Artamonova E.N., Tаlpasheva D.

Saratov State Technical University, Russia

CALCULATION OF LONG-TERM STRENGTH ELEMENTS OF POLYMER MATERIALS

In assessing the strength reliability of structural elements necessary to solve the problem of long-term strength - the decline of strength of materials over time under load [1], and the definition of the laws of the behavior of different physical systems, based on some general principles, is one of the main problems of mechanics. Analysis of the experimental data shows that the characteristics of the temperature dependence of the relaxation processes and destruction of viscoelastic polymers with the same activation energy value for each material. Combinations of different approaches to the description of these processes, i.e. formulating a general mathematical theory of deformation and fracture of polymers depends on the strain of studying the relationship, and the destruction of voltage steps, temperature, corrosive factors in the whole range of working time element. Viscoelastic behavior reflects the combined viscous and elastic response of the material under mechanical stress. Viscoelastic properties of polymers depend on several variables, such as temperature, pressure and time; chemical composition, molecular weight and weight distribution and crystallinity; dilution with solvents or plasticizers; A mixture with other materials to form composite systems. It is known that the physical destruction process can be divided into three stages (Fig. 1): scattered devastation, developed cracks, the intensive growth of the main crack.

                                

                                  

                                                   Figure 1

In engineering calculations on the structural strength of materials made the assumption that the appearance of the main crack is equivalent to total destruction.
The paper presents research results in the calculation of long-term strength of the elements of nonlinear viscoelastic polymers, built the mathematical expression of generalized criteria for the stress-strain state of the samples with the terms of destruction. According to the kinetic approach of destruction it is represented as a gradually developing in time the process of changing the element particle microstructure parameters during the load operation. This approach is appropriate in connection with the growing use of structures made of composite materials based on polymers, in which the problem of forecasting performance is complicated due to irreversible and reversible processes change the molecular and supramolecular structures during the operation [2]. Сreep curves and the instantaneous deformation is used to build long-term strength theories. These various sources of experimental data from experiments and long-term creep strength can be schematically summarized as a time variation curves with fixed voltage level [2]. We choose to approximate the curves σ-е (stress-strain) at fixed time points corresponding to the ratio of how instantaneous deformation curves of the equation. For mathematical expressions experimental data dependences σ-е can be grouped as follows: diagram σ-е polymer samples obtained at different times, under different influences of aggressive actions and a particular voltage level; Creep curves; curves of long-term strength of the material; continuous curves from fracture limit strain fracture time for different operating conditions; Data on the longevity of the material in various conditions.

On the basis of the sharing of experimental data can be described to construct the generalized criteria limit the stress-strain state of the samples with the terms of destruction and cause a geometric interpretation of the stress-strain state at time t in the form of surfaces in the space of σ, е, t [3].

The equations of the kinetics of degradation are based on the premise that the degradation of the mechanical properties of ω - a process, not an instantaneous act, ie, function t, σ, ε (time, stress and strain) is not the value of w, and its speed:

                           dω/dt = F(σ, ε, ω, t, T˚, …).

 

Representing the equation of state in the form of the equations of state of a viscoelastic medium

                                               t

                                         (1)

                                              0

you can set the form of the function ω (t). Equation (1) - Volterra integral equation II- kind where e (t) and σ (t) - relative deformation and stress change over time; K (t-τ) - the core of transient creep, which, as experiments show, is well described, for example, the expression:

                                                 K(t-τ)=δe-δ1(t-t0) ,                     (2)
where δ, δ1 - creep parameters; determined by the results of tests of long polymer.
The results obtained in the criteria [3] have significant commonality caused integral dependence on the deformation history, and allow to evaluate viscoelasticity manifestation, long-term strength of materials, taking into account the impact of the load and the environment, based on the interconnected physically reasonable hypothesis of viscoelasticity and creep strength.

      References:

      1. Н. Ф. Морозов, Ю. В. Петров. Проблемы динамики разрушения твердых тел, СПб.: Изд-во СПбГУ, 1997. 

      2. Е. В. Ломакин, Т. А. Белякова, Ю. П. Зезин. Нелинейное вязкоупругое поведение наполненных эластомерных материалов, Изв. Сарат. ун-та. Сер. Математика. Механика. Информатика. Т.8, 2008, с.56-65

      3. И. Ф. Подкомарная, В.Ю. Артамонов. Определение длительной прочности материалов конструкций, Тр. межд. студ.конф. МНСК-50, Новосибирск, 2012.

Пальмов В. А. Определяющие уравнения термоупругих, термовязких и термопластических материалов. СПб.: Изд-во Политехн. ун-та, 2008.