A. M. Stalevich

A version of modeling of nonlinear-hereditary viscoelasticity of polymer materials

We propose a version of the mathematical model of nonlinear-hereditary viscoelasticity of polymer materials, which is used to predict strain processes of various complexity, from simple relaxation and simple creep processes to complicated strain recovery processes and reverse relaxation processes with alternating loading and unloading.

Prediction of Reverse Relaxation and Deformation—Recovery Processes in Synthetic Fibres

Use of “force” and “geometric” “deformation” variants of the nonlinear-hereditary viscoelasticity equation for prediction of complex processes by calculation is examined on the example of deformation-recovery and reverse relaxation processes in Lavsan synthetic fibres. A comparison of the calculated and measured values allows recommending the method of calculated prediction in which an elementary function — the normalized arctangent of the logarithm of the reduced time serves as the normalized relaxation or creep function.

Variant of the Relaxation and Retardation Spectra for Amorphous Crystalline Synthetic Fibres

The relaxation (retardation) spectrum of amorphous crystalline synthetic fibres is totally determined by the mean statistical relaxation (retardation) time and the structural coefficient that essentially characterizes the intensity of the relaxation (creep) process. With respect to the physical meaning, the relaxation function (retardation function) is obtained by integration of the relaxation (retardation) spectrum. Methods are developed for determining the relaxation and retardation spectra.

Calculated and Experimental Estimation of Absorbed Mechanical Work in Deformation of Synthetic Fibres

Methods are proposed for obtaining the elastic and absorbed components of deformation and mechanical work expended in the region of a nondestructive mechanical effect from the stress-strain diagrams or by calculated prediction. The closeness of the values of the absorbed and correspondingly the elastic components obtained with the measured or predicted stress-strain diagram totally confirm the satisfactory reliability of modeling the physicomechanical properties of a fibre in the form of an integral equation in which the nonlinear-hereditary kernel analytically reflects the activating character of the mechanical effect combined with the concept of the deformation-time analogy in normalized form [5].

Methods of Refinement and Control of Predictable States of Synthetic Materials

Methods of integral monitoring of the accuracy of calculated determination of viscoelastic characteristics were developed and make it possible to indicate the confidence intervals of the values of the determined parameters. The selection of a mathematical model for which the relative error of difference of the calculated values of the parameters from the average values is smallest will allow increasing the accuracy of prediction. The use of methods of refining the calculated parameters based on experimental stress—strain diagrams and iterative recalculation of these parameters brings the calculated values of the parameters closer to the experimental values, narrowing the confidence intervals and thus increasing the accuracy of the prediction.

Determination of the Viscoelastic Characteristics of Polymer Materials on the Example of Polyacrylonitrile Fibre

Methods are developed for determining viscoelastic characteristics with the results of brief laboratory measurements based on both independent processing of families of relaxation and creep curves and on their combined processing using a new mathematical model and the normalized arc tangent of the logarithm of the reduced time as the relaxation function and the creep function. The expediency of using these methods is demonstrated on the example of polyacrylonitrile fibre. The results of the calculations are confirmed by the experimental data.

Variant for Prediction of Deformation of Synthetic Fibres

A new function with certain advantages over the previously used functions is proposed for use as the integral relaxation kernel for predicting the stress—strain states of synthetic fibres and other textiles by calculation in the region of nondestructive loads using an indicial equation. The range of prediction of the viscoelastic properties was expanded and the working equations were simplified. Correction of the calculation of the viscoelastic properties with the points on the experimental stress—strain diagram will allow increasing the reliability of prediction of deformed states.

Analytical prediction of deformation of polycaproamide cloth

A method of combined approximation of isothermal “families” of creep and relaxation curves is proposed for obtaining more precise numerical values of the viscoelastic characteristics of cloth. The applicability of the equation of nonlinear-hereditary elasticity designed for analytical prediction of the stress—strain state of the fabric and in particular, stress—strain diagrams and more complex strain regimes was demonstrated.

Determination of the deformation characteristics of polycaproamide fabrics

The applicability of a previously developed fast method of determining the viscoelastic characteristics of synthetic thread with the measured relaxation curve to polycaproamide fabrics was demonstrated. This fast method can be used to model the physicomechanical properties of cloth for goal-oriented solution of problems of the mechanical technology of these fabrics and the study of their properties in use.

Characteristics of creep in polycaproamide cloth

The applicability of a fast method of determining the creep characteristics by brief measurements, developed for synthetic fibres, to polycaproamide cloth was demonstrated. The advantages of the proposed method are the minimum characteristics used and for this reason, the stability of the numerical values of these characteristics.