Abstract:
Inelastic materials, in particular, composites are
widely used in industry. This necessitates the development and
research of mathematical models to describe the rheological
properties of such materials at different temperatures and
types of loads. The principle of heredity for the study of
composite materials leads to the construction of the most
general equations that take into account hereditary effects, the
influence of speed, types of loading, operating conditions, etc.
such prominent relations are integral equations of the Voltaire
type. According to the law of inheritance and the principle of
superposition, the total deformation of a body consists of the
instantaneous deformation, which is determined by the stress
acting at a given moment in time and related to it by Hooke's
law, and the inherited deformation. The heredity principle is
the most general principle that can be the basis of studies of the
rheological properties of inelastic materials. The article
formulates and describes a mathematical model based on this
principle, which describes the behavior of composite materials
in different loads and temperatures modes. The purpose of the
article is to develop an adequate model of the environment,
quite simple and convenient for describing the rheological
properties of composites under conditions of various loads and
elevated temperatures. Objectives of the article: to present the
developed model for describing the rheological properties of
composite anisotropic materials; show the method of
determining viscosity and temperature parameters for inelastic
materials; to demonstrate the possibility of predicting the
behavior of composites in different modes of loads and
temperatures. The mathematical model is an integral equation
with a creep nucleus. The nucleus of the model is chosen in the
form of the Abel nucleus. The parameters of the Abel nucleus
are determined by experiments on samples of anisotropic
composites. The loading mode can be any, for example,
stretching the sample at different load speeds, or stress
relaxation at constant deformations. As determined,
temperature heredity is not significant. The behavior of the
material is determined only by the value of temperature at a
given time. The temperature effect function can be selected as a
normal degree dependence. The model is determined by three
parameters. The parameter determination problem can be
solved analytically, for simple load cases. More complex load
cases, require the use of computer technology and methods of
approximate calculations. The advantage of the proposed
model is the possibility to transfer certain parameters from one
load mode to another. The basic relations are given; the
method of determining the parameters of the hereditary model
is described; theoretical and experimental research is
presented; the possibility of predicting the behavior of
composite materials at different temperatures is shown.
