08 / 26 / 2011 - 12:14 — viktoriya

**УДК 539.3**

** DEPENDING ON THE PROPERTIES OF STRUCTURAL ELEMENTS OF TIME AND COORDINATES OF THE STATE SPACE**

**Artamonova Elena Nikolaevna, D-r of Techn. Sciences, Professor Saratov State Technical University**

*To describe the strain state and fracture in the framework of a generalized model of vickoelasticity is necessary to consider the history of deformation of the sample. Кеу words: vickoelasticity, deformation, mehanicheskie properties, degradatio*n.

In assessing the reliability of strength design must address the long-term strength ( or static fatigue)-the decline of strength of materials over time under the load.The phenomenon of longterm strength inherent in all materials , but essentially manifested dangerous when changes in physical and mechanical properties of the material with time(creep,corrosive media).If there are currently a large number of physical relationships creep theory,theory,describing the interactions of structural elements with aggressive media , in their infancy. These theories in accordance with the accepted model of the material - a model of a continuous medium - used a phenomenological approach, i.e internal microstructure of the material is not studied.

This approach allows us to construct mathematical equations, which even in the absence of clarity in fact occurring in the material complex internal processes , that well reflect their external manifestations in the range of variation of process parameters , which conducted an experimental study of the mechanical properties of the material.

To determine the conditions of structural strength during the period of operation necessary know the strength characteristics of the material design.The basis for the construction of theories of long -term strength is the long -term strength curve that relates the time of destruction with the value of a permanent as well σ.Effect of long-term strength is manifested in the exhaustion of the store strength with time,which can be explained damage accumulation during deformation,which lead to the appearance of cracks to fracture even at relatively small deformations.

As is known,for example,from [2], the physical process of destruction of materials can be divided into three stages:

1 - stage scattered destruction , during which the accumulation of microdamage, ending with the formation of macroscopic cracks;

2 - stage developed cracks;

3 - stage destruction (intensive growth of main crack).

In engineering calculations on the strength of structural elements that do not have defects in the form of surface sinks,foreign inclusions,etc.,usually based on the assumption that the appearance main crack is equivalent to the total destruction , and for the ultimate resistance of the material considered only the stage - the process of accumulation of scattered damages. The accumulation of damage has an impact on physical and mechanical properties of the material , so the degree of accumulated damage can be introduced into the equation of state.In the simplest case to describe the extent of accumulated damage parameter is introduced ω [1,2]. In this paper, some results of studies in the calculation of longterm strength of structural elements of the nonlinear viscoelastic materials under various operating conditions on the basis of determine the extent of accumulated damage. It solved at least two problems: the need to describe the change in the stress- strain state of the material in time and build strength criteria for structures made of material . Consider the well - known from the literature scattered data macroscopic experiments that characterize the deformation of the polymer up to fracture at the main types of loading ( tension , compression , shear),the basic modes (constant and variable strain rates, creep), in natural conditions and under the influence of the active medium.

Under these conditions , can be obtained by a set of features, allowing to set the fracture, the influence of the parameters of the material at his trial,particularly the destruction of polymer, is more complicated than the processes associated with the destruction of usual materials . The most important characteristic of polymers is their deformability, the most important information about the deformation of materials under different operating conditions of the diagrams σ - ε . Analysis of experimental data [ 3 ] suggests characteristics of the temperature dependence of relaxation processes and fracture for elastic- polymers with the same energy value activation for each material.

Both aspects of the strength of polymers ( short - term and long - term loading ) depend on the local structural changes that primarily can be linked with the process of accumulation of damage,education grid hairline cracks.Combining different approaches to describing these both processes,i.e.formulation of general theory of deformation and fracture of polymers depends on the study of the relationship of deformation , destruction and voltage , temperature, aggressive factors in the whole time interval of operation of the element . Relaxation properties influence the process of destruction , enhancing the growth of microdamage. This is explained by the fact, that in the this process of development forced highly elastic deformation near the damage is mechanical energy into heat [ 4 ]. Influenced by aggressive actions are subject to change and constant material properties,for example, [ 2 ] gives numerical data elastic modulus E of nylon moisture C %, and placed table with numeric data , reflecting the change in elastic modulus polypropylene in solutions of different concentrations. In [ 2 ] systematized experimental data on the rate of decline over time and changes in concentration among the moduli of elasticity and durability of materials in various environments.Change the modules reflects the interaction of the relaxation and elastic processes determining the details of the mechanical behavior.

Experimental data [ 2 ] on creep of polymers show an acceleration processes of creep with increasing stress and concentration of the medium . However , the hostile environment is distributed over the volume of the material unevenly , and data on changes in the mechanical characteristics are approximate,the most suitable for comparing resistance of various materials in the same conditions. An examination of these experimental data one can draw conclusions that should be taken into account when constructing the conditions of fracture:

1. Mehanicheskie properties and the process of destruction of polymer materials substantially

depend on time and operating conditions.

2. Destruction is a two -stage process. At the first stage of degradation of the properties of the material , the accumulation of damage , microcracks occur. The stage ends at a time when the merger of microdamage formed macroscopic crack . This moment is short - lived and by their physical nature is a loss of stability of equilibrium microdefects [1].

3. At failure, the material from corrosion or silent creep value of the first stage is so large,that the evaluation time of destruction the destruction process can be generally described as the[1] accumulation of damage and degradation properties of plastic.

4. Given the irreversibility of the process of destruction is determined not only the current [3] values of parameters characterizing it, but the entire prior history of these parameters.

5. Because of the private nature of the experimental data on the effect of environment on the construction of the general behavior of plastic materials for materials the phenomenological description of fracture, based on mechanical performances due to the difficulties and serious shortcomings. It is therefore necessary and molecular interpretation of macroscopic changes in the material. Thus, the phenomenological theory of temporal dependence as would provide a common framework, which must fit the theory of material behavior, and that put a detailed mechanical theory of change of macroscopic and microscopic properties of the polymer. This need arises in the interpretation of the parameters of the phenomenological equation, allowing you to identify not only the common features, as well as the difference between the materials. 6. Because of significant time effects for polymers the process of their destruction [1 ] more difficult than traditional materials , the phenomenon of viscous and brittle fracture occur simultaneously.Fracture criterion in this case must take into account the achievement of the instantaneous and destructive values σ , ε at the moment t?, and their dependence on the development of degradation of material properties.

7. From the analysis of a number of stress-strain curves, it follows that when the ambiguity of physical and mechanical characteristics in the process of corrosive media on polymers some of their characteristics do not change or vary monotonically . For example, [ 2 ] for polyolefins yield stress σ? elongation at yield point ε? up to the brittle fracture remains practically unchanged , and the breaking stress , and tensile , elongation at break decrease, respectively , to yield strength and elongation at up to yield point . After this happens , the catastrophic decline in the strength of [2] . Based on the above dm highly elastic materials can be selected as the characteristic parameter , sufficiently sensitive to the degradation of its properties and responsible for the performance of the polymer , elongation at break, and as a stability criterion - elongation at yield point. This choice can be linked with molecular changes, since the limiting mutual distance of the molecules, which corresponds( ε?) to the mechanical characterist, attraction between them is weakened, there is a gap.

8.The degradation of physical and mechanical properties of the material over time the main influence of microstresses.

9. Degradation of material properties under the influence of stress and aggressive influence leads to a drop in voltage. Extrapolation of this dependence on the coordinate of the stress gives conditional equilibrium voltage ,which can be considered an equilibrium, relegated to the invariable initial state of the material, apply to it the thermodynamic relations.

**References:**

- 1.Moskvitin V.V. Cyclic loading cell konstruktsiy.-M.: Science, 1981.-344 S.
- 2.Euric F.G. Smith T.L. Molekulyar mechanical aspects damage elastomer insulated. //Destruction.-M.: World 1976.V.7.P.II. - S.104-390.
- 3.Gomenyu S.I.,GrebenyukS.N.,TarkhovaV.M.Space-time finite element to determine the viscoelastic materials VAT ./ /Problems computational mechanics and durability structures, is.14, 2010. - S.109-115.
- 4.PobedryaB.E.Numerical methods for solving boundary value problems in mechanics of composites and nanocomposites . / / Internat. scien. konfer. “ Modern problems of mathematics, mechanics and computer science.”: Tula, 2010.-S.193-194.

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## vickoelasticity