Driving forces for localized corrosion-to-fatigue crack transition in Al–Zn–Mg–Cu
J. T. BURNS
Air Force Research Laboratory Materials and Manufacturing Directorate (AFRL/RX), Wright-Patterson Air Force Base, OH 45433, USA
Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904, USA
Search for more papers by this authorJ. M. LARSEN
Air Force Research Laboratory Materials and Manufacturing Directorate (AFRL/RX), Wright-Patterson Air Force Base, OH 45433, USA
Search for more papers by this authorR. P. GANGLOFF
Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904, USA
Search for more papers by this authorJ. T. BURNS
Air Force Research Laboratory Materials and Manufacturing Directorate (AFRL/RX), Wright-Patterson Air Force Base, OH 45433, USA
Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904, USA
Search for more papers by this authorJ. M. LARSEN
Air Force Research Laboratory Materials and Manufacturing Directorate (AFRL/RX), Wright-Patterson Air Force Base, OH 45433, USA
Search for more papers by this authorR. P. GANGLOFF
Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904, USA
Search for more papers by this authorABSTRACT
Research on fatigue crack formation from a corroded 7075-T651 surface provides insight into the governing mechanical driving forces at microstructure-scale lengths that are intermediate between safe life and damage tolerant feature sizes. Crack surface marker-bands accurately quantify cycles (Ni) to form a 10–20 μm fatigue crack emanating from both an isolated pit perimeter and EXCO corroded surface. The Ni decreases with increasing-applied stress. Fatigue crack formation involves a complex interaction of elastic stress concentration due to three-dimensional pit macro-topography coupled with local micro-topographic plastic strain concentration, further enhanced by microstructure (particularly sub-surface constituents). These driving force interactions lead to high variability in cycles to form a fatigue crack, but from an engineering perspective, a broadly corroded surface should contain an extreme group of features that are likely to drive the portion of life to form a crack to near 0. At low-applied stresses, crack formation can constitute a significant portion of life, which is predicted by coupling macro-pit and micro-feature elastic–plastic stress/strain concentrations from finite element analysis with empirical low-cycle fatigue life models. The presented experimental results provide a foundation to validate next-generation crack formation models and prognosis methods.
REFERENCES
- 1 Bucci, R. J., Konish, H. J. and Shaw, B. J. (1995) A technical plan to address aircraft structural problems arising from corrosion/corrosion fatigue. USAF Corrosion/Fatigue Planning Meeting, WP-AFB, OH.
- 2 Cole, G. K., Clark, G. and Sharp, P. K. (1997) The implication of corrosion with respect to aircraft structural integrity, Report DSTO-RR-0201. Melbourne, Australia.
- 3 Koch, G. H., Hagerdorn, E. L. and Berens, A. P. (1995) Effect of preexisting corrosion on fatigue cracking of aluminum alloys 2024-T3 and 7075-T6, Contract AFRL-VA-WP-TR-2004–3057. WP-AFB, OH.
- 4
Smith, C. J. E. (2010) Management of corrosion of aircraft (Edited by
J.A.R. Tony). Shreir's Corrosion. Elsevier,
Oxford
, pp. 3175–3197.
10.1016/B978-044452787-5.00165-7 Google Scholar
- 5 Hoffman, M. E. and Hoffman, P. C. (2001) Corrosion and fatigue research – structural issues and relevance to naval aviation. Int. J. Fatigue 23, S1–S10.
- 6 ASTM. (2004) E606–05 Standard Practice for Strain-Controlled Fatigue Testing. Vol. 03.01. ASTM International, West Conshohocken, PA.
- 7 (1997) Fixed Wing Aircraft Structural Life Limits, Instruction 13120.1. Naval Air Systems Command.
- 8 (1998) JSSG-2006 Joint Services Specification Guide – Aircraft Structures. Department of Defense.
- 9 (2005) MIL-STD-1530 (USAF) Department of Defense Standard Practice – Aircraft Structural Integrity Program (ASIP). Department of Defense.
- 10 Weiland, H., Nardiello, J., Zaefferer, S., Cheong, S., Papazian, J. and Raabe, D. (2009) Microstructural aspects of crack nucleation during cyclic loading of AA7075-T651. Eng. Fract. Mech. 76, 709–714.
- 11 Papazian, J., Anagnostou, E. L., Christ, R. J., et al . (2009) DARPA/NCG Structural Integrity Prognosis System, HR0011-04-C-0003. DARPA, Arlington, VA.
- 12 Bozek, J. E., Hochhalter, J. D., Veilleux, M. G., et al . (2008) A geometric approach to modeling microstructurally small fatigue crack formation: I. Probabilistic simulation of constituent particle cracking in AA 7075-T651. Model Simul. Mater. Sc. 16, 1–28.
- 13 Emery, J. M., Hochhalter, J. D., Wawrzynek, P. A., Heber, G. and Ingraffea, A. R. (2009) DDSim: A hierarchical, probabilistic, multiscale damage and durability simulation system – Part I: Methodology and Level I. Eng. Fract. Mech. 76, 1500–1530.
- 14 Bennett, V. P. and McDowell, D. L. (2003) Polycrystal orientation distribution effects on microslip in high cycle fatigue. Int. J. Fatigue 25, 27–39.
- 15 Lukas, P. and Kunz, L. (2003) Small cracks – nucleation, growth and implication to fatigue life. Int. J. Fatigue 25, 855–862.
- 16 Rosenbloom, S. N. and Laird, C. (1993) Fatigue-crack nucleation based on a random slip process. 1. Computer-model. Acta Metall. Mater. 41, 3473–3482.
- 17 Repetto, E. A. and Ortiz, M. (1997) A micromechanical model of cyclic deformation and fatigue-crack nucleation in fcc single crystals. Acta Mater. 45, 2577–2595.
- 18
Gangloff, R. P. (2003) Hydrogen assisted cracking of high strength alloys (Edited by
J. Petit and
P. Scott). Comprehensive Structural Integrity: Environmentally Assisted Fracture. Elsevier,
New York
,
NY
, pp. 31–101.
10.1016/B0-08-043749-4/06134-6 Google Scholar
- 19 Vasudevan, A. K. and Sadananda, K. (2009) Classification of environmentally assisted fatigue crack growth behavior. Int. J. Fatigue 31, 1696–1708.
- 20 Petit, J. and Sarrazin-Baudoux, C. (2010) Some critical aspects of low rate fatigue crack propagation in metallic materials. Int. J. Fatigue 32, 962–970.
- 21 Kim, S., Burns, J. T. and Gangloff, R. P. (2009) Fatigue crack formation and growth from localized corrosion in Al-Zn-Mg-Cu. Eng. Fract. Mech. 76, 651–667.
- 22 Burns, J. T., Kim, S. and Gangloff, R. P. (2010) Effect of corrosion severity on fatigue evolution in Al-Zn-Mg-Cu. Corros. Sci. 52, 498–508.
- 23 Sharp, K., Mills, T., Russo, S., Clark, G. and Liu, Q. (2001) Effects of exfoliation corrosion on the fatigue life of two high-strength aluminum alloys. FAA/DoD/NASA Aging Aircraft 2000, St. Louis, MO.
- 24 Liao, M., Renaud, G. and Bellinger, N. C. (2007) Fatigue modeling for aircraft structures containing natural exfoliation corrosion. Int. J. Fatigue 29, 677–686.
- 25 Gruenberg, K. M., Craig, B. A., Hillberry, B. M., Bucci, R. J. and Hinkle, A. J. (2004) Predicting fatigue life of pre-corroded 2024-T3 aluminum from breaking load tests. Int. J. Fatigue 26, 615–627.
- 26 Crawford, B. R., Loader C, Ward, A. R., et al . (2005) The EIFS distribution for anodized and pre-corroded 7010-T7651 under constant amplitude loading. Fatigue Fract. Eng. Mater Struct. 28, 795–808.
- 27 Van Der Walde, K., Brockenbrough, J. R., Craig, B. A. and Hillberry, B. M. (2005) Multiple fatigue crack growth in pre-corroded 2024-T3 aluminum. Int. J. Fatigue 27, 1509–1518.
- 28 DeBartolo, E. A. and Hillberry, B. M. (2001) A model of initial flaw sizes in aluminum alloys. Int. J. Fatigue 23, S79–S86.
- 29 Sankaran, K. K., Perez, R. and Jata, K. V. (2001) Effects of pitting corrosion on the fatigue behavior of aluminum alloy 7075-T6: modeling and experimental studies. Mat. Sci. Eng. a-Struct. 297, 223–229.
- 30 Medved, J. J., Breton, M. and Irving, P. E. (2004) Corrosion pit size distributions and fatigue lives – a study of the EIFS technique for fatigue design in the presence of corrosion. Int. J. Fatigue 26, 71–80.
- 31 DuQuesnay, D. L., Underhill, P. R. and Britt, H. J. (2003) Fatigue crack growth from corrosion damage in 7075-T6511 aluminium alloy under aircraft loading. Int. J. Fatigue 25, 371–377.
- 32 Van Der Walde, K. and Hillberry, B. M. (2007) Initiation and shape development of corrosion-nucleated fatigue cracking. Int. J. Fatigue 29, 1269–1281.
- 33 Gao, Y. X., Yi, J. Z., Lee, P. D. and Lindley, T. C. (2004) The effect of porosity on the fatigue life of cast aluminium-silicon alloys. Fatigue Fract. Eng. Mater Struct. 27, 559–570.
- 34 As, S. K., Skallerud, B. and Tveiten, B. W. (2008) Surface roughness characterization for fatigue life predictions using finite element analysis. Int. J. Fatigue 30, 2200–2209.
- 35 Rusk, D. T. and Hoppe, W. (2009) Fatigue life prediction of corrosion-damaged high-strength steel using an equivalent stress riser (ESR) model Part I: Test development and results. Int. J. Fatigue 31, 1454–1463.
- 36 Rusk, D. T., Hoppe, W., Braisted, W. and Powar, N. (2009) Fatigue life prediction of corrosion-damaged high-strength steel using an equivalent stress riser (ESR) model. Part II: Model development and results. Int. J. Fatigue 31, 1464–1475.
- 37 Cheong, K. S., Smillie, M. J. and Knowles, D. M. (2007) Predicting fatigue crack initiation through image-based micromechanical modeling. Acta Mater. 55, 1757–1768.
- 38 Patton, G., Rinaldi, C., Brechet, Y., Lormand, G. and Fougeres, R. (1998) Study of fatigue damage in 7010 aluminum alloy. Mat. Sci. Eng. a-Struct. 254, 207–218.
- 39 McDowell, D. L. (2007) Simulation-based strategies for microstructure-sensitive fatigue modeling. Mat. Sci. Eng. a-Struct. 468, 4–14.
- 40 Dowling, N. E. (1999) Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue. 2nd edn. Prentice Hall, Upper Saddle River , NJ , xviii, 830 p.
- 41 Kermanidis, A. T., Petroyiannis, P. V. and Pantelakis, S. G. (2005) Fatigue and damage tolerance behaviour of corroded 2024 T351 aircraft aluminum alloy. Theor. Appl. Fract. Mech. 43, 121–132.
- 42 Petroyiannis, P. V., Kermanidis, A. T., Papanikos, P. and Pantelakis, S. G. (2004) Corrosion-induced hydrogen embrittlement of 2024 and 6013 aluminum alloys. Theor. Appl. Fract. Mech. 41, 173–183.
- 43 Hardie, D., Holroyd, N. J. H. and Parkins, R. N. (1979) Reduced ductility of high-strength aluminium alloys during or after exposure to water. Metal. Sci. 13, 603–610.
- 44 Scamans, G. M., Alani, R. and Swann, P. R. (1976) Pre-exposure embrittlement and stress-corrosion failure in Al-Zn-Mg alloys. Corros. Sci. 16, 443–459.
- 45 Gangloff, R. P. (2002) Environment Sensitive Fatigue Crack Tip Processes and Propagation in Aerospace Aluminum Alloys (Edited by A. Blom). Fatigue 2002. EMAS, Stockholm , Sweden .
- 46 Petit, J., Henaff, G. and Sarrazin-Baudoux, C. (2003) Environmentally asisted fatigue in the gaseous atmosphere (Edited by J. Petit and P. Scott). Comprehensive Structural Integrity: Environmentally Assisted Fracture. Elsevier, New York , NY , pp. 962–970.
- 47 Burns, J. T., Larsen, J. M. and Gangloff, R. P. (2011) Effect of initiation feature on microstructurally small fatigue crack propagation in Al-Zn-Mg-Cu. Int. J. Fatigue In press.
- 48 Burns, J. T. (2010) The effect of initiation feature and environment on fatigue crack formation and early propagation in Al-Zn-Mg-Cu. PhD Dissertation . Materials Science and Engineering. University of Virginia, Charlottesville , VA .
- 49 Burns, J. T. (2006) Modeling fatigue behavior of pre-corroded aluminum alloys using linear elastic fracture mechanics. MS Thesis . Materials Science and Engineering. University of Virginia, Charlottesville , VA .
- 50 Ro, Y. J., Agnew, S. R., Bray, G. H. and Gangloff, R. P. (2007) Environment-exposure-dependent fatigue crack growth kinetics for Al-Cu-Mg/Li. Mat. Sci. Eng. a-Struct. 468, 88–97.
- 51 Ro, Y., Agnew, S. R. and Gangloff, R. P. (2008) Environmental fatigue-crack surface crystallography for Al-Zn-Cu-Mg-Mn/Zr. Metall. Mater. Trans. A 39A, 1449–1465.
- 52 Slavik, D. C. and Gangloff, R. P. (1996) Environment and microstructure effects on fatigue crack facet orientation in an Al-Li-Cu-Zr alloy. Acta Mater. 44, 3515–3534.
- 53 Piascik, R. S. and Gangloff, R. P. (1993) Environmental fatigue of an Al-Li-Cu Alloy. 2. Microscopic hydrogen cracking processes. Metall. Trans. A 24, 2751–2762.
- 54 Wei, R. P. and Gao, M. (1990) Hydrogen embrittlement and environmentally assisted crack growth (Edited by N.R. Moody, and A.W. Thompson). Hydrogen Effects on Material Behavior. TMS, Warrendale , PA , pp. 789–813.
- 55 Gao, M., Pao, P. S. and Wei, R. P. (1988) Chemical and metallurgical aspects of environmentally assisted fatigue crack-growth in 7075-T651 aluminum-alloy. Metall. Trans. A 19, 1739–1750.
- 56 Hirth, J. P. (1980) 1980 Institute of metals lecture the metallurgical-society-of-aime – effects of hydrogen on the properties of iron and steel. Metall. Trans. A 11, 861–890.
- 57 Carter, R. D., Lee, E. W., Starke, E. A. and Beevers, C. J. (1984) The effect of microstructure and environment on fatigue crack closure of 7475-aluminum alloy. Metall. Trans. A 15, 555–563.
- 58 Vasudevan, A. K. and Suresh, S. (1982) Influence of corrosion deposits on near-threshold fatigue crack-growth behavior in 2xxx and 7xxx series aluminum-alloys. Metall. Trans. A 13, 2271–2280.
- 59 Oriani, R. A. (1987) Whitney Award Lecture 1987 – Hydrogen – the Versatile Embrittler. Corrosion 43, 390–397.
- 60 Davidson, D. L. and Lankford, J. (1983) The effect of water-vapor on fatigue crack tip mechanics in 7075-T651 aluminum-alloy. Fatigue Eng. Mater. 6, 241–256.
- 61 Toribio, J. and Kharin, V. (2006) Fractographic and numerical study of hydrogen-plasticity interactions near a crack tip. J. Mater. Sci. 41, 6015–6025.
- 62 Wei, R. P., Pao, P. S., Hart, R. G., Weir, T. W. and Simmons, G. W. (1980) Fracture-mechanics and surface-chemistry studies of fatigue crack-growth in an aluminum-alloy. Metall. Trans. A 11, 151–158.
- 63 Robertson, I. M. (2001) The effect of hydrogen on dislocation dynamics. Eng. Fract. Mech. 68, 671–692.
- 64 Lynch, S. P. (1982) Mechanisms of environmentally assisted cracking in Al-Zn-Mg single-crystals. Corros. Sci. 22, 925–&.
- 65 Birnbaum, H. K., Buckley, C., Zeides, F., et al . (1997) Hydrogen in aluminum. J. Alloy Compd. 253, 260–264.
- 66 Gangloff, R. P., Burns, J. T. and Kim, S. (2005) Laboratory characteriztion and fracture mechanics modeling of corrosion-fatigue interaction for aluminum alloy substitution, Contract F09650–03-D-001. WPAFB, OH.
- 67 Payne, J., Welsh, G., Christ, R. J., Nardiello, J. and Papazian, J. M. (2010) Observations of fatigue crack initiation in 7075-T651. Int. J. Fatigue 32, 247–255.
- 68 Jones, D. A. (1996) Principles and Prevention of Corrosion. 2nd edn. Prentice Hall, Upper Saddle River , NJ , xvi, 572 p.
- 69 ASTM. (2007) G34–01: Standard test method for exfoliation corrosion susceptibility in 2xxx and 7xxx series aluminum alloys, Vol 03.02. ASTM International, West Conshohocken , PA .
- 70 ASTM. (2007) E466–07: Standard practice for conducting force controlled constant amplitude axial fatigue tests of metallic materials. Vol. 03.01. ASTM International, West Conshohocken, PA.
- 71 ASTM. (2005) E1012–05: Standard practice for verification of test frame and specimen alignment under tensile and compressive axial force application. Vol. 03.01. ASTM International, West Conshohocken, PA.
- 72 Hertzberg, R. W. (1996) Deformation and Fracture Mechanics of Engineering Materials. 4th edn. J. Wiley & Sons, New York , xxi, 786 p.
- 73 Sunder, R., Porter, W. J. and Ashbaugh, N. E. (2003) The role of air in fatigue load interaction. Fatigue Fract. Eng. Mater Struct. 26, 1–16.
- 74 Sunder, R. (2005) Fatigue as a process of cyclic brittle microfracture. Fatigue Fract. Eng. Mater Struct. 28, 289–300.
- 75 Fawaz, S. A. (2003) Equivalent initial flaw size testing and analysis of transport aircraft skin splices. Fatigue Fract. Eng. Mater Struct. 26, 279–290.
- 76 Noda, N. A., Kobayashi, K. and Oohashi, T. (2001) Variation of the stress intensity factor along the crack front of interacting semi-elliptical surface cracks. Arch. Appl. Mech. 71, 43–52.
- 77 Lam, K. Y. and Phua, S. P. (1991) Multiple crack interaction and its effect on stress intensity factor. Eng. Fract. Mech. 40, 585–592.
- 78 Loehnert, S. and Belytschko, T. (2007) Crack shielding and amplification due to multiple microcracks interacting with a macrocrack. Int. J. Fract. 145, 1–8.
- 79 Ro, Y. (2008) Characterization of exposure dependent fatigue crack growth kinetics and damage mechanisms for aluminum alloys. PhD Dissertation . Materials Science and Engineering. University of Virginia, Charlottesville , VA .
- 80 Toribio, J. and Kharin, V. (1997) K-dominance condition in hydrogen assisted cracking: The role of the far field. Fatigue Fract. Eng. Mater Struct. 20, 729–745.
- 81 Pressouyre, G. M. (1980) Trap theory of hydrogen embrittlement. Acta Metall. 28, 895–911.
- 82 Ro, Y., Agnew, S. R. and Gangloff, R. P. (2007) Environmental exposure dependence of low growth rate fatigue crack damage in Al-Cu-Li/Mg alloys (Edited by J.E. Allison, J.W. Jones, J.M. Larsen, R.O. Ritchie). Fourth International Conference on Very High Cycle Fatigue. TMS-AIME, Warendale , PA , pp. 407–420.
- 83 Gupta, V. K. and Agnew, S. R. (2011) Fatigue crack surface crystallography near crack initiating particle clusters in precipitation hardened legacy and modern Al-Zn-Mg-Cu alloys. Int. J. Fatigue. In press.
- 84 Prevey, P. S. and Cammett, J. T. (2002) Restoring fatigue performance of corrosion damaged AA7075-T6 and fretting in 4340 steel with low plasticity burnishing. FAA/DoD/NASA Aging Aircraft 2002, San Francisco , CA .
- 85 Kaufman, J. G. (2008) Properties of Aluminum Alloys: Fatigue Data and the Effects of Temperature, Product form, and Processing. ASM International, Materials Park , Ohio , vii, 559 p.
- 86 Scully, J. R., Young, G. A. and Smith, S. W. (2000) Hydrogen solubility, diffusion and trapping in high purity aluminum and selected Al-base alloys. Mater. Sci. Forum 331–3, 1583–1599.
- 87 Wolverton, C., Ozolins, V. and Asta, M. (2004) Hydrogen in aluminum: First-principles calculations of structure and thermodynamics. Phys. Rev. B 69, 144109-1–144109-16.
- 88 Cerit, M., Genel, K. and Eksi, S. (2009) Numerical investigation on stress concentration of corrosion pit. Eng. Fail Anal. 16, 2467–2472.
- 89 Zhu, G. Q., Ritter, J. E., Jakus, K. and Bhattacharya, S. (1997) Stress intensity factor for a peripherally cracked spherical cap. J. Am. Ceram. Soc. 80, 2445–2448.
- 90
Pilkey, W. D. and
Peterson, R. E. (1997) Peterson's Stress Concentration Factors. 2nd edn.
Wiley,
New York
, xxxii, 508 p.
10.1002/9780470172674 Google Scholar
- 91 Turnbull, A., Horner, D. A. and Connolly, B. J. (2009) Challenges in modelling the evolution of stress corrosion cracks from pits. Eng. Fract. Mech. 76, 633–640.
- 92 Chakravarti, I. M., Laha, R. G. and Roy J (1967) Handbook of Methods of Applied Statistics. Wiley, New York , 2 v.
- 93 Ostash, O. P. and Chepil, R. V. (2003) Local strain measurement for prediction of fatigue macrocrack initiation in notched specimens. Strain 39, 11–19.
- 94 Fan, H., Keer, L. M. and Mura, T. (1991) The effect of plastic-deformation on crack initiation in fatigue. Int. J. Solids Struct. 28, 1095–1104.
- 95 Fatemi, A. and Socie, D. F. (1988) A critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fatigue Fract. Eng. Mater Struct. 11, 149–165.
- 96 Papadopoulos, I. V. (1995) A high-cycle fatigue criterion applied in biaxial and triaxial out-of-phase stress conditions. Fatigue Fract. Eng. Mater Struct. 18, 79–91.
- 97 Manonukul, A. and Dunne, F. P. E. (2004) High- and low-cycle fatigue crack initiation using polycrystal plasticity. P Roy Soc. Lond. Mat. 460, 1881–1903.
- 98 Mcdowell, D. L. and Berard, J. Y. (1992) A Delta-J-based approach to biaxial fatigue. Fatigue Fract. Eng. Mater Struct. 15, 719–741.
- 99 Smith, K. N., Watson, P. and Topper, T. H. (1970) A stress-strain function for the fatigue of metals. J. Mater. 5, 167–778.
- 100 Herman, W. A., Hertzberg, R. W. and Jaccard, R. (1988) A simplified laboratory approach for the prediction of short crack behavior in engineering structures. Fatigue Fract. Eng. Mater Struct. 11, 303–320.
- 101
Neuber, H. (1961) Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law.
Trans. Am. Soc. Eng., J. Appl. Mech.
28, 544–550.
10.1115/1.3641780 Google Scholar
- 102 Harter, J. A. (2008) AFGROW Program Version 4.12.15.0. http://www.stormingmedia.us/13/1340/A134073.html. AFRL/VASM, WPAFB, OH.
- 103 DiMatteo, N. D. and Lampman, S. R. (1996) ASM Handbook: Fatigue and Fracture, Volume 19. ASM International, Materials Park , OH .
- 104 McDowell, D. L. and Dunne, F. P. E. (2010) Microstructure-sensitive computational modeling of fatigue crack formation. Int. J. Fatigue 32, 1521–1542.
- 105 Wang, L., Daniewicz, S. R., Horstemeyer, M. F., Sintay, S. and Rollett, A. D. (2009) Three-dimensional finite element analysis using crystal plasticity for a parameter study of microstructurally small fatigue crack growth in a AA7075 aluminum alloy. Int. J. Fatigue 31, 651–658.
- 106 Cavanaugh, M. K., Buchheit, R. G. and Birbilis, N. (2009) Evaluation of a simple microstructural-electrochemical model for corrosion damage accumulation in microstructurally complex aluminum alloys. Eng. Fract. Mech. 76, 641–650.
- 107 Harlow, D. G., Nardiello, J. and Payne, J. (2010) The effect of constituent particles in aluminum alloys on fatigue damage evolution: Statistical observations. Int. J. Fatigue 32, 505–511.
- 108 Harlow, D. G., Wang, M. Z. and Wei, R. P. (2006) Statistical analysis of constituent particles in 7075-T6 aluminum alloy. Metall. Mater. Trans. A 37A, 3367–3373.
- 109 Harlow, D. G. and Wei, R. P. (1998) A probability model for the growth of corrosion pits in aluminum alloys induced by constituent particles. Eng. Fract. Mech. 59, 305–325.
- 110 Wei, R. P., Liao, C. M. and Gao, M. (1998) A transmission electron microscopy study of constituent-particle-induced corrosion in 7075-T6 and 2024-T3 aluminum alloys. Metall. Mater. Trans. A 29, 1153–1160.
- 111 Reed, R. E. and Wilcox, P. R. (1970) Stress concentration due to a hyperboloid cavity in a thin plate, NASA Technical Note D-5955. Moffett Feild, CA .
- 112 Noda, N. A. and Takase, Y. (2002) Stress concentration factor formulas useful for all notch shapes in a flat test specimen under tension and bending. J. Test Eval. 30, 369–381.
- 113 Birbilis, N., Cavanaugh, M. K. and Buchheit, R. G. (2006) Electrochemical behavior and localized corrosion associated with Al7Cu2Fe particles in aluminum alloy 7075-T651. Corros. Sci. 48, 4202–4215.
- 114 Newman, J. C. and Abbott, W. (2009) Fatigue-life calculations on pristine and corroded open-hole specimens using small-crack theory. Int. J. Fatigue 31, 1246–1253.