The linearity domain for the viscoelastic properties of high-molecular organic fibers is determined. The linearity criteria are coincidence of experimental compliance curves and linearity of isochronic creep curves. Statistical criteria are used to establish linearity. The influence function in the constitutive equation of linear viscoelasticity is an Abel-type power kernel. The calculated and experimental creep strains are in good agreement both at the initial stage of deformation and after long-term loading Introduction. To determine the deformation and strength characteristics of composite materials from the properties of their components, it is necessary to determine these properties experimentally and define them analytically [10,13]. In the case of viscoelastic composites, the deformation properties of their components are determined from creep curves [4,7].A great variety of constitutive equations have been proposed to describe the creep of viscoelastic materials. The theory of hereditary viscoelasticity has been used most widely. The concept of linear viscoelasticity is well developed and widely applied. However, the parameters of constitutive equations are determined by approximating experimental creep curves plotted for several levels of stresses and averaging the resulting values. This necessitates extensive long-term creep tests and lead to significant errors in creep strains calculated using average coefficients. The issues remaining to be resolved are determining the linearity domain of viscoelastic properties and selecting a heredity kernel.A generalized rheological model based on the hypothesis of a unified isochronic deformation curve has been developed in [1]. The model allows us to predict the nature of creep (whether linear or nonlinear) and includes an easily implementable procedure of identifying the material constants. In the present paper, we use the model from [1] to calculate the linear creep strains of organic fibers used as reinforcement in organofibrous and hybrid composites. We will determine the domain of linear viscoelastic deformation of organic fibers and justify the structure of the heredity kernel that describes the features of creep of the fibers over the whole time interval.1. Problem Formulation. Subject of Research. The deformation properties of a linear viscoelastic medium under uniaxial tension may be described within the framework of small-deformation theory by the following constitutive equations of the Boltzmann-Volterra hereditary theory of viscoelasticity [9]:

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The nonlinearity of the creep of nylon fibers is justified based on the similarity of a set of isochronous creep curves, which also includes the instantaneous deformation curve. Nonlinear hereditary constitutive equations of creep are derived. The real values of the influence function are determined as the basic rheological characteristic of the material. The applicability of Boltzmann's, Abel's, Rzhanitsyn's, and Rabotnov's kernels is estimated quantitatively. The choice of an Abel-type kernel is justified. The calculated and experimental data are in satisfactory agreement for a loading duration of up to 1,000 hours and an order of magnitude change in the stresses Introduction. The creep of metals at high temperatures and most polymeric and composite materials occurs in the nonlinear domain of deformation [1,7,10,17]. In this domain, experimental compliance curves do not agree and there is no a unified creep function. Also, depending on the type of material and loading conditions, either the initial creep curves or the isochronous creep curves are similar.There are many publications devoted to nonlinear hereditary models. Some of these models, methods for determining their material constants, and their results were discussed in [8, 10-16, 19, 21, 22, 24-27, 30, 31]. The best justification was given to Rabotnov's constitutive equation of nonlinear viscoelasticity [16,17] based on the similarity conditions for isochronous creep curves.The similarity condition for isochronous creep curves is used in [29] to formulate the concept of a unified isochronous deformation curve. This curve also includes the instantaneous tension curve as an isochrone at time zero. The same concept underlies a generalized rheological model describing both linear and nonlinear creep. This model was used in [3,4] to analyze the linear creep of viscoelastic fibers. In the present paper, we employ this model to analyze the nonlinear creep strains of viscoelastic nylon fibers.1. Problem Formulation. Subject of Inquiry. Let us analyze the nonlinear creep of viscoelastic organic fibers that are long subjected to a tensile force. The external load does not vary during creep, and the tensile stress σ(t) is defined by