Mathematical Modeling and Methods of Determination of Functional-Use Relaxation-Recovery Properties of Polymer Textile M
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Fibre Chemistry, Vol. 52, No. 3, September, 2020 (Russian Original No. 3, May-June, 2020)
PAPERS AT THE INTERNATIONAL CONFERENCE “INNOVATIVE DIRECTIONS OF DEVELOPMENT OF SCIENCE ON POLYMER FIBER AND COMPOSITE MATERIALS,” ST. PETERSBURG, 2020. MATHEMATICAL MODELING AND METHODS OF DETERMINATION OF FUNCTIONAL-USE RELAXATION-RECOVERY PROPERTIES OF POLYMER TEXTILE MATERIALS A. G. Makarov, N. V. Pereborova, E. A. Buryak, and A. A. Kozlov
UDC 539.434:677.494
Mathematical models and methods of determination of functional-use relaxation-recovery properties of textile industry materials having decisive importance for comparative analysis and qualitative sampling of materials having specific properties are reviewed.
Functional-use and performance properties of textile industry materials are based primarily on determination of the physicomechanical properties of these materials, to the study of which paramount attention must be paid. For a comprehensive study and prediction of the functional-use and performance properties of textile industry materials to improve the quality of goods therefrom, it is proposed to conduct investigations of the basic relaxationrecovery and deformation-performance processes, i.e., relaxation and creep, which characterize the key physicomechanical properties of the materials [1-3]. It is expedient to conduct such study making use of mathematical modeling, followed by computer-aided prediction of relaxation and creep. Although relaxation and creep processes are different in physical nature, they are, in fact, reciprocal processes harmoniously complementing each other. Because of this, the study of relaxation and deformation properties of textile industry materials relating primarily to the class of viscoelastic solids is an essential and, in some cases, an urgent task [4-6]. Relaxation process implies a change in the stress σt (or force Ft) applied to a material over a time t under the action of deformative ε: σ = σ (t ) =
F (t ) . s
(1)
A key property of relaxation process is relaxation modulus Eεt = σt/ε, which has two asymptotic values:modulus of viscoelasticity E ∞ = lim E εt
(2)
E0 = lim Eεt .
(3)
t →∞
and modulus of elasticity [7-9]
t →0
St. Petersburg State University of Industrial Technologies and Design. E-mail: [email protected]. Translated from Khimicheskie Volokna, No. 3, pp. 3-7, May-June, 2020 0015-0541/20/5203-0135© 2020 Springer Science+Business Media LLC
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E(ε,t), GPa
E0
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E(ε,t)
2
E∞ ln(t/t1), t1 = 1
0 -5 -4
-3 -2
-1
0
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Fig. 1. Graph depicting experimental “family” of relaxation curves of 33.3 tex Nitron yarn at constant deformation values. The relaxation modulus Eεt can be modeled mathematically using increasing normalized relaxation function ϕεt that acquires significance in the segment [0.1]: E εt = E 0 − (E0 − E ∞ )ϕεt .
(4)
Let us take the normalized arc tangent of logarithm (NAL) that characterizes the Cauchy integral distribution as the relaxation function ϕεt [10, 14]: ϕ εt =
⎛ 1 1 1 t ⎞ + arctg ⎜⎜ ln ⎟⎟, τ 2 π b ε ⎠ ⎝ nε
(5)
w
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