facebook
twitter
vk
instagram
linkedin
google+
tumblr
akademia
youtube
skype
mendeley
Wiki
Page translation
 

ON THE MODEL OF THE MECHANICAL BEHAVIOR OF ELEMENTS WHEN EXPOSED TO AGGRESSIVE ENVIRONMENTS

ON THE MODEL OF THE MECHANICAL BEHAVIOR OF ELEMENTS WHEN EXPOSED TO AGGRESSIVE ENVIRONMENTS
Elena Artamonova, professor, doctor of technical science, full professor

Svetlana Shatokhina, lecturer

Saratov State Technical University, Russia

Championship participant: the National Research Analytics Championship - "Russia";

The objective of this study is to the development of incremental model and methods of calculation of structural elements in situations actions of mechanical loads, viscoelasticity and  surrounding  aggressive environment.

Keywords: modulus of elasticityaggressive environment,stress, strain, chemical agents, degradation deformation

 

The development of methods of calculation taking that take into account the material to work in aggressive environmentsis the actual problem.

 It is known that under the influence of aggressive properties of material change, and this change is uneven in terms of products, design element or structure. Numerous experimental data indicate that the surface area of the product in direct contact with the aggressive material change of tensile strength, modulus of elasticity is more intense than in the depth of the product volume. But until now, all calculation methods in the analysis of the action of aggressive media in the design work as the fundamental design characteristics of strength, modulus of elasticity used data obtained by testing samples of material (prisms, cubes, cylinders), exposed to corrosive environments. The thus obtained integral estimates strength, elastic modulus does not reflect the actual operation of the product when exposed to an aggressive environment. In recent years, to study the properties of the material change processes under the influence of aggressive environment more widely used methods of micromechanical tests. They make it possible to accurately determine the mechanical characteristics of the material and changes in both time and volume of product.

 

                                                                                           

                                                             Fig.1. Example of the effect of the environment on building elements

 

Accounting for the real work of the material makes it possible for a new approach to the construction of computational models of structures, located under the combined action of mechanical stress and corrosive media, make an assessment of the durability of a more accurate and to improve operational safety of such products, structures. From the extensive bibliography presented [6], the article concluded that there is no development of structures under the influence of aggressive environments of the most general physical relations of the theory of viscoelasticity.

To eliminate this gap, in this paper, we will use as the most general - the equation of the state of viscoelasticity:            

                                                                                                                                                                                                                                                                                                  ,                                 (1)

where e(t)  and σ(t)–relative deformation and stress, time-varying; K(t,τ,ω)– core transient creep,Volterra integral operators, as experience shows, is well described by the expression: K(t)=δe-δ1(t),

where δ, δ1– creep parameters; determined by the results of sample testing. The law of change ω in time is usually is given by the kinetic equation.

The final result of interaction with an aggressive environment is the irreversible change in the microstructure and chemical composition of the material, leading, from the point of view of mechanics of the deformed body, to a change both in its deformative properties and in the strength properties of the structural element. In (1) to describe the residual strength, a parameter of the damage ω is introduced, depending on the characteristics of the medium, the material, and the stress state at the point in such a way that ω= 0 for the undamaged raw material and ω= 1 at the  is destroyed.  It is usually assumed that the design is destroyed when the parameter of the damage reaches the conditional limit value (unit) at least at one point. Although all parameters can be introduced formally, by assigning the corresponding kinetic equations that determine the time variation of the parameters, they are usually endowed with physical meaning. A separate problem is the definition of a specific type of kinetic equation (structural identification), as well as the specification of the values of the constants entering into these equation (parametric identification). The solution of the problem is based on the available a information on the physics of the processes that are taking place and depends to also extent on the art of the researcher [2].

The need to take corrosion into account, one way or another, is associated with the problem of determiningdurability of the structural element under the influence of workloads and media and, accordingly, with the problem of strength.

From the various approaches to the calculation of the effect of aggressive environment in application to loadable structures, the following is the most widely used in calculating the stress state and durability of loaded structures: the use of the theory of structural parameters based on the mechanics of a continuous deformed environment [4]. To the usual parameters of the latter, additional macroparameters reflecting the effect of corrosion are added.For incompressible material we have the following physical equation

                                                                                        (2)
where - deviator of deformations, - deviator strain, - secant modulus, take into account the viscoelastic properties according (1),  taking into account the level of concentration of the aggressive environment.

The impact of aggressive environment take into account by introducing the definition of secant modulus function, characterized by its degradation when exposed to aggressive environments     , where - secant material unit into contact with aggressive media, - the intensity of the strain, - intensity of deformations, K(т)-Volterra integral operators,F (B)- function secant modulus degradation satisfying the condition under: [1].

Under the influence of an aggressive environment (corrosive effect) is understood the process of gradual change (deterioration) of design parameters when surface contact with some liquid or gaseous medium. Characteristics of the corrosion process are determined mainly by the chemical composition of the pair of aggressive media - the material of the structure, the microstructure of the material surface, the temperature and the stress-strain state.

In order to build a model of incremental bending plate of viscoelastic material thickness hinteracting with aggressive environment, it is necessary to have incremental equations relating stress increments in increments of deformations. Such incremental physical relationships in the case of a plate bending problem are as follows:

 

                                        

 

where-the increment of stress caused by the increment of external influences, - the increment of linear and angular deformities, -tangent modulus after exposure to aggressive environment, - tangent modulus prior to contact with aggressive media,-the increment of aggressive media concentration.

Changing the concentration of aggressive environment on the thickness of the damaged layer is determined from the solution of mass transfer equation. The concentration of the working environment on the surface of the material .This denote the value assumed to be constant throughout the period of the interaction of the material with aggressive environment. - the concentration of aggressive environment at any point of the plate material, - the depth of penetration of aggressive environment in the thickness of the material. With these designations concentration of aggressive environment at any point will be considered as a function of the thickness of the layer of corrosion damage . In view of the smallness of the thickness of the damaged layer, although this is not essential, we believe, that the concentration of the corrosive environment varies according to the law of the triangle. Obviously, this a solution with durability.

Assuming a fair hypothesis Kirchhoff, write the deformation in the middle plane of the plate by the deflection and strain increment, respectively, by the increment of deflection :

                          

The incremental equation of equilibrium of the middle plane of the plate element is of the form:

                                    (3)

We get:

                         (4)

 

                       

 

Substituting (4) into equation (3) we obtain the equation given a plate bending aggressive environment exposure

 

               (5)

 

- "fictitious " load, depending on the time, reflecting the effects of creep and aggressive environment:

                          

Numerical realization of the equation (5) is made in two stages. The first of them is done step by step loading of the plate to a predetermined load level.At the same time, sequentially solving the equations of the form (5) with the load  . At the second stage settlement of the deformed scheme of the achieved level of loading load. The sequential increase in the damaged layer thickness of the plate deflection increases. At this stage, successively increasing layer thickness of the affected aggressive environment, solve the equation with the load .

Numerical realization of the plate bending equations in two stages. The first step is a step by step up to the plate loading a given load level. And the second - make a step by step calculation of the time t. Used Vlasov-Kantorovich method, according to which at each stage of the load deflection increment plates looking as the product of two functions, each of which depends only on one variable where the approximating function φ (y) must satisfy the given boundary conditions.

Modules in the damaged area and change from initial values at the boundary of these modules front degradation to the smallest (on the sample surface). To account for the degradation of material properties, modules take the form:

  .                               

Experimental studies of polymer allowed to write a function in the form of degradation:

                                                  ,

 χ-experimental factor characterizing the degree of degradation of the material index of the material.

,ie in the absence of aggressive environment secant modulus degradation does not occur. The increment of the concentration of aggressive environment at any point corroded plate layer calculated by the formula .

We must have an analytical expression of the stress-strain curve to determine the state of a variable stiffness. Instant curve can be approximated by a cubic parabola

                                                                                    

Thus, the decision of the plate bending problem of nonlinear viscoelastic material in view of corrosion processes caused by the action of aggressive environment consists of two stages. At the first stage the solution is reduced to the solution of multiple linear integro-differential equation whose coefficients are recalculated after each stage of loading. Solutions is continued until the predetermined load value.

In the second stage, which takes into account the impact of aggressive environment, the decision comes down to solving multiple linear equation whose right-hand side  rates are adjusted after each offset by the amount of degradation of the Δδ. Process solutions continues until it reaches the stress in the plate dangerous values.

Having chosen the model of motion of the degradation front, it is possible to set the time and longevity when the plate voltage reaches dangerous levels.

 

References:

  • 1. Petrov V.V,  Penina O.V, Selyaev P.V. Plates calculation of nonlinear deformable material with an arbitrary deformation diagram for the effects of aggressive operational environment// Academia. 2008. №3. –P. 87–92.
  • 2. Artamonova E.N. Relations in viscoelasticity // София: БялГРАД-БГ. 2016.–P.71–79.
  • 3. Khelif R., Chateauneuf A, Chaoui K. Reliability-based assessment of polyethylene pipe creep lifetime// Int. J. Pres. Ves. Pip., 84 (12). 2009. – P. 697–707.
  • 4. Овчинников И.Г., Почтман Ю.М. Тонкостенные конструкции в условиях коррозионного износа. Расчет и оптимизация. // Днепропетровск: изд-во ДГУ. 1997. –С. 192.
  • 5. Зеленцов Д.Г. Напіваналітичні алгоритми розв’язання систем диференціальних рівнянь у задачах довговічності кородуючих конструкцій // Комп‘ютерне моделювання в наукоємних технологіях. Праці міжнародної науково-технічної конференції (м. Харків, 26–31 травня 2016 р.). – Харків: ХНУ ім. В. Н. Каразіна, 2016. – С.
  • 153–155.
  • 6. Ovchinnikov I.I. and ot. Problem of optimum design of the loaded constructions which are exposed to influence of aggressive environments (review)//– Режим доступа: http://publ.naukovedenie.ru/PDF/109tvn412.pdf
0
Your rating: None Average: 9.5 (2 votes)
Comments: 4

Babayev Naqibullo Habibullayevich

Доклад авторов данной работы является очень интересной и представляет как фундаментальный, так и прикладное значение для науки. авторам работы следовало бы привести адекватности разработанной модели. Работу оцениваю оценкой 9 балов. елаю дальнейщих творческих успехов. С уважением д.т.н., проф. Накибулло Бабаев

Elena Artamonova

Уважаемый Накибулло Хабибуллаевич, благодарим за отзыв. В процессе проведения численных расчетов их результаты по напряженно-деформированному состоянию и долговечности элементов сопоставляются с экспериментальными, так у нас проводится проверка пригодности модели. Дальнейших успехов Вам в технике и философии!

Vladimir Karlov

Уважаемые авторы! На примере изгиба пластины с учетом воздействия агрессивной среды в докладе разработана строгая математическая модель, решение которой сведено к двух этапному численному решению нелинейного дифференциального уравнения второго порядка. Оценка доклада высокая. С уважением Владимир Карлов.

Elena Artamonova

Большое спасибо, уважаемый Владимир Анатольевич, за внимание к докладу и его оценку. Успехов!
Comments: 4

Babayev Naqibullo Habibullayevich

Доклад авторов данной работы является очень интересной и представляет как фундаментальный, так и прикладное значение для науки. авторам работы следовало бы привести адекватности разработанной модели. Работу оцениваю оценкой 9 балов. елаю дальнейщих творческих успехов. С уважением д.т.н., проф. Накибулло Бабаев

Elena Artamonova

Уважаемый Накибулло Хабибуллаевич, благодарим за отзыв. В процессе проведения численных расчетов их результаты по напряженно-деформированному состоянию и долговечности элементов сопоставляются с экспериментальными, так у нас проводится проверка пригодности модели. Дальнейших успехов Вам в технике и философии!

Vladimir Karlov

Уважаемые авторы! На примере изгиба пластины с учетом воздействия агрессивной среды в докладе разработана строгая математическая модель, решение которой сведено к двух этапному численному решению нелинейного дифференциального уравнения второго порядка. Оценка доклада высокая. С уважением Владимир Карлов.

Elena Artamonova

Большое спасибо, уважаемый Владимир Анатольевич, за внимание к докладу и его оценку. Успехов!
PARTNERS
 
 
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
image
Would you like to know all the news about GISAP project and be up to date of all news from GISAP? Register for free news right now and you will be receiving them on your e-mail right away as soon as they are published on GISAP portal.