mags LIERARY I {222111232} State Um: u‘sity K--. ._._ w ‘— This is to certify that the dissertation entitled EFFECT OF MULTI-FUNCTIONAL INHIBITORS ON THE ELECTROCHEMISTRY WITHIN A COR- ROSION CRACIéresemed by Hiroyuki Omura has been accepted towards fulfillment of the requirements for ph.D Metallurgy degree in Major professor Robert Surmitt Date é {1’99}er ’?&$/ MSU is an Affirmative Action/Equal Opportunity Institution 0-12771 MSU LIBRARIES “ RETURNING MATERIALS: Piace in book drop to remove this checkout from your record. FINES wiii be charged if book is returned after the date stamped below. EFFECT OF MULTI-FUNCTIONAL INHIBITORS ON THE ELECTROCHEMISTRY WITHIN A CORROSION CRACK By Hiroyuki Omura A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Metallurgy, Mechanics and Materials Science 1984 ABSTRACT EFFECT OF MULTI-FUNCTIONAL INHIBITORS ON THE ELECTROCHEMISTRY WITHIN A CORROSION CRACK BY Hiroyuki Omura The electrochemical and mass transport mechanisms in stress cor- rosion cracking, which depend on the rate of metal dissolution and production of hydrogen, have been used to establish analytically the electrode potential distribution within the crack. When crack growth occurs by enhanced anodic dissolution of the plastically strained tip, the electrode potential at the crack tip always is more active than at the crack mouth because of the electric potential gradient which exists in the electrolyte within the crack. This also gives rise to additional or alternate electrochemical reactions such as hydrogen evolution and anodic dissolution at the crack tip. Futhermore, because of the potential difference from the crack mouth, the electrochemical driving force becomes more favorable for the development of corrosion inside the crack. The analysis predicts the distribution of electrode potential within a crack, and theoretical results have been compared with experimental measurements recorded from a model electrode system. Under free corrosion, a small potential difference may cause a concentration change of Cl- ion and increase the chloride attack. In order to reduce the chloride and hydrogen attack, multifunctional inhibitors, such as borax-nitrite with small amounts of surfactant such as NET or amino-methyl-prOpanol, are excel- lent inhibitors. The surfactant interferes in the dissolution reaction and blocks active chloride ion and hydrogen ion by interacting synergistically with the passive film produced by the borax-nitrite, which results in de— velopment of a stronger and thicker protective film. ACKNOWLEDGMENT The author would like to express his deep gratitute and appeciation to his academic advisor, Dr. Robert Summitt whose guidance and assistance were invaluable throughout the authors graduate program and especially during the course of this investigation. Thanks are also due the other members of the authofs guidance committee, Dr. J. Martin, Dr. K. N. Subramanian and Dr. A. Timnick for their inspiration. Thanks are extended to U. 8. Air Force, Wright-Aeronautical Laboratories, NASA Lewis Research Center, U. S. Army Construction Engineering Research Laboratories, U. S. Office of Naval Research, the Department of Metallurgy, Mechanics and Materials Science,and the Division of Engineering Research at Michigan State University for the financial assistance rendered during the Doctoral program. ii TABLE OF CONTENTS Page LIST OF TABLES 00.00.000.00...OOOOOOOOOOOOOOOOOOOOOOOO iv LIST OF FIGURES .................. ....... ..... ....... . v I. INTRODUCTION .............................. 1 II. THEORETICAL BACKGROUND .................... 11 III. EXPERIMENTAL TEST PROCEDURE AND APPARATUS ................................. 25 IV. EXPERIMENTAL RESULTS ...................... 40 V. DISCUSSION ........... ........ .. .......... . 85 VI. CONCLUSION ......... ...... ................. 105 REFERENCES .00....0000.0.0..OOOOOOOOOOOOOOOOOOOOOOOC 108 iii Table LIST OF TABLES Page Chemical Analysis of Test Specimen ........ .................. 35 Mechanical Properties of 7075—T6 Al Alloy ... ................ 36 The Inhibitors and Surfactant ......... ....... ...... ......... 39 Chemical Composition of Tap Water .... ..... . ................. 47 iv LIST OF FIGURES Figure Page 1 Theoretical Electrochemical System with Two Oxidation- Reduction Reactions 0 O O O O C I O O O O C O O O O O O O O O O O O O O O O O O ..... O 17 2 Motion of Electrolyte ions in a Crack .......... ....... 22 3 Simplified Experimental System .... ..... . ..... . ........ 26 4 Bare Surface Specimen.................................. 29 5 A Modified Artificial Crevice.......................... 29 6 Block Diagram of Simplified Experimental System in Control EOperationOOOOOO0.00.0.0...00.0.00.........OOCOOOOOOOOO 31 7 Steady-State Open-Circuit Potential for 7075 T6 Al Alloy in 1.0 Wtoyo NaCl SOlutionOOOOOCOOO......IOOOIOOOOIOIOOO 33 8 Modified WOL-type Constant Deflection Specimen ........ 38 9 Anodic Polarization of 7075 T6 Al Alloy in Dilute Sodium Chloride Solution Without Stirring at 20°C : 2°C ....... 41 10 Cathodic Polarization of 7075 T6 A1 Alloy in 1 wt.% NaCl Solution Without Stirring at 20°C i 2°C ....... 42 ll Cathodic Polarization of 7075 T6 Al Alloy in 3 wt.% NaCl Solution Without Stirring at 20°C + 2 oC .......... 43 12 Anodic Polariztion of 7075 T6 A1 Alloy in Distilled Water Without Stirring at 20°C:2°C 45 13 Anodic Polarization of 7075 T6 Al Alloy in Tap Water Without Stirring at zooCizoC ....0.0.0..........OOOOOOOOOOOOO~ 46 14 Anodic Polarization of 7075 T6 Al Alloy in 1 wt.% NaCl and Inhibitor Without Stirring at 20°C i 2°C 43 15 Anodic Polarization of 7075 T6 Al Alloy in 1 wt.% NaCl and Inhibitor Without Stirring at 20°C 1 2°C ..... ...49 16 Anodic Polarization of 7075 T6 Al Alloy in 1 wt.% NaCl and Inhibitor Without Stirring at 20°C i 2°C .........51 Figure 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Anodic Polarization of 7075 T6 A1 Alloy in 1 wt.% NaCl and Inhibitor Without Stirring at 20°C -_i-_ 2°C Anodic Polarization of 7075 T6 A1 Alloy in 1 wt.% NaCl, Inhibitor and Surfactant without Stirring at 20°C i12°C Cathodic Polarization of 7075 T6 Al Alloy in 1 wt.% NaCl and Inhibitor Without Stirring at 20°C i 2°C .... Linear Polarization of 7075 T6 Al Alloy in 1 wt.% NaCl Under Various Condition Without Stirring at 20°C i 2°C Linear Polarization of 7075 T6 Al Alloy in 1 wt.% NaCl Without Stirring at 200C:20C ......OOOOOOOOOOOOOOO. Linear Polarization of 7075 T6 Al Alloy in 1 wt.Z NaCl Without Stirring at 200C120C .....IOOOOIOOOOOOOOOO Anodic Polarization of 7075 T6 A1 Alloy in 1 wt.% NaCl Under Stress Without Stirring at 20°C i 2°C ......... Anodic Polarization of 7075 T6 Alloy in Dilute NaCl SOlution 0..........000............OOOOOOOOOOOOOOOOOO Potential - pH Equilibrium Diagram for the System Aluminum - Water at 25°C .......................... Cathodic Polarization of 7075 T6 Al Alloy in 1 wt.% NaCl Solution and Crevice Without Stirring at 20°C 1 2°C Cathodic Polarization of 7075 T6 A1 Alloy in 3 wt.% NaCl Solution and Crevice Without Stirring at 20°C 1 2°C Steady - State Open - Circuit Potentials for Open and Crevice 7075 T6 Al Alloy in Dilute NaCl Solution With and Without Inhibitors .....OOOOOOOOOOOOOOIOOC0...... Steady - State Open - Circuit Potentials for Open and Crevice 7075 T6 A1 Alloy in Dilute NaCl Solution .... Anodic Polarization for Open and Crevice 7075 T6 Al Alloy in 1 wt.% NaCl Solution Without Stirring at 20°Ciz°c.. ..... . ..... ............. .. ....... vi Page 52 55 57 59 60 61 62 64 66 67 68 69 72 73 Figure . Page 31 Anodic Polarization for Various Condition of Crevice in Dilute Solution Without Stirring at 200C3t 2°C....... 74 32 Steady - State Open - Circuit Potential for Open and Coupled Crevice 7075 T6 Al Alloy in 1 wt.% NaCl Solution Without Stirring at 20°C :;2°C ......................... 77 33 Steady - State Open - Circuit Potential Difference for Open and Coupled Crevice 7075 T6 Al Alloy in 1 wt.Z NaCl SOlution .000.000.000.00...0.00.00.00.00...0.0.0.0000... 78 34 The Potential Difference for Open and Crevice 7075 T6 Al Alloy Under Active State in 1 wt.% NaCl Solution ........ 79 35 Steady - State Open - Circuit Potential Under Stress in 1 wt.% NaCl Solution .... ......... ....................... 82 36 Rate of Cracking Versus Stress Intensity for Dilute NaCl solution 0......00........................OOCIOOOOOOOOO 84 37 Schematic Representation of the Crack .................. 96 38 Schematic Polarization Diagram of the Electrochemical Reactions Occurring at the Specimen Surface Showing the Influence of Potentiostatic Polarization ............... 97 vii I. INTRODUCTION A. General Introduction This thesis describes an experimental investigation of the electro- chemical and mass transport behavior inside a crack, under both stressed and unstressed conditions, and in the presence of aqueous chloride ion. In order to investigate these corrosion processes, electrochemical cor- rosion methods have been found to be useful because these techniques ac- celerate the corrosion process and allow rate data to be obtained in a short time. Additionally, these techniques can be used to characterize the corrosion of alloys in specific environments. In this research, electrochemical potentiodynamic polarization techniques were used to determine (1) the electrochemical and mass transport mechanism of 7075 T6 A1 alloys between the external environment and the crack tip; (2) the relation between micro-electrochemistry and an external environment cont- rolled by an inhibitor; and (3) the relations between microchemistry at the crack tip and external chemistry in the presence of chloride ion. Generally, the results show that crevice corrosion of the aluminum alloy depends on the width of the crack, the difference between the rate of the process in the crevice and on an Open surface. The polarization behavior at the crack is different from the outer surface. Furthermore, intensive corrosion of aluminum alloys in a narrow crack is the result of a marked negative change of the potential. The value of the potential of aluminum inside the crack reaChes a certain. value which provides as well for the possible cause of the corrosion process because of the re- action of hydrogen evolution. Crevice corrosion leads to the formation of localized cells where the solution may attain very high ionic concentration. During the very initial stage of the formation of localized cells, the electric mass transport ( migration ) has been regarded as predominating over diffu- sion. The latter, on the contrary, mainly determines the concen- tration profile as soon as steady conditions of growth are reached. The transport number of the highly hydrated corrosion products is nearly zero and migration Should play a secondary role. It will be shown that high ionic concentration and especially halide enrichment, ionic migration, acidity because of hydrolysis, ionic solvation, and low water-to-iron ratio allow a more realistic picture of the electrochemistry of the localized cells to be obtained. A model is preposed for the combined effect of mass transfer, polar- ization on the current and potential profiles inside the crack. Further- more, a mathematical model has been extended which links several param- eters so that quantitative predictions can be made for crack corrosion behavior of 7075—T6 Al alloy in sodium chloride environments. Experimental work associated with providing selected input data for the model and also with providing verification of the model are described. B. General Background And Resarch Objective High strength aluminum alloys are notoriously susceptible to stress corrosion cracking in aqueous chloride solution. Several ap- proaches have been used in efforts to overcome the problem, including variations in heat treatment, alloy composition, and thermomechanical processing. An attractive alternate approach is to modify the envi- ronment itself by the use of corrosion inhibiting substances. In- hibitors have been used successfully to prevent corrosion of aluminum alloys, and have been found to be somewhat effective in reducing stress corrosion cracking.(l)’ (2) Inhibitors can function yi§_either cathodic or anodic mechanisms. (3) Mechanisms whereby cathodic inhibitors ( e.g., borax ) function ap- parently are to provide an oxygen diffusion barrier at the metal surface, and, since the films also usually are poor electronic conductors, they are incapable of promoting oxygen reduction at the film-sclution interface. On the other hand, anodic inhibitors ( e.g., nitrite ion ) react pref- erentially at electron sink sites, and promote the formation of protective oxide films. In the case of nitrite ion, the film is formed by adsorp- tion of nitrite on the metal surface followed by a reaction to form ox- ides. The reduction product of the nitrate inhibitor is soluble, hence a protective film would be formed containing metal ion, oxygen and pos- sibly hydrated oxide. The oxide layer which is formed by the combined action of nitrite and oxygen is continuous and adherent. Several theoretical models have been proposed to describe electro- (4) chemical conditions in an unstressed crack. The earliest, by Evans , was based on a differential aeration mechanism. Differential aeration effects, resulting in oxygen concentration gradients, produce a cathodic reaction effect and also drive corrosion at locally variable rates under an electrolyte film of nonuniform thickness. If the local corrosion rate is limited by the oxygen flux, the attack would be most .severe for thin films. Rosenfe1d(5) has proposed an alternate mechanism in which the metal within the crack suffers anodic attack as a result of restricted oxygen supply, and the external ( aerated ) surface forms a large cathode. Inside the crack, anodic dissolution, together with hydrolysis of the product metal ion, can cause an increase of hydrogen ion concentration. If the net corrosion reaction plus hydrolysis should lead to an increase of hydrogen ion concentration, the process would occur independently of any other process, and would accelerate with time to a steady state where diffusion out of the crack tip region would limit the buildup. If the corrosion reaction plus hydrolysis should lead to no net change in H+ concentration, merely an acid solution in a crack would be created. If the corroding solution contains some chloride ion, these transferred anions may be chloride ions, and acid formed inside the crack is hydro- (6) chloric acid. Pourbaix has claimed that this is one reason why chlorides are particularly harmful in promoting crevice corrosion and stress corrosion cracking. (7) ’ .(5) McCafferty adapts the systematic approach of Rosenfeld 3 paper in order to investigate polarization kinetics aspects of a simple crevice system, and confirms the conclusion of Rosenfeld. According to McCafferty, in a crevice where the internal sample is not short- circuited to external metal, the anodic corrosion rate is determined by the limiting current for oxygen reduction. The limiting cathodic current resulting from oxygen reduction was independent of pH and Cl- concentration. Because the crevice height is comparable with the thickness of the oxygen diffusion layer, diffusion of oxygen into the crevice is impeded, hence the corrosion rate is reduced. This results from cathodic control. Fontana(8)and Greene suggested another mechanism, based on electroneutrality, where chloride ions migrate into the crack to balance the otherwise increasingly positive charge resulting from metal ion concentration. This gives rise to an accumulation of aggressive anions at the crack tip. Alkire and Siitari (9)’(10) offered a quantitative mathematical model, as well as experimental data, for a mass transfer control process according to Fontana's mechanism. Another mechanism for the initiation of corrosion inside the crack (11) was proposed by Eklund , based on electron microscopic investigations of crack regions, which describes corrosion initiation at sulfide inclusions in the metal surface. Models of corrosion with stress in a crack have been proposed for (12).(13) (14) aluminum alloys These include active crack-path mechanism, stress assisted dissolution by a mechanochemical mechanism, or by film rupture(15), brittle rupture(l6) (16) , hydrogen embrittlement , and struc- turally—determined dissolution resulting from compositional differences in the grain boundary region. All of these mechanisms can be categorized generally for aluminum-base alloys under NaCl solution as involving (a) pre-existing active paths, (b) strain-generated active paths, or (c) Specific adsorption at sub-critical stress sites. Pre-existing reaction path models assume that localized dissolution occurs because the aluminum alloy contains locally active sites associated with segregated impurities. Some aluminum alloys exhibit intergranular corrosion in the unstressed state partly because of the solubility of the corrosion products. If these are insoluble and relatively nonporous, one function of the imposed stress would be to rupture the protective film. Such mechanisms of strain-generated active paths have been pro- posed by several researchers(l7)’(l8). A dissolution-controlled mechanism assumes that dissolution follows a narrow path as a result of imposing a stress on a specimen. It arises from the interaction of elastically strained metal, produced by the stress, with the solution. (18)’(19) have centered around the role of Several discussions dislocations ( one of the most important elements of this mechanism ) which are considered to be reactive with respect to the matrix because of their movement or compositional differences arising from atomic rearrangements around stacking faults or regions of short range order. (15)’(18) showed that static dislocations in metals Several researchers did not show evidence of chemical activity derived from the strain energy of their core, but the segregation of solution to dislocations in metals did not Show evidence of chemical activity derived from the strain energy of their core, but the segregation of solution to dis- locations can result in localized attack. Another type of mechanism of strain-generated active path is a so—called film rupture mechanism(ls). High strength aluminum alloys owe their electrochemical inactivity to a relatively inert aluminum oxide film, which forms on the exposed surface of aluminum and aluminum alloys, so that the active metal is separated from the corrosive en- vironment. If the protective aluminum oxide film is mechanically ruptured, the metal is exposed to chemical attack until such time as the protective film can reform, and thereafter further reaction is stifled until the film is again ruptured. Elastic strain in the underlying metal may be sufficient to bring the protective film to its fracture point, thus exposing metal. The active path along which the crack prop— agates is generated cyclically as disruptive strain and film buildup alternate with one another. Hoar(20) showed experimentally that cur— rents associated with electrodes under stress may be much larger than those observed at static surfaces, a difference which suggests that the reaction rate upon straining is controlled by the rate of oxide rupture caused by slip-step emergence and by the subsequent passivation rate of the newly bared metal.' The mechanism of specific adsorption at subcritically stressed sites has been proposed. Where the local dissolution rate at the crack tip is under cathodic control, the ratio of hydrogen evolved to hydrogen ad- sorbed may play an important role in determining what proportion of a fracture is caused by dissolution and what proportion by hydrogen. Even when hydrogen embrittlement is the major cause of fracture, the minor role of the dissolution process will, under open-circuit condition, determine the rate of hydrogen ion discharge. Each of these corrosion cracking models, with or without stress, in the presence of NaCl solution, has key features: (1) role of chloride and hydrogen ions; (2) cathodic reduction; hydrogen or oxygen reduction; (3) the potential gradient inside a crack; and (4) the potential effects of inhibitors. A significant role of Cl- ion inside the crack with and without (6) . <7) . (9). stress has been demonstrated Chloride ion is one of the primary factors responsible for the pr0posed dissolution process related to the mechanism of a pre-existing active path and film rupture mechanism. (10)’(21)also postulate the importance of Cl- Alkire, Hebert and Siitari inside the crack. If accumulation by migration of Chloride ions within the crevice is significant, it is possible that the activation behavior (23) would depend on Cl- concentrations. Pryor believes that the manner in which Cl- promotes pitting is caused by a defect structure set up where Cl- ions exchange with 0-2 ions on the A1 0 lattice, electrical 2 3 neutrality being maintained by the passage of an appropriate number of Al3+ ions from the oxide into solution. The influence of Cl- concentration on pitting also has been studied by Bogar and Foley(22). At the higher Cl-concentration, the following reaction will take place. Al + 4 CI‘ -- AlClZ + 3e’ , Al + 4 C1‘ + 3H+ -- AlCl; + 3/2 H2 . This action of Cl- promotes pitting. The importance of the cathodic reaction (hydrogen evolution re- action), as well as H+ ion on the side wall and external surface, has been investigated. Pickering and Frankenthal<24), Pickering and Ateya (25) (2°), Siitari and Alkire(27), observed hydrogen , Seys and Brabers gas evolution from both real and artifical pits or crevices in aluminum during kinetics experiments. The gas extracted from the electrolyte was analyzed in a mass spectrometer and was found to be hydrogen gas. This evidence is important because it supports the mechanism of hydrogen em- (26) brittlement. Furthermore, Seys and Brabers reported that hydrogen evolution is not an essential part of the pitting mechanism, but note that stress corrosion cracking commonly arises as a result of hydrogen (28) gas formation. Evans and Edeleanu proposed the mechanism of auto- catalytic pit propagation resulting from the hydrogen evolution reaction and a buildup of acidity. (29) Alkire and Siitari , showed quantitative mathematical models (21) under mass transfer control and presented later a more developed model . It was demonstrated that cathodic processes can occur within the crack as well as on adjacent exterior surfaces and largely is influenced by the potential and concentration distribution inside the crack. Pickering and Frankenthal<24) showed that the large potential drops in solution are caused by formation of bubbles within regions of corrosion in the crack. The presence of gas bubbles on the electrode surface causes an increase of the electrolyte layer, adjacent to the electrode surface. The ohmic resistance increase is closely related to the bubble departure radius. The electrode-potential gradient between the crack and the external environment also is important as the driving force for mass transport between the crack tip and bulk environment. There are three forms of mass transport: migration, diffusion and convection. The transport of reactants and products in the crevice region is thus restricted so as to give rise to conditions different than those encoun- tered by metal freely exposed to bulk electrolyte(29). Although in a general way the corrosion mechanism of aluminum alloys is clear, individual aspects of the key features call for more clear elucidation. The activation mechanism of aluminum alloys in aqueous chloride solutions remains unclear: is there a gradual shift of the stationary potential to the negative side in the crevice because of acidification and transport of the metal from a passive to an active state? In this connection, it is highly important to ascertain more definitely the value of potentials or of other parameters at which localized corrosion develops. 10 Furthermore, the influence of geometrical factors on change in the com— position of the medium and distribution of potentials and current, demand special study. Consequently, an experimental program was conducted to provide information on the polarization kinetics, potential distribution in a crack, and other parameters under various conditions. The approach taken here is (7) (5). similar to that developed by McCafferty and others II. THEORETICAL BACKGROUND A. Electrode Kinetics. The rate of a simple anodic electrochemical reaction where metal ions M+ are produced from the solid metal phase M(s), may be written M(s) -> M+ + e", or as an anodic current density, ia = F Ka’ (l) and, similarly, the rate of the reverse (cathodic) reaction also may be written as a current density, 1 =-FKC+, (2) where the quantities Ea and Re are heterogeneous electrochemical rate constants which depend on the electrical potential, and CM} is the concentration of M+ . Anodic currents are taken to be positive and cathodic currents are negative. The potential dependence of each of the rate constants is defined to be - _ a. r 1‘. ‘KaexM—W)’ <3) RC =Kcexp(-°‘R'§ a), (4) where the potential O is taken with respect to a reference electrode, e.g., hydrogen or saturated calomel electrode. The constants Ka and Kc are the fundamental heterogeneous rate constants and are independent of potential. The constants F and R are the Faraday constant and gas constant, respectively, and T is the absolute temperature The pa- rameters da’ and dc are intrinsic kinetic parameters of the system, and usually have the value of 1/2 for elementary one electron trans- fer reactions. With these definitions, the anodic and cathodic ll 12 reactions may be written ia = F Ka exp ( EL%—¥— ¢ ) , (5) and _ (i F iC — - F ( K CM+ ) exp ( - -§fEr-¢ ). (6) ( For the above reaction, the cathodic reaction is first order in MI and the cathodic rate is a linear function of the concentration of + M . The anodic process also could be considered first order with respect to M, but the metal concentration does not change during the reaction and is absorbed in the rate constant for convenience.) The net current density for the reaction will be i = i8 + iC , (7) or LIE- = Ka exp ( é—fi‘ri— a ) - ( KC CM+ ) EXP ( ' Elf—i;— ¢ )0 (8) At steady state, the net current is zero so that and the equilibrium potential ¢° therefore is o _ R T K C + Q) — F (da +dc) 1n CK M ° (10) a Defining a quantity called the exchange current density, K C + c M olflol + cl 0 a Ka ) a a C? (11) the net current density may be written i=ioiexpt°Lg-‘T’—<¢-¢°>i-expt-iri—g—(w-WH]. (12) One may further define the surface overpotential, 13 _ _ o 73—¢ ¢’ (13) and obtain d i=iolexpté-g—f;—?S>—exp(-—§-§—?SH, (14) Equation (14) is known as the Butler - Volmer expression for the electrode - kinetics of the single step. Expressing the net rate of an electrode reaction in terms of the exchange current density and overpotential is equivalent to expressing it in terms of the heteroge- neous rate constants and the potential.(32)’(33)’(34) 14 B. Corrosion Reaction The general relationship for current balance at the corrosion potential is A heterogeneous surface will satisfy the overall current balance expressed in equation (15) although it is not obeyed loCally. If the heterogeneous surface is a collection of locally homogeneous areas A on which the current density is uniform, the current balance equation is XikAk =-[ij Aj . (l6) Attention will be given to homogeneous surfaces which satisfy the current density balance at each point on the surface, i.e., the current equation is [.k = {13. (17) For the special case of a single metal dissolution reaction coupled with a single cathodic reaction, 1a = - 1c = 1corr ’ (18) and the last relationship identifies the corrosion current. Substituting the Butler-Volmer equation for each reaction, ioaiuptiga%<¢*-¢§>i-epr-ign'—§—<¢*-¢§>i= [Egg—(rating)i-expi-égegl-<¢*-¢c>11. (19) n where the potential, O, is the corrosion potential, and it lies between 0 o o o ¢a and ¢c . Given the values of ioa’ ioc’ and ¢a’ ¢c one can compute the corrosion potential. A closed form solution for equation (19) can be found when the 15 values are all equivalent, cl =ol =ol =ol 88. CC 8C C3. (20) Additionally, if all theCX values are equal to 1/2, equation (19) may be * rearranged to give the corrosion potential ¢ , o * R T ln ioa exp (F/2RT) ¢a + 10c exp ( F/2RT) ¢c (21) F O 0 10a exp (-F/2RT) ¢a + i0C exp ( -F/2RT) ¢c When the equilibrium potentials for the two reactions are widely separated, the reverse reaction for either or both reactions may be (35) negligible. Stern and Geary first treated this superposition for metal dissolution and hydrogen evolution, and obtained icorr 10a exp (JLdR TF) ( ¢x - 0: ) = 10C exp ( - iffii) ( (6* - (I): ). (22) The corrosion potential can be calculated from equation(22) i * _ R T cc 0 o (0‘ aa + dcc) ¢ _ F In ( ioa ) +01cc ¢c + o(aa¢a ° (23) Introducing the definition for the current density [ Eq. (22) ] and corrosion potential [ Eq. (23) ], the total current density is given by ( cf. Stern<36)’(37)’(38)) i = i8 + ic = icorr [ exp (3L§3%—) ( ¢ - ¢*) - exP ( -9£§S%-( ¢ - ¢*)) ]- (24) This equation resembles the Bulter-Volmer equation for a single reaction, where the corrosion potential and corrosion current density have replaced the equilibrium potential and exchange current density. Neglect of the reverse reaction is valid for large positive potential ( with respect to the equilibrium potential ) for the anodic reaction. Neglect of the oxide reaction is valid for large negative potentials ( with 16 respect to the equilibrium potential ) for the cathodic reaction. At the corrosion potential, both conditions are assumed to be fulfilled simultaneously for the Stern treatment and each reaction is said to be under the Tafel condition. The teatment is illustrated in Figure l, i.e., if ia)»iC , the current i is i=1cmex p<-ae—) (¢-¢*), (25) and if iC > ia, it is 1=-icorrexp(-°—‘§£§—(¢-¢*>). (26) Equation (25) can be rewritten as S l 6. ll 1n - , (27) or * ”S. l '8. ll 3.; l i, 28 daaF“ " * Figure 1 shows a schematic plot of Eq. 28 as O - ¢ vs 1 . The value of the anodic Tafel lepe is * d t W - 0.) _ 2.303 RT (27) d log 1 — daa F Extrapolation of Tafel branches to their interaction at the corrosion potential gives the corrosion current density, ic , and is shown by orr the solid-dashed line, and the deviation from the extrapolated curves indicates the increased importance of the other, superposed, reaction as the corrosion potential is approached from either Tafel extreme. The Tafel extrapolation technique for measurement of corrosion kinetic parameters may be used to determine the anodic and cathodic Tafel lepes as well as the corrosion current density. This technique has been used widely for the investigation of corrosion kinetics, with the most ( volts ) Potential 0.1 0.0 -0.1 -002 -0.6 17 Oxidation Curve ...... ‘6-.._.__-..--._-._- Equilibrium Potential ‘ Reduction Curve .fi 133 e t‘A—t .r l Corrosion . Current Oxidation | Curve ............................. 5_ - - - - - - - Corrosion Potential Activation Tafel region Polarization ‘?.__. Equilibrium Potential Limiting _.._.. _.. _.._.. _.-. _.. Current Concentration Polarization 9“ \ \ 4 I 1r 5 l i ‘ 0.01 0.1 1.0 10 100 1000 Log Current Density, log ix (,(A/cmz) FIGURE 1 THEORETICAL ELECTROCHEMICAL SYSTEM WITH TWO OXIDATION - REDUCTION REACTIONS 18 success in acidic solutions and other systems in which there are soluble reaction products. Aside from limitations caused by the precipitation of insulating and protective films, the Tafel technique has limitations caused by ohmic and mass transfer effects. (1) Ohmic Effects Ohmic resistance between the reference electrode and the polar- ized electrode contributes to total overvoltage measured. The re- sistance is a function.of solution conductivity, distance between the reference electrode and the sample, and the geometry of the system. (39) Barnatt has presented an analysis of the magnitude of the IR drop expected as a function of both the current density and the solution conductivity. According to Barnatt<39), the resistance is a linear function of current and can be expressed as Ci F L = k 6 K R T i ave ’ (29) where L is a characteristic dimension for the system, and K is the electrolyte conductivity. The magnitude of 5 depends on the level of current and reflects the increased importance of ohmic effects at high current density in Tafel polarization measurements. (2) Concentration Polarization At high overvoltages, the measurement of activation overvoltage may be complicated by an interfering phenomena called concentration polarization. Concentration polarization occurs when the reaction rate or the applied external current is so large that the species being l9 oxidized or reduced cannot reach the surface at a sufficiently rapid rate. The solution adjacent to the electrode surface becomes depleted of the reacting ions and the rate then is controlled by the rate at which the reacting species can diffuse to the surface. Analytically, it is given by Uhlig(58) as follows: *_RT 1 ¢ - ¢ - —Z—F ln ( 1 -.IL ), (30) where iL is the limiting current density for a cathodic process and i is * the applied current density. As i approaches 1 ¢ - ¢ approaches L, * infinity. This is shown by the plot of O - ¢ versus 1 in Fig. l. The limiting current density can be evaluated from the expression 1 = 2 F D c , L I” where D is the diffusion constant for the ion being reduced, 2 is the (31) number of unit charges transported per ion in the diffusion process, X'is the thickness of the stagnant layer of electrolyte next to the electrode surface, and c is the concentration of diffusion ion in moles/ liter. 20 C. Mass Transfer The simplest electrode reactions are those in which the kinetics of all elecron transfer and associated chemical reactions are very rapid compared with those of the mass transfer process. Under these conditions, the chemical reactions can usually be treated in a particulary simple way. If, for example, an electrode process involves only fast heterogene- ous charge transfer kinetics and mobile, reversible homogeneous reactions, one finds that (a) the homogeneous reactions may be regarded as being at equilibrium and (b) the surface conCentrations of species involved in the faradaic process are related to the electrode potential by an equation of the Nernst form. Mass transfer results either from differences in electrical or chemical potential, or from movement of a volume element of solution. The modes of mass transfer (40) are 1. Migration, movement of a charged body under the influence of an electric field ( electrical potential gradient ). 2. Diffusion, movement of a species under the influence of a chemical potential gradient ( concentration gradient ). 3. Convection, stirring or hydrodynamic transport. Generally fluid flow occurs because of natural convection ( convection caused by a thermal or density gradient ), or forced convection, and ,may be char- acterized by laminar flow and turbulent flow. The modelling of diffusion, migration, and convection in solution is described by the four relationship: 1. The flux equation for charged species, ZiDiciF Ni =-—-R_T_ V0 -D1VC:l + C1V. (32) 21 2. The current equation in solution, 1=FXZiNi° (33) 3. The material balance, ’bCi E)t = - Y7. N1 + Ri . (34) 4. The equation of electroneutrality, [2 c =0. (35) i i i In equation (32), N is the flux of species i ( mole sec-l cm ) i at distance x from the surface, D is the diffusion coefficient ( cm2/sec ), i VCi, or , in one dimension,bci , is the concentration gradient at 15X distance x, O is the potential, 21 and C1 are the charge and concentration of species 1, respectively, and v is the velocity ( cm/sec ) with which H- a volume element in solution moves along the x axis. The quantity R1 is a certain function of concentrations of the components participating in the reaction. The three terms on the right-hand side represent migration, diffusion and conveCtion respectively to the flux. In equation (34), this equation can be written as 3C1 2 21 15—?— + vVCi=DiV Ci+—R—,f— FD1V(CV¢)+Rio (36) 22 C. 2. Equation of Motion of Electrolyte ions in Crack Suppose two metal surfaces fornia narrow slit filled with an electro- lyte solution. Let S denote a middle surface, equidistant from the side walls of the slit. The slit width is assumed small compared with the radius of curvature of S at any point. Let u, v be fixed orthogonal Gaussian coordinates of a point on the surface S. The solution contains ions of n species, the concentration of each species being equal to C1' Let h denote the part of the slit width outside the double layer in which O, as well as true concentrations, may be considered constant along the normal to the surface S. This situation is shown in Fig. 2. /////////////.,z_z\zzzazzaam W . _fJ k—r—y fl//////////// i777777777 u—tfi—i Figure 2 . Structure of elastic potential in a narrow crevice filled up with electrolyte. 23 The value of the liqid flow velocity v is assumed to be zero, and the double-layer thickness negligibly small compared with h. Chemical reaction occurs in the thin-layer metal-electrolyte between the boundaries of the layer A and the slit, therefore on the boundaries of the layer A, there exists a flow of ions ( or, hence electric current ) in the direction of the normal to the surface S. The law of mass conservation in the layer A may be expressed by the following equations on the surface S: 1301 2 .21 ,M +vvci = Div C1 + H FD1V(CV¢)- %N1(¢,Ci). (37> where Ni( O, Ci) is the number of ions of the i-th species passing over into the double layer from a layer A per unit time per unit area of the the middle surface; vector operations being carried out along the surface S. The functions Ni( ¢, Ci) are determined by the polarization.curves which depend on the kinetics of chemical reactions and phase transitions in the double.layer. Equation (37) is obtained from rigorous three-dimensional equations of the electrolyte motion in the following way. In the first place, Eq. (36) lies In the orthogonal curvilinear system of coordinates (u, v, w) so that the surface S should coincide with the surface w = 0. Then we introduce the following two assumptions: (1) vector v at any point of the layer A is independent of w, its component along the normal to the surface S being equal to zero ; (ii) the derivatives 3¢/2u and D¢lav at any point of the layer A are independent of w. Taking these assumptions into account, the exact equations are integrated with respect to w within the layer A from -h/2 to h/2, and average concentrations over the layer 24 thickness are introduced. The quantities Ni ( ¢, Ci) are equal to N=D(ztia¢+’aCi)h/2 R T iaw 3w -h/2 . (38) They represent the flows of the corresponding chemical reagents into the double layer. The solution in the layer A is electrically neutral. Equations (35) and (37) represent a closed system with respect to the required functions Ci( u, v ) and O ( u, v ). The system should be supplemented with initial and boundary conditions. At any moment the following equations of electrochemical kinetics are to be obeyed at the crack front: 3C1 Di 21 F '30 'OII R T 29m and F1=21F[KaexP(%¢)_(.KCCM+)eXp(-%)'(4O) Equation(40) is the same as Eq.(8) . The crack growth rate V may be found from the mass conservation law MD ‘aC z F 90 E: ’a'n R T M'EDn ) . (41) The following symbols are used: DM’ CM’ ZM, and M are the corresponding quantities referring to the ions of the metal being dissolved, n the direction of the normal to the crack front on the surface S, and 5 the volume fraction of the metal anodic component being dissolved owing to the anode reaction at the crack root. III. EXPERIMENTAL TEST PROCEDURE AND APPARATUS Electrochemical techniques often are employed to evaluate crevice corrosion. Critical potential values such as the crevice corrosion potential<6l> (62) , and a crevice protection potential , have been proposed to indicate crevice corrosion tendency. From a practical point of view, it is useful to know the corrosion kinetic behavior within crevices. The polarization method, widely used in order to study the kinetic behavior, shows good accuracy for general corrosion. In the case of crevice cor- rosion, however, the reliability of this method seems to be poor in corrosion kinetic behavior of metal in neutral solution because of an instability of polarization potential during measurement. This instability is consid- ered to be because of an existence of thick oxide film on the surface of metal. In the case of aluminum, however, the corroding surface is exposed to the solution with reduced pH and enriched ion concentration and consequently, is expected to have little film on it. This gives rise to a stability of polarization potential. Therefore, the polarization method is expected to be applicable. A polarization cell is shown in Figure 3 and is arranged in the system circuit shown in Figure 3. The function of the circuit is to develop sequentially increasing or decreasing potentials on a test electrode and to measure the corresponding current associated with the potential. This results in a polarization curve of the potential versus current which " of the corrosion behavior of the material-environment is a " foot print combination. The relative positions of the curves can be used to compare corrosion behavior of various materials and environments. Additionally, the potentio-dynamic polarization technique is useful to determine the 25 26 MODEL I73 Potentiostat AUX WE REF <9 9 9 MODEL 178 G <5 Electra-Probe Q a L0 (‘3 R E F A U X W E Polarization Cell FIGURE 3 SIMPLIFIED EXPERIMENTAL SYSTEM 27 effect of inhibitor, corrosion rates, and kinetics behaviors without resorting to more tedious and less accurate weight change methods. Three types of crevices were investigated for the NaCl solution: (1) An " isolated " artificial crevice, where the crevice metal was not " coupled " artificial crevice, coupled to the open external metal ;(2) a where crevice metal was coupled to the external metal ; and (3) a real crack with stress. The first configuration allowed study of local cell activity within a crevice, the second simulated the more practical case, and the third studied the real crack. The kinetics behaviors, polarization behaviors and pH of solution were studied for the first and second types of crevices. The corrosion potential inside the real crack with stress was studied for the third case. A. Experimental System The experimental system was divided into the following basic units; (1) Potentiostat (2), Corrosion Cell, (3) Electrometer Probe . The simplified experimental system is also shown in Figure 3. (l) Potentiostat The potentiostat was a Princeton Applied Research Model 173. The instrument features a current capability of one ampere, with compliance voltages as high as 100 V in either polarity, and a slew rate of 10 V per microsecond. It incorporates two independently built-in potential/current sources, each adjustable to any voltage in the range of i 4.999 V as well as logic and switching circuity for controlling the sources from the front panel or by externally derived trigger. 28 (2) Corrosion Cell (a) Working Electrode The working electrode , shown in Figure 6 & 7, was fabricated in the local machine shop. (b) Reference Electrodes A standard calomel electrode (SCE) was used as the reference elec- trode to give a reduction potential of 0.24 V. Such an electrode is not easily poisoned or contaminated, and it is insensitive to electrolyte composition because of its design. To avoid mutual contamination of the test solution and the reference electrode, the two usually are isolated by means of a salt bridge or liquid junction. (c) Auxiliary Electrode. Platinum can be used in almost any solution over a wide range of temperature without special precautions, and its rate of polarization is very low, hence it was used as an auxiliary electrode to supply current. (3) Heat Source Since solution temperature was a variable, some means of control- ling this parameter was needed. The cell was placed on top of a variable control Thermolyne electric heater and was manually controlled to about 1: 100 C. The heater was also equipped with a magnetic stirrer. 29 ----.---.. J-_-Il Figurei4 A.rectanglular specimen for bare surface test l Figure.5. A modified artificial crevice 3O (4) Electrometer Probe A PAR model 178 Electrometer Probe was supplied with the Potentiostat so that the potential at high-impedance ( Reference Electrode ) could be monitored. After placing the probe at the end of a cable it could be positioned very near the monitored potential. As a result, stray ca- pacitance loading was minimized with a subsequent Optimization of stability. B. System Assembly (1) Corrosion Cell The polarization cell and its components were cleaned in laboratory detergent solution followed by rinsing in distilled water. The solution and a stirring magnet were placed in the large beaker, and the working electrode and standard calomel electrode were inserted. With the SCE in place, the working and auxiliary electrodes and thermometer were positioned with respect to an imaginary horizontal plane established by the tip of the SCE. Vertical alignment of the electrodes and ther- mometer were maintained by the specimen-holding unit because they had enough depth to provide the support needed to prevent lateral movement of these items. The specimen-holding unit was designed in order to maintain an equal distance between all three electrodes. (2) Control System F1gure_4_is a simplified diagram of the test system consisting of the Princeton Applied Research Model 173 potentiostat, the Model 178 probe and an electrochemical cell. The potentiostat was furnished with two special interconnecting cables to interface the electrochemical cell. One interconnecting cable also has three different colored cables : P30 <\m 31 z. “.5. .06. ..CG zoEéBo A ofiémofizfiom v m goEzoo 2H seamen geezsfimmmxm omEHEsz so resin Moose o ESE ..OF mmumDOm szmwhz m w < lm z_ .05.... mtDUmZU Jomhzou I“ z. ...:th 32 (l) a red cable clip, connected to the Counter Electrode of the electro- chemical cell; (2) a green cable clip, connected to the Working Electrode; and (3) a black clip which is not connected or connected to the ground. Another cable from the Model 178 Electrometer Probe must be connected in Control E Operation. The Electrometer Probe Connector on the front panel provides 1:24 volts and also carries the probe output signal back to the potentiostat. For proper Operation in the Control E mode ( Se- lector switch set to Ext Cell in the front panel ) the probe must be connected to the Reference Electrode at the cell. C. Equilibration Specimen preparation was conducted during the time the solution was being stirred. After stirring was terminated, the assembled working electrode was placed in the corrosion cell and properly positioned. In order to find the time to come to equilibrium, the Open circuit cor- rosion potential was measured as a function of time. In the case Of the bare surface eleCtrOde, after the electrode was placed in solution ( 1 wt. 2 NaCl ), there was a little increase in Open circuit potential from -O.755 to -O.73O V. Electrode potential slightly increased with time. After 3.5 hr ( the induction time ), the potential remained at a constant value, about -O.710 V ( vs SCE ). This is shown in Fig. 5 . Therefore, 7075 T6 Al alloy specimen was held in the 1 wt. Z NaCl solution for 3.5 hours in order to allow it to come to equilibrium before any data were taken. During this time, the electrodes were electrically disconnected from the control system. 33 22 l‘ 4 1. _ (hr) " 5 -0.6 -0.7 -0.8 -0.9 ( V vs SCE ) Figure 7 STEADY-STATE OPEN-CIRCUIT POTENTIAL FOR 7075 T6 A1 alloy in 1.0 wt;Z NaCl SOLUTION 34 D. System Operation. (1) Initial Stage It was necessary to allow the system to stabilize thermally for several hours before data were taken. This warm-up period coincide with the equilibration period for the corrosion cell. (2) Second Stage In the three-electrode configuration, Control E Operation auto- matically compensates for the system internal resistance. (3) Measurement of Corrosion Potential The equipment was set up and connected to the system as shown in Figure 3. Whenever the potentiostat was connected to the cell, the potential of the Working electrode vs. the Reference electrode was auto- matically displaced. In order to measure the corrosion potential,the Cell Select switch was set to Ext. Cell., and the meter should deflect to the left° The A Channel polarity switch was set to correspond to the meter reading. The Operating Modal switch is set to Null and Channel A Applied Potential/Current controls are adjusted as required to Obtained a zero meter induction. The setting Of the Channel A Applied Potential Current control will then correspond to the corrosion potential. (4) Operation Control E Operation Of potentiostat was always used. After the cell connection was made, the cable connects to the Model 258 digital Multimeter. When ready to start, the Selector switch was set to EXT CELL. The Counter electrode was driven to whatever potential was required to establish the Working electrode. 35 E. Test Material (1) Chemical Analysis. Commercial aviation—grade 7075-T6 aluminum alloy was used for the study. This was from the same lot used in an earlier PACER LIME test (75) program. NO further information is available beyond the nominal chemical (74) analysis, Table 1. Table 7075-T6 Al Alloys Element Zn Mg Cu Cr Mn Z 5.52 2.76 1.41 0.23 0 (2) Mechanical Analysis. In order to analyze the mechanical prOperties Of Commercial 7075-T6 aluminum alloy, mechanical tests were performed. Tensile strength and yield strength were measured with an Instron tensile test machine. Table 2 shows the mechanical properties for this material. 36 Table 2 Mechanical Properties of 7075-T6 Al Alloys Tensile Strength Yield Strength Hardness ( psi ) ( psi ) ( Rockwell ) Specimen 72,000 66,000 B 76 Handbook(74) 83,000 73,000 B 85 (3) Specimen Preparation (3) Polarization Kinetic Test. Rectangular specimen, for bare surface test and a modified artificial crevice specimen, as shown in Figure 6 and 7, respectively, 37 first were ground with 240 grit paper and then polished with 600 grit paper. Oxide scale and surface defeCO3were removed during the grinding Operation. The specimens were measured to the nearest 0.001 cm., and the surface area was calculated. The samples were cleaned thoroughly in acetone 2 and alcohol, and finally degreased with petroleum ether(3 ). (b) Stress Corrosion Test. Modified WOL—type, constant deflection specimens were used§4l)’(42) (43)’(44)( Figure 8), The specimens Of 7075-T6 aluminum alloy were S-T oriented, i.e., stress was applied On the short transverse direction to the grain structure. The stress intensity factor KI of the crack tip is : V E F K = . (42) I w1/2 C where W ( = 2.55 B ) is the width Of the specimen, E is Youngs modulus, V is the initial displacement; F is a function of a/w ( a is crack length ), F( 3- )=(30.96-195.8( 5‘- )+730.6( :- )1/2-1186( g )3 +254.6( 3 )4) , (43) and C is the compliance. F. Test Solution (1) Material used. Each specimen was tested in a series of solutions of various concentrations Of sodium chloride with and without inhibitors, and 38 Ln W ll “His-‘1 l H—c- L. GEOMETRY FOR l-T: B = l.00n W '2. 55n W" 3020f! “5‘06 2511 0520.625n Hp‘ I.OOn Op 3 0.70n ON 30.77 n N :0,094n (DIMENSIONS IN INCH ES) _______ .. _JL _.— ————— : N "" """ —E" r---\ L___—"'..i :1 [___"—:—-—-J (Q): 0.486 n: thickness (41) FIG.8 —WOL fracture specimen. 39 with one Of several surface-active agents. The inhibitors and surface-active agents are listed in Table 3. Table 3 The inhibitors and surfactant Type Inhibitor Surfactant Type I NaNOz, NaSCN. 2—Amino-2-Methyl Type II CH3COON, (COONa)2 l'pr°pa°°l Type III NazB407 (1) Preparation: Solutionswere prepared fresh just prior to testing. Concentrations were in weight percent solute, based on the total weight of the solution. C. pH Test In order to analyze the small amount Of corrodent present without chemical changes, alkacid paper was used for measurement Of pH within the crack. The pH paper tests permitted accurate estimates of the acidity inside the crack. IV. EXPERIMENTAL RESULTS A. Effect Of Cl- concentration. In Figure 9, anodic profiles at the bare surface are presented for concentrations between 0.1 wt.% and 3 wt.% NaCl at room temperature without stress and inhibitors. The figure shows that the corrosion potential Of corroding 7075-T6 Al alloy depends strongly on the solution concentration, i.e., increasing corrosion potentials correspond to decreasing Cl- concentrationw Furthermore, increasing corrosion current corresponds to increasing Cl- concentration, i.e., the current density is dependent upon the Cl- concentrations. All profiles in Figure 9 were continuous, but were not adaptable to Tafel analysis because of a short linear region. During the course of the experiment, formation of a very thin dark gray adherent film on the surface of the specimen was visually Observed at the beginning Of the experiment. In Figures 10 and 11, cathodic profiles at the bare surface are shown for concentrations 1 Z and 3 Z NaCl at room temperature without stress and inhibitors. These figures show that the current density Of corroding 7075-T6 Al alloy is independent of the solution concentration. All profiles in Figures 10 and 11, show the limiting current density resulting from the oxygen reduction or oxide passivation. As the potential is decreased, no deposit continues to accumulate at the surface Of the specimen, and no gas evolution nor bubble formation were Observed at the specimen surface. According to these results, the anodic profiles in Figure 9, showed that the current density depends upon the Cl- concentration. Cathodic profiles in Figures 10 and 11, 40 10 10 ( flA/cmz) 10 10 41 l/TIIIIH p P Solution 0 -- 0.1 wt.°/. NaCl : O -- 0.2 wt.7. NaCl 3 u-- 0.5 wt.°/. NaCl - *- ‘-- 100 Wtoz NaCl ’- A-fiz 3.0 wt.°/. NaCl __ NO Stress, NO Inhibitor P E l—- I I I I -0.3 -0 4 -0.5 -0.6 ( V vs SCE ) I l Llll I IIIIIIII I IIIIIIII I J Illml I I IIIIIII FIGURE 9 ANODIC POLARIZATION OF 7075 T6 A1 ALLOY IN DILUTE SODIUM CHLORIDE SOLUTION WITHOUT STIRRING AT 200C 3: 2°C 42 : I I I I I I = p. Z 10" E T. b- V Z P - 103. 5' '5 2 ' _. (NA/cm) ._ q r- i _. 102 :— '5 Limiting Current i : CE) 10 :— __ : J :1 r — I I I I I '005 -006 -Oo7 -008 -009 -l.0 ( V vs SCE ) FIGURE 10 CATHODIC POLARIZATION OF 7075 T6 A1 ALLOY IN 1 wt.°/. NaCl SOLUTION WITHOUT STIRRING AT 20°C i 2°C 43 E I I I I I I I '1 10" 5" Z 103 :' —: 2 .. _. ()uA/cm ) 102 :- '3': Limiting Current . __ > o 9 _— 10 F:- o E l I I A l 1 -0.6 -007 -008 -009 -100 -101 ( V vs SCE ) FIGURE 11 CATHODIC POLARIZATION OF 7075 T6 A1 ALLOY IN 3 wt.7. NaCl SOLUTION WITHOUT STIRRING AT 20°C 1 2°C 44 however, show that the current density is independent of the Cl- concentration. In Figures 12 and 13, Anodic profiles are shown for distilled water and tap water, respectively, at room temperature without stress, stirring, or inhibitors. Table 4 shows the chemical composition Of tap water<72). The figures show that the corrosion potential Of tap water for corroding 7075-T6 Al alloy is lower than the corrosion potential of distilled water because Of chemical elements effects as shown in Table 4. The profile in Figure 12 was continuous with no discontinuites and may be adaptable to Tafel analysis and, the corrosion current density can be found. However, the profile in Figure 13 was not adaptable to Tafel analysis because Of a short linear region. By means of the Figure 12 and Tafel methods , the corrosion current density, about 30 )UA/cm2 can be found. A. 2. Effect of Inhibitors Figures 14 and 15 show the anodic polarization behavior Of 7075-T6 Al alloy in the inhibitor solutions such as NaNO2 + Na2B407 ( 0.1 wt. Z ) and 0.1 wt.Z NaSCN, respectively, with l wt.Z NaCl. The anodic polarization curves contained no discontinuities, which normally are associated with film formation, and no passivation. The corrosion potential Of the corroding A1 alloys was independent of the addition Of the inhibitors to the solution. (47) .(48) It is known that these inhibitors, NaNO NaNO -+ Na B O 2’ 2 2 4 7 combined, and NaSCN increase passivation against Chloride attack. The nitrite ion affects the potential, that is , those salts whose anions have high redox potentials. For example, 10 10 (HA/cmz) 10 10 45 _-_- l I W i I | _-; Z. q — c-l "" 'l _ C-l — —I :7 1: I— c- _ - L. .. — -'l — d In— — I- -I '- -l - m — u-I '- .- — - ~O\K _ :— lIllllIl I I IIIIII I I Irvrl I I lllLlLI I I I I I II I I 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 ( V vs SCE ) FIGURE 12 ANODIC POLARIZATION OF 7075 T6 Al ALLOY IN DISTILLED WATER WITHOUT STIRRING AT 20°C i 2°C 46 _ I I I I I I : 4 1° F‘ '1 F'- :1 -' I: 1__ : 103 :— 1 E I P - ( MA/cm2> r- \ ._ 102 :— ._ Z’ I: b- ._ L. "l 10 I— _- : 2: E I I L I I l I -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 ( V vs SCE ) FIGURE 13 ANODIC POLARIZATION OF 7075 T6 A1 ALLOY IN TAP WATER WITHOUT STIRRING AT 20°C : 2°C 47 Table 4 The Chemical Composition of Tap Water Element Concentration ( mg/l ) Magnesium ( Mg ) less than 0.1 mg/l Chlorides ( Cl ) 8 mg/l Sulfates ( SO4 ) 0.3 mg/l Nitrates ( NO3 ) less than 0.01 mg/l Nitrites ( NO2 ) 0.03 mg/l Ammonia ( NH4 ) less than 0.1 mg/l Zinc ( Zn 1 0.025 mg/l Copper ( Cu ) less than 0.11 mg/l Nickel ( Ni ) 0.2 mg/l Iron ( Fe ) 0.5 mg/l Aluminum ( Al ) 0.332 mg/l 48 : I I I T I I 3 : - 10“ E” t: Z ""1 _. n 103 r ':I : I - m 2 (MA/cm) .. -I 102 :' T: : 2 E i I- u-I - 4 Inhibitor 0.1 wt.Z NaNO2 + 10 - . 1: : 0.1 wt./. Nasz’O7 :1 I. 21 u— ...I l I l I I I -003 -004 -005 -006 -007 -008 ( V vs SCE ) FIGURE 14 ANODIC POLARIZATION OF 7075 T6 A1 ALLOY IN 1 wt.Z NaCl AND INHIBITOR WITHOUT STIRRING AT 20°C i 2°C 49 I I 5} cl ‘ .I 104 .. .2 ._ -'I -I _ °\ .. 103 _'_— 1 Z .2 - -l 2 "’ —I (MA/cm ) .1 102 :- _— Z : : I .. Inhibitor -- 0.1 wt.Z NaSCN '- 10 I J L- I I— d - -l l LL, 1 I “I I "003 -004 -005 -006 -007 -008 ( V vs SCE ) FIGURE 15 ANODIC POLARIZATION OF 7075 T6 A1 ALLOY IN 1 wt.Z NaCl AND INHIBITOR WITHOUT STIRRING AT 20°C i 2°C 50 N03 + 8H+ + 6e 2 NH: + 2H20 E = + 0.90 v, SHE The anodic profile in Figure 14 shows a small effect Of NaNO2 and NaZB4Q7 inhibitors upon the polarization behavior Of 7075-T6 Al alloy, but Figure 15 shows no effects Of inhibition. It may be suggested that the passive film formed by NaNO2 in this range Of inhibitor concentration still is weak and ineffective against chloride attack when chloride ion is present in high concentration without a high concentration Of inhibitors. It also is known that oxidizing inhibitors, such as NaNOZ, raise the corrosion potential and can have adverse results if they are present at insufficient concentration. Oxidising inhibitors or passivators, by providing an additional cathodic reactant, effectively reduce cathodic polarization, so that the corrosion current will be increased. I Therefore, if added in insufficient quantity, oxidising inhibitors can have disastrous consequences. If no passivation results, as in these experimental results, anodic dissolution increases or the passive film is weak. Figures 16 and 17 show the anodic polarization behavior Of 7075-T6 Al alloy in the inhibitor solutions, CH COONa and ( COONa )2, respectively, 3 with 1 wt.Z NaCl. Acetate and oxalate ions are chelating agents, ions or molecular species with two or more atoms with unshared pairs Of electrons. The chelating agent can donate the unshared electron pair to a metal atom to form a stable 5- or 6-member ring resembling a "claw ", with the result that the metal atom is held in a stable config- guration and the chelate produced usually does not exhibit the proper- ties Of the metal atom or the chelating agent. In the case Of aluminum 10 10 (MA/cmz) 10 10 51 I: I I I I I I :1 I I b - —O~ _ :- —+ '- Inhibitor --- 0.1 th CH3COONa T '- :- -:: '_" I — —J l L I I “I 1 -O.3 -0.4 -0.5 -0.6 -0.7 -0.8 ( V vs SCE ) FIGURE 16 ANODIC POLARIZATION OF 7075 T7 Al ALLOY IN 1 wt.Z NaCl AND INHIBITOR WITHOUT STIRRING AT 20°C i 2°C 52 Z I I I I I I : o— .- 104 _.. : I 103 r '- 2 - - (MA/cm ) I 102 ::- I) "' I— 10 E- Inhibitor --- 0.1 wt.Z ( COONa )2 O -: u | l u (I l -0-3 -o.4 -o.5 -0.6 -o.7 - 0.8 ( v vs SCE ) FIGURE 17 ANODIC POLARIZATION OF 7075 T6 A1 ALLOY IN 1 wt. NaCl AND INHIBITOR WITHOUT STIRRING AT 20°C 1 2°C 53 alloys, the chelating agent can react with the aluminum cation in the oxide film. Depending on the chelating agent, the resulting compound may be stable and insoluble, or it may be a stable, soluble, complex ion with a solubilizing function on the oxide. In these experiments, there was no change essentially in corrosion potential as well as anodic polarization curves when sodium acetate and sodium oxalate were added to 1 Z NaCl. Metallographic examination of the samples showed a general corrosion on the surface. It is known that a chelating agent, as an inhibitor, reacts with aluminum to form an insoluble aluminum oxalate or acetate compound, and prevents aluminum corrosion by a precipitation type effect. In chloride solutions, the possibility of inhibition should be viewed from the point of interfering with the reaction A13+ + 2 c1“ + 20H“ ZZZ A1 (OH)2 01;, by which the oxide film is thinned. A species may form a complex ion which may be stable and soluble, Al3+ + nR- '23: AlR3-n. and accelerate corrosion. 0n the other hand, the species may react as - + - -4> 3 (___ Al + 3 R Al R 3, wherein the species Al R3 is stable, uncharged and very slightly ionized and resides at or near the aluminum surface. Although these precipitation type of inhibitors are known to prevent aluminum corrosion in the presence of chloride, Figures 16 and 17 show no effect of these type of inhibitors upon the polarization behavior of 7075-T6 A1 alloy . Figure 18 shows the anodic polarization behavior of 7075-T6 A1 alloy 10 10 (MA/c113) 10 10 54 I I lll1| I III_ I ITIIIII l_lJIill IIIII I III IIIII u I IIIIIJ llllllll l I IIIIII Inhibitor -- 0.1 wt.Z NaNO2 + 0.1 wt.Z N323407 Surfactant -- 2-Amino-2-Methyl-l-propanol T I ITIlIr l I I unl I I I I I 0.0 -o.2 -o.4 -O.6 -0.8 -1.0 I ( V vs SCE ) FIGURE 18 ANODIC POLARIZATION OF 7075 T6 A1 ALLOY IN 1 wt.Z NaCl, INHIBITOR AND SURFACTANT WITHOUT STIRRING AT 20°C :_2°c 55 in the presence of borate-nitrite (0.1% NaNO + Na ) inhibitor, 2 23407 with small additions of surfactant, such as Z-Amino-Z-Methyl-l-propanol, to the 1% NaCl solution. According to Khobaib, Quakenbush and Lynch's research(5?)small additions of some surfactants improve the inhibition of borate-nitrite systems and, these mixtures provide good protection to aluminum alloys in high chloride-containing solutions. Figure 18 shows that the corrosion potential has been moved in the active direction by the addition of surfactant, from -O.710 V (vs SCE) to —l.049 V. The corrosion potential was greatly altered by 2-Amino-2-Methyl-l-propanol. During the equilibration, a very thick black oxide films formed. With the potential increasing to -0.630 V, the current density remains constant because of oxide formation on the specimen surface. At a potential of —0.550 volt (vs SCE), the oxide slightly breaks down and the anodic current density increases because of the occurrence of gas or bubble formation at the surface. As the potential is increased, the oxide film continues to form at the surface of the specimen. According to Figure 18, a small, addition of surfactant, Z-Amino-Z-Methyl-l-propanol very much affects the anodic polarization curve, and it may be suggested that this surfactant provides good protection to A1 alloys in the present of chloride solution. It is suggested that the small additions of surface active compounds, such as Amino-Methyl-propanol interferes with the dissolution reaction by interacting with the passive film already provided by the inhibitor formation which results in the development of a stronger and possibly thicker adsobed protective film. Potentiodynamic cathodic polarization curves at room temperature and at l wt.Z NaCl and 1 wt.Z NaCl + 0.1 wt. Z NaNO2 are shown in 56 FigureSlO and IQ, respectively. The cathodic polarization curve of Figure 10 indicated the limiting current density because of the hydrogen evolution reaction occurring from —l.08 V ( vs SCE ) to —0.715 ( vs SCE ). The limiting current density is about 11.5 (AAA/cmz). Throughout the experiment, a small amount of bubble formation and gas evolution on the surface was observed. As the potential is decreased, the gas evolution is increased. In Figure 19, the anodic polarization curve also indicated the limiting current density resulting from oxygen reduction or hydrogen evolution reaction between -O.9lO ( vs SCE ) and -O.715 ( vs SCE ). The limiting current density is about 15.5 (MA/cm2 ). The inhibitor, NaNO2 effects a raising of the potential. It is also known that NaNO2 has good ability for increased passivation against chloride attack. Although nitrite is known to prevent aluminum corrosion in the presence of chloride-containing solutions, Figure 19 shows that NaNO2 either reduces cathodic pOlarization or induces the limiting current density. In view of these results, it may be suggested that nitrite, a passivator' in the range of concentrations ( 0.1 wt.Z NaNOZ), may be ineffective against chloride attack because of the reducing cathodic polarization. The linear polarization technique appeared to be the most suitable approach for determination of corrosion rates. Instead of imposing a very large change in voltage, typical of the Tafel method, the linear polarization method involves only 10-30 mV swings positive or negative from the corrosion potential, in increments of about 1 mV. A direct plot of current vs. potential yields a straight line according to the (35) Stern-Geary equation, ( AIS/AI >E_0 B/ 1 p corr’ I SO I (44) I l T I T I ’- —I Z '1 F’ _ 104 L1" Inhibitor --— 0.1 wt.Z NaNO2 : = 1: _ -I F -. b - 103 __ _ T- : t" .. 2 " - (INA/cm,) '— c—I 102 :: I: P I __ Limiting Current -— Io .. / _= E O = b - : I I I— .... r- .. I L I l l I -006 -007 “0.8 -009 *1.0 -101 ( V vs SCE ) FIGURE 19 CATHODIC POLARIZATION OF 7075 T6 A1 ALLOY IN 1 wt.Z NaCl AND INHIBITOR WITHOUT STIRRING AT 20°C i 2°C 58 where Rp is polarization resistance, and icorr is the corrosion current density. In Figure 20, polarization measurements on these specimens of 7075-T6 A1 alloys, without inhibitor and surfactant, with only surfactant, with surfactant and inhibitor are shown. Values of Rp are taken from the initial slopes of the curves and are tabulated with corresponding corrosion potentials in Figures. In Figures 21 and 22, polarization measure- ments on 7075-T6 Al alloy with inhibitors only ( 1 wt.% NaCl solution ) are shown. According to these results, the inhibitor may be effective on a bare surface specimen and in the presence of chloride ions. If, however the surfactant is added to the inhibitors, the combination will prevent chloride from attacking A1 alloys. B. Effect of Stress In Figure 23, the anodic profile is presented for the concentration 1 wt.% NaCl at room temperature with stress, but no inhibitors. The figure shows that the corrosion potential of corroding 7075—T6 Al alloy moved 15 mV in the active direction as a result of applied stress. Furthermore, applied stress affects the increasing current density. The profile in Figure 23 is continuous, but is not adaptable to Tafel analysis because of a short linear region. Throughout the experiment, formation of a thin white adherent film on the surface of the specimen was observed. As the potential is increased, a deposit continued to accumulate at the surface of the specimen and, simultaneously, gas evolution on the specimen surface was observed. In view these observations,it can be concluded that the applied stress affects the polarization behavior of 7075-T6 Al alloy and raises the current density. 59 RP=36x10—2(Vm2/A) -* 15 Rp= 11 x 10’ -30 -20 (MA/cmz) O-- 1 wt.Z NaCl wt.Z NaNO2 + A.M.P o-— 1 wt.Z NaCl + A.M.P" fl 1 -I IIIIIIIIIILII FIGURE 20 LINEAR POLARIZATION OF 7075 T6 A1 ALLOY IN 1 wt.Z NaCl UNDER VARIOUS CONDITIONS WITHOUT STIRRING AT 20°C i 2°C 60 R = 22.7 x 10’2 v m2/A 15 P 10 mV vs SCE 5 I I I I I I I I I I I ' I I I -30 -20 -1O 10 20 30 40 2 (fiA/cm ) -* Inhibitor -- 0.1 wt.‘7o NaNO2 C I I I I J I I J I I I J FIGURE 21 LINEAR POLARIZATION OF 7075 T6 A1 ALLOY IN 1 wt.% NaCl WITHOUT STIRRING AT 20°C :_2°c 61 O... l wt.Z NaCl I I I I I I I I I_J, I fl _I _2 R = 4.95 x 10 ' Rp= 2.7 x 10 p n 15 "I' (V mz/A) 0 O o - 0 0 mV 10 ..I... O .. vs CI () SCE . . .J I, q 5 ._ 0 d I l I ' I I I 4 I I I 4 I I I T -30 -20 ~10 ‘I 10 20 30 40 o -I O . 2 ( A/cm ) O M - O _ . 0.1 wt.% NaN02+ l wt.°/. 0 NaCl J FIGURE 22 LINEAR POLARIZATION OF 7075 T6 A1 ALLOY IN 1 wt.Z NaCl WITHOUT STIRRING AT 20°C 1 2°C 10 103 (MA/cmz) 10 10 62 C l l I I I I : ; Cf-<¥~ : - O~o. .. E : L. I — .J :- _. .. I - u I- .. I- _- - -I P — I I I I I (I I -O.3 -o.4 -o.5 -o.6 -O.7 -O.8 ( V vs SCE ) FIGURE 23 ANODIC POLARIZATION OF 7075 T6 A1 ALLOY IN 1 wt.% NaCl UNDER STRESS WITHOUT STIRRING AT 20°C i 2°C 63 Furthermore, stress affects the type of oxide film formation at the surface of specimen. C. Crack Electrochemistry. Experiments on crack or crevice corrosion were carried out on 7075-T6 Al alloy in l wt.Z NaCl solution with and without inhibitors at ambient temperature. Additionally, the effect of applied stress has been analysed. When artificial cracks are immersed in an aqueous chloride solution, rapid corrosion or accelerated crack electrochemistry may occur. This accelerated dissolution arises because the crevice restricts mass transport of dissolved corrosion products away from the metal surface. Consequently, the chemical system of the crack electrolyte may change, and species which are aggressive to the metal surface may accumulate there. Several mechanisms have been proposed for corrosion inside the crack, all of which involve three basic components, alone, or in combination: differential aeration, localized acidification, and migration of chloride ions into the crack. The type of cracks have been analysed for NaCl solution without inhibitors: (1) an " isolated " crevice, where The'crevice metal was not coupled to the Open external metal; and (2) a n coupled " crevice, where crevice metal was coupled to the open external metal. D.. Isolated Crevices. In Figgre 24, anodic profiles are presented for 0.5, 1 and 3 wt.Z NaCl concentrations at bare surfaces and in isolated cracks. According to the anodic polarization curve for the isolated crack in Figure 24 , 64 I I IIIII O I I I III A A I l 10 4 AI" A A LIIIIII A I I _________.‘Is A A A . I 103 (MA/cmz) I FIIIIII A I I IIIIIH l #A 10 I IIIIIII ILJ ILLuI O-- 1.0 wt.Z. NaCl Isolated Crevice O-- 0.5 wt.Z NaCl Isolated Crevice U-- 3.0 wt.Z NaCl Isolated 10 II Crevice A -— 1.0 wt.Z NaCl bare surface I IIIIIII TBubbli - & Gas formati I . | gIIIII . J I . I -O.3 -0.4 -0.5 -0.6 -0.7 -0.8 ( V va SCE ) FIGURE 24 ANODIC POLARIZATION OF 7075 T6 A1 ALLOY IN DILUTE NaCl SOLUTION 65 gas bubbles were visually observed in the potential range between -0.850 V to - 0.600 V. Also negative current has been observed. Above this potential, the curves are linear with smooth slopes. Anodic profiles for isolated crevices show that anodic dissolution inside the isolated crevice is independent of the concentration of NaCl. Anodic dissolution inside the crevice, however is much higher than at the bare surface. The experimental data show that , in the potential range between -0.850 to -0.600 V, the hydrogen evolution reaction may take place, i.e., _ 1 _ H20+e --> -2-H2 + OH, because negative current under anodic condition and profuse bubble formation could be observed. The gas extracted from electrolyte was analysed in chemical flame test. The gas was hydrogen. According to Figure 25, this reaction can take place thermodynamically. This hydrogen reduction reaction proceeded slowly in neutral aqueous media. In Figure 26 and 27, cathodic profiles are presented for concentra- . tions of 1 and 3 wt.Z NaCl inside the isolated crack. According to the cathodic polarization curve for the isolated crack in Figures 26 and 27, gas bubbles were observed in the entire range of potentials. Cathodic profiles for isolated crevices show the limiting current. Also it is shown that cathodic polarization curves are dependent of the concentration of NaCl. With increasing NaCl concentration, the current density increased. The Open circuit corrosion potential was measured as a function of time. An isolated artificial crack is immersed in various concentra- tions of NaCl with and without inhibitors. Figure 28 shows the results for several conditions. The solution ( 1.0 wt.Z NaCl with and without 66 ”:2 -I 0 I 2 3 I. s s 7 8 9 10 II I2 I3 It. Is I6 HVI b I ‘I a 2 a 5 (i) I I ‘1 T’ I T I I I I IA '2 _ \\\\N I '5 '9 '2 D - I,2 I .. “N ' \\VK\ -I \ 0,8 I" \\\."N a 0,8 “‘46 \\ 0.5 *- ~\\\ - 0,6 0". '— \\\ L c- 0". l \\ Q2_. 'Al _‘01 \@ l 203.;H20 0 - \\ I hydrargIIII'te .- 0 \\~~ - "0,2 -- "‘\.\\ “Oz-.02 HI\ ’0}: .. \ - ' \\\‘\ CI 0,“ '0,6 I- I \\\~ “-06 \ 0 '0,8 _ - \\.\\ -I'0.8 \\ ‘l - A1”? \..-I l 4,2 .— I «"2 -I _ I - ’h 3 I -l I,“ -I,6 _ I“ .415 5+ L I “1.8 I? I I ‘ - -2-4-6 " IB -2 b I Z __2 I I ~22- I - ‘2'“ ~ I 4-23. -2,6 I I I I I I II I I I I I I 10.2L- I 5 -2.5 - -I 0 l 2 3 ‘9 5 6 7 8 9 IO II 12 13 III 15 I6 - pH Fig. 25 Potential-pH Equilibrium diagram for the System Aluminum- Water, at 25°C. (77) 10 10 (NA/c1112) 10 10 67 I [111 TIIIII I j ITIIIII[ I IIJIIIIII I I I [I'll] I_IJ I IIIII llIlllIl I I IIIIIJ I I Limiting Current I I IIIlII IIIIIIII -O.7 -O.8 -0.9 -1.0 -1.1 -1.2 ( V vs SCE ) FIGURE 26 CATHODIC POLARIZATION OF 7075 T6 Al ALLOY IN 1 wt.Z NaCl SOLUTION AND CREVICE WITHOUT STIRRING AT 20°C i 2°C 68 _ 3 L. — r - 10“ r: :4 I j 103 __ —I :2 2 ' 4 _ 2 " .— (pA/cm ) 102 t.— '1: " -+ - Limiting Current ‘ '- 10 _ _ 3 I I. _ I I I I I I -O.8 -0.9 -1.0 -1.1 -1.2 -1.3 ( V vs SCE ) FIGURE 27 CATHODIC POLARIZATION OF 7075 T6 Al ALLOY IN 3 wt.Z NaCl SOLUTION AND CREVICE WITHOUT STIRRING AT 200C + 2°C 69 mMOHHmHmzH 8305:» DE EH3 ZOHHDAOm Howz NEDAHQ zH >042 H< on. we mnom muH>mmo 92¢ zmmo mom mAQuo wnu wvwmcH II 0 noufiflfii €53 mummuam 0.3m II 4 I acuwnwsafi usozufis moa>muu mnu wvfimaH II nu Hmuanwncfi unocufia mommHSm wuwm II D II 0 I101 I9 I01 .41 I 44 \\l.'.- IL I II III ‘ LIII I. ... 4 III 4 4 I 4I 4 4 m.OI mom m> > w.on mél c.0I 70 0.1 wt.Z NaNO2 + 0.1 wt.Z Na23407 ) was aerated and without stirring dur— ing the experiment. In the caSe of the bare surface electrode ( no con- nection to crack ), after the electrode was placed in solution ( 1 wt. Z NaCl without inhibitor ), there was a little increase in open circuit potential from -O.755 to -O.73O V vs SCE. Electrode potential slightly increased with time. After 3.5 hr. ( the induction time ), the potential remained at a constant value, about -O.710 V vs SCE. On the other hand, after the electrode was placed in solution ( l wt.Z NaCl + 0.1 wt.Z NaNO 2 + 0.1 wt.Z Na B O ), there was a rapid increase in potential from -1.016 2 4 7 to -0.924 V. After 2 hr, the potential remained at a constant value, about -0.710 V, which was the same as the potential at a bare surface electrode. In the case of an isolated crack electrode, after the electrode was placed in solution ( l wt.Z NaCl without inhibitor ), the corrosion potential moved toward the active direction, and the potential attained a value of about -O.880 V. After 7 hr, the potential remained at a constant value of about —O.810 V, which is much less than the value obtained with the bare surface electrode ( no connection to crack electrode ). After the artificial crevice electrode was place in solution ( l wt.Z NaCl with 0.1 wt.Z NaNO2 + 0.1 wt.Z Na2B407 ), the corrosion potential moved very rapidly in the noble direction from -O.890 to -O.820 V. As time passes, the electrode potential consistantly increased. After, 4 hr. the corrosion potential attained a value about -0.550 V which is much different from the other conditions. After 20 hr, the potential remained at a constant value, about -0.630 V which was higher than the bare surface electrode, with and without inhibitor, and the cracked electrode ( isolated ) without inhibitor. 71 Figure 29 shows the open circuit corrosion potential at the different position of inside the crack as a function of time. The solution ( 1.0 wt.Z NaCl without inhibitors ) was aerated with no stirring during the experiment. The results show a small potential drop inside the crack ( isolated crack ). E, Coupled Crack. We have confined ourselves to a consideration of electrochemical and corrosion behavior of Al alloys inside the crack alone. In reality, for existing structures, the crevice always is in contact with A1 alloy outside the crack. In this experiment, the polarization behavior of a " coupled " crevice, where crevice metal was coupled to the Open external metal was studied. In Figure 30, anodic profiles are presented for 1 wt.% NaCl on a bare surface, not coupled to the any other metal and a coupled crack. According to the anodic polarization curve for a coupled crack in Figure 30, gas bubbles were observed in the potential range between -0.850 V to —O.700 V both on the bare surface and inside the crack, and current oscillation was observed. Above this potential, the curves are linear with smooth slopes. The anodic profiles for a coupled crevice shows that anodic dissolution inside the crack is much higher than is the case for a bare surface. (54)’(55) Show that the cathodic reaction ( oxygen Some references reduction ) continues outside the crack after the oxygen within the crack has been consumed, and anodic reaction is confined to the crack. Figure 31 also compares the current densities for the isolated ( uncoupled ) crack to that for Al alloy couples under various concentrations. According to the polarization curves for the coupled crack, in solutions 72 on9340m Homz MEDAHQ zH >OHA< H< OH mNON moH>mmo 924 zmmo mom mHQouo mnu mvaaH II I I. A canoe ecu Eoum Eu H v moH>muo wsu opHmaH II Au Howz N.u3 H cH mommusm whom II 0 o/o oIIIIIoI IloH\\\II.YlI-\!n m.OI mom w> > w.OI n.0I c.0I 73 B I I I I I II . I I 104’ :7 _H r I r- .. b - 103 E. _ (pA/cmz) : I P - _ q I 102 .—- -—q I Z - d p» .4 O-- Bare Surface in l wt.Z NaCl 10 :— O-- Coupled Crevice in l wt.°/. NaCl L '1: P Bubble & Gas formation. '- l I I I J} I -O.3 -0.4 -0.5 -O.6 -O.7 -O.8 ( V vs SCE ) FIGURE 30 ANODIC POLARIZATION FOR OPEN AND CREVICE 7075 T6 Al ALLOY IN 1 wt.Z NaCl SOLUTION WITHOUT STIRRING AT 20°C 1'. 2°C 10 10 ()I A/cmz) 10 10 74 lIllll I [III — '—I I 2.1 _ 1 — —I .. .J c\ : C) I: I— \ - P O '— ? 0 —-Isolated Crack :' (1 wt.Z NaCl ) ‘E : 0 -— Coupled Crack — : (l wt.Z Nacl ) : _ D -— Coupled Crack _1 _ (3 wt.Z NaCl ) _ I -- Counled Crack (1 wt.? NaCl + 0.1 wt.Z NaNn + ”.1 wt.7 NaB407 I I I ITIII IIIIIIII —0.6 -0.7 —0.8 ( V vs SCE ) FIGURE 31 ANODIC POLARIZATION FOR VARIOUS CONDITION OF CREVICE 7075 T6 A1 ALLOY IN DILUTE SOLUTION WITHOUT STIRRING AT 20°C i 2°C 75 ( 3 wt.Z NaCl and l wt.Z NaCl ), Figure 31, gas formation as well as bubbling were observed in the potential range between —O.800 V to -0.730 V at bare surface as well as inside the crack. The rate of gas formation as well as bubbling inside the crack were less than at the bare surface. Above this potential, the curves are linear with smooth slopes. The anodic profile for 3 wt.Z NaCl solution shows that anodic dissolution inside the crack is higher than for 1 wt.Z NaCl solution. At higher C1_ ion concentration, gas formation and bubble formation are less than at the low Cl- ion concentration inside the crack. In Figure 31, anodic profile is presented for a coupled crack at 1 wt.Z NaCl + 0.1 wt.Z NaNO2 + 0.1 wt.Z Na2B407 inhibitive solution. According to the anodic polarization curve for a coupled crack, Figure 31, gas ‘bubbling was Observed in the potential range between -0.85 V to - 0.710 V at both bare the surface and inside the crack, and oscillations in current were observed. In the potential range between -0.850 V to -0.710 V, the profile shows discontinuities because of cathodic reduction, gas bubbling, and depolarization. At the bare surface ( external surface ), formation of a very thick black adherent film on the specimen surface was observed. Above the potential, -0.710 V, the curve is linear. Inside the crack, no gas bubble formation was observed. Figure 31, compares the anodic polarization curve for a coupled crack in the non-inhibitive solution with that for a coupled crack in an inhibitive solution. In the former case, the break- down anodic dissolution potential is a little higher than that in the non- inhibitive solution. The nitrite ion effects a raising. of the potential, that is, - + - —-> + No2 + 8H + 6e (w- NH4 + 21120, 76 E = + 0.90 V SHE. However, the current density is almost the same for both cases. From the experimental results, these concentrations of inhibitors may be a little more effective inside the crack, but, the inhibitive action is weak. The open circuit corrosion potential was measured as a function of time. A coupled artificial crack was immersed in l wt.Z NaCl without inhibitor, (Figure 32). The solution ( l wt.Z NaCl ) was aerated and not stirred during the experiment.- In all c8888 ( open circuit corrosion potential, anodic polarization and cathodic polarization ), the measurements were made at the same position inside the crack. The cracked specimen of 7075-T6 Al alloys and the external Al alloy were coupled for a few minutes. Upon coupling, the corrosion po- tential of the external specimen shifted to the more noble direction, compared with the bare surface specimen ( uncoupled to other electrode ), whereas the corrosion potential of the cracked specimen shifted to the more active direction compared with the isolated specimen. After 6 hr, a steady-state condition was attained, at a potential difference of about 150 mV, which corresponds to Rosenfelds data. Since this value is not small, an IR drop between the crack interior and outer electrode must be large. Figure 33 shows the potential difference between the crack interior and outer electrode as function of time. After 6 hr, steady- state was attained. The electrode potential was measured as a function of time under the active state. After several hours, the potential differences were attained at a steady state condition of about 150 mV, i.e., the same value as that under the nonsteady-state conditions. Figure 34 shows the results,i.e., the potential difference between the external specimen and the cracked specimen under the active state. 77 DON H UOON H< ozHéHHm HDOFHHS ZOHHDAom Homz N35 H zH MOAA< PH. when mUH>mmD omamaou Qz< zmmo. mom iHHzmHOHH HHDOMHUIZWQO 932% I figmem NM ”550”; A moo: V mN mm «H mH NH HH OH m m N o m a m N H a d _ _ _ _ _ _ _ _ q H _ _ _ fi _ H J #098 I vmaasoo mo ovumuam Hose—H IIO ovumusm 055 II I :1 m6: 0 o lo! trio 1 H mum m> > V I w.ol I fio- 78 ZOHHDAOm Homz N.u3 H zH >OAA< H< c8 when moH>mmu qumboo Qz< zmmo mom mozmmmmmHQ AHHo< mmoz: >OHH< H< oH mmon mUH>mmu az< zmmo mom mozmmmmmHa H > v n.0l 83 A schematic representation of crack velocities of aluminum alloys as a function of stress intensity typically yields a curve with three distinctive regions(48). These regions are as follows: Region I, where crack growth is initially observed and changes rapidly with stress intensity; Region II, the " plateau " region which may be nearly parallel to the stress intensity axis; and a sharply increasing crack growth rate region ( Region III ) just prior to failure. In our experiments, a stress intensity factor (Kl = 12 Mpalfi), corresponding to Region II was used for SCC because in this region crack growth appears to be mainly environmentally controlled, and independent of K. Figure 36 shows the experimental result together with reference values<78). During crack propagation, the length of the crack can be measured in an optical microscope whenever necessary, then data for the da/dt vs. K1 plot can be obtained. The specimen of configuration shown in Figure 8 was loaded using a torque wrench to a torque of 12.7 (N~m), with the equilibrium relationShip expressed mathematically, T = G D 1309), (44’) where, T is Torque (N~m), D is the Nominal bolt diameter (m), P is the induced force or clamp load (N), and is C an empirical constant, which takes into account friction and the variable diameter under the head and in the threads where friction is acting. The P in Equation 1 (Novak and Rolfe<41)) and Equation 42 yielded KI = 12 MPaI'. (tn/soc) RATE OF STRESS CORROSION CRACK 84 ALUMINUM 7075-T6. '0-8 ,. O 0.01 N NaCl ( Referenceggg) A 0.6 N NaCl ( Reference ) I 0.35 N NaCl Experimental data I Io'9. '040 A . . ‘ L ; 5 IO IS 20 25 3O smtss INTENSITY (MN/«3’4 FIGURE 36 RATE OF CRACKING VERSUS STRESS INTENSITY FOR DILUTE NaCl SOLUTION V. DISCUSSION A. Bare Surface Corrosion. Polarization profiles in Figure 9 show that since the bare surface dissolution rate is dependent on chloride content, the reaction involves complexes of chloride anion. Corrosion of Al and 7075—T6 A1 alloy at the bare surface, in solutions containing dilute NaCl, is accompanied by the consumption of hydrogen, oxide, chloride, and sodium ions. The most probable reactions mechanism accompanying the initial stage of the corrosion process of 7075 T6 Al alloys in NaCl is as follows<45): -> 3+ - Al <- Al + 3e , (a) Al + H20 23 H+ + A10H2+, (b) A13+ + c1" 2 A1C12+, (c) Alon2+ + 21420 23 Al(OH)2Cl + 211+ , (c) A1012+ + 21120 (1'1) Al(OH)2C1 + 211+, (d) A1(OH)C1+ + H20 23 Al(OH)2Cl + H": (f) Al(OH)2Cl + H20 2 A1<0H)3 + 11+ + (31‘. (g) (45).(46) It is believed ’ that the hydrated aluminum ion, Al(H20)+? is formed rapidly ( about 1 sec ). The hydrated A13+ ion also undergoes a very fast hydrolysis reaction written as Equation (b). Later, both the Al3+ and Al(OH)2+ ion can react with Cl- ions, i.e., Equations (c) and (e). Reaction (e) is faster, however, than reaction (d). From these experimental results, it may be suggested that both reactions (c) and (e) may take place as an anodic dissolution 85 86 mechanism. On the other hand, the over-all cathodic reaction in nearly neutral solutions, based on the experimental results, is oxygen reduction, 02 + 2H20 + Ae’ ----> 4011’. (h) From Figures 10 and 11, the limiting current density ( iL ) is lOflA/cm2 for both concentrations ( 1 wt.Z and 3 wt.% NaCl ). Oxygen is relatively insoluble in NaCl solution at room temperature. According to Eq. (29), this low solubility in turn means that there is a small limiting current density for the cathodic reduction of oxygen. In Figure 25, the applied stress affects the polarization behavior of A1 7075-T6 and raises the current density. Stress corrosion cracking of the 7075-T6 aluminum alloys in chloride ion environments is because of the formation and ,growth of cracks of an almost brittle nature, which propagate along the grain boundaries. (51) . (52) . (53) A number of mechanisms have been proposed IX) account for the phenomenon. Three of the proposed mechanisms which have received wide attention are the film rupture<15)'(16) (14) model , the pre-existing 2 , and the hydrogen embrittlement mechanism(51)’(5 ), active path model In the pre-existing path umdel, emphasis is placed on the micro- structural and electrochemical parameters. Chemical inhOmogeneities in the material are regarded as being the key factor. An example often quoted is the segregation of alloying elements in the form of precipitates at grain boundaries in 7075 T6 aluminum alloy, creating a precipitate- free zone, in the adjacent material. In a corrosive environment a highly localized electrochemical reaction can be established between the 87 precipitates and the adjacent material. Although this is an adequate explanation for intergranular corrosion, it does not account for the important role of tensile stresses in producing SCC ( stress corrosion cracking ). According to the film rupture model,the role of the tensile stress is to rupture the protective or passivating oxide film. This exposes highly localized regions of fresh metal surfaces with electrochemical potentials quite different from the surrounding areas still protected by the oxide film. Thus corrosion is envisaged to occur at these sites until a new passivating oxide film can reform. This fresh film will in turn be ruptured and the corrosion and repassivation processes repeated, thereby generating an active path for SCC. In this mechanism, the rate of re- passivation is the key factor. If repassivation is very rapid, insufficient corrosion will occur to promote SCC. The mechanism of hydrogen embrittlement involves diffusion of water molecules or hydrogen ions down the crack, reduction of these species to adsorbed hydrogen atoms at the crack-tip surface, surface diffusion of adsorbed atoms to a preferred surface site, adsorption of the adatoms into the metal matrix, and followed by diffusion of hydrogen atoms to a position in front of the crack-tip. Nevertheless if hydrogen is indeed the basis of the embrittlement during SCC, the kinetics may still be influenced, if not controlled, by such processes as hydrogen permeation or stress induced rupture of the oxide film. The possible crack-advancement mechanisms, that is, dissolution and hydrogen ion reduction, will be controlled at a given potential by three subsidiary factors: the oxide rupture rate, the solution-renewal rate, and passivation rate including repassivation rate. In these experiments, it can be found that passivation rate at the stress 88 concentration region, which is common to both mechanisms, that is film rupture ( activation control ) and hydrogen-embrittlement ( diffusion control ) mechanism, is the rate controlling reaction in the stress cor- rosion process. B. Crack Electrochemistry. According to the polarization curves in Figures 24, 26, and 27, hydrogen gas formation and bubbling were observed near the corrosion potential region. Under the experimental results, two major cathodic reactions may be considered, i.e., reduction of oxygen and hydrogen, 02 + 2 H20 + 4e —-%> 4 OH, - 1 _ and H20 + e -"'> ‘2' H2 + OH . If both cathodic reactions may take place, the effect of the depolarization can be considered. Because of this effect, the corrosion rate will increase. Figure 24 shows that the polarization profiles inside the isolated crack differ from the bare surface specimen. Furthermore, the pH inside the crack is also different from that of the external surface. In the case of the bare surface specimen, no hydrogen gas bubbling was observed. These results show that the chemical and electrochemical environment of the crack tip may be different from the bulk exterior environment. There also may be the possibility of additional or alternative electro- chemical and/or chemical reactions such as hydrogen reduction inside the crack. 89 Figure 24 shows that 0.1 wt.Z NaNO2 + 0.1 wt.Z Na2B407 inhibitors may affect the chloride attack inside the crack, although Figure 14 shows only a small effect of these inhibitors. This is because of the establishment of a special, more complex microchemical or electrochemical environment within the crack which is different from the bulk exterior environment. Although localized corrosion is complex and involves many processes which occur simultaneously, many suggestions can be considered for this reason. If accumulation, by migration, of chloride ions within the crevice, and hydrogen by hydrogen evolution are another significant factor ( hydrogen evolution is the main factor based on the results of the anodic polarization ), it is possible that electrochemical behaviors would depend upon [ Cl- ] and [ H+ ]. In the case of a coupled crack, Figure 30 and 31 show that the cathodic reaction ( probably oxygen reduction and hydrogen reduction ) takes place outside the crack and a little anodic reaction as well as hydrogen reduction occurs inside the crack. Figure 31 also shows that the anodic profile of an isolated crack is different from the profile of a coupled crack. The evidence of a different corrosion potential, the active potential and the anodic profiles probably result from the hydrogen evolution reaction. This cathodic reduction may control this corrosion mechanism or suppress the anodic dissolution. According to Pourbaix(6), the surfaces which are outside the crack and are in direct contact with NaCl solution, are often passivated by oxygen, and are acting as aerated cathodes where oxygen is being reduced to water, for example, 90 + - 02 + 4 H + 4 e ---> 2 H20 The surfaces which are inside the crack are active and are acting as non-aerated anodes where the metal undergoes corrosion and hydrolyzes with a decrease of pH, for example, Al --> A13+ + 3e- Al3+ + 3 H20 ---9'Al( on )3 + 3H+. The experimental result shows the decrease of pH inside the coupled crack and indicates weak acidity inside the crack, and chloride ion inside the crack affects the anodic dissolution . (55) Rosenfeld shows a general mechanism of real crack involving the effects of chloride ion and acidity, Me + H20 - 2e --> MeO + 2H+, Me + 2 H20 - 2e --> Me( OH )2 + 2H+, Me + 2 Cl- - 2e -—> Me C12( ads ) + H20 -m> -H> MeO + 2H+ + 2C1". Our experimental results show that hydrogen evolution and oxygen reduction ( secondary ) take place cathodically, and anodic dissolution may take place anodically ( anodic condition ). (24) showed that large potential Pickering and Frankenthal drops attributed to constrictions are caused by trapped hydrogen gas bubbles. For our experimental results, the following two cathodic processes can be considered. (1) Hydrogen evolution and (2) ionization of oxygen. These may proceed by independent but parallel stages and are related 91 to one another only as they provide an overall electrochemical potential on the corroding surface. However, the hydrogen evolution reaction may take an important role as the main controlling cathodic process. The hydrogen evolution process possesses high diffusion mobility and a high rate of migration in an electric field. .An increase in the rate of hydrogen evolution with consequent evolution of hydrogen bubbles will decrease the thickness of the diffusion layer of liquid ajacent to the surface of the metal, because of the additional mixing. As a result, the limiting diffusion current for-oxygen reduction also will increase, as is evident from Equation (34). The presence of hydrogen bubbles on the metal surface may decrease oxygen diffusion, either as a result of a smaller electrolyte cross section, or by removal of oxygen from the metal surface by entrapment with the evolved bubbles of hydrogen. In our experimental results, the principal effect of hydrogen evolution on the limiting diffusion current density for oxygen has been suggested to consist of a decrease in the thickness of the diffusion layer as a result of increased agitation caused by hydrogen evolution. Uhlig<58> suggested the importance of hydrogen evolution in a different role as a controlling factor. When aluminum dissolves 3 and Al+ are formed, initially the univalent anodically, both Al+ ion which then reduces water to form the trivalent ion. During formation of a surface oxide film, the hydrogen evolution reaction takes place simultaneously at the anode as well as at the cathode. In the anodic dissolution process, hydrogen evolution is responsible for increased local corrosion action. Many actions of hydrogen as well as migration are probably responsible for the potential drop as well as 92 separation of the anodic and cathodic sites. Another experimental result in the case of an isolated crack, shows that the current density is independent of the concentration of 01- ion, i.e., the rate of corrosion inside the crack is controlled by a cathodic process. When aluminum dissolves anodically, both A13+ and Al+ may be formed. Initially, the univalent ion then reduces water to form the trivalent ion, 4- _ Al + H20 --> AlOHadS + H +e , AlOHadS + 5 H20+H+ --> A13+ 6H20 + 2e- 2 AlOHadS + H20 --> A1203 + 4 11+ + 4e- or Al+ + 2H 0 ---> Al+2 + H + 20H-. 2 2 During these processes, in the rate-determining steps, these reactions do not involve complexes with C1- ion . 93 . Mathematical Model Several models for crevice corrosion or corrosion cracking have been proposed(21)’(22)’(25) which yield distributions of current, voltage, and composition in the crevice and nearby regions. The results indicate that the approach shows promise, especially in predicting crevice gap/depth ratios that are the most critical for localized attack. Porous elec- trode theory (63) can also be used to predict the depth at which the an- odic reaction may be driven by an external cathodic current. Ohmic drOp restricts the penetration of current into a small—gap, occluded region. At greater depths in the gap, the metal is isolated from the external (64) surface reactions. Newman calculated the depth to which a reaction may penetrate the walls of pipe. Turnbull<65) showed improved math- ematical modelling of mass transport of oxygen in a crevice or crack for an estimation of the oxygen concentration. Diffusion and acid hydrolysis were included in a mathematical model for crevice corrosion by Galvele<66). A sophisticated model for stress corrosion cracking of titanium (76) was developed by Beck; transport limitations, wall reactions and nonlinear kinetics were included in the model. Alkire and Hebert (21) developed improved mathematical modelling for initiation of corrosion of pure alu- minum. His model accounts for electrode reactions of aluminum, oxygen and hydronium ion; and for transport by unsteady state diffusion and migration. In our research, inside the crack, hydrogen evolution reaction takes place cathodically and anodically, although the reaction is a cathodic process. The electrode potential of the metal inside the crack is lower than the hydrogen equilibrium potential in the relevant 94 solution. The anodic corrosion reaction is not the only possible one; a cathodic evolution of hydrogen according to 2H+ + 2e- --> H2 also may occur inside the crack under the anodic condition. Our results show that near the corrosion potential, only cathodic evolution of hydrogen may take place and hinders the anodic dissolution so that Pickering and Ateya's(25) mathematical model may be useful and can describe the mass transfer of the electrolyte taking place by molecular diffusion and ionic migration according to the Nernst-Einstein relation. From the ideas discussed in an earlier section ( theoretical background ), the following model can be written. According to Pickering and Ateya, dc+ _ H F d¢ _ 1 J H+ ' DH+ ( dx + CH+ R T dx ) ‘ F , (45) dC - _ Cl _ F _g¢ _ J c1+ ’ " D01" ( dx ' C01 R T dx ) ' 0’ (46) where D + is the diffusivity of H+ ion, H is the diffusivity of C1: D01" C is the concentration of the indicated species, ¢ is the local electrical potential in the crack, and i is the local current density of the hydrogen evolution reaction; T' is the absolute temperature, F is the Faraday constant,and R is the gas constant. The equation of electroneutrality is {:21 c1 = o, (47) ' i.e., CH+ = col. = C. (47) The experimental results also show that after a few hours, the potential and current attain a steady-state condition. Acorroding to the Pickering model, 95 c=coexp<£f~ ). <48) Modifying Equation(48), by Equation(47) and substituting in Equation(45) gives JH+ = ' 2 DH+ Co RFT g g eXP ( E g ). (49) Pickering derived the following equation, —1§1232{I [W1] . where x = ( DH+ Co F a/ is ) , 18=1o exp (%’)’ or i=is( go ) exp (3%). where P is the transfer coefficient of the hydrogen evolution reaction, and ¢ is the local electrical potential in the crack and solution. Figure 35 shows the experimental results of the Open circuit corrosion potential vs a function of time inside the real crack. According to Figure 35, the potential difference from outer surface is about 40 mV. Mathematically, the potential difference 0 can be calculated from Equation (50), that is, R T cosh [ ( L - x ) / X ] ¢ F l“ cosh [ ( L / X ) ] ’ (50) within the crack. Values for the relevant parameters are as follows: -5 2 RT X = (DH + Co F a/ is), DH + + 5 x 10 cm /sec, §r'= 25mV. The crack length (L) is l em, and crack width (a) is 0.01 cm. Co = 0.17 mole/l, F = 96500 c/mole, 18 can be obtained from the experimental results (Figures 26 and 27). From the experimental data (Figure 26), 96 is = 20 )JA/cmz = 20 x 10-6MA/cm2 , X = ( DH+ Co F a / is ) = 0.64 Thus, the potential g R T cosh [ ( L - x ) / X ] ¢ F 1n cosh [ ( L/X ) ] =18 mV According to the calculation, ¢ = 18 mV, about 20 mV, which this theoretical value is not in very good agreement with the experimental value. Another important mathematical model with a different approach has been proposed by Doig and Melvillé69)’ (70)’ (73). They show that when stress corrosion cracks, growing by enhanced anodic disolution, are subjected to an external polarization, an electrode potential distribution is established within the crack. Figure 37 shows the schematic diagram of a crack of width w in the Z direction and length x in the X direction and width y in the Y direction. The width y is very much greater than the width w so that it may be considered to be of infinite length. In our experiment ( Figure 37 ). following crack was used for analysis 7§7F:==' i (E) x)—DI(x) Fig ‘3'? Schematic mutation of the crack 97 However, -3Z(-.- (<0 so that we may assume that the effect of variation of crack width may be neglected. Figure 38 shows the Evans polarization diagram. fl 1 I I I I I —‘ Elodmdo humid .. ..--------- n- -- N I by. anon! density - Figure 38 Schematic Polarization Diagram of the Electrochemical Reactions Occurring at the Specimen Surface Showing the Influence of Potentiostatic Polarization Ec is the corrosion potential at external surface, 1 is the corrosion current density at potential Ec and lacis the potential at position x (73) within a crack ( V )- According to Doig and Flewitt , the net anodic ia PP at E is iven b app 8 Y Eapp - Ec EaPE- EC (51) iapp=1c[exp( d ) -exp( -9 )]. More generally, the net current density, ix, at any potential Ex is given by Ex — EC Ex - EC 1x = ic [ eXp (-———;:—__. ) - exp (-f:?§——-*) ] . (52) According to Doig and Flewitt, the net anodic current flow within the crack at a distance x from the free surface is the integrated sum of the net anodic current generated on the crack surface at distance greater than X, 98 f _ d x - 2 1x, (53) and d Ex if=-WC(—-a—;—'). (54) Consequently, from Equation(53) and the differential Equation (54), we obtain d E E - E E - E x = - 2 i c [ ex ( x c ) _ ex ( x 2 W c p p C a -B )1. (55) In order to apply this model to real experimental conditions, it was , modified, following Melville's (70’71) line of reasoning, According to Melville, the variation of potential is described under more general conditions. If E(x) is the potential of the specimen relative to the solution at a position, X, in the crack, there is a change dI, in the current down the crack over a length, dx, given by, d1 = 2 ti (E ) dx. (56) I Ohms law gives the change in the potential, dB of the solution over a length dx as _ I dE — t W C dx. (57) If I(x) is the current down the crack, and C is the conductivity of the solution, _...SE = - _..—I , (58) x T w c then d2E 2 i (E) d x = ’ (59) 99 and d E = dE d 2 dx d O‘D- NIT! ). (60) If the potential remains close to the free corrosion potential for the passivated sides of the crack, Ek, the function i(E), describing the electrochemical reactions on the crack sides may be approximated by i(U)=KU, (61) where U = ( E - Ec ), and (62) __.+czxo Io < .0” yl/z) ] (79) K1(ok1/2 3,172) 10(41/2 y1/2) ' where yo = wo/b and y1 = ( l + wo/b ). This may be evaluated at y = y0 to give the potential at the crack tip as , 103 It 1 E=E--—-——g(]—.wl). (90) t C wo where wl = w1/wo, and w1 and wo are the widths of the crack at the mouth and crack tip, respectively. Then 1/2 1/2 1/2 T- ( wl - 1) 11 (1.1 2) K6 ( 1_1/2 wi/z) 1/2 1/2 1/2 Ko( T. wl ) Jo(]- ) ], (91) 1 2 1 2 l 2 K1(r/) Jo