Statistical modeling for the corrosion fatigue of aluminum alloys 7075-T6 and 2024-T3

It is well known that corrosion and simultaneous cyclic loading have a detrimental impact in the integrity of devices or structures. Understating these mechanisms is critical to ensure safety of aircraft. This work presents an extensive literature review on issues of corrosion mechanisms including pitting, exfoliation and intergranular attack. Moreover, models for phases of life and pitting corrosion are presented. Relevant definitions related to these failure modes are presented. The nucleation of fatigue cracks from corrosion pits was investigated by evaluating the effects of two variables on the fatigue life of dog-bone specimens of aluminum alloys 7075-T6 and 2024-T3. The specimens were exposed to different levels of corrosion in an acidified saline solution of 3.5% NaCl. In addition, the specimens were exposed to concomitant fatigue and corrosion until failure by fracture occurred. SEM analysis indicated that fatigue cracks formed/nucleated from each pit, and subsurface mechanisms of degradation were identified associated with the pitting nucleation sites including subsurface pitting, cracking, tunneling and intergranular attack. Failure data were analyzed by ANOVA methods and three transformations were evaluated to minimize the variance, including natural log, inverse square root and power with a lambda of 1/3. Contour and surface plots were developed to show how these variables impact the response of cycles to failure for the conditions evaluated. The effects of stress are more detrimental than corrosion time on the fatigue life of the specimens for the values previously defined by the DOE matrix. The research reported herein presents a methodology for accelerated corrosion fatigue of high strength aluminum alloys in an acidified saline environment. Subsequently a statistical based methodology to assess the impact of multiple variables into the fatigue life of specimens is presented. Statistical models are developed to assess the effect of two variables, stress and corrosion time into the fatigue life of the specimens. Stress levels were chosen to simulate conditions of current aircraft, such as fuselage bulkheads in the F-16. Development of statistical models to predict the behavior of materials will increase our ability to predict and prevent catastrophic structural failures thereby increasing the safety of our aircraft structures.

STATISTICAL MODELING FOR THE CORROSION FATIGUE OF ALUMINUM ALLOYS 7075-T6 AND 2024-T3 by Carlos A. Arriscorreta A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Mechanical Engineering The University of Utah May 2012 Copyright © Carlos A. Arriscorreta 2012 All Rights Reserved The University of Utah Graduate School STATEMENT OF DISSERTATION APPROVAL The dissertation of Carlos A. Arriscorreta has been approved by the following supervisory committee members: David W. Hoeppner , Chair 3/5/2012 Date Approved Timothy Ameel , Member 3/5/2012 Date Approved Donald S. Bloswick , Member 3/5/2012 Date Approved Charles B. Elliott III , Member 3/5/12 Date Approved Kimberli Jones , Member 3/5/2012 Date Approved and by Timothy Ameel , Chair of the Department of Mechanical Engineering and by Charles A. Wight, Dean of The Graduate School. ABSTRACT It is well known that corrosion and simultaneous cyclic loading have a detrimental impact in the integrity of devices or structures. Understating these mechanisms is critical to ensure safety of aircraft. This work presents an extensive literature review on issues of corrosion mechanisms including pitting, exfoliation and intergranular attack. Moreover, models for phases of life and pitting corrosion are presented. Relevant definitions related to these failure modes are presented. The nucleation of fatigue cracks from corrosion pits was investigated by evaluating the effects of two variables on the fatigue life of dog-bone specimens of aluminum alloys 7075-T6 and 2024-T3. The specimens were exposed to different levels of corrosion in an acidified saline solution of 3.5% NaCl. In addition, the specimens were exposed to concomitant fatigue and corrosion until failure by fracture occurred. SEM analysis indicated that fatigue cracks formed/nucleated from each pit, and subsurface mechanisms of degradation were identified associated with the pitting nucleation sites including subsurface pitting, cracking, tunneling and intergranular attack. Failure data were analyzed by ANOVA methods and three transformations were evaluated to minimize the variance, including natural log, inverse square root and power with a lambda of 1/3. Contour and surface plots were developed to show how these variables impact the response of cycles to failure for the conditions evaluated. iv The effects of stress are more detrimental than corrosion time on the fatigue life of the specimens for the values previously defined by the DOE matrix. The research reported herein presents a methodology for accelerated corrosion fatigue of high strength aluminum alloys in an acidified saline environment. Subsequently a statistical based methodology to assess the impact of multiple variables into the fatigue life of specimens is presented. Statistical models are developed to assess the effect of two variables, stress and corrosion time into the fatigue life of the specimens. Stress levels were chosen to simulate conditions of current aircraft, such as fuselage bulkheads in the F-16. Development of statistical models to predict the behavior of materials will increase our ability to predict and prevent catastrophic structural failures thereby increasing the safety of our aircraft structures. This work is dedicated to: my Mom for unconditional love, my brother and sisters for their support. If we knew what it was we were doing, it would not be called research, would it? - Albert Einstein Amat Victoria Curam TABLE OF CONTENTS ABSTRACT .....................................................................................................................iii ACKNOWLEDGMENTS ...............................................................................................ix CHAPTER 1. INTRODUCTION ..................................................................................................1 Hypotheses .............................................................................................................3 Experimental Program ............................................................................................4 Dissertation - Structure and Overview ...................................................................10 References ...............................................................................................................13 2. EXFOLIATION CORROSION (EC) AND PITTING CORROSION (PC) AND THEIR ROLE IN FATIGUE PREDICTIVE MODELING: STATE OF THE ART REVIEW. ................................................................................................................17 Abstract…………………………………… ...........................................................17 Introduction .............................................................................................................18 Phases of Life and Modeling………………………… ..........................................19 Corrosion in Aircraft Structural Aluminum Alloys ................................................31 Intergranular and Exfoliation Corrosion .................................................................37 Corrosion Fatigue....................................................................................................40 Corrosion Pillowing and its Effect on Structural Integrity of Aircraft Lap Joints ................................................................................................................42 Pitting Nucleation Theories ....................................................................................43 Pitting Corrosion………………………………… .................................................44 Formation of Passive Films and their Growth ........................................................46 Structure of the Passive Film in Aluminum ............................................................47 Pitting Potential and Induction Time ......................................................................52 Pit Growth Rate and Pit Morphology .....................................................................53 Mechanisms of Pit Nucleation ................................................................................55 Ion Migration and Penetration Models ...................................................................60 Mechanical Film Breakdown Theories Chemico-Mechanical Breakdown Theories ..............................................................................................63 Pitting Corrosion Fatigue ........................................................................................66 Environmental Effects on "Short" Crack Behavior of Materials ............................72 Conclusions and Recommendations…………………… .......................................73 viii Appendix .................................................................................................................77 References ...............................................................................................................84 3. CORROSION FATIGUE MODELING OF ALUMINUM ALLOY 7075-T6 ......104 Abstract…………………………………………………………………………...104 Introduction……..………………………………………………………………..105 Experimental Procedures………………………………………………………....108 Results…………………………………………………………………………….111 Discussion………………………………………………………………………...123 Conclusions……………………………………………………………………….124 References………………………………………………………………………...126 4. EFFECTS OF PRIOR CORROSION AND STRESS IN CORROSION FATIGUE OF ALUMINUM ALLOY 7075-T6……………………………………………..129 Abstract……………………………...……………………………………………129 Introduction……………………………………………………………………….130 Methodology………………………………...……………………………………137 Results………………………………...…………………………………………..139 Fractography……………………………………………………………………...143 ANOVA -Box-Cox Transformations…………………………………………. 148 Discussion………...………………………………………………………………153 Conclusions……………………………………………………………………….155 References………………………………………………………………………...157 5. EFFECTS OF PRIOR CORROSION AND STRESS IN CORROSION FATIGUE OF ALUMINUM ALLOY 2024-T3…………………………………………….162 Abstract……………………………………...……………………………………162 Introduction………………………………………...……………………………..163 Experimental Procedures…………………………………………………………168 Results and Discussion…………………………………………………………...171 Weibull Analysis…………………………………………………………………185 Conclusions…………………………………………………………….…………190 References………………………………………………………………………...191 6. CONCLUSIONS AND RECOMMENDATIONS .................................................195 Research Contribution ............................................................................................197 Recommendations ...................................................................................................199 ACKNOWLEDGMENTS I would like to thank my committee members, Dr. Hoeppner, Dr. Ameel, Dr. Bloswick, Dr. Elliott, and Dr. Jones, for their guidance. Particularly, Dr. Hoeppner has been an inspiration for me, not only to become a better student, a better engineer, but also a better person. I will always be grateful for his advice. I would like to thank QIDEC members Ms. Amy Taylor and Mr. Larry Smiltneek. Their frienship and assistance made my time in the lab more enjoyable. Finally, I would like to express my gratitude and love for my mom and dad. Especially to my mom, for her advice, love, patience and support. Thanks to my brother and sisters, Edgar, Carolina and Alejandra, for their love and support. CHAPTER 1 INTRODUCTION It is well known that aircraft are exposed to the effects of environment and fatigue, and in many occasions the fatigue life is exceeded in aging aircraft. Understanding the mechanisms of corrosion and fatigue is critical to make decisions of life extension and incorporating this knowledge into design of new aircraft. Due to the inherent variability of these processes, statistical models are needed to make accurate assessments. Corrosion fatigue has been studied since the late 1800s. Jones and Hoeppner summarized some of the authors that have been involved understanding these mechanisms [1]. Since 1837, failures from metal fatigue were noticed, with the first documented mention of corrosion fatigue was by Haigh in 1917 and McAdam in 1929 [2]. Research in the areas of pitting corrosion fatigue has been performed by Harmsworth [3], Chen, Liao, Wan, Gao and Wei [4], Lindley, McIntyre and Trant [5], Kondo [6], Kawai and Kasai [7], Hoeppner [8], and Goswami and Hoeppner [9]. These investigators concluded that pitting corrosion adversely affects the fatigue life of the structures. Clark and Hoeppner found that corrosion pits often would nucleate cracks, and the critical pits associated with these cracks were usually not from the deepest pit [10]. 2 Corrosion fatigue involves a significant amount of variables, which makes modeling of this mechanism a challenging endeavor. Several scientists and engineers have proposed models, including the following: Harlow and Wei [11], Shi and Mahadevan [12], Xiuling and Rong [13], Atkinson et al.[14], Hoeppner, Chandrasekaran and Taylor [15], Hoeppner and Goswami [9], Hoeppner [16], Khan and Younas [17], Murtaza and Akid [18], Swift [19], Wanhill [20], Clark, G. [21], P. Bressolette, A. Chateauneuf [22], Liao, Bellinger and Komorowski [23], Ramsamooj and Shugar [24], and Rong [25]. In addition, research to understand the effects of corrosion and corrosion fatigue in high strength aluminum alloys has been documented. Such authors include Jones K et al. [26], Liao, Renaud and Bellinger [27], Wei et al. [28], Clark P. and Hoeppner [29], Jones K and Hoeppner [30, 31], Birbilis and Buchheit [32-33], Cavanaugh, Buchheit and Birbilis [34], Jones K and Hoeppner [35-36], Gangloff, Kiam and Burns [37], Sankaran, Perez and Jata [38], and Hoeppner [39-40]. Aluminum alloys 7075-T6 and 2024-T3 frequently are used in the manufacture of airframe components that are critical to assurance of airworthiness. Understanding the effects of corrosion fatigue on these alloys is essential for the integrity and reliability of these components. Research focusing on statistical modeling, such as reported herein, will increase the understanding of a structure through the phases of life and diminishing the effects of corrosion fatigue on structural integrity. Thus, it is envisioned that this work is one of the steps needed to continue to make aircraft structures safer, relative to the potential degradation from corrosion fatigue. 3 Hypotheses The research reported herein focuses on developing models to predict with confidence the life of a structure exposed to simultaneous corrosion and fatigue. The following hypotheses were used as guidance for this research: Hypothesis I. Aluminum alloys 7075-T6 and 2024-T3 will dissolve by pitting when pre-exposed to an acidified saline environment. Furthermore, cracks will nucleate from pits and propagate until failure by fracture is reached. 3.5% NaCl was used as the corrosive environment acidified to a pH~3. This is a common environment found in the literature. This hypothesis was clearly identified by use of metallurgical and scanning electron microscopes (SEM). The second technique allowed for subsurface evaluation, which revealed very interesting results, which are shown in subsequent chapters. Hypothesis II. Stress magnitude will have a greater deleterious impact as compared with corrosion exposure time on the fatigue life of the specimens. The effect of two variables into the life of the specimens was studied. Those variables included maximum stress and corrosion time. Statistical analyses of the results show what variables have greater impact in the life of the specimens. Knowing which variable has greater detrimental impact in the structural integrity of a structure is critical to make decisions, such as extending the life of structure, etc. Hypothesis III. Statistical models will predict with confidence the life of specimens exposed to stress and an acidified saline environment with limits defined by a DOE matrix. 4 The ultimate goal of this research was to develop statistical significant models to predict the effects of stress and corrosion time in the life of the specimens. This was accomplished by developing protocols based on design of experiments (DOE) and analyzing the results with statistical methods include analysis of variance (ANOVA), with Box-Cox transformations to stabilize the variance. Statistical significant models were developed to predict the life of specimens as a function of maximum stress and corrosion time. Experimental Program This section discusses the experimental program and procedure used in the research reported herein. It shows the polishing regime, specimen preparation, pre-corrosion conditions and corrosion fatigue parameters. Specimen Configuration and Polishing A schematic of the fatigue test specimen selected for this study is shown in Fig. 1.1. All specimens were polished according to the following guidelines. Each specimen was polished through six steps. Each step produced a more refined surface finish. The steps included the following: 1) 240 grit silicon carbide polishing paper. 2) 320 grit silicon carbide polishing paper. 3) 400 grit silicon carbide polishing paper. 4) 600 grit silicon carbide polishing paper. 5) 1.0 mm alpha silica compound on a 12 inch diameter polishing cloth. 6) 0.3 mm alpha silica compound on a 12 inch diameter polishing cloth. 5 Fig. 1.1: Dog-bone Specimen for Corrosion Fatigue. 0.250" R1.112" 4.000" 3.000" 1.500" 0.625" 0.500" Ø0.380" 1.000" 2.000" 1.000" 0.500" 6 The side of the specimen not corroded was polished with steps 1 thru 4. The edges of the specimens were polished with 800 grit polishing paper, to minimize fatigue cracks nucleating from the edges or corners. Specimens were then cleaned with acetone in an ultrasonic bath and stored in a dessicator. Prior Corrosion of Specimen All specimens were prior corroded according to the following steps: 1) Solution preparation: a. Using distilled water, a 3.5 % NaCl solution was prepared. This is accepted in the literature to simulate the salinity of sea water. A calibrated scale was used to measure the NaCl. b. The solution was acidified with a 1 molar solution of HCl, until a pH of 3 was obtained. It is well known that aluminum alloys are prone to corrode at relatively low and high pH values. It was expected that at a pH of 3, conditions for pitting would be favorable. Calibrated pH meters were used to measure pH. 2) Prior corrosion: two sets of experiments were performed with different exposure times to the corrosive solution. The first set included preliminary studies performed on aluminum alloy 7075-T6 and the second set corresponded to experiments on AA 2024-T3. Prior to exposure to the solution specimens were coated with a finger nail polish. Experimentation was started after the nail polish had dried, usually about 30 minutes. A specific area on the surface of each specimen was left exposed for corrosion reaction. The area of exposure was approximately 40 mm2. 7 a. Preliminary studies on AA7075-T6. i. Approximately half liter of solution was poured into a beaker. ii. Specimens were pre-exposed to an acidic saline environment for 24 and 48 hours. Two blocks were used, the first one with agitation of solution using a magnetic Fisher stirring plate, at a speed of three; and the second block with a stagnant solution. Specimens were exposed to the solution according to a DOE matrix (see chapter 3). iii. After corrosion the specimens were cleaned up with acetone in an ultrasonic bath, and stored in a dessicator. b. Prior corrosion on AA 2024-T3 i. Specimens were coated and immersed as indicated previously. However, time of exposure was modified to 24 or 72 hours according to a DOE matrix (see chapter 5). Multiple pilot tests were performed to assess the effect of prior corrosion at different levels from 24 to 120 hours. It was found that after 72 hours no significant impact of the corrosive solution was observed. Pitting Characterization Upon completion of prior corrosion, each specimen was examined to characterize pitting damage. This was accomplished utilizing a confocal microscope. Pitting damage was examined primarily for pit depth and topography. 8 Corrosion Fatigue Specimens were simultaneously exposed to the acidified saline environment and cyclic loading as follows: 1) Corrosion: solution was prepared following the same procedure as explained previously. The flow rate through the environmental chamber was controlled to approximately 1 mL/min. The solution was not recycled. Fig. 1.2 is the environmental chamber used in this study. 2) Fatigue: testing was performed utilizing a 3.3 kip servo-hydraulic, controlled MTS load frame, provided by FASIDE International, Inc. The loading was controlled by an MTS TestStar system with TestWare to supply a waveform. Phenolic shims were used to minimize fretting between the specimen and machine grips.The parameters used include the following: a. Loading: i. Preliminary studies for AA7075-T6 included 17.5 ksi and 35 ksi. The first value is commonly used by previous investigators at the University of Utah. The upper value was approximately half of the yield strength of the material. ii. Additional testing for AA2024-T3, included loading values of 17 ksi and 22 ksi. It is known that aircraft such as the F-16 operate with stresses between 17 and 22 ksi, including critical areas such as the fuselage bulkheads. This was done to assure that the stress levels used had some degree of validity related to an operating fleet of aircraft. 9 Fig. 1.2: Environmental chamber setup b. Stress ratio: R=0.1 c. Loading frequency: 10 Hz, loading frequency was reduced to 0.5 Hz during inspection intervals. This was done such that the crack could be accurately measured. Inspection intervals lasted 10-20 cycles. d. Waveform was sinusoildal. e. Loaded in L-T direction. f. Specimens were exposed to simultaneous corrosion fatigue until failure by fracture was obtained. 3) Postfracture characterization: as soon as the specimens failed by fracture, the fracture surface was analyzed with a scanning electron microscope. This enables identification of critical discontinuity and also characterization of subsurface damage such as tunneling, pitting, cracks, etc. 10 Dissertation - Structure and Overview This dissertation was structured as a compilation of manuscripts that have been published or have been submitted for publication, as follows:  Chapter 2 - Exfoliation Corrosion (EC) And Pitting Corrosion (PC) and their role in Fatigue Predictive Modeling: State-of-the-Art Review. This manuscript is a comprehensive study of the literature to establish a solid background for this research. It covers important aspects such as phases of life and modeling, corrosion in aluminum alloys, pitting corrosion, environmental effects on short crack behavior, etc. A compilation of definitions related to corrosion fatigue are presented. This manuscript was recently published by International Journal of Aerospace Engineering (Hindawi Publishing Corporation, Volume 2012, Article ID 191879, 29 pages). It was the result of approximately 3 years of work, which included extensive literature research (243 references), compilation of definitions, etc. In addition, this paper was invited for a special manuscript submission by Hindawi; however, other authors for unknown reasons did not present manuscripts for review and the paper was published in a regular journal issue.  Chapter 3 - Corrosion Fatigue Modeling of Aluminum Alloy 7075-T6. Once a solid background was established by performing a comprehensive literature review, it was time to develop hypotheses and test these in the lab. As indicated in the previous section, a methodology to develop models was desired. It was important to base such experiments with statistical methodologies so that the results could be analyzed accordingly. Since the effect of two variables into the response was desired, design of experiments (DOE) was utilized to setup a testing 11 protocol. Initially, a full factorial design was chosen, with two levels of corrosion time and stress magnitude. The results were analyzed with ANOVA and Box-Cox transformations. Specimens were analyzed by using metallurgical and scanning electron microscopes (SEM) to establish the origin of failure. A statistical significant model was developed and is presented on this chapter. This manuscript was recently submitted for publication in Corrosion Science.  Chapter 4 - Effects of Prior Corrosion and Stress in Corrosion Fatigue of Aluminum Alloy 7075-T6. Once the methodology for testing was established and found to be adequate, further modeling was performed. Two additional Box-Cox transformations were evaluated, inverse square root, and power with lambda of 1/3. ANOVA indicates that these models are statistical significant. SEM revealed subsurface mechanisms, including pitting, tunneling and IGA. This paper was submitted and recently accepted for publication by Corrosion - The Journal of Science and Engineering, by NACE.  Chapter 5 - Effects of Prior Corrosion and Stress in Corrosion Fatigue of Aluminum Alloy 2024-T3. Once the methodology for testing and developing models was established and found to be statistical adequate, it was desired to expand to other materials, including AA 2024-T3. Communications with Dr. Jones and Dr. Bloswick were helpful to improve the testing protocol by using stress levels of current applications such as bulkheads in the F-16, and increasing the number of replicates to ensure adequate confidence in the results. With such feedback the protocol was modified accordingly. Following the same methodology, specimens were exposed to both corrosive environment and fatigue 12 until failure. Post fracture analysis was done with SEM. Finally, analysis of data was performed as indicated previously with ANOVA and Box-Cox transformations including natural log and power with lambda of 1/3. Models obtained from this study were found to be statistical significant, and data fits Weibull distributions with 95% confidence. This paper was also recently submitted to Corrosion - The Journal of Science and Engineering, by NACE.  Chapter 6 is a summary of conclusions and recommendation from this study. 13 References [1] K. Jones, D.W. Hoeppner, Pit-to-crack transition in pre-corroded 7075-T6 aluminum alloy under cyclic loading, Corrosion Science 47 (2005) 2185-2198. [2] W. Schütz, Engng. Fract. Mech. 54 (2) (1996) 263-300. [3] C.L. Harmsworth, Effect of corrosion on the fatigue behavior of 2024-T4 aluminum alloy, ASD Technical Report 61-121, 1961, pp. 1-7. [4] G.S. Chen, C.M. Liao, K.C. Wan, M. Gao, R.P. Wei, Pitting corrosion and fatigue crack nucleation, in: W.A. Van Der Sluys, R.S. Piascik, R. Zawierucha (Eds.), Effects of the Environment on the Initiation of Crack Growth, ASTM STP 1298, American Society for Testing and Materials, 1997, pp. 18-31. [5] T.C. Lindley, P. McIntyre, P.J. Trant, Met. Technol. 9 (1982) 135-142. [6] Y. Kondo, Corrosion 45 (1989) 7-11. [7] S. Kawai, K. Kasai, Fatigue Fract. Engng. Mater. Struct. 8 (2) (1985) 115-127. [8] D.W. Hoeppner, Model for Prediction of Fatigue Lives Based Upon a Pitting Corrosion Fatigue Process, ASTM STP 675, American Society for Testing and Materials, 1979, pp. 841-870. [9] T. Goswami, D.W. Hoeppner, J. Mech. Behavior Mater. 10 (5-6) (1999) 261- 278. [10] P.N. Clark, D.W. Hoeppner, J. Mech. Behavior Mater. 13 (2) (2002) 91-105. [11] D.G. Harlow, R.P. Wei, Probability modeling and material microstructure applied to corrosion and fatigue of aluminum and steel alloys, Engineering Fracture Mechanics 76 (2009) 695-708. [12] P. Shi, S. Mahadevan, Damage tolerance approach for probabilistic pitting corrosion fatigue life prediction, Eng Fracture Mech 68 (2001) 1493-1507. [13] Z. Xiulin, W. Rong, On the corrosion fatigue crack initiation model and expression of metallic notched elements, Eng Fracture Mech 57 No. 6 (1997) 617-624. [14] J. D. Atkinson, J. Yu, Z. Y. Chen, Z. J. Zhao, Modeling of corrosion fatigue crack growth plateux for RPV steels in high temperature water, Nuclear engineering and design 184 (1998) 13-25. 14 [15] D. W. Hoeppner, V. Chandrasekaran, A.M.H Taylor, Review of pitting corrosion fatigue models, Proceedings of 20th ICAF Symposium, Structural Integrity for the Next Millenium, Dayton OH, 2000 pp 253-276. [16] D. W. Hoeppner, Model for prediction of fatigue lives based upon a pitting corrosion fatigue process, American Society for Testing and Materials, 1979. [17] Z. Khan, M. Younas, Corrosion-fatigue life prediction for notched components based on the local strain and linear elastic fracture mechanics concepts, Int. J Fatigue Vol. 18 No. 7, pp 491-498, 1996. [18] G Murtaza, R Akid, Empirical corrosion fatigue life prediction models of a high strength steel, Eng Frac Mech, 67, (2000) 461-474. [19] S. Swift, Sticks and stones: could the words of aeronautical fatigue hurt us? 26th ICAF Symposium - Montreal June 2011. [20] R. Wanhill, T. Hattenberg, Fractography based estimation of fatigue crack "initiation" and growth lives in aircraft components, NLR Technical Publication NLR-TP 2006-184, National Aerospace Laboratory, Amsterdam, Netherlands. [21] G. Clark, Fleet recovery and life extension - some lessons learned. ICAF 2011: Structural integrity, influence of efficiency and green imperatives [22] P. Bressolette, A. Chateauneuf, Probabilistic lifetime assessment of RC structures under coupled corrosion-fatigue deterioration processes, Structural Safety 31 (2009) 84-96. [23] M. Liao, N. C. Bellinger, J. P. Komorowski, Modeling the effects of prior exfoliation corrosion on fatigue life of aircraft wing skins, Int J Fatigue 25 (2003) 1059-1067. [24] D. V. Ramsamooj, T. A. Shugar, Modeling of corrosion fatigue in metals in an aggressive environment, Inh J Fatigue 23 (2001) S301-S309. [25] W. Rong, A fracture model of corrosion fatigue crack propagation of aluminum alloys based on the material elements fracture ahead of a crack tip, Int J Fatigue 30 (2008) 1376-1386. [26] K. Jones, S. R. Shinde, P. N. Clark, D. W. Hoeppner, Effect of prior corrosion on short crack behavior in 2024-T3 aluminum alloy, Corrosion Science 50 (2008) 2588-2595. [27] M. Liao, G. Renaud, N. C. Bellinger, Fatigue modeling for aircraft structures containing natural exfoliation corrosion, Int J Fatigue 29 (2007) 677-686. 15 [28] R. P. Wei, G. S. Chen, K-C Wan, T. H. Flurnoy, Transition from pitting to fatigue crack growth - modeling of corrosion fatigue crack nucleation in a 2024-T3 aluminum alloy, Materials Science and Eng A219 (1996) 126-132. [29] P. N. Clark, D. W. Hoeppner, Corrosion pitting behavior of 2024-T3 aluminum considering the effects of loading and sheet thickness, (2001) ASC 01-2552. [30] K. Jones, D.W. Hoeppner, Prior corrosion and fatigue of 2024-T3 aluminum alloy, Corrosion Science 48 (2006) 3109-3122. [31] K. Jones, D. W. Hoeppner, Pitting corrosion, grain boundaries, and constituent particles: which will win the crack nucleation race? ICAF 2005, Hamburg, Germany. [32] N. Birbilis, R. G. Buchheit, Electrochemical characteristics of intermetallic phases in aluminum alloys, Journal of Electrochemical Society 152 (4) B140- B151 (2005). [33] N. Birbilis, R. G. Buchheit, Investigation and discussion of characteristics for intermetallic phases common to aluminum alloys as a function of solution pH, Journal of Electrochemical Society 155 (3) C117-C126 (2008). [34] M. K. Cavanaugh, R. G. Buchheit, N. Birbilis, Modeling the environmental dependence of pit growth using neural network approaches, Corrosion Science 52 (2010) 3070-3077. [35] K. Jones, D. W. Hoeppner, Pit-to-crack transition in pre-corroded 7075-T6 aluminum alloy under cyclic loading, Corrosion Science 47 (2005) 2185-2198. [36] K. Jones, D. W. Hoeppner, The interaction between pitting corrosion, grain boundaries, and constituent particles during corrosion fatigue of 7075-T6 aluminum alloy, Int J Fatigue 31 (2009) 686-692. [37] R. P. Gangloff, S. Kim, J. T. Burns, Fatigue crack formation and growth from localized corrosion in Al-Zn-Mg-Cu, Eng Fracture Mech 76 (2009) 651-667. [38] K. K. Sankaran, R. Perez, K. V. Jata, Effects of pitting corrosion on the fatigue behavior of aluminum alloy 7075-T6: modeling and experimental studies, Materials Science and Eng A297 (2001) 223-229. [39] D. W. Hoeppner, The formation/nucleation of fatigue cracks in aircrafts structural materials, 26th ICAF Symposium Montreal (2011). 16 [40] D. W. Hoeppner, D Mann, J Weekes, Fracture mechanics based modeling of the corrosion fatigue process, NATO AGARD CP316 Corrosion Fatigue CESME Turkey 1981 CHAPTER 2 EXFOLIATION CORROSION (EC) AND PITTING CORROSION (PC) AND THEIR ROLE IN FATIGUE PREDICTIVE MODELING: STATE OF THE ART REVIEW 6 Abstract Intergranular attack (IG) and exfoliation corrosion have a detrimental impact on the structural integrity of aircraft structures of all types. Understanding the mechanisms and methods for dealing with these processes and with corrosion in general has been and is critical to the safety of critical components of aircraft. Discussion of cases where IG attack and exfoliation caused issues in structural integrity in aircraft in operational fleets is presented herein along with a much more detailed presentation of the issues involved in dealing with corrosion of aircraft. Issues of corrosion and fatigue related to the structural integrity of aging aircraft are introduced herein. Mechanisms of pitting nucleation are discussed that include adsorption-induced, ion migration-penetration and chemico-mechanical film breakdown theories. In addition, pitting corrosion fatigue models are presented as well as a critical 6 Reprinted with Permission from © Hindawi: Publishing Corporation. "Exfoliation Corrosion and Pitting Corrosion and Their Role in Fatigue Predictive Modeling: State-of-the-Art Review," International Journal of Aerospace Engineering, vol. 2012, Article ID 191879, 29 pages, 2012. doi:10.1155/2012/191879 18 assessment of their application to aircraft structures and materials. Finally environmental effects on short crack behavior of materials are discussed, and a compilation of definitions related to corrosion and fatigue is presented. Key Words: Aircraft Structural Integrity, Corrosion Effects, Exfoliation Corrosion; Pitting Corrosion; Fatigue; Intergranular Attack; Corrosion Fatigue, Structural Integrity. Introduction This review article deals with the effects of intergranular attack and exfoliation corrosion on structural integrity of aircraft structures and materials with emphasis on aluminum alloys used over many decades for airframe components of military, commercial and general aviation aircraft. Aluminum alloys have been the material of choice for many components of airframes in the past and remain so even though some aircraft are using more titanium alloys and resin based composites in many airframe components. The general background on phases of life and methods for dealing with corrosion in general and aspects of HOLSIP (Holistic Structural Integrity Processes) paradigm are presented to some extent. (See www.holsip.com.) This is followed by a discussion of corrosion effects on SI (Structural Integrity) with some detail provided on significant effects of corrosion on maintainability and reliability of structures with extensive background material. Subsequently a section that describes intergranular attack and exfoliation in general terms follows which then is followed by a discussion of cases where IG attack and exfoliation caused significant structural integrity issues in aircraft in operational fleets. Studies oriented toward evaluating the effects of IG and exfoliation on fatigue behavior with emphasis on the long crack aspects is presented. The final section then presents recommended studies in order to develop and validate models to allow 19 prediction and management of IG attack and exfoliation as part of a Holistic Structural Integrity Processes paradigm [1-69]7. Phases of life and modeling The phases of life of a structure may be classified according to the division in the Table 2.1. Thus, the total life (LT) of a structure is LT= L1+L2+L3+L4. Fig. 2.1 presents a depiction of the degradation process from a holistic perspective. The regions shown in Fig. 2.1, e.g. 1, 2, 3, and 4, illustrate the portion of life, on the abscissa, and the corresponding growth in discontinuity size plotted schematically on the ordinate. This article concentrates on the phases of life L1 and L2. That is, the corrosion process or processes that results in the formation or nucleation of a specific form of corrosion generating a specific form of discontinuity that is not necessarily a crack like discontinuity (EDS or MDS- see list of definitions in the appendix), and the development of short cracks and their propagation from the initial discontinuity state or from the evolved or modified discontinuity state (IDS- see the list of definitions in the appendix) formed by the mechanism in question. The requirement of the community to come up with design methods to deal with corrosion or other time based degradation, i.e. fatigue, creep, and wear, is essential and some of the elements are depicted in Fig. 2.2. This figure illustrates that most of the quantitative methods that have been developed used the concepts of mechanics of materials with an incorporation of fracture mechanics. The sections of this article that follow will discuss the following major areas:  General effects of corrosion on structural integrity. 7 Numbers in parentheses refer to the references in order of appearance. 20 Table 2.1: Phases of Life. See Fig. 2.1. {from Hoeppner, 1971[69], 1982 [38], 1985 [39]}  FORMATION OR NUCLEATION OF DEGRADATION/DAMAGE BY A SPECIFIC PHYSICAL OR CORROSION PROCESS INTERACTING WITH THE FATIGUE PROCESS IF APPROPRIATE. CORROSION AND OTHER PROCESSES MAY ACT ALONE TO FORM/NUCLEATE THE DAMAGE. A TRANSITION FROM THE FORMATION/NUCLEATION STAGE TO THE NEXT PHASE MUST OCCUR. PHASE L1 TO SOME OTHER PHASE.  MICROSTRUCTURALLY DOMINATED CRACK LINKUP AND PROPAGATION ("SHORT" OR "SMALL" CRACK REGIME). PHASE L2.  CRACK PROPAGATION IN THE REGIME WHERE LEFM, EPFM, OR FPFM MAY BE APPLIED BOTH FOR ANALYSIS AND MATERIAL CHARACTERIZATION (THE "LONG" CRACK REGIME). PHASE L3.  FINAL INSTABILITY. PHASE L4. NOTE: In some cases in practice not all the phases cited above occur. 21 Fig. 2.1: A depiction of the degradation process {after Hoeppner-1971 [69], 1982 [38] 1985 [39]}. Discontinuity Size Life A 4 A= "FIRST" detectable crack 1. Nucleation phase, "NO CRACK" 2. "SMALL CRACK" phase-steps related to local structure (Anisotropy) 3. Stress dominated crack growth, LEFM, EPFM 4. Crack at length to produce instability 1 2 3 The degradation process 22 Fig. 2.2: Methods for each life phase {after Hoeppner-1971 [69], 1982 [38] 1985 [39]}. 23  Intergranular attack and Exfoliation Corrosion (EC) in Aircraft Structural Aluminum Alloys. Efforts to date on Modeling Effects of Exfoliation Corrosion in Aircraft Structure with emphasis on fatigue and fatigue crack propagation behavior. The issue of the effects of corrosion on structural integrity of aircraft has been a question of concern for some time [1-36]. The potential effects are many and they can be categorized as follows: (An attempt has been made to provide as simple a statement of each potential problem as possible. In the discussion below the use of the terms global and local refers to the likely extent of the corrosion on the surface of a component. Global means the corrosion would be found on much of the component whereas local means the corrosion may be localized to only small, local areas.): 1) Reduction of section with a concomitant increase in stress (e.g., thickness change, etc.). Global or local. 2) Production of stress concentration. Local. 3) Nucleation of cracks. Local, possibly global. Source of Multiple-site cracking. 4) Production of corrosion debris. This may result in surface pillowing by various means, which may significantly change the stress state and structural behavior. Local and global. 5) Creation of a situation that causes the surfaces to malfunction. Local and global. 6) Cause environmentally assisted crack growth (EACG) under cyclic (corrosion fatigue or corrosion-fatigue) or sustained loading (SCC) conditions. Local. 24 7) Create a damage state that is missed in inspection when the inspection plan was not developed for corrosion or when corrosion is missed. Local and global. 8) Change the structurally significant item due to the creation of a damage state not envisioned in the structural damage analysis or fatigue and strength analysis. If the SSI is specified, for example, by location of maximum stress or strain, then the corrosion may cause another area(s) to become significant. Local or global. 9) Create an embrittlement condition in the material that subsequently affects behavior. Local or global. 10) Create a general aesthetic change from corrosion that creates maintenance to be done and does damage to the structure. Local or global. 11) Corrosion maintenance does not eliminate all the corrosion damage and cracking or the repair is specified improperly or executed improperly thus creating a damage state not accounted for in the design. Local or global. 12) Generation of a damage state that alters either the durability phase of life or the damage tolerant assessment of the structure or both. 13) Creation of a widespread corrosion damage (WCD) state or a state of corrosion that impacts the occurrence of widespread fatigue damage (WFD) and its concomitant effects. [1, 3, 4, 13, 15, 26, 27, 28, 32, 33, 34, 35, 36]. 14) Produce a condition that may cause a loss of fail safety in conjunction with one or more issues noted above. The question of whether corrosion, corrosion fatigue, corrosion/fatigue or and stress corrosion cracking (see appendix for definitions used herein) are safety concerns or just maintenance/economic concerns has been a point of discussion related to aircraft 25 structural integrity for over 50 years. Nonetheless, a great deal of the aircraft structural integrity community believes that corrosion related degradation is just an economic or maintenance concern. The issue of type of corrosion and its effects on structural integrity has been addressed in other summaries. This brief introduction gives a summary of some of the compilations of information related to corrosion in general. The major section that follows presents more information on the studies to date that have focused or are focusing on intergranular attack and exfoliation corrosion. It was with the issue of safety or economic concerns that led Campbell and Lehay [12] and Wallace, Hoeppner and Kandachar [13] to pursue the presentation of technical facts and knowledge to illustrate the potential for a safety issue as well as maintenance and/or economic issue. Finally, Hoeppner et al. [28] reviewed failure data obtained from USAF, USN, USA, FAA, and the NTSB related to aircraft incidents and accidents in the USA from 1975-1994 to evaluate further the potential for corrosion and fretting related degradation to be significant safety issues. A quote from the introduction to the paper [28] follows: "On July 25, 1990, a pilot and crew were killed when the right wing outboard of the engine nacelle separated from their Aero Commander (now Twin Commander) 680 while performing a geological survey. The aircraft entered an uncontrolled decent and crashed into a field near Hassela, Sweden. Investigations revealed that the wing failed due to corrosion pits, which nucleated fatigue cracks in the lower spar cap"[28]. Although the accident occurred in Sweden, this accident sparked inspections of other Twin Commander aircraft worldwide. In November of 1991, Twin Commander released a service report detailing extensive cracking problems found in the lower spar cap of a 26 U.S. registry airplane. The Australian Civil Airworthiness Authority (CAA), on behalf of the Federal Aviation Administration (FAA), conducted fractographic analyses on ten cracks found in the component. The CAA determined that the cracks formed by intergranular attack, pits and resulted in stress corrosion cracks and that further extension occurred by fatigue. These failures will be referred to later in the section on IG and exfoliation and more detail will be provided. The mechanism overlap (two or more corrosion or degradation mechanisms being involved in change of damage state) frequently has been observed as documented by reference 13 as well. The above example illustrates how corrosion pits and IG attack can severely jeopardize the structural integrity and safety of aircraft. In addition to corrosion, fretting and fretting fatigue have proven, on occasion, to be significant safety hazards. This article will not deal with fretting and fretting fatigue as the first author has written extensively about this elsewhere and these mechanisms of degradation were not to be included in this brief summary. Although the aircraft industry directs a great deal of attention to safety concerns, for many years it has relegated corrosion and fretting to maintenance, economic, and inspection issues. While the industry has developed some corrosion/fretting prevention programs, it has not done what it possibly should to quantitatively evaluate the effects of corrosion/fretting on structural integrity. What attempts have been made in this area are sporadic and limited in number [28]. Walter Schütz addressed this issue further in the Plantema Lecture at ICAF [26]. Furthermore, anyone that doubts the potential catastrophic consequences of corrosion related degradation of aircraft structure would be assisted by reading Steve Swift's 27 insightful presentation related to "The Aero Commander Chronicle" [27]. As a part of a technical paper delivered by Hoeppner et al. at ICAF-1999, they found the following with regard to pitting corrosion and pitting corrosion fatigue as listed in Table 2.2. The examples shown in the table, taken with the general information cited in the references clearly show that corrosion related degradation is a significant safety issue in the assurance of structural integrity of aircraft. No such compilation has been done for exfoliation alone but needs to be done in the authors' opinion. In recent years more emphasis has been placed on this issue of corrosion effects on structural integrity-especially after the fleet surveys subsequent to the Aloha Airlines accident (AA243) in 1988 [16]. Even though the NATO-AGARD community authorized the production of a manual on corrosion case studies and a great deal of information was presented in the manual published by AGARD [13] it is essential that the RMS deficiencies that may arise before accidents occur be recognized. This clearly has not been the case in all major fleets of aircraft whether they are military or commercial [12, 16, 19-22, 23, 26-28]. Another issue that is clear is that deficiencies in the analysis of failures and the databases exist [28, 29]. The potential regrettable occurrence of accidents from corrosion related crack formation/nucleation is a constant threat to aircraft safety. The following quote from the recent NATO RTO conference on fatigue in the presence of corrosion adds some understanding to the need for greater effort to understand the potential role of effects of corrosion on structural integrity. "Some of the workshop papers discussed the significance of corrosion-fatigue as a safety issue or an economic issue. There is ample data to support the contention 28 Table 2.2: Incidents from Pitting Corrosion and Corrosion Fatigue. that it is definitely an economic issue. There is also ample data to support the contention that it has not been a significant safety problem. However, the problem is certainly a potential safety concern if maintenance does not perform Aircraft Location of Failure Cause Incident Severity Place Year From Bell Helicopter Fuselage, longeron Fatigue, corrosion and pitting present Serious AR 1997 NTSB DC-6 Engine, master connecting rod Corrosion pitting Fatal AK 1996 NTSB Piper PA- 23 Engine, cylinder Corrosion pitting Fatal AL 1996 NTSB Boeing 75 Rudder Control Corrosion pitting Substantial damage to plane WI 1996 NTSB Embraer 120 Propeller Blade Corrosion pitting Fatal and serious, loss of plane GA 1995 NTSB Gulfstrea m GA-681 Hydraulic Line Corrosion pitting Loss of plane, no injuries AZ 1994 NTSB L-1011 Engine, compressor assembly disk Corrosion pitting Loss of plane, no injuries AK 1994 NTSB Embraer 120 Propeller Blade Corrosion pitting Damage to plane, no injuries Canada 1994 NTSB Embraer 120 Propeller Blade Corrosion pitting Damage to plane, no injuries Brazil 1994 NTSB Mooney Mooney 20 Engine, interior Corrosion pitting, improper approach Minor injuries TX 1993 NTSB C-130 Bulkhead 'Porkchop' Fitting Fatigue, corrosion pitting Pressurization leaks - 1995 LMAS C-141 FS998 Main Frame Corrosion pitting, stress corrosion cracking Found crack during inspection - 1991 LMAS 29 their task diligently. In addition, management must continuously update established maintenance and inspection practices to address additional real-time degradation threats for aircraft operated well beyond their initial design certification life. The economic issue alone is sufficient to motivate the support of research and development that can reduce the maintenance burden. This research will also reduce the threat of catastrophic failure from the corrosion damage." [Lincoln, J., Simpson, D., Introduction to Reference 36]. Another quote from a different reference sheds further light on this issue [34-page 1-1]. "At the present time, structural life assessments, inspection requirements, and inspection intervals, are determined by Durability and Damage Tolerance Assessments (DADTAs) using fracture mechanics crack growth techniques in accordance with the Aircraft Structural Integrity Program (ASIP). These techniques do not normally consider the effects of corrosion damage on crack initiation or crack growth rate behavior. Also, these techniques do not account for multiple fatigue cracks in the DADTAs of the structural components susceptible to WFD. For aircraft that are not expected to have significant fatigue damage for many years, such as the C/KC-135, this approach has severe limitations since it does not account for corrosion damage or WFD. The impact of corrosion damage and WFD on stress, fatigue life, and residual strength must be understood to ensure maintenance inspections and repair actions are developed and initiated before serious degradation of aircrew/aircraft safety occurs." 30 Thus, the community clearly now recognizes the potential impact of corrosion related degradation on structural integrity of aircraft. The need to understand the potential for the occurrence of corrosion on aircraft components is critical. Thus, to even begin the assessment of this potential the community needs to know the following:  The chemical environment likely to be encountered on the structure of interest at the location of interest, The material from which the component is manufactured,  The orientation of the critical forces (loads) applied externally and internally with respect to the critical directions in the material. The susceptibility of the material to occurrence of a given type of corrosion. The temperature of exposure of the component. The type of forces applied (i.e., sustained force or cyclic force-constant amplitude loading or variable amplitude loading). The type of exposure to the chemical environment (i.e., constant, intermittent), concomitant with the forces (corrosion fatigue or stress corrosion cracking) or sequentially with force (corrosion/fatigue or corrosion-fatigue),  The rates of corrosion attack. The potential influence of the effects of corrosion on fatigue crack nucleation and propagation,  The impact of any related corrosion degradation to residual strength,  The potential for widespread corrosion damage to occur (WCD), and  The potential impact of corrosion on the occurrence of widespread fatigue damage (WFD) and its impact on structural integrity. Obviously this is a formidable list but the assessment of these items is possible to some degree to make the estimation of the effects of corrosion more accurate than they have been to date. 31 This article deals with the identification of the issues to be dealt with in establishing methods of estimating (predicting) the effects of corrosion. To do this various models are employed to be able to identify methods of establishing those components most susceptible to the ravages of corrosion. Corrosion in Aircraft Structural Aluminum Alloys General Corrosion is an electrochemical reaction process between a metal or metal alloy and its environment [37]. For corrosion to occur, four conditions must exist viz. an anode, a cathode, an electrolyte, and an electrical path (flow of electrons). The anode and the cathode could be of two dissimilar metals or anodic and cathodic cells could be formed in the same metal alloy because of the potential difference in the constituent chemical elements or grain interior and grain or phase boundaries. Moreover, depending on the availability of oxygen (differential aeration cells) and electrolyte (differential concentration cells) on the surface of the metal alloy, special types of localized corrosion could occur. 2xxx (Al-Cu alloys) and 7xxx (Al-Zn alloys) series aluminum alloys are most commonly used in manufacturing aircraft structural components. This is currently true and has been true for some time. Depending upon strength and toughness requirements, different types of aluminum alloys such as 2024, 7075, 7178, and many others are used for commercial and military aircraft fuselage skins, wing skins, and other extrusions and forging such as stringers, and fuselage frames. In general, 2024-T3 is used for skins and 7075-T6 for stringers and frames although many applications of these and other alloys in the 2xxx and 7xxx families exist. Lap or butt splices are the common configuration for longitudinal joints whereas butt joints are for circumferential joints. A 32 common joining method is riveting and in some cases it is in combination with adhesive bonding. In older aircraft, spot welding also can be found. As Wallace and Hoeppner mentioned in their AGARD report on "Aircraft Corrosion: Causes and Case Histories", in the initial stages, corrosion is in the form of filiform or pitting in the interior and exterior of fuselage skins [38]. Moreover, as noted in their report, crevice corrosion between the riveted sheets in fuselage joints is a significant issue and it is usually associated with the trapped small "stagnant solution." Furthermore, depending upon the chemical conditions this could lead to a combination of pitting, galvanic or exfoliation corrosion. As well, it is recognized that fretting corrosion/wear in faying surfaces and within fastener holes plays a role in the corrosion mechanisms within aircraft joints [38]. The process of corrosion may start early in the process of manufacturing and continues when the aircraft enters its service. Therefore, it has been realized that the corrosion prevention and control program (CPCP) should be planned concurrently from the initial design until the aircraft is out of service. Furthermore design allowables should be established as with other major integrity issues. Many types of corrosion mechanisms such as intergranular, exfoliation, pitting, crevice, fretting, microbiologically influenced corrosion, stress corrosion cracking, and hydrogen embrittlement have been found to occur in aircraft structural aluminum alloys [38]. Moreover, the synergistic effects of corrosion and the loading conditions have been found to initiate the corrosion fatigue failure process and the stress corrosion cracking failure process of aluminum alloy aircraft structural components. As identified, recently, in a report by the National Research Council's National Materials Advisory Board [39], corrosion in aircraft structural joints would result in the following: (i) significant changes 33 in the applied stress because of material loss as well as corrosion product buildup that may cause "pillowing" or bulging of aluminum alloy sheet, (ii) hydrogen embrittlement that may result in reduced toughness, strength, and ductility of the material, and (iii) increase in fatigue crack growth rates that may severely hamper the planned inspection intervals. These issues have been discussed in workshops presented for the US-FAA and UCLA as well as FASIDE Int. Inc. workshops since 1971. In addition, the first author has frequently discussed the following other potential effects of corrosion on structural integrity.  Production of localized stress concentrations that act as crack nucleation sites.  Change of the structurally significant item (SSI).  Modification of the fail safety by any of the above. Moreover, recently, an attempt has been made to model loss of thickness due to crevice corrosion growth in a corroded lap joint. Several metallurgical, mechanical and environmental factors influence the corrosion process in aluminum alloys [40]. Metallurgically induced factors include heat treatment, chemical composition of alloying element, material discontinuities such as the presence of voids, inclusions, precipitates, second phase particles, and grain boundaries as well as grain orientation. Environmental factors include temperature, moisture content, pH, type of electrolyte, and the time of exposure. Aircraft often are exposed to both external and internal environments. External surfaces of the aircraft are exposed to a variety of environments including rain, humidity, acid-rain, deicing fluid, industrial pollutants, hot and cold temperatures, dust, high content of deposits of exhaust gases from engines, and salts. In addition, the inside of the aircraft is affected by condensed 34 moisture, spilled beverages, cargo leak, deicing fluid, lavatory seepage, and accumulated water in the fuel tank as well as others. Moreover, aircraft are exposed to wide ranges of environment depending upon their route and geographical location viz. tropical, marine, industrial and rural [38, 52]. In both military and commercial aircraft, internal and external wing structures as well as the fuselage bilge areas and flight control surfaces are found to be most affected by corrosion in a marine and tropical environment [41]. The major causes of corrosion in aging aircraft as observed in Indonesian aging aircraft were found to be due to spillage of toilet liquid, contamination due to spillage or evaporation from the cargo compartment, and contamination due to high humidity [42]. In addition, in these aircraft, corrosion was often found in the area surrounding the cargo compartment, wing structure, and landing gear. The types of corrosion found in these aircraft were of exfoliation, galvanic, filiform, and stress corrosion and among these exfoliation corrosion was found in most cases [42]. Several "structural issues" such as exfoliation, pitting, stress corrosion cracking, fatigue cracking, fastener corrosion, wear, fatigue and corrosion, delamination and disbonds have been observed in the U.S. Air Force aging aircraft as shown in Table 2.3 [39]. For example, in C/KC 135 fleet, crevice corrosion in the spot welded lap joint/doubler and corrosion around the steel fasteners on the upper wing skin have been recognized as significant corrosion issues [43]. In the later case, as was noted, there was a possibility of moisture from condensation or deicing solution trapped around fastener heads forming a galvanic couple. This was observed to result in intergranular attack of the grain boundaries leading to exfoliation [43]. 35 Table 2.3: Corrosion and Fatigue Issues in the US Air Force Aging Aircraft. Type of aircraft Issues 1 C/KC 135 (Tanker aircraft) Corrosion between fuselage lap joints and spot welded double layers, around fasteners in the 7178-T6 aluminum upper wing skins, between wing skins and spars, between bottom wing skin and main landing gear trunnions, between fuselage skin and steel doublers around pilot windows, Stress Corrosion Cracking (SCC) of large 7075-T6 aluminum forging (fuselage station 620, 820, and 960), corrosion and SCC of fuselage station 880 and 890 floor beams, wing station 733 closure rib, and corrosion in the E model engine struts. 2 C-141B (Transport aircraft) Widespread Fatigue Damage (WFD) in the fuel drain holes in the lower surfaces of the wings, corrosion and SCC in the upper surface of the center wing, fatigue cracking and SCC around the wind shield, fatigue cracking in the stiffeners in the aft pressure door, SCC in the fuselage main frames, and corrosion in the empennage. 3 C-5 (Airlifter) SCC of the 7075-T6 aluminum mainframes, keel beam, and fittings in the fuselage, 7079-T6 fuselage lower lobe and aft upper crown. 4 B-52H (Bomber) Cracking in the bulkhead at body station 694, fatigue cracking in flap tracks and in the thrust brace lug of the forward engine support bulkhead, cracking in the side skin of the pressure cabin, aft body skins, and upper surface of the wing. 5 F-15 (Fighter aircraft) Low-cycle fatigue cracking in the upper wing surface runouts, upper wing spar cap seal grooves, front wing spar conduit hole, upper in-board longeron splice plate holes, corrosion in nonhoneycomb structure including fuselage fuel tank, the outboard leading-edge structure of the wings, and the flap hinge beam. 6 F-16 (Fighter aircraft) Cracking of the vertical tail attachment bulkhead at fuselage station 479, fuel vent holes of the lower wing skin, the wing attach bulkhead at fuselage station 341, the upper wing skin, fastener problems on the horizontal tail support boxbeam, and the ventral fin. 36 Table 2.3 Continued 7 A-10 (Attack aircraft) Fatigue cracking in the wing auxiliary spar cutout of the center section rib at wing station 90, outer panel front spar web at wing station 118 to 126, outer panel upper skin at leading edge. Fatigue cracking in the center fuselage forward fuel cell floor at the boost pump, forward fuselage gun bay compartment, forward fuselage lower longeron and skin at fuselage station 254, and center fuselage overwing lower floor panel stiffeners. Fatigue cracking in the aft nacelle hanger frame, thrust fitting and the engine inlet ring assembly skin/frame. Fatigue cracking in the main landing gear shock strut outer cylinder. Exfoliation corrosion in the 2024-T351 aluminum lower wing skin, 7075-T6 aluminum upper wing at the leading edge, 2024-T3511 aluminum lower front spar cap, 7075-T6 aluminum fuselage bottom skin 2024-T3/7075-T6 aluminum fuselage side skin and beaded pan, and 2024-T3511 aluminum horizontal stabilizer upper spar caps. Pitting corrosion in the 9Ni-4Co-0.3C steel wing attach fitting bushing and lug bore, main landing gear fitting attach bolts, 7075-T6 aluminum aft fuel cell aft bulkhead, and 2024-T351 center fuselage upper longeron. SCC in the wing attach bushing flange, and the main landing gear attach bolts. 8 E-3A (Airborne Warning and Control System) Fatigue and corrosion in the 7178-T6 rudder skins, and spoiler actuator clevis. Exfoliation corrosion in the 7178-T6 upper wing skin, leading edge slats, main landing gear door, fillet flap, fuselage stringer 23, and magnesium parts. Delamination and disbonds in the windows, floor panels, and nose radome core. Wear in the antenna pedestal turntable bearings. 9 E-8 (Joint Surveillance and Attack Radar System) "Small" fatigue cracks in fastener holes in the 7075-T6 aluminum stringers, in the 2024-T3 aluminum skins. 10 T-38 (Air training command aircraft Fatigue cracking in the lower surface of the wing, lower wing skin fastener holes, wing skin access panel holes, milled pockets on the lower wing skin, and the fuselage upper cockpit longerons. SCC in the fuselage cockpit upper and lower longerons, fuselage forgings. honeycomb corrosion in the horizontal stabilizer (due to water intrusion), and the landing gear strut door 37 Examination of C/KC 135 fuselage lap splices (stiffened aluminum lap joint) revealed that outer skin corrosion was predominantly intergranular and exfoliation [44]. Moreover, extensive cracking was noted at these sites in the outer skin. In addition, extensive "pillowing" with more than 300% change in volume due to corrosion products along the faying surfaces was observed. In the rivet/shank region, severe localized corrosion and intergranular corrosion were observed. The fracture of rivet heads was attributed to high local stress due to environmentally assisted cracking at the junction. As well, in this study, solution samples were collected from selected areas of lap splice joints and the solution analysis showed the presence of several cations such as Al3+, Ca2+, Na+, K+, and Ni2+ and also anions Cl-, SO42-, and NO3-. Subsequent potentiodynamic tests using solution containing these ions led to the belief that dissolution rates could completely penetrate the fuselage outer skin during service life [44]. Thus, in addition to fatigue cracking, different corrosion mechanisms occur in aircraft structures depending upon their location, geometry, exposure to environment, and loading conditions. Research studies conducted within the Quality and Integrity Design Engineering Center (QIDEC) at the University of Utah as well as other related studies are briefly discussed below. Intergranular and Exfoliation Corrosion Exfoliation corrosion is believed to be a manifestation of intergranular corrosion. Intergranular corrosion results from either the segregation of reactive impurities or from the depletion of passivating elements at the grain boundaries. This makes the regions at or surrounding the grain boundaries less resistant to corrosion resulting in preferential 38 corrosion. The high strength aluminum alloys such as 2xxx and 7xxx series are highly susceptible to intergranular corrosion [37]. Exfoliation corrosion is a form of intergranular attack that occurs at the boundaries of grains elongated in the rolling direction. The 7xxx series aluminum alloys are particularly less resistant to exfoliation corrosion because during heat treatment (to achieve maximum desirable strength) their constituent elements copper and zinc accumulate at grain boundaries leaving the adjacent region free of precipitates. As aluminum and aluminum intermetallic compounds are highly reactive in the EMF series as well as aluminum is anodic to copper in the galvanic series, the resulting galvanic couples cause the grain boundaries to preferentially corrode (intergranular attack). McIntyre and Dow have related the localized corrosion problems in the 7075-T7352 fuel tanks of underwater weapon systems to intergranular corrosion [45]. In their study, aluminum alloys 7075 and 6061 were exposed to artificial seawater containing nitrate ions. It was observed that accelerated intergranular corrosion occurred in 7075 alloys. From the test results, they hypothesized that refueling the improperly cleaned fuel tank may cause the propellant in contact with the small quantity of sea water remaining in the fuel tank. This resulted in the release of nitrate ions from an hydrolysis process leading to reduced pH that may cause the dissolution of the oxide film (localized corrosion). They further hypothesized that corrosion eventually propagates to the bulk regions of the alloy due to intergranular attack by the preferential corrosion of reactive MgZn2 intermetallic compounds located at grain boundaries. This was found to be true for 7075 aluminum alloy but not for 6061 aluminum alloy because the latter does not contain either Cu or Zn as alloying element [45]. 39 Reducing the impurities such as iron and silicon as well as heat treatment modifications in aluminum alloys have resulted in an increase in the resistance to exfoliation corrosion [46]. For example, overaged 7075-T7 alloys are more resistant to exfoliation corrosion when compared to 7075-T6 alloys. In addition, Rinnovatore showed that in the T6 temper, exfoliation corrosion resistance was found to be greater for forgings produced from rolled bar stock than forgings from extruded bar stock [47]. Moreover, it was shown that rapid quenching from the solution temperature in cold water increased exfoliation corrosion resistance of forgings tempered to T6. Fatigue and exfoliation interactions have been studied. Mills reports that most of the studies have been performed during the last five years on this issue although Shaffer in 1968 reported significant reduction in the fatigue life of exfoliated extruded 7075-T6 spar caps [48]. Moreover, multiple crack nucleation sites were observed in 7075-T651 [49], and 2024-T3 [50] aluminum alloy specimens when the specimens were subjected to exfoliation corrosion and then fatigue tested under positive R values with constant amplitude loading. Mills found an 88% decrease in the fatigue life of the specimens with prior exfoliation corrosion damage when compared to specimens tested without prior corrosion damage. Chubb et al. showed in their study using panels containing fastener holes that the end grains exposed in the rivet holes would be the potential corrosion sites that could eventually result in multiple site damage. In a recent study [48], experiments were performed to determine the effect of exfoliation on the fatigue crack growth behavior of 7075-T651 aluminum alloy. First the specimens were subjected to prior-corrosion damage using ASTM standard EXCO corrosive solution and then fatigue tested in corrosion fatigue environments of dry air, 40 humid air, and artificial acid-rain. Test results indicated that prior-corrosion damage resulted in higher crack growth rates than when tested in dry air as well as in acid-rain environments when compared to uncorroded specimens. Fractographic analysis showed quasi-cleavage fracture close to the exfoliated edge of the specimens tested in all the three environments indicating embrittlement by prior-corrosion. Thus, embrittlement by prior-corrosion was stated to "result in accelerated crack nucleation, faster short crack growth, and earlier onset of fatigue phenomena such as multiple-site damage." Corrosion fatigue Corrosion fatigue is defined as "the process in which a metal fractures prematurely under conditions of simultaneous corrosion and repeated cyclic loading at lower stress levels or fewer cycles than would be required in the absence of the corrosive environment" [40]. Corrosion acting conjointly with fatigue can have major effects on materials in structures of aircraft. First, corrosion can create discontinuities (pits, cracks, etc.) that act as origins of fatigue cracks with significant reductions in life at all stress levels. In crack propagation, corrosion effects are well known to produce accelerated fatigue crack propagation. The combination of aggressive environment and cyclic loading conditions has been observed to accelerate crack growth rates in aluminum alloys. Several mechanisms were proposed to explain the corrosion fatigue process [37]. They are: (i) dissolution of material at the crack tip in corrosive environment, (ii) hydrogen embrittlement in which diffusion of hydrogen (a by product of corrosion process) into the lattice space that could weaken the atomic bonds thereby reducing the fracture energy, (iii) theory of adsorbed ions in which the transport of critical species to the crack tip results in lowering of the energy required for fracture, and (iv) film-induced 41 cleavage in which it is hypothesized that crack speed would increase at the film-substrate interface when the crack grows through the low toughness oxide layer leading to the rupture of the film. In general, corrosion fatigue effects on crack propagation are more pronounced at lower stress intensities whereas at higher stress intensities the crack propagates at such a high rate that the effects of chemical dissolution or localized embrittlement will be negligible. Several parameters affect corrosion fatigue crack propagation rates. For example, crack growth rates increase with increase in the stress intensity range. Also, at lower frequency corrosion fatigue effects will be more severe than at higher frequency because of the time dependent nature of the process. Increase in R value has been found to generally increase corrosion fatigue crack propagation rates. As well, increasing the concentration of corrosive species, lowering the pH, increasing the moisture content, and temperature usually result in more severe effects [40]. The most common corrosion fatigue environment that is simulated in laboratory testing is 3.5% NaCl as it is believed to result in severe general corrosion rates as well as it represents roughly the salinity of sea water. In addition, other environments such as humid air, salt sprays, and artificial acid rain (to simulate industrial pollutants) also are used to characterize corrosion fatigue crack growth behavior of aluminum alloys. As aircraft are exposed to several complex chemical environments both inside and outside, no single environment could simulate the actual condition. Therefore, a few studies used sump tank water that was considered close to a "realistic chemical environment" [51]. The quest for realistic corrosion fatigue environment led Swartz et al. [52] to collect and analyze solution samples from bilge areas, external galley and lavatories of five different 42 airplanes. As a result, a new chemical environment was developed to perform corrosion fatigue crack growth experiments on 2024-T351, 2324-T39, 7075-T651, and 7150-T651 aluminum alloys. For all the alloys studied the fatigue crack propagation rates in synthetic bilge solution were found to be between the dry air and the 3.5% NaCl data. In another study [53], cyclic wet and dry environment was simulated in characterizing the corrosion fatigue crack growth rates in 2024-T351 aluminum alloy. It was hypothesized that during the dry cycle the partial evaporation of the aqueous solution may allow some chemical species to get deposited at the crack tip and then in the wet cycle when the rehydration occurs, corrosion could occur at a greater rate than before. To simulate aircraft service corrosion, fatigue crack growth studies were conducted on service corroded 2024-T3 aluminum panels extracted from a C/KC-135 aircraft [54]. Test results showed that in some cases fatigue crack growth rates were two or three times greater in the corroded material, however, in other cases, there was little difference. It was observed that "the difference in the crack growth rates was due to high variability in the amount of corrosion damage between specimens". Corrosion Pillowing and its Effect on Structural Integrity of Aircraft Lap Joints Recently, some studies have shown that the increase in stress levels is not only because of the thickness loss due to corrosion but also due to the volume of the corrosion product build-up in a joint [55]. Also, evidences show that lap joints contain "faying cracks" under the rivet heads in the corroded areas. The complexity of this issue as explained by Komorowski et al. is that "the majority of the cracks had not penetrated the outer skin surface and appeared to grow more rapidly along the faying surface creating a 43 high aspect ratio semi-elliptical crack and it is difficult to detect and affects the structural integrity of the joint" [55]. As reported by Krishnakumar et al. [56], the major corrosion product in the lap splices is found to be aluminum oxide trihydrate, an "oxide mix" which has a high molecular volume ratio to the alloy. As the oxide is insoluble, it is found to remain within the joint and in turn is responsible to deform the skins in the joint which usually gives a bulging appearance, commonly termed as "pillowing". Moreover, finite element analysis revealed that for a two layer joint the stresses due to 6% thinning due to corrosion resulted in stress more than the yield strength of 2024-T3 aluminum alloy [57]. In addition, "pillowing induced deformation" was observed on the corroded joints after removal of the rivets and the separation of the skin. Moreover, multiple cracks were found to nucleate from rivet holes. Fracture mechanics analysis has shown that as the pillowing increases, the stress intensity factor for the crack edge along the faying surface increases [58]. On the other hand, the stress intensity factor decreases for the crack edge along the outer surface. Therefore, it was hypothesized that pillowing produces compressive stresses in the rivet area on the outer surface because of the resultant bending stresses. At the same time, high tensile stress is produced on the faying surface resulting in more rapid growth of faying surface cracks in the direction of the row of rivets than through the skin towards the outer surface [58]. Pitting Nucleation Theories Pitting corrosion is defined as "localized corrosion of a metal surface, confined to a point or small area that takes the form of cavities" [40]. Pitting is a deleterious form of localized corrosion and it occurs mainly on metal surfaces which owe their corrosion resistance to passivity. The major consequence of pitting is the breakdown of passivity, 44 i.e. pitting, in general, occurs when there is breakdown of surface films when exposed to pitting environment. Pitting corrosion is so complicated in nature because "oxide films formed on different metals vary one from another in electronic conduction, porosity, thickness, and state of hydration" [59]. The empirical models that have been developed to understand the pitting process are closely related to the integrity of the metal oxide film. The salient features of the empirical theories related to pit nucleation mechanisms are mentioned in Table 2.4. Therefore, nucleation of pits generally involves certain localized changes in the structure and properties of the oxide film. However, propagation of pits is related to the dissolution of the underlying bulk metal. Further discussion on this subject is presented later in this article. Pitting Corrosion Overview Pitting is classified as a localized attack that results in rapid penetration and removal of metal at "small" discrete areas [84]. An electrolyte should be present for pitting to occur. The electrolyte could be a film of condensed moisture, or a bulk liquid. How and when pitting occurs on a metal depends on numerous factors, such as, type of alloy, its composition, integrity of its oxide film, presence of any material or manufacturing induced discontinuities as well as chemical and loading environment, to name a few. Many metals and their alloys are subject to pitting in different environments. These include alloys of carbon steels, stainless steels, titanium, nickel, copper, and aluminum [85]. 45 Table 2.4: Pit Nucleation Theories Proposed by Theory Evans et al. [60] (1929-30) Proposed penetration theory. Ability of a chloride ion to penetrate the film was linked to the occurrence of pitting. Halide ions are assumed to be transported from the film-solution interface to the metal-oxide interface either by the application of electric field or exchange of anions. Hoar et al. [61, 62] (1960s) Assumed the adsorption of anions on the oxide surface as the key aspect in the pit nucleation process. Proposed "ion-migration" model that involves activating anions that enter the oxide film lattice without exchange thereby increasing the ionic conductivity of the film resulting in local high anodic dissolution rates and pitting. Proposed "mechanical" model in which it was assumed that adsorption of anions at the oxide-solution interface lowers the interfacial energy resulting in the formation of cracks in the protective oxide film under the influence of the "electrostatic repulsion" of the adsorbed anions. Suggested a concept of local acidification of pit as a critical factor in pit growth. Uhlig [63] and Kolotyrkin [64] (1961- 1967) Proposed adsorption theory in which at a certain value of the potential (pitting potential) the adsorption of aggressive anions on the metal surface displaces the passivating species such as oxygen. Kolotyrkin suggested that adsorption of anions at preferred sites forming soluble complexes with metal ions from the oxide. Once such species leave the oxide, thinning of the film starts locally increasing the electric field strength which accelerates the dissolution of the oxide. Sato [65, 66] (1971, 1982) Proposed that at a critical potential an internal film pressure exceeds the critical compressive stress for film fracture. Considered thinning of film at local sites and suggested that pitting occurs only when a critical concentration of aggressive anions and a critical acidity is locally built up. Macdonald et al. [67] (1981) Proposed that metal vacancies may accumulate as a result of the diffusion of metal cations from the metal/film to the film/solution interface, forming voids at the metal/film interface. When the voids grow to a critical size the passive film will collapse leading to pit growth. 46 In passivated metals or alloys that are exposed to solutions containing aggressive anions, primarily chloride, pitting corrosion results in local dissolution leading to the formation of cavities or "holes". The shape of the pits or cavities can vary from shallow to cylindrical holes and the cavity is approximately hemispherical [86]. The pit morphology depends on the metallurgy of the alloy and chemistry of the environment as well as the loading conditions. As observed first by McAdam in 1928, these pits may cause local increase in stress concentration and cracks may nucleate from them [87]. According to Foley [88], pitting corrosion of aluminum occurs in four steps: (1) adsorption of anions on the aluminum oxide film, (2) chemical reaction of the adsorbed anion with the aluminum ion in the aluminum oxide lattice, (3) penetration of the oxide film by the aggressive anion resulting in the thinning of the oxide film by dissolution, and (4) direct attack of the exposed metal by the anion. The susceptibility of a metal to pitting corrosion as well as the rate at which pitting occurs on its surface depends on the integrity of its oxide film. Therefore, a brief overview of the mechanisms of the formation of passive film is discussed below. Formation of Passive Films and their Growth The following discussion on the oxide film formation and its growth is extracted from ref. [89]. Early investigators examined the effects of natural waters on metals by placing them outside. One investigator, Liversidge, in 1895, observed that an aluminum specimen, ... "lost its brilliancy, and became somewhat rough and speckled with grey spots mixed with larger light grey patches; it also became rough to the feel, the grey 47 parts could be seen to distinctly project above the surface, and under the microscope they presented a blistered appearance. This encrustation is held tenaciously, and does not wash off, neither is it removed on rubbing with a cloth" [90]. Liversidge proposed that a hydrated aluminum oxide had formed, but did not confirm this with further testing of the layer. He did, however, note that when weighed, the aluminum specimens gained weight with exposure, rather than losing weight [91]. It was later confirmed that the weight gain was due to formation of an oxide film [92]. Although Liversidge suggested the formation of an aluminum oxide film, subsequent investigators proposed other theories to explain the passive behavior of aluminum. Some of these were changes in the state of electric charge on the surface, changes in valence at the surface, and a condensed oxygen layer [93]. Dunstan and Hill proved the presence of the oxide film on the surface of the metals in 1911. Through experiments with iron, they determined that the passive film was reduced at 250 °F, the temperature at which magnetic iron oxide is reduced. Similar films were found on other metals [93]. Barnes and Shearer attempted to determine the constitution of passive films on aluminum and magnesium in 1908. They determined that aluminum formed hydrogen peroxide when reacting with water and that the passive film consisted of Al2(OH)6 [92]. This was later determined to be incorrect [94]. Structure of the Passive Film in Aluminum It later was determined that this film on aluminum consists of an aluminum oxide created when the aluminum comes in contact with an environment. Generally, this film is 48 amorphous; however, under certain circumstances it will develop one of seven crystalline structures: 1. Gibbsite (also called hydrargillite): (-Al2O3•3H2O) 2. Bayerite: (-Al2O3•3H2O) 3. Boehmite: (-Al2O3•H2O or AlO•OH) 4. Diaspore: (-Al2O3•H2O) 5. Gamma alumina: (-Al2O3) 6. Corundum: (-Al2O3) 7. Combinations of aluminum oxides with inhibitors, for example (2Al2O3•P2O5•3H2O) Gibbsite and diaspore structures are not found during corrosion of aluminum, but are frequently found in bauxite ores. Boehmite, bayerite, gamma alumina, and corundum are sometimes found in the passive layers of aluminum under certain conditions. Additionally, bayerite is frequently found as a corrosion product during pitting of aluminum. Combinations of aluminum oxides with inhibitors are not understood very well in the literature, but it is known that they will combine with oxide layer to form improved corrosion resistance through changing the passive film structure. Several researchers have studied changes in the amorphous structure of the oxide film. In one investigation, the passive film formed on the pure aluminum sheet revealed changes in structure with an increase in temperature and oxygen content. Prior to heating, the structure was reported to be amorphous oxide. As the temperature was increased, the amorphous film thickened, formed boehmite, and bayerite. The rate of film formation increased with temperature, and with an increase in oxygen content, intergranular attack began. The researcher suggested the following sequence of events in the formation: 49 boehmite is nucleated at dislocation centers that are at the surface of the amorphous film; it then grows by a diffusion mechanism. During thickening of the boehmite, a process occurs that allows aluminum ions to escape into the solution, which results in bayerite growth [95]. Other investigations revealed that aluminum in the molten state would develop an oxide film of gamma alumina which will convert to corundum when exposed to dry air. Aluminum sheet in water at temperatures below 70 to 85 °C after long aging will develop a passive film consisting of bayerite. Boehmite is found on aluminum exposed to water at high temperatures (above 70 to 85 °C) [94]. More recently, researchers have found small regions of crystallized -alumina within the amorphous layers created during anodizing [96]. During exposure to air and water, alumina will form a passive film with a duplex structure. The film will consist of two layers, a permeable outer layer, and a protective, nonporous layer next to the metal's surface. In the case of an air environment, the protective layer is thicker and the permeable layer is comparatively thin. In the case of an immersion in water, the permeable layer is thicker and the protective layer is thinner. In both cases, the total thickness of the duplex film is the same [94]. The protective layer will quickly reach maximum thickness, with the permeable layer growing slower. The growth rate of each layer depends on a few parameters. In air, it is dependent on temperature; in water, it is dependent on temperature, oxygen content, pH, and the type of ions present in the electrolyte; and in anodization procedures, it depends on electrolyte and applied potential. The film is typically formed on pure aluminum when the pH of the solution is between 4.5 to 8.5 [94]. 50 Other researchers have suggested that the permeable outer layer consists of hexagonal close-packed pores in pure aluminum. The size of these pores will depend on conditions of formation. Sealing processes in an attempt to improve the characteristics of the passive film sometimes controls these conditions of formation. In sealing processes, the pores are blocked or made smaller by boehmite or gamma alumina formation, nickel acetate is added to obstruct the pores, or dichromates or chromates can be added to create pores of a different structure [97]. The passive film formed on metals will differ according to the environment in which it forms. Studies done by Seligman and Williams in the 1920s illustrate this difference. In experiments with tap water, the presence or absence of certain impurities caused either the passive film to breakdown and the metal to corrode or, the film will become thick and less susceptible to corrosion. They determined that nitrates and chromates would combine with the passive film and serve to increase resistance of the passive film to localized corrosion [98]. Later studies emphasized this conclusion. One researcher found a film of 55,000 angstroms in distilled water and another found a film of only 4,800 angstroms for the same alloy (AA-1099) immersed in tap water [94]. Additionally, experiments performed by Bengough and Hudson on aluminum in sea water showed that the passive film varied with corroding liquid and with different alloying elements [91]. In a more recent paper, researchers determined that the reaction between aluminum and water takes place in three steps: formation of the amorphous oxide, dissolution of the oxide, and deposition of the dissolved products as hydrous oxide. In the first step, the amorphous oxide layer is formed and grows by the anodic and cathodic 51 reactions present at the water/metal interface. The second step involves a hydrolysis reaction with the surface which depends on temperature, pH and aluminum concentration and the last step is accomplished when the resulting hydroxide is deposited on the surface. The rate at which the film will grow is controlled by the diffusion of water molecules through the existing layers. At temperatures between 50 and 100 °C, pseudoboehmite grows on the amorphous oxide. At 40 °C, however, bayerite crystallization occurs and with time will overcome the pseudoboehmite [99]. Upon exposure of an air-formed-film to water, the air-formed-film will break down and another film will form that is thicker and contains more water. The rate at which the film is reformed depends on the anions present and the temperature [94]. In more recent work, the water in the aluminum passive film has been stated to be a medium for the mobilization for aluminum cations and deposited anions [100]. In air, the thickness of the passive film is dependent on humidity. In higher humidity, the oxide layer is thicker. The growth rate of the film, however, does not depend on humidity. Rosenfeld et al. found that in high purity air, the growth rate was not changed. However, when small amounts of impurities were added, growth was accelerated in humid air [101]. In addition to impurities, the growth of the film is highly dependent on temperature. Below 200 °C, the film will grow only to a few hundred angstroms, above 300 to 400 °C, the rate gradually increases, between 400 and 600 °C, the film will grow to a thickness of 400 angstroms, at 450 °C, the film will crystallize to gamma alumina [94]. 52 Pitting Potential and Induction Time According to Smialowska [85], the susceptibility of a metal or alloy to pitting can be estimated by determination of one of the following criteria:  Characteristic pitting potential,  Critical temperature of pitting,  Number of pits per unit area, or weight loss and  The lowest concentration of chloride ions that may cause pitting. One of the most important criteria to determine an alloy's susceptibility to pitting corrosion is to find the pitting potential, i.e., the potential at which the passive film starts to break down locally. The potential above which pits nucleate is denoted by Ep and the potential below, which pitting does not occur and above which the nucleated pits can grow, is often indicated by Epp. Once the passive film begins to breakdown, the time it takes to form pits on a passive metal exposed to a solution containing aggressive anions, for example, Cl-, is called the induction time or incubation time [85]. The induction time is meaningful in a statistical sense as it represents the average rate of reaction over the whole surface to produce a measurable increase in current. It should not be considered as the time to form the first pit. This is because "micro" pits have been observed to form during the induction time [88]. The induction time is usually denoted by . It is measured as the time required producing an appreciable anodic current at a given anodic potential. It is expressed as 1/ = k (E-Ep), where E is the applied potential and K is a function of Cl- ion concentration [102]. In general, pitting potential decreases with increasing Cl- ion concentration. 53 The most commonly used relation for estimating t is based on an exponential relationship between time and activation energy i.e. 1/ = Ae-Ea/RT; the activation energy needed for pit nucleation can be obtained from an Arrhenius plot of log (1/) vs. 1/temperature [88]. As well, Hoar and Jacob [103] have proposed a relationship 1/ = K (Me)m (X-)n to estimate the induction time. Where Me is the metal ion concentration, X-is the halide ion concentration, and m and n are orders of reaction which are determined experimentally. Subsequent to the nucleation of pits it has been observed they grow. The following subsection presents a discussion of pit growth. Pit Growth Rate and Pit Morphology Godard [104] developed a simple but effective relation based on the experimental data to estimate the rate at which pits grow. The empirical relation he developed was d = K (t1/3). Even though he found this relation when tested using aluminum, it was observed to be true for other materials in different types of water environments. In general, the rate of pit growth depends on several factors such as temperature, pH, properties of passive films, chloride ion concentration, presence of anions and cations in solution, and the orientation of the material [5]. The pit growth can be viewed as a direct interaction of the exposed metal with the environment. Upon observing the geometry of the pits formed on 7075 aluminum alloy in halide solutions, Dallek [105] proposed a pit growth rate expression i - ip = a (t - ti)b in which current was expressed as a function of time. In this expression, i is the dissolution current, ip is the passive current, t is the time, ti is the induction time, a is the constant depending on the halide, and b is the constant depending on the geometry of the pit. 54 From this expression, a plot of log (i - ip) vs. log (t - ti) will give the slope b. Dallek predominantly observed pits of hemispherical shape. However, Nguyen et al. [106] have observed hemispherical pits at low potential on 1199 aluminum alloy in chloride solutions and at high potential they observed a porous layer film covered on the pit mouth with orifice at the center. This study indicated the effect of potential on the morphology of pits. Chloride ion concentration also was found to affect the pit morphology. Baumgartner and Kaesche [107] observed that in dilute to medium concentrated solutions, pit morphology was "rough" whereas at high concentration, pits were found to be "smooth and rounded." In addition, a recent study by Grimes [89] showed clearly the effect of loading conditions on the morphology of pits. This study was conducted on 7075 - T6 aluminum alloy in 3.5% salt water under three different loading conditions, viz. zero, sustained and cyclic. It was found that the pits propagated under cyclic loads were three times larger in cross sectional area when compared to those grown under sustained or zero load conditions. Also, it was found that most of the pits originated from the grain boundaries. This study concludes that the effect of both mechanical and chemical environment must be considered in pitting corrosion studies. However, when studying the effect of pitting on the fatigue life of aluminum alloy 7075- T6 in 3.5% NaCl solution, Li [108] found that although the test frequency (5 and 20 Hz) had a pronounced effect on the total corrosion fatigue life, the fatigue test frequency did not have any effect on the pit morphology. On the other hand, Chen et al. [109] have found that the size of the pit from which a crack nucleated was comparatively larger at the lower frequencies and stresses than at higher frequencies and stresses when fatigue tested using 2024-T3 aluminum alloy. 55 Mechanisms of Pit Nucleation In general, pit nucleation mechanisms are classified into three categories. (i) Adsorption-induced mechanisms, (ii) Ion migration and penetration models, and (iii) Mechanical film breakdown theories. Adsorption-Induced Mechanisms In this section mechanisms of pit nucleation based on the adsorption of aggressive anions at energetically favored sites are discussed. Many researchers including Uhlig et al. [110-112] Hoar et al. [103, 113] and Kolotyrkin [114] have suggested mechanisms related to the ion-adsorption concepts (see Table 2.5). Many of the mechanisms proposed in the literature consider this as a necessary step in the pit nucleation process. Uhlig [110- 112] and Kolotyrkin [114] independently proposed that both oxygen and chlorine anions can be adsorbed onto the metal surfaces. When the metal is exposed in air, oxygen is adsorbed by the metal resulting in the formation of passive oxide film. Consequently, a chemical bond is established between the oxygen anion and the metal cation. This process is known in corrosion terminology as "chemisorptions." Chemisorption results in the formation of a metal-compound that covers the surface of a metal. If aluminum is exposed in oxygen, the resulting compound is aluminum oxide, i.e., Al2O3. However, the type of compound that is formed on the metal surface depends on the environment in which the metal is exposed. For example, in the case of salt water, Cl- ions in addition to oxygen are present. When oxygen is adsorbed, passivation of metal occurs whereas if chlorine anion is adsorbed, it does not result in passivation but breakdown of passivity occurs. 56 As proposed by Kolotyrkin [114], below the pitting potential, metals may prefer to adsorb oxygen and above this critical potential metals may adsorb halides, such as Cl- This mechanism is termed "competitive adsorption" as the presence of different anions will compete with the oxygen to be chemisorbed by the metal. Therefore, at or above the pitting potential, chlorides and other aggressive anions if present, combine with the metal and then diffuse from the metal's surface into the solution. Subsequently, it combines with water in solution to form metallic oxides, hydrogen and chloride ions. These chloride ions are attracted to the surface of the metal and the process begins again. It was hypothesized by many researchers that the chloride ions might diffuse to regions of high energy such as inclusion, dislocations and other form of discontinuities. Hoar et al. [103, 113] originally proposed a "complex ion formation theory" which stated that the formation of Cl- containing complexes on the film-solution interface might lead to a locally thinned passive layer. This was proposed because Cl- - containing complexes are more soluble when compared to complexes formed in the absence of halides. They assumed that a high-energy complex is formed when a small number of Cl- ions jointly adsorb around a cation in the film surface, which can readily dissolve into solution. This creates a stronger anodic field at this site that will result in the rapid transfer of another cation to the surface where it will meet more Cl- and enter into solution. Experimental support was provided for this concept by Strehblow et al [115] by conducting an investigation on the attack of passive iron by hydrogen fluoride. They found that the breakdown process occurred with complete removal of the passivated oxide layer. It was observed that hydrogen fluoride catalyzed the transfer of Fe3+ and Ni2+ ions from oxide into the electrolyte. As mentioned in a paper by Bohni [116], 57 similar observation was made in another study by Heusler et al. regarding the influence of chloride containing borate and phthalate solutions on the passive film breakdown of iron. Different behavior of Cl- and F- ions in the pit nucleation process was proposed in a model by Heusler et al. Cl- ions were suggested to form only two dimensional "clusters" leading to the localized thinning of the passive layer. However, it was proposed that F-ions adsorb homogeneously on the oxide surface thereby promoting a general attack. It should be noted that the proposed models did not take into account material discontinuities such as point "defects", dislocations, inclusions, voids and others. Also, another model based on the concept of an increased probability of "electrocapillary film breakdown" was proposed by Sato [117] (see Table 2.5). Although Sato includes the effect of dislocations in this purely theoretical approach, no experimental evidence was found in the literature to support his model. However, Sato's theoretical model proposed that n-type passive oxide films are more stable than p-type films because of the difference in the band structure of electron levels. From these studies it can be concluded that in addition to chloride anions, other anions such as chromate and sulphate also get adsorbed changing the nature of the compound. In addition, as observed by Richardson and Wood [118], enhanced adsorption takes place at the "imperfections or flaws" in the oxide film. These discontinuities in the film usually become the sites of anion adsorption. Nilsen and Bardal [119] have observed by measuring the pitting potential of four aluminum alloys (99% pure Al, Al-2.7Mg, Al- 4.5Mg-Mn, and Al-1Si-Mg) and found that the pitting potential values for the four alloys were within only 25 mv. From this study, they concluded that alloy composition does not directly depend on the adsorption step of the process. 58 Table 2.5: Adsorption-Induced Mechanisms Proposed by Summary Description Limitations 1 Uhlig et al. 1950-69 Kolotyrkin 1961 Hoar 1967  Proposed concepts based on either competitive adsorption or surface complex ion formation.  In competitive adsorption mechanism Cl-anions and passivating agents are simultaneously adsorbed. Above a critical potential Cl-adsorption is favored resulting in the breakdown of passivity.  Kolotyrkin suggested that there were critical Cl-/inhibitor concentration ratios, depending on the potential above which pitting would occur.  Occurrence of induction times varying with passive film thickness cannot be explained. 59 Table 2.5: Continued 2 Sato 1982  Proposed a theoretical concept based on the potential dependent transpassive dissolution which depends on the electronic properties of the passive film.  The electrochemic al stability of a passive film depends strongly on the "electron energy band structure" in the film.  Stated that the critical potential above which potential-dependent dissolution of the film occurs will be less noble at the sites of chloride ion adsorption.  As a result of the increased dissolution rate above the critical potential, local thinning of the passive films occurs until a steady state is reached.  Proposed that the local thinning of the oxide film as a mechanism of pit "initiation"  Included the effect of dislocations similar to the influences of Cl-ions.  Knowledge of the electronic properties of passive films has not been fully understood.  Experimental evidence for this mechanism is lacking. 60 Ion Migration and Penetration Models A few models (see Table 2.6) were proposed based on either penetration of anions from the oxide/electrolyte interface to the metal/oxide interface or migration of cations or their respective vacancies. This theory is based on the concept that Cl- ions migrate through the passive film and results in breakdown of the film once they reach the metal/film interface. Hoar and Jacob [103] explain that when a critical potential is reached, smaller ions, like Cl-, may penetrate the film under the influence of an electrostatic field which exists across the film. These aggressive anions prefer the high energy regions like grain boundaries and impurities as sites for migration because these regions produce thinner passive film locally. During the migration, the ions either pass through the film completely or they may combine with the metal cation in the midst of the film resulting in the formation of what is called a "contaminated" film, which is a better conductor than the "uncontaminated" film. This process results in an autocatalytic reaction, which encourages more ions to penetrate the film. This hypothesis is supported by some researchers as they have observed a higher concentration of Cl- ions over thin films on the surface of iron as well as that the time to breakdown the film increases with the thickness of the film [120]. It was further hypothesized that Cl- ions first fills anion vacancies on the surface of the passive film and then migrates to the metal/oxide interface. However, other works revealed that the time required for Cl- to penetrate through the film is much longer than the induction time measured experimentally [116]. Later, Macdonald et al. [121] proposed a model in which the growth of the passive film was explained by the transport of both anions (e.g., oxygen ion) and cations (e.g., metal ion). Diffusion of anion from film-solution interface to metal-film interface 61 Table 2.6: Ion Migration and Penetration Models Proposed by Summary Description Limitations 1 Hoar et al. 1965  Presented that when the electrostatic field across the film/solutio n interface reaches a critical value correspondi ng to the critical breakdown potential, the anions adsorbed on the oxide film enter and penetrate the film.  Favored sites for ion migration are suggested to be high-energy regions like grain boundaries and impurities where thinner passive films are produced.  If the aggressive ions meet a metal cation, contaminated film is produced that encourages further ions to penetrate the film. Then, this process continues as an autocatalytic reaction.  Did not explain the observation that pits often form from mechanical breaks in the oxide film or from scratches. 2 Macdonal d et al. 1981  Presented a theoretical model to explain the chemical breakdown of passive film.  Proposed that metal vacancies may accumulate as a result of the diffusion of metal cations from the metal/film to the film/solution interface, forming voids at the metal/film interface. When the voids grow to a critical size the passive film will collapse leading to pit growth.  Surface discontinuities such as grain boundaries etc. were not considered in developing the model.  No direct observation of void formation was made.  As the measured induction times usually show a large scatter, definite quantitative agreement is difficult to obtain. 62 results in thickening of the film. Cation diffusion from the metal-film interface to the film-solution interface results in the creation of metal vacancies at the metal/film interface. These metal vacancies usually "submerge" into the metal itself. However, if the cation diffusion rate is higher than the rate of vacancy submergence into the bulk metal, the metal vacancies will increase leading to the formation of voids at the metal/film interface. This process is known as "pit incubation". Subsequently, when the void reaches a critical size, the pit incubation period ends leading to the local rupture of the passive film. This eventually results in pit growth at that local site. Based on this theory, Macdonald et al expressed a criterion for pit "initiation" as stated below. (Jca - Jm) * (t - ) =  where, Jca is the cation diffusion rate in the film, Jm is the rate of submergence of the metal vacancies into the bulk metal, t is the time required for metal vacancies to accumulate to a critical amount x  is a constant, Also, in this model, the role of the halide ion in accelerating the film breakdown by increasing Jca was suggested. The ion penetration and migration theories do not include the effect of mechanical breakdown of the oxide film that may result because of the scratches from which pits can nucleate. Nor is the mechanical breakdown of the oxide film included that results from strain and local cracking of the oxide film. In addition MacDonald et al [122] have proposed a "point defect" model for anodic films to calculate Jca for "thin" films on the order of 10-40 A. Also, the "point 63 defect" model could be used to calculate incubation times. Although, the "point defect" model was one of the most detailed models proposed, this model has some limitations as mentioned in Table 2.4. Mechanical Film Breakdown Theories - Chemico-Mechanical Breakdown Theories Pit nucleation models proposed so far based on the concepts of the "chemico-mechanical" breakdown of films have not included the effect of externally applied stresses (see Table 2.7). Sato [123] showed that a significant film pressure always acted on "thin" films that he attributed to "electrostriction". Sato expressed a relation between the film pressure, thickness and surface tension of the film as follows. p = po + [((-1)2)/8] -/L where p is the film pressure, po is the atmospheric pressure,  is the film dielectric constant,  is the electric field,  is the surface tension, and L is the film thickness. According to his hypothesis, both  and L have significant influence on film pressure p. Based on this relation, Sato suggested that the adsorption of chloride ion significantly reduces the surface tension  thereby increasing p. Also, he proposed that when p is above the critical value, the film might break down. In addition, Sato proposed that breakdown of the film occurs when it attains a thickness at which mechanical stresses caused by "electrostriction" become critical. Therefore, building up of critical stresses in the film could cause pitting. In addition to the aforementioned theory, some researchers have observed the influence of mechanically produced discontinuities (such as scratches in the passive film) on the formation of pits along those scratches [124]. 64 Table 2.7: Chemico-Mechanical Breakdown Theories Proposed by Summary Description Limitations 1 Sato 1971  Proposed a breakdown mechanism for anodic films from thermodyna mic consideratio ns.  Showed that thin films always contain film pressure due to "electrostriction".  Hypothesized that both the surface tension of the film and the film thickness has a significant effect on film pressure.  Proposed that adsorption of chloride ions, depending on their concentration, greatly reduces surface tension.  Experimental proof is not found. 2 Sato 1982  Derived an equation for the work required to form a cylindrical breakthrough pore in the passive film.  Proposed that for a pit nucleus to grow to macroscopic size a critical radius corresponding to critical pore formation energy must be exceeded.  Experimental proof is not found.  Microstructura l parameters such as grain boundaries, inclusions that may influence pitting "initiation" were not considered. If there is a scratch in the passive film that sets up a local anodic site, which will eventually, be the preferred site for pit to form. This smaller anode/cathode ratio results in higher local potential leading to the nucleation of pits. Other researchers proposed a similar theory that is related to the value of product of the length of the discontinuity and the current density. Assuming a unidirectionally growing pit, if this value exceeds a critical value, the discontinuity such as "fissures" in the oxide film may form a local area 65 of low pH leading to the formation of pits from them. This happens due to the difference in the pH at the local site (fissure) when compared to the bulk solution. It was proposed that a fissure of size in the order of 10-6 cm could be a limiting condition for this to happen [125]. Hoar [113] also assumed that the presence of pores or "flaws" could mechanically stress and damage the passive films in contact with an aggressive solution. Moreover, Hoar assumed that aggressive anions would replace water and reduce surface tension at the solution-film interface by repulsive forces between particles, producing cracks. In conclusion, there is no full agreement among the researchers regarding the mechanisms of pit nucleation. However, as the pitting process itself is a complex one, the commonly accepted view is that the first step in the pit nucleation process is the localized adsorption of aggressive anions on the surface of the passivated metal. Several experimental studies also have indicated that the preferred sites for the passage of anions through the oxide film are the discontinuities present in an alloy. Such discontinuities are non-metallic inclusions; second phase precipitates, pores or voids, grain or phase boundaries as well as other mechanical damages [85]. These discontinuities eventually may become pit nucleation sites. The aforementioned theories on pit nucleation are based purely on electrochemical concepts. However, the breakdown of surface film is dependent not only on the solution conditions (e.g., pH), and the electrochemical state at the metal/solution interface, but also on the nature of the material as well as the stress state. In addition, the aforementioned pit nucleation mechanisms did not take into account the material parameters such as the microstructural effects, inherent discontinuities such as voids, inclusions, second phase particles as well as the externally 66 applied stress. Moreover, localized corrosion also may take place at slip bands during fatigue loading [126]. Once the pit is formed, the rate of pit growth is dependent mainly on the material, local solution conditions and the state of stress. Cracks have been observed to form from pits under cyclic loading conditions. Therefore, to estimate the total corrosion fatigue life of an alloy, it is of great importance to develop some realistic models to establish the relationship between pit propagation rate and the stress state. Furthermore, pitting corrosion in conjunction with externally applied mechanical stresses, for example, cyclic stresses has been shown to severely affect the integrity of the oxide film as well as the fatigue life of a metal or an alloy. Therefore, to understand these phenomena, some models based on pitting corrosion fatigue mechanisms have been proposed as discussed below. Pitting Corrosion Fatigue Linear Elastic Fracture Mechanics (LEFM) concepts are widely used to characterize the crack growth behavior of materials under cyclic stresses in different environmental conditions. It is important to note that both pitting theory and crack growth theory have been used in model development as follows. Pit growth rate theory proposed by Godard is combined with fatigue crack growth concepts. The time to form/nucleate a Mode I crack from the pit (under cyclic loading) could be modeled using LEFM concepts. Based on this idea, a few models [127-130] were proposed since 1971 (see Table 2.8). All of the models assume hemispherical geometry for the pit shape and the corresponding stress intensity relation is used to determine the critical pit depth using 67 Table 2.8: Pitting Corrosion Fatigue Models [137-235]. Proposed by Summary Description Advantages/ Limitations 1 Hoeppner (1971 - current)  Proposed a model to determine critical pit depth to nucleate a Mode I crack under pitting corrosion fatigue conditions.  Combined with the pit growth rate theory as well as the fatigue crack growth curve fit in a corrosive environment, the cycles needed to develop a critical pit size that will form a Mode I fatigue crack can be estimated.  Using a four parameter Weibull fit, fatigue crack growth threshold (Kth) was found from corrosion fatigue experiments for the particular environment, material, frequency, and load spectrum.  The stress intensity relation for surface discontinuity (half penny shaped crack) was used to simulate hemispherical pit. i.e.) where,  is the applied stress, a is the pit length, and Q is the function of a/2c, Sty.  Using the threshold determined empirically, critical pit depth was found from the stress intensity relation mentioned above.  Then, the time to attain the pit depth for the corresponding threshold value was found using where, t is the time, d is the pit depth, and c is a material/environment parameter.  This model provides a reasonable estimate for hemispherical geometry of the pits.  This model is useful to estimate the total corrosion fatigue life with knowledge of the kinetics of pitting corrosion and fatigue crack growth.  This model did not attempt to propose mechanisms of crack nucleation from corrosion pits.  Quantitative studies of pitting corrosion fatigue behavior of materials can be made using this model.  This model is valid only for the conditions in which LEFM concepts are applicable.  Material dependent. K = 1.1   a Q      t = d c     3 68 Table 2.8: Continued 2 Lindley et al. (1982)  Similar to Hoeppner's model, a method for determining the threshold at which fatigue cracks would grow from the pits was proposed.  Pits were considered as semi-elliptical shaped sharp cracks  Used Irwin's stress intensity solution for an elliptical crack in an infinite plate and came up with the relationship to estimate threshold stress intensity values related to fatigue crack nucleation at corrosion pits. i.e.) where,  is the stress range, a is the minor axis, and c is the major axis of a semi-elliptical crack.  From the observed pit geometry i.e. for a/c ratio, threshold stress intensity can be calculated.  For the corresponding a/c ratio, critical pit depth can be estimated.  The proposed stress intensity relation can be used in tension - tension loading situations where stress intensity for pits and cracks are similar.  Critical pit depths for cracked specimens can be estimated using the existing threshold stress intensity values.  This model is valid only for the conditions in which LEFM concepts are applicable.  Material dependent. Kth   a 1.13 0.07 a  c1  2    1 1.47 a  c 1.64    1 2 69 Table 2.8: Continued 3 Kawai and Kasai (1985)  Proposed a model based on estimation of allowable stresses under corrosion fatigue conditions with emphasis on pitting.  As corrosion is not usually considered in developing S-N fatigue curves, a model for allowable stress intensity threshold involving corrosion fatigue conditions was proposed.  Considered corrosion pit as an elliptical crack.  Based on experimental data generated on stainless steel, new allowable stresses based on allowable stress intensity threshold was proposed. i.e.) Where, Kall can be determined from a da/dN vs. K plot for a material, hmax is the maximum pit depth, and F is a geometric factor.  Using this model, allowable stress in relation to corrosion fatigue threshold as a function of time can be estimated.  Material dependent.  This model is valid only for the conditions in which LEFM concepts are applicable.  all  kall F hmax 70 Table 2.8: Continued 4 Kondo (1989)  Corrosion fatigue life of a material could be determined by estimating the critical pit condition using stress intensity factor relation as well as the pit growth rate relation.  Pit diameter was measured intermittently during corrosion fatigue tests.  From test results, corrosion pit growth law was expressed as 2c  Cp t1/3 where, 2c is the pit diameter, t is the time, and Cp is an environment/material parameter. Then, critical pit condition (Kp) in terms of stress intensity factor was proposed by assuming pit as a crack. where, a is the stress amplitude, a is the aspect ratio, and Q is the shape factor.  Critical pit condition was determined by the relationship between the pit growth rate theory and fatigue crack growth rates. c = cp (N/f)1/3 Where, N is the number of stress cycles, f is the frequency, and 2c is the pit diameter.  The pit growth rate dc/dN was developed using K relation as given below. dc/dN was determined using experimental parameter Cp.  Finally, the critical pit size 2Ccr was calculated from the stress intensity factor relation. i.e.) 2Ccr = (2Q/)( Kp/2.24a)2  The aspect ratio was assumed as constant.  Material and environment dependent. Kp  2.24 a  c Q dc dN  1 3    Cp 3 f 1 2 2Q2 2.24 a   71 the crack growth threshold (Kth) that is found empirically. For hemispherical pit geometry, these models provide a reasonable estimate for the total corrosion fatigue life. However, it is well known that corrosion pit morphology varies widely. Thus, this aspect must eventually be dealt with in LEFM models that attempt to deal with pit growth and the ultimate nucleation of crack(s) from pit(s). As mentioned before, the combined effect of corrosion and the applied cyclic loading have been shown to produce cracks from corrosion pits. In addition, pits have frequently been the source of cracks on aircraft that are operating in fleets. Depending upon the fatigue loading and corrosion conditions, some studies have shown that the crack formation/nucleation site may change from slip bands to corrosion pits [132]. This observation was made when fatigue tested at reduced strain rates in Al-Li-Cu alloy. Another study also showed an anodic dissolution in slip bands in Al-Li-Zr alloy at high stress levels whereas at low stress levels fatigue cracks nucleated from corrosion pits [133]. Therefore, it was hypothesized that at higher stress levels, conditions are favorable to form cracks from slip bands before the corrosion pit reaches the critical condition to favor the nucleation of crack from it. In addition, a recent study also showed that larger pit was formed at lower stress and frequency. It also was observed in 2024-T3 (bare) aluminum alloy in NaCl solution that once pits formed from the constituent particles, because of the applied cyclic stresses, the pits coalesced, laterally and in depth to form larger pits from which crack was observed to nucleate [134]. Therefore, modeling the transition of a pit first to a "short" crack and then to a "long" crack is considered to be important in characterizing the total corrosion fatigue life of a material as discussed in the next section [127, 135,136]. 72 Environmental Effects on "Short" Crack Behavior of Materials A few "small" crack studies under corrosion fatigue conditions have been performed to characterize the transition of a pit to a "small" crack. In 2024 aluminum alloy, Piascik and Willard have shown a three times increase in crack growth rates of "small" cracks in salt water environment when compared to air. Moreover, their studies clearly have observed the transition of pits formed at the constituent particles to intergranular "microcracks" and then to transgranular fracture path once the crack reaches the depth of 100 mm. In addition, the increase in "small" crack growth rates was observed even at very low mode I K (<1 MPa m). As well, Kondo (1989) also observed in two low alloy steels that "short" cracks from pits propagated at K that is well below the threshold value of a long crack for these materials. In a recent in-situ fatigue study, prior pitted 2024-T351 and 7075-T651 aluminum alloy specimens exhibited faster crack growth rates in the "short" crack regime when compared to specimens without prior corrosion damage (A. Hoeppner [now A. Taylor] 1996). This study showed that prior corrosion damage did influence the "small" crack growth rates. It also was observed that the 7075 aluminum alloy specimen had faster crack growth rates compared to the 2024 aluminum alloy specimens. Also, in this study cracks were observed to form from pits on the prior corroded specimens whereas on the specimens without any prior corrosion damage, cracks formed from constituent particles. In addition to a few previous studies (Hoeppner, 1971, 1979) in which pitting was modeled statistically with different materials and specimen types, recently, as discussed before in this article, there was a study demonstrating corrosion fatigue induced "short" crack formation from pits (Akid and Murtaza, 1992). Also, recent studies (Ma and D. Hoeppner, 1994, Grimes, 1996, and A. Hoeppner, 1996) have shown that pits form in 73 different shapes depending upon environment and loading conditions in contradiction to general assumption that pits have hemispherical shape. Although this assumption simplifies the modeling part of research (Kondo, 1989), further studies to characterize the formation of cracks from pits in the "short" crack regime must be evaluated as indicated by A. Hoeppner (1996). Apart from these studies the literature search