Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments

Based on standpoints of the surface physics, fracture mechanics and electrochemistry, a mathematical model of the physical and chemical processes near the crack tip of a metal under mechanical loads in aqueous electrolyte solutions is developed. Calculations of the energy and electrochemical charact...

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Дата:	2017
Автори:	Yuzevych, V.M., Dzhala, R.M., Koman, B.P.
Формат:	Стаття
Мова:	English
Опубліковано:	Інститут металофізики ім. Г.В. Курдюмова НАН України 2017
Назва видання:	Металлофизика и новейшие технологии
Теми:	Металлические поверхности и плёнки
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/130471
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Цитувати:	Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments / V.M. Yuzevych, R.M. Dzhala, B.P. Koman // Металлофизика и новейшие технологии. — 2017. — Т. 39, № 12. — С. 1655-1667. — Бібліогр.: 16 назв. — англ.

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spelling	irk-123456789-1304712018-02-14T03:03:31Z Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments Yuzevych, V.M. Dzhala, R.M. Koman, B.P. Металлические поверхности и плёнки Based on standpoints of the surface physics, fracture mechanics and electrochemistry, a mathematical model of the physical and chemical processes near the crack tip of a metal under mechanical loads in aqueous electrolyte solutions is developed. Calculations of the energy and electrochemical characteristics are performed for the steel 20 in the 3% solution of sodium chloride. Parameters of the Tafel-type relationship between the anode current and the difference of electrode potentials are analysed. Well-known Kaeshe expression for the current density on the juvenile surface of a crack bottom is generalized both by linear approximation of the dependence of corrosion current density on surface energy of plastic deformation of the metal and with accounting for increase of mechanical tensile stress up to yield limit. Исходя из положений физики поверхности, механики разрушения и электрохимии сформулирована математическая модель физико-химических процессов в вершине трещины металла при его механическом нагружении в водном растворе электролита. Проведены расчёты энергетических и электрохимических характеристик для стали 20 в 3% растворе хлорида натрия. Проанализированы параметры уравнения типа Тафеля между анодным током и разницей электродных потенциалов. В линейном приближении связи плотности коррозионного тока с поверхностной энергией пластического деформирования металла и с учётом увеличения механических растягивающих напряжений до предела текучести обобщено известное соотношение (Kaeshe) для плотности тока на ювенильной поверхности дна трещины. З позицій фізики поверхні, механіки руйнування та електрохемії сформульовано математичний модель фізико-хемічних процесів у вершині тріщини металу при його механічному навантаженні у водному розчині електроліту. Проведено розрахунки енергетичних та електрохемічних характеристик для криці 20 у 3% розчині хлориду натрію. Проаналізовано параметри рівняння типу Тафелевого між анодним струмом і ріжницею електродних потенціялів. У лінійному наближенні зв’язку густини корозійного струму з поверхневою енергією пластичного деформування металу та з урахуванням зростання механічних розтягувальних напружень до границі плинности узагальнено відоме співвідношення (Kaeshe) для густини струму на ювенільній поверхні дна тріщини. 2017 Article Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments / V.M. Yuzevych, R.M. Dzhala, B.P. Koman // Металлофизика и новейшие технологии. — 2017. — Т. 39, № 12. — С. 1655-1667. — Бібліогр.: 16 назв. — англ. 1024-1809 PACS: 62.20.mt, 68.35.bd, 68.35.Gy, 68.35.Md, 81.40.Np, 81.65.Kn, 82.45.Bb DOI: doi.org/10.15407/mfint.39.12.1655 http://dspace.nbuv.gov.ua/handle/123456789/130471 en Металлофизика и новейшие технологии Інститут металофізики ім. Г.В. Курдюмова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Металлические поверхности и плёнки Металлические поверхности и плёнки
spellingShingle	Металлические поверхности и плёнки Металлические поверхности и плёнки Yuzevych, V.M. Dzhala, R.M. Koman, B.P. Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments Металлофизика и новейшие технологии
description	Based on standpoints of the surface physics, fracture mechanics and electrochemistry, a mathematical model of the physical and chemical processes near the crack tip of a metal under mechanical loads in aqueous electrolyte solutions is developed. Calculations of the energy and electrochemical characteristics are performed for the steel 20 in the 3% solution of sodium chloride. Parameters of the Tafel-type relationship between the anode current and the difference of electrode potentials are analysed. Well-known Kaeshe expression for the current density on the juvenile surface of a crack bottom is generalized both by linear approximation of the dependence of corrosion current density on surface energy of plastic deformation of the metal and with accounting for increase of mechanical tensile stress up to yield limit.
format	Article
author	Yuzevych, V.M. Dzhala, R.M. Koman, B.P.
author_facet	Yuzevych, V.M. Dzhala, R.M. Koman, B.P.
author_sort	Yuzevych, V.M.
title	Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments
title_short	Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments
title_full	Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments
title_fullStr	Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments
title_full_unstemmed	Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments
title_sort	analysis of metal corrosion under conditions of mechanical impacts and aggressive environments
publisher	Інститут металофізики ім. Г.В. Курдюмова НАН України
publishDate	2017
topic_facet	Металлические поверхности и плёнки
url	http://dspace.nbuv.gov.ua/handle/123456789/130471
citation_txt	Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments / V.M. Yuzevych, R.M. Dzhala, B.P. Koman // Металлофизика и новейшие технологии. — 2017. — Т. 39, № 12. — С. 1655-1667. — Бібліогр.: 16 назв. — англ.
series	Металлофизика и новейшие технологии
work_keys_str_mv	AT yuzevychvm analysisofmetalcorrosionunderconditionsofmechanicalimpactsandaggressiveenvironments AT dzhalarm analysisofmetalcorrosionunderconditionsofmechanicalimpactsandaggressiveenvironments AT komanbp analysisofmetalcorrosionunderconditionsofmechanicalimpactsandaggressiveenvironments
first_indexed	2025-07-09T13:39:45Z
last_indexed	2025-07-09T13:39:45Z
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fulltext	1655 МЕТАЛЛИЧЕСКИЕ ПОВЕРХНОСТИ И ПЛЁНКИ PACS numbers: 62.20.mt, 68.35.bd, 68.35.Gy, 68.35.Md, 81.40.Np, 81.65.Kn, 82.45.Bb Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments V. M. Yuzevych, R. M. Dzhala, and B. P. Koman* Karpenko Physico-Mechanical Institute, N.A.S. of Ukraine, 5 Naukova Str., UA-79060 Lviv, Ukraine Ivan Franko National University of Lviv, Faculty of Electronics and Computer Technologies, 1 Universytetska Str., UA-79000 Lviv, Ukraine Based on standpoints of the surface physics, fracture mechanics and electro- chemistry, a mathematical model of the physical and chemical processes near the crack tip of a metal under mechanical loads in aqueous electrolyte solu- tions is developed. Calculations of the energy and electrochemical character- istics are performed for the steel 20 in the 3% solution of sodium chloride. Parameters of the Tafel-type relationship between the anode current and the difference of electrode potentials are analysed. Well-known Kaeshe expres- sion for the current density on the juvenile surface of a crack bottom is gen- eralized both by linear approximation of the dependence of corrosion current density on surface energy of plastic deformation of the metal and with ac- counting for increase of mechanical tensile stress up to yield limit. Key words: metal, crack, juvenile surface, mechanical tension, electrochemi- cal overpotential, surface energy, corrosive current. З позицій фізики поверхні, механіки руйнування та електрохемії сфор- мульовано математичний модель фізико-хемічних процесів у вершині тріщини металу при його механічному навантаженні у водному розчині електроліту. Проведено розрахунки енергетичних та електрохемічних характеристик для криці 20 у 3% розчині хлориду натрію. Проаналізова- Corresponding author: Bohdan Petrovich Koman E-mail: sonce_28@ukr.net Please cite this article as: V. M. Yuzevych, R. M. Dzhala, and B. P. Koman, Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments, Metallofiz. Noveishie Tekhnol., 39, No. 12: 1655–1667 (2017), DOI: 10.15407/mfint.39.12.1655. Ìåòàëëîôèç. íîâåéøèå òåõíîë. / Metallofiz. Noveishie Tekhnol. 2017, т. 39, № 12, сс. 1655–1667 / DOI: 10.15407/mfint.39.12.1655 Îòòèñêè äîñòóïíû íåïîñðåäñòâåííî îò èçäàòåëÿ Ôîòîêîïèðîâàíèå ðàçðåøåíî òîëüêî â ñîîòâåòñòâèè ñ ëèöåíçèåé 2017 ÈÌÔ (Èíñòèòóò ìåòàëëîôèçèêè èì. Ã. Â. Êóðäþìîâà ÍÀÍ Óêðàèíû) Íàïå÷àòàíî â Óêðàèíå. https://www.multitran.ru/c/M.exe?t=437966_1_2&s1=%EC%E5%F5%E0%ED%E8%EA%E0%20%F0%E0%E7%F0%F3%F8%E5%ED%E8%FF https://doi.org/10.15407/mfint.39.12.1655 https://doi.org/10.15407/mfint.39.12.1655 1656 V. M. YUZEVYCH, R. M. DZHALA, and B. P. KOMAN но параметри рівняння типу Тафелевого між анодним струмом і ріжни- цею електродних потенціялів. У лінійному наближенні зв’язку густини корозійного струму з поверхневою енергією пластичного деформування металу та з урахуванням зростання механічних розтягувальних напру- жень до границі плинности узагальнено відоме співвідношення (Kaeshe) для густини струму на ювенільній поверхні дна тріщини. Ключові слова: метал, тріщина, ювенільна поверхня, механічне напружен- ня, електрохемічне перенапруження, поверхнева енергія, корозійний струм. Исходя из положений физики поверхности, механики разрушения и электрохимии сформулирована математическая модель физико-химичес- ких процессов в вершине трещины металла при его механическом нагру- жении в водном растворе электролита. Проведены расчёты энергетиче- ских и электрохимических характеристик для стали 20 в 3% растворе хлорида натрия. Проанализированы параметры уравнения типа Тафеля между анодным током и разницей электродных потенциалов. В линейном приближении связи плотности коррозионного тока с поверхностной энер- гией пластического деформирования металла и с учётом увеличения ме- ханических растягивающих напряжений до предела текучести обобщено известное соотношение (Kaeshe) для плотности тока на ювенильной по- верхности дна трещины. Ключевые слова: металл, трещина, ювенильная поверхность, механиче- ское напряжение, электрохимическое перенапряжение, поверхностная энергия, коррозионный ток. (Received November 10, 2017) 1. INTRODUCTION It has been established that physical and chemical description of corro- sion process on surfaces of metal constructions as a stationary process of oxidation with formation of passivating films on the metal surface does not reflect adequately the whole complexity of degradation pro- cesses in metals [1–3]. In particular, real technical system is normally operated under conditions of aggressive environments and mechanical fields (stress corrosion [4, 5]) followed by formation of cavities, corro- sion pits and cracks, and their growth. Thus, corrosion processes in such objects should be treated comprehensively with taking into ac- count the mechanical factor and probable electrochemical processes. In another words, the corrosion as by its essence is an electrochemical process with formation of new surfaces and developed cracking. The paper is concerned with an impact of external corrosive envi- ronment and mechanical loading on variations in mechanical and elec- trochemical parameters characterizing corrosion current in the crack tip under mechanical loading within zero to yield limit T of a metal. This study aims to analyse macroscopic relationships of surface phys- ANALYSIS OF CORROSION UNDER CONDITIONS OF MECHANICAL IMPACTS 1657 ics, destruction mechanics, and electrochemistry to establish relation- ships between energy variations and plastic deformation of the surface, overpotential of anodic reaction for a -wide juvenile surface (JS) (of the width ), and electric current in the crack tip at the boundary of elas- tically deformed metal and ambient corrosive environment. 2. OBJECT OF STUDY AND MATHEMATICAL MODEL The object of study is a loaded metal with a crack on its surface in aqueous electrolyte solution. Passive films presented on the surface are destroyed at the crack tip under loading, and the wide JS and plastic deformation zone appear [3]. The said juvenile surface is the just formed surface of a metal, free of oxides and other contaminations [3, 4]. In the first approximation, we treat the geometric parameter at the crack tip as its opening dis- placement 1С. The crack tip and the JS in particular extend into the body volume. Near the crack tip, the cathode and anode reactions take place. Corrosive dissolution corresponds to the metal anode reaction. We address the crack tip as an anode (A), beyond it on the side surfaces there is the cathode region (K) [4]. The ‘А–K’ system forms an electro- chemical couple. To obtain quantitative assessment of impact of aggressive environ- ment on energy characteristics of surface layers, we use analytical ex- pressions, which connect cracking parameters and intensity of electro- chemical reactions in the cracks vicinity. The stress intensity coefficient (SIC) K1SCC [Pa m1/2] relates to the crack tip opening displacement 1С and overpotential of the metal dis- solution reaction by relationships [3, 6, 7] (here, the overpotential means deviation of the electrode potential from its equilibrium ther- modynamic value during live electrode polarization [8, 9]): 2 1SCC pL si 1SCC 1C ( / ) /(1 ), , T K W z F M E K E (1) where zsi—formal charge of solvated ions, F—the Faraday constant, —width of approaching micro crack front [m], М—molecular mass of a metal [g/mole], K1SCC—threshold value of the SIC (minimal value cor- responding to onset of the corrosive crack propagation), WpL—specific energy spent for plastic deformation of the subsurface level when new (juvenile) surface is formed in it, E and —elastic modulus and Pois- son’s coefficient, respectively, T—yield limit of metal. Parameter WpL can be found in well-known Griffith–Irwin–Orowan relationship (the strength criterion) [10]: 2 pL * pL 4 /[ (1 )], 4 /( ), T T EW L EW L (2) https://www.multitran.ru/c/M.exe?t=4794_1_2&s1=%EA%EE%EB%E8%F7%E5%F1%F2%E2%E5%ED%ED%FB%E9 1658 V. M. YUZEVYCH, R. M. DZHALA, and B. P. KOMAN where LT—length of the crack. Here in formulae (2), first formula is written for a plane defor- mation, second one—for a plane stressed state, —critical stress, WpL J/2, J—the Rice’s integral having energetic meaning [11]. In paper [9], empirical relationship linking the SIC to the WpL has been established based upon the study of contact deformation of dif- ferent steel brands: 1/2 8 1/2 1SCC 1 pL 2 1 2 N , 2.26 10 , 6.98MPa m . m K a W a a a (3) The Kaeshe relationship for the current density Ias at the crack tip complements the model [4]: ak as , ln([ ]/ ) I h c r (4) where —angle at the crack tip, —electric conductivity of electro- lyte, ak—ohmic variation of potential between anode and cathode sections (anode—a tip, cathode—edges of a crack), с—crack depth, h c r—total depth of defect (cavity and crack), h—depth of cavity, r—curvature radius at the crack tip. Expression (4) was written for a crack in unloaded metal. However, to operate elements of real constructions like pipelines, one needs to take into account conditions of corrosion under loading (stress corro- sion) [12]. Therefore, it is necessary to modify expression (4) by adding mechanical parameters. For this purpose, let us consider a model of cylindrical pipe of radius R and wall thickness d, having aforementioned defects and being in conditions of aggressive environment (Fig. 1). Let us assume that the metal is in an electrolyte solution and has a surface defect in form of the cavity with a crack at its tip. Figure 2 Fig. 1. Element of pipe with cavity (h) and crack (с) under impact of internal pressure p in corrosive environment. ANALYSIS OF CORROSION UNDER CONDITIONS OF MECHANICAL IMPACTS 1659 shows projection of it on the xOy plane. External corrosive environ- ment (in both the cavern and the crack) is an aqueous electrolyte solu- tion. Under impact of mechanical load (uniaxial tension in the direction of the Oy axis with corresponding stresses y), destruction of passive films at the crack tip occurs and the JS of width and length L is formed as well as the region of plastic deformations when yy T ( T—material yield limit). We model projection of the JS by a semicircle r (Fig. 2). The crack tip and the JS extend into the body volume in the direction of the x-axis toward the pipe centre almost perpendicularly to the boundary. Near the crack tip, the cathode and anode electrochemical reactions take place characterizing corrosion process of the metal dis- solution. We consider the crack tip as an anode (A), and beyond its lim- its on the side surfaces, there is the cathode region (K). The ‘А–K’ sys- tem forms an electrochemical couple (Fig. 2). In the first approximation, we assume that the empirical relation- ship between the crack opening displacement 1С and geometric param- eter characterizing the JS width holds true 1C , and corresponding value of the empirical constant 1. In paper [9], relationship (4) is generalized by accounting for the WpL and internal pressure pcr acting upon the cylindrical pipe: Fig. 2. A cavity (h) with a crack (c) in a pipe with markings of cathode (K) and anode (А) sections. Total depth of the defect h c r; , 1C—angle and the crack tip opening displacement, ak—difference of potentials between the anode and cathode sections, Ia—density of anode corrosive current. 1660 V. M. YUZEVYCH, R. M. DZHALA, and B. P. KOMAN ak a as pL pL (1 ) (1 ), ln( / ) W W I I W W c (5) 4 0 cr 4 2 2 4 t 0 0 0 0 (1.5 )( )2 2 , 3 ( ) 0.5 ( ) zT K r cd p K D r c r r c r (6) where 1 3 1 0 0 0 01 3 1 0 t 11 0 2( ) 3 , , 2 3 ( ) 1 z W d c r r r rd c d K d c r K d cd c r Kt (2.021 1.301 0.727 2 0.147 3)d(d1 c)—the notch sensitivi- ty index, whose procedure of calculation is presented in [13], W— empirical coefficient of proportionality, r—radius of curvature at the crack tip, r0—critical value of r when plastic deformations occur at the crack tip. The critical pressure (6) corresponds to a condition of reaching lim- iting, plastic, state according to the Huber–Mises–Hencky yield crite- rion [12]: 2 2 2 /3, / (2 ), / (2 ), y z y z T y z pD d p D d (7) where T—yield limit of the pipe metal, x, y, z—rectangular Cartesian coordinates, p—internal pressure inside the pipe. In the relationships (7), we took into account for the mechanical stresses tensor y yy and for z that the pipe thickness d is considera- bly less than diameter D. Relationships (1)–(7) compose a mathematical model for assessment of changes in the effective surface energy during plastic deformation, elec- trochemical overpotential and in the current density of the metal disso- lution reaction at the crack tip on the metal surface during its loading in aqueous electrolyte solution (i.e. under conditions of stress corrosion). 3. BEHAVIOUR OF ENERGY AND ELECTROCHEMICAL PARAMETERS 3.1. Accounting for a Resistive Layer The specific of cracking in electrolyte solution is emergence of a ‘resis- tive layer’ (RL) of the HL thick and with practically dry its surface [14]. It is called a layer of complete hydration (solvation). Resistance of the RL is larger than the resistance of the diluted solution by 2–3 orders of magnitude [14]. Over time, when crack resides in the electrolyte, its thickness increases. ANALYSIS OF CORROSION UNDER CONDITIONS OF MECHANICAL IMPACTS 1661 Let r(t), (t) be radius vectors of internal and external surfaces of the RL, correspondingly; (t) 2 2(t), (t) 2 r2(t)—areas of internal and external surfaces of the RL, which we assume to be concentric hemispheres. In vector form, with accounting for spherical symmetry, relation- ships for the HL will be L ( ) ( ).t tH r (8) Motion of surfaces (t), (t) with radii r(t), (t) is defined by the re- lationship [14]: a si si ( ) , ( ) . M M t z F t z F r I I (9) Here, Ia( ), I ( ) are densities of currents outflowing from these sur- faces and depending on coordinates of the points, zsi—valence, — density of material, M—molar mass. The dissolution current of the crack bottom ia( ) ia( , cas, cbs) de- pends on threshold concentrations of activated ions cas, aqueous sol- vent cbs and polarization of the metal. Polarization ( ) of the metal is connected with anode potential by relationship [14]: a rs 0 ( , ) ( , ) ( ),r r r (10) where rs( , r), 0(r)—ohmic potential drops in the volume of the RL. Losses in the electrolyte are relatively small. In the first approximation, for the radius change, it is possible to use formula following from considerations of spherical symmetry and accounting for the Faraday law [14]: 1/3 3 ( ) . 2 IMt r t zF (11) 3.2. Calculation of the Change in Effective Energy and Overpotential at the Crack Tip For the steel 20 (T 20 C and p 100 kPa), physical and mechanical characteristics are as follow [15, 16]: zsi 2, E 213 GPa, T 245 МPa, 0.3, 7860 kg/m3. (12) With using (1)–(3), (12) and numerical data of paper [3], we obtain 1662 V. M. YUZEVYCH, R. M. DZHALA, and B. P. KOMAN changes in effective energy during plastic deformation of the metal subsurface layer WpL f1( / T) and overpotential of anodic dissolution reaction f2( / T). Results corresponding to calculations of these de- pendences are presented in Fig. 3. One can see from the dependences of Fig. 3 that the effective surface energy WpL during plastic deformation grows by 9.5 times, and the overpotential decreases by 40 times. These changes can be assessed quantitatively by the difference of maximal and minimal values at- tributed to their mean value: pL max pL min max min 1 2 pL max pL min max min 2 1.62, 2 1.90. W W w w W W (13) 3.3. Calculation of Electrochemical Parameters To assess impact of tensile stresses on intensity of corrosion processes in the steel 20 residing in the 3% NaCl solution, in particular, at the crack tip at the moment of passive films’ destruction (when anode cur- rent ia considerably grows), we will use experimental data [3] approxi- mated by the Tafel-type expression [3]: a 0 0 a exp( / ), ,I I DE a DE E E (14) where a—the Tafel parameter for anode process. Fig. 3. Dependences of surface energy of plastic deformation WpL( / T) [J/m2] (1) and overpotential ( / T) [mV] (2) within the range of mechanical tensile stresses / T 0–1 for the steel 20 in the 3% NaCl solution. ANALYSIS OF CORROSION UNDER CONDITIONS OF MECHANICAL IMPACTS 1663 By these data, we calculate values of the DE and a, presented in Fig. 4. Minimal values of the DE( / T) and f4( / T) determined by the data of Fig. 4 are DEmin 156 mV when / T 0.8 and a 38.6 mV when / T 0.39, correspondingly. Because DEmax 177 mV when / T 0 and amax 43.1 mV when / T 1.0, then we obtain the relative variations of the parameters: max min max min 3 4 max min max min 2 0.126, 2 0.110. DE DE a a w w DE DE a a (15) By comparing expressions (13) and (15), it is evident that the rela- tive variations of the effective energy and overpotential during in- crease of mechanical stress are considerable larger than the relative variations in the Tafel equation. Comparison of data of Figs. 3 and 4 allows to state that there is no corre- lation between the WpL, on the one hand and the DE, a( / T) on the other. At the same time, in Fig. 3, we can allocate three ranges of the / T variation. In the first range ( / T 0–0.16), DE and a are decreased. In the second range ( / T 0.16–0.84), parameters DE and a are changed insignificantly. In the third one ( / T 0.84–1), they grow considerably. Assessments of the said parameters can be indicative of changes of the electrode reaction type on the JS. 3.4. Generalization of Relationship between Electric Voltage and Current at the Crack Tip with Accounting for Mechanical Stress Let us use experimental dependences [3] of current density ia for the steel 20 in corrosive environment with different values of crack open- Fig. 4. Dependences of the electrode potential difference DE( / T) [mV] (1) and the Tafel coefficient a( / T) [mV] (2) of the relative tensile stress within the range of / 0.2 0–1 for the steel 20 in the 3% NaCl solution. 1664 V. M. YUZEVYCH, R. M. DZHALA, and B. P. KOMAN ing displacement 1С for stresses / T 0–1. From dependences pre- sented, ia f(lg 1С) and ia f( / T), one can see that until / T 0.59 ( 1С 1.9 m), density of anode current practically does not change, but after / T 0.59, the ia grows nonlinearly. Results of calculations by the LS-method has shown that dependence of the plastic deformation energy WpL on the ia (ia f5(WpL)) after / T 0.59 is practically linear (Fig. 5). With considering the data of [3], for expression (5), we have: Ias 19.86 A/m2, W 0.0000843 m 2/J (WpL 1400–5456 J/m2). (16) With accounting for the approximation (6) with respect to E0, Ea [3], which contains the surface layer energetic characteristic, WpL, we gen- eralize well-known relationship (Kaeshe) (4) for the current density at the crack tip: / /ak a as pL pL (1 ) (1 ). ln( / ) DE a DE a W W I I e W e W c (17) Expression (17) describes dependence of the anodic dissolution current on electrochemical characteristics of the crack tip , ak, DE, a, the ge- ometric , , c, and the effective energy of plastic deformation WpL. Let us consider an example of a pipe made of the pipe steel X-70. Ac- cording to [3], the limiting value of the crack critical depth сcrg 3 mm is the criterial one. Let us set following parameters: Р 5 MPa 50 atm, h 4 mm, d 10 mm, d1 6 mm, Fig. 5. Dependence of anodic dissolution current ia [A/m2] on the plastic de- formation energy WpL [J/m2] within the range of / T 0.59–1 for the steel 20 in corrosive environment. ANALYSIS OF CORROSION UNDER CONDITIONS OF MECHANICAL IMPACTS 1665 D 2R 0.76 m, 372 MPa, * cr 9.3MPa.p (18) With accounting for (12), (19) by means of (6), we obtain: сcr0 1.52 mm. (19) Here, сcr0—initial value of the crack critical depth when condition of plasticity holds true at the crack tip. Then, the crack expands from сcr0 to сcrg due to corrosion (anodic dissolution). Let initial condition for anodic current is: a 0 mm 1 for 0.3 mm. year I c (20) With taking into account data [3], information in Figs. 1–3, and re- lationships (8)–(11), (17)–(20), we obtain the dependence Ia Ia(c) (Fig. 6) and assessment for a pipeline resource (Table 1) for three options of the corrosion initial speed. 4. CONCLUSIONS Fig. 6. Dependence of the corrosion current ia on the crack length с. TABLE 1. A pipeline resource. Option Corrosive rate, mm/year The time of achieving a crack of critical depth of 0.7d over the years (17), years 1 0.3 8.9 2 1.0 2.6 3 1.5 1.8 1666 V. M. YUZEVYCH, R. M. DZHALA, and B. P. KOMAN A mathematical model based on standpoints of the surface physics and electrochemistry was expanded for assessment of the surface energy of plastic deformation, overpotential and current density for the reaction of metal dissolution at the tip of crack for loaded metal in aqueous electro- lyte solution. Dissolution of metal on the juvenile surface has been treated with accounting for the coefficient of stresses intensity. The Kaeshe rela- tionship for current density at the crack tip for loaded metal under uniax- ial tension has been generalized with accounting for the WpL. Based on analysis of dependences among the surface energy of plastic deformation, WpL, the anode energy overpotential, , and the load (with stress / T), it is found that, within the range of variation of tensile stresses from zero to the yield limit for the steel 20 in the 3% NaCl so- lution, the WpL grows by 9.5 times, and the decreases by 40 times. Dependences of the electrode potential difference DE and coeffi- cient a in the Tafel-type equation on the relative tensile stress / T 0–1 for the steel 20 in 3% NaCl solution were calculated. Based upon these dependences, we obtained information on changes in the character of electrode reactions on the juvenile surface. The proposed technic of study of the energetic and electrochemical parameters of the stress-deformed state of metal pipe structures can be used for assessment of a number of physical and mechanical parame- ters of the corroding technical system (a pipeline), necessary to in- crease its service life. REFERENCES 1. A. Philip and P. E. Schweitzer, Fundamentals of Corrosion—Mechanisms, Causes and Preventative Methods (Boka Raton: CRC Press: 2010). 2. A. J. Bard and L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications (New York: Wiley: 2001). 3. I. M. Dmytrak and V. V. Panasyuk, Influence of Corrosive Media on the Local Destruction of Metals near Stress Concentrators (Lviv: FMI: 1999) (in Ukrainian). 4. H. Kaeshe, Die Korrosion der Metalle. Physikalisch–Chemische Prinzipien und Aktuelle Probleme (Berlin–Heidenberg–New York: Springer-Verlag: 1979). 5. V. P. Astakhov, Tribology in Manufacturing Technology (New York: Springer: 2013), p. 1. 6. T. K. Christman, Corrosion, 46, No. 6: 450 (1990). 7. D. A. Horner, B. J. Connolly, S. Zhou, L. Crocker, and A. Turnbull, Corrosion Science, 53, No. 11: 3466 (2011). 8. A New Directory of Chemist and Technologist. Electrode Processes. Chemical Kinetics and Diffusion. Colloid Chemistry (Ed. S. A. 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Popov, and Yu. V. Alekseev, Itogi Nauki i Tekhniki. Ser. Corrosion and Corrosion Protection, 9: 88 (1982) (in Russian). 15. Tables of Physical Quantities. Reference Book (Ed. I. K. Kikoin) (Moscow: Atomizdat: 1976) (in Russian). 16. G. Dieter, Mechanical Metallurgy (New York: McGraw-Hill: 1986). https://doi.org/10.1016/0022-5096(77)90003-5 https://doi.org/10.1016/0022-5096(77)90003-5 https://doi.org/10.1115/1.3601206

Analysis of Metal Corrosion under Conditions of Mechanical Impacts and Aggressive Environments

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