre properties (shear rigidity μ_f. Young's modulus ε_f, Poisson's ratio σ and coefficient of friction f), that is
Then, by the application of same method to torsional displacement of fibre in a bundle which are twisted by _??_ per unit length, the effects of amount of _??_ on structure factors L, R and _??_ of system are determined theoretically by the following:
where, E is Young's modulus, Σ is Poisson's ratio of untwisted sliver:
And S is applied tensile stress of sliver. If sliver is twisted with constant length, it may be put:S=1/2ER²_??_².

抄録全体を表示

The stationary creep phenomena of the untwisted sliver subjected to various constant loads has been observed by one of the authors, previously.
In this paper, the theoretical relationship between external load and stationary creep velocity is derived assuming that the slippage of individual fiber in assembly may occur when the fiber tension increases to reach the value larger than the static frictional force.
The increment of this tension is determined by the pulling rate of force.
The complete expression for the stationary creep velocity becomes where, W=external load, P=inter-fiber pressure per unit length, N=number of fibers in cross section, l=length of fiber, E=Young's modulus of fiber, A=area of cross-section of fiber, μ₀=coefficient of static friction, μ_k=coefficient of kinetic friction, and α=constant determined by the nature of contacting fibers.
A comparison of this theoretical expression with experiment was satisfactory in the range in which fiber number N remains constant for various loads.

抄録全体を表示

By the application of the principle of double elasticity theory to the torsional displacement of sliver-like fibre system in which Young's modulus E, Poisson's ratio ∑, Shear modulus G, and structure factor L, R, ρ are given by the same expressions as in the previous paper, the theoretical formula of the relationship between torsional moment and twist angle per unit length, M(θ), are derived in the following:
And assuming that λ=0 or λ=1, this formula will be deduced to the case of spun yarn of staple fibres or multi-filament yarn, respectively.

抄録全体を表示

In this paper the correspondence of the induced pressure in twisted sliver with the compressed paessure in loaded wad was measured under such equilibrium condition that both of frictional forces at the two ends of metal wire inserted partly in the wool wad and partly in the twisted wool sliver were balanced (see fig. 1). At the balanced frictional state (see fig. 2), the experimental relations between the twist angle θ (deg/cm) of sliver having fullness (1-ε)_s and the applied load R (g/cm²) of wad having fullness (1-ε)_w are shown in fig. 4. On the other hand, the effect of R on the withdrawal force F_w (g/cm) of single fibre from this wad was described by inverse sigmosoidal curve in fig. 5, and the dependence of F_w on R/(1-ε)_w was obtained linearly as shown in fig. 7. Thus, frictional coefficient of wool fibre was estimated to μ₀=0.26 by Postle-Ingham's method²³⁾. And then, the dependence of average frictional force F_t (g/cm) of a fibre in wool sliver on its twist number n (cm^-1) was estimated from the load-elongation curves of twisted wool sliver. In fig. 10, this relation of F_t and n was plotted exponentially.
From these experimental results, detailed assignments of the mechanical state of a fibre in twisted sliver have been made as follows:
(1) In fig. 12 it is shown that the value of radial pressure P_w (g/cm) produced on the unit length of axial centre line of twisted sliver increases quadratically as twist number n increases.
(2) Inter-fibre frictional force F_t of twisted sliver increases with two sets of factors: one is bulk density increment of sliver by twisting, and another the curvature increment of fibre arrangement. The observed values of the former efiects on the frictional force of single fibre are given as F_w/4 in fig. 10, and those of the latter effect as (F_t-(F_w/4)) in fig. 10.
(3) The tortional behavior of wool sliver as a whole is similar to the spongy material, for the orientation of fibre in a twisted sliver was not arranged to regular spiral configuration, but intercected mutually as the results of fibre migrations. This makes possible to suggest that the value of inter-fiber frictional cofficient μ in twisted sliver is larger than that of μ₀ in untwisted wool wad. Actually, inserting the observed values of F_t/(F_w/4), the average ratio of frictional force along the generating line of unit length, into eqs. (6), (7), calculated value of μ was about 1.

抄録全体を表示