Hysteresis of Tensile load — Strain Route of Knitted Fabrics under Extension and Recovery Processes Estimated by Strain History

Abstract

Hysteresis phenomenon of tensile load (stress) under extension and recovery processes were estimated in terms of time dependence of tensile load by using several kinds of knitted fabrics. The measurements were done under strip biaxial extension corresponding to uniaxial extension with a fixed dimension in the direction perpendicular to elongation. The present concept was based on tensile load (stress) relaxation in elongation and restricted sides. To attempt mathematical evaluation, a simple hypothesis described by hereditary integral was proposed to explain the hysteresis of tensile load (strain), strain routes under extension, and recovery processes, in which the extension and recovery routes were formulated as addition and subtraction of step function of strain history, respectively. The calculated curves were in good agreement with the experimental curves in the large deformation region. The theoretical calculation to give the best fit with experimental curve could be realized by using n adopted as an exponent to describe the “linearizing method” ( F = Yen, where F is the tensile load and e is strain of a fabric) proposed by Kawabata et al. The present evaluation improved on their proposal, since the present theory can represent the hysteresis routes by using the same value of parameter n.

Auxetic deformation of the weft-knitted Miura-ori fold

“…Due to microstructural deformation and fiber slippage, the knitted fabric is a type of viscoelastic material, which usually shows a time-dependent elastic behavior leading to a viscoelasticity. 39 A cyclic axial tensile testing method 40 was used to measure the mechanical property of the WMF for testing the viscoelasticity, and the unloading strain was used to evaluate the hysteresis effect of the auxetic structure. The fabric samples were cut into 50 mm  80 mm rectangular shapes; 30 mm out of the 80 mm length was for fixing the samples on the MTS, and therefore the actual testing area was 50 mm  50 mm, conditioned for 24 hours at 25 AE 1 C and 65% humidity before mechanical experiment and Poisson's ratio measurement.…”

Clothing Pressure of Knitted Fabrics Estimated in Relation to Tensile Load Under Extension and Recovery Processes by Simultaneous Measurements

“…To pursue the more detailed analysis, the relationship between tensile load and pressure under extension and recovery processes was analyzed in terms of the hysteresis phenomenon based on the concept that the drastic decrease of tensile load is attributed to the tensile load (stress) relaxation mode [12]. If the strain is due to time dependence described as a summation of step functions concerning strain history, tensile load (stress) under extension process can be represented by using hereditary integral according to the Boltzmann superposition principle.…”

“…In equation (6), A, B, α and β are the coefficient to represent time dependence of strain against the external applied tension [12]. They are given by (7) As discussed in our previous paper [13], equation (7) representing two relaxation modes is only a formula to represent tensile load (stress), but the origin of actual time dependence is obviously attributed to a number of unknown factors such as plastic deformation, slippage and Figure 7 Tensile load (on left hand) and pressure (on right hand) against strain under extended and recovery processes measured for specimen A.…”

“…Apart from their concepts for fitting of fabrics to human bodies in terms of geometrical aspects, this study aimed to deal with characteristics of knitted fabrics based on the direct measurement of clothing pressure by an air-packing method developed by Ito et al [8,9]. The pressure by an air pack and the tensile load by a strip biaxial tensile tester were measured simultaneously and the relationship between the pressure and the tensile load established for a curved thin liquid film has been mainly discussed in terms of clothing material science by using two kinds of knitted fabric discussed in previous papers [10][11][12][13]. The two kinds of plain knitted fabrics had simple structures.…”

Modelling the hysteretic wale-wise stretching behaviour of technical plain knits

“…Popper (1966) assessed the role of friction in the biaxial behaviour of knitted fabrics through a theoretical analysis and demonstrated that its effect is very important even if the value of the coefficient of kinetic friction is low (0.1). This effect being opposed to the sliding direction, its contribution acts inversely during loading and unloading steps, leading to a very pronounced hysteretic behaviour of knitted fabrics under biaxial (Popper, 1966) and uniaxial (Matsuo and Yamada, 2009) tension. The sensitivity to friction is exacerbated by the exponential form of the drive belt formula that may apply at the loops crossing points due to yarn curvature (Popper, 1966).…”