Fatigue Crack Growth Models

  1. Fatigue Crack Growth Models List
  2. Fatigue Crack Growth Models Pictures
  3. Fatigue Crack Growth Models 2017
  4. Business Growth Models
  5. Fatigue Crack Growth Models List
  6. Fatigue Crack Growth Models 2016

AFGROW (Air Force Grow) is a Damage Tolerance Analysis (DTA) framework that allows users to analyze crack initiation, fatigue crack growth, and fracture to predict the life of metallic structures. Originally developed by The Air Force Research Laboratory, AFGROW[1] is mainly used for aerospace applications, but can be applied to any type of metallic structure that experiences fatigue cracking. AFGROW is now being independently developed and maintained commercially by LexTech, Inc.

  • 2History

Software architecture[edit]

Crack-growth results, based on studies on “long” (3mm) cracks, show fatigue-crack propagation rates to be markedly power-law dependent on the applied stress-intensity range, ΔK, with a. First class of phase-field models of fatigue crack growth to reproduce the Paris law. Yields different Paris law exponents characteristic of brittle and ductile materials. Describes fatigue growth of multiple interacting cracks in arbitrarily complex geometries without explicit front tracking. Jun 19, 2018  The UniGrow model is modified by 2 different methods, namely the “short crack stress intensity correction method” and the “short crack data‐fitting method” to estimate the total fatigue life including both short and long fatigue crack propagations. Metal Fatigue Crack Growth Models. Jovica Riznic. Shripad Revankar. Jovica Riznic. Shripad Revankar. Download with Google Download with Facebook or download with email.

The stress intensity factor library provides models for over 30 different crack geometries (including tension, bending and bearing loading for many cases). In addition, an advanced, multiple crack capability allows AFGROW to analyze two independent cracks in a plate (including hole effects), non-symmetric corner cracked. Finite Element (FE) based solutions are available for two, non-symmetric through cracks at holes as well as cracks growing toward holes. This capability allows AFGROW to handle cases with more than one crack growing from a row of fastener holes.

AFGROW implements five different crack growth models (Forman Equation,[2] Walker Equation,[3] Tabular lookup, Harter-T Method and NASGRO Equation[4] ) to determine crack growth per applied cyclic loading. Other AFGROW user options include five load interaction (retardation) models (closure,[5][6]Fastran,[7] Hsu, Wheeler,[8] and Generalized Willenborg[9]), a strain-life based fatigue crack initiation model, and the ability to perform a crack growth analysis with the effect of the bonded repair. AFGROW also includes useful tools such as: user-defined stress intensity solutions, user-defined beta modification factors (ability to estimate stress intensity factors for cases, which may not be an exact match for one of the stress intensity solutions in the AFGROW library), a residual stress analysis capability, cycle counting, and the ability to automatically transfer output data to Microsoft Excel.

AFGROW provides COM (Component Object Model) Automation interfaces that allow users to build scripts in other Windows applications to perform repetitive tasks or control AFGROW from their applications.

AFGROW also has new plug-in crack geometry interface that allows AFGROW to interface with any structural analysis program capable of calculating stress intensity factors (K) in the Windows environment. Users may create their own stress intensity solutions by writing and compiling dynamic link libraries (DLLs) using relatively simple codes. This includes the ability to animate the crack growth as is done in all other native AFGROW solutions. This interface also makes it possible for FE analysis software (for example, StressCheck) to feed AFGROW three-dimensional based stress intensity information throughout the crack life prediction process, allowing for a tremendous amount of analytical flexibility.

History[edit]

AFGROW's history traces back to a crack growth life prediction program (ASDGRO) which was written in BASIC for IBM-PCs by Mr. Ed Davidson at ASD/ENSF in the early-mid-1980s. In 1985, ASDGRO was used as the basis for crack growth analysis for the Sikorsky H-53 Helicopter under contract to Warner-Robins ALC. The program was modified to utilize very large load spectra, approximate stress intensity solutions for cracks in arbitrary stress fields, and use a tabular crack growth rate relationship based on the Walker equation on a point-by-point basis (Harter T-Method). The point loaded crack solution from the Tada, Paris, and Irwin Stress Intensity Factor Handbook[10] was originally used to determine K (for arbitrary stress fields) by integration over the crack length using the unflawed stress distribution independently for each crack dimension. After discussions with Dr. Jack Lincoln (ASD/ENSF), a new method was developed by Mr. Frank Grimsley (AFWAL/FIBEC) to determine stress intensity, which used a 2-D Gaussian integration scheme with Richardson Extrapolation which was optimized by Dr. George Sendeckyj (AFWAL/FIBEC). The resulting program was named MODGRO since it was a modified version of ASDGRO.

Early years[edit]

Fatigue crack growth models pictures

Fatigue Crack Growth Models List

Many upgrades were made during the late 1980s and early 1990s. The primary improvement was modifying the coding language from BASIC to Turbo Pascal and C. Numerous small changes/repairs were made based on errors that were discovered. During this time period, NASA/Dryden implemented MODGRO in the analysis for the flight test program for the X-29.

Recent times[edit]

In 1993, the Navy was interested in using MODGRO to assist in a program to assess the effect of certain (classified) environments on the damage tolerance of aircraft. Work began at that time to convert the MODGRO, Version 3.X to the C language for UNIX to provide performance and portability to several UNIX Workstations.

Fatigue Crack Growth Models Pictures

In 1994, the results of the Navy project were presented to the Navy sponsor and MODGRO was renamed AFGROW, Version 3.X.

Fatigue Crack Growth Models 2017

Since 1996, the Windows-based version of AFGROW has replaced the UNIX version since the demand for the UNIX version did not justify the cost to maintain it. There was also an experiment to port AFGROW to the Mac OS. The Mac version had the same problem (lack of demand) as the UNIX version. An automated capability was added to AFGROW in the form of a Microsoft Component Object Model (COM) interface. The AFGROW COM interface allows users to use AFGROW as the crack growth analysis engine for any Windows based software.

Present Day[edit]

An advanced model feature has been added to allow users to select cases with two, independent cracks (with and without holes). This feature continues to be improved and expanded to cover more combinations of corner and through-the-thickness cracks. A user-defined plug-in stress intensity model capability has also been added to AFGROW. This allows users to create their own stress intensity solutions in the form of a Windows DLL (dynamic link library). Drawing tools have been included in AFGROW to allow the user-defined solution to be animated during the analysis. Interactive stress intensity solutions have been demonstrated using AFGROW to perform life predictions while sending geometric data to an external FEM code, which returns updated stress intensity solutions back to AFGROW.

Verification testing is a continuing process to improve AFGROW and expand the available database. There are plans to continue to add new technology and improvements to AFGROW. A Consortium has been started with users in Government and Industry to combine the best fracture mechanics methods available.

References[edit]

  1. ^Harter, James A. (2003). AFGROW Reference Manual (version 4.0). Wright-Patterson Air Force Base, AFRL/VASM.
  2. ^Forman, R. G.; Hearney, V. E.; Engle, R. M. (1967). 'Numerical analysis of crack propagation in cyclic-loaded structures'. Journal of Basic Engineering. 89: 459–464.
  3. ^Walker, K. (1970). 'The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminum'. Effects of Environment and Complex Load History for Fatigue Life. American Society for Testing and Materials. pp. 1–14.
  4. ^NASGRO Fracture Mechanics and Fatigue Crack Growth Analysis Software, Version 4.02. SwRI. 2002.
  5. ^Elber, Wolf (1970). 'Fatigue crack closure under cyclic tension'. Engineering Fracture Mechanics. 2: 37–45.
  6. ^Elber, Wolf (1971). The Significance of Fatigue Crack Closure, ASTM STP 486. American Society for Testing and Materials. pp. 230–243.
  7. ^Newman, Jr., J. C. (1992). FASTRAN II -- A fatigue crack growth structural analysis program, Technical Memorandum 104159. NASA.
  8. ^Wheeler, O. E. (1972). 'Spectrum Loading and Crack Growth'. Journal of Basic Engineering. 94: 181–186.
  9. ^Willenborg, J. D.; Engle, R. M.; Wood, H. A. (1971). 'A crack growth retardation model using an effective stress concept'. NASA.Cite journal requires |journal= (help)
  10. ^Tada, Hiroshi; Paris, Paul C.; Irwin, George R. (1973). The stress analysis of cracks handbook. Del Research Corporation.

External links[edit]

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Fatigue Crack Growth Models List

Retrieved from 'https://en.wikipedia.org/w/index.php?title=AFGROW&oldid=905427960'

Fatigue Crack Growth Models 2016

  1. P. Paris, M.P. Gomez and W.E. Anderson, A Rational Analytical Theory of Fatigue, The Trend in Engineering, University of Washington 13 (1961) 9–14.Google Scholar
  2. W. Elber, Fatigue Crack Closure under Cyclic Tension, Engineering Fracture Mechanics 2 (1970) 37–45.CrossRefGoogle Scholar
  3. W. Elber, The Significance of Fatigue Crack Closure, Damage Tolerance in Aircraft Structures, ASTM STP 486 (1971) 230–242.Google Scholar
  4. A.J. McEvily, On Crack Closure in Fatigue Crack Growth, Mechanics of Fatigue Crack Closure, ASTM STP 982 (1988) 35–43.Google Scholar
  5. D.L. Davidson, Fatigue Crack Closure, Engineering Fracture Mechanics 38:6 (1991) 393–402.CrossRefGoogle Scholar
  6. P. Lalor, H. Sehitoglu and R.C. McClung, Mechanics Aspects of Small Crack Growth from Notches—The Role of Crack Closure, The Behavior of Short Fatigue Cracks, EFG Pub. 1, Mechanical Engineering Publications, London (1986) 369–386.Google Scholar
  7. R.C. McClung and H. Sehitoglu, Closure Behavior of Small Cracks under High Strain Fatigue Histories, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (1988) 279–299.Google Scholar
  8. J.C. Newman, Jr., A Nonlinear Fracture Mechanics Approach to the Growth of Small Cracks, in Proceedings of the 55th AGARD Meeting on Behaviour of Short Cracks in Airframe Components, Toronto (1982).Google Scholar
  9. J.C. Newman, Jr., A Crack-Closure Model for Predicting Fatigue Crack Growth under Aircraft Spectrum Loading, Methods and Models for Predicting Fatigue Crack Growth under Random Loading, ASTM STP 748 (1981) 53–84.Google Scholar
  10. H.L. Ewalds and R.T. Furnee, Crack Closure Measurement Along the Fatigue Crack Front of Center Cracked Specimens, International Journal of Fracture 14 (1978) R53-R55.Google Scholar
  11. D.S. Mahulikar, W.P. Slagle and H.L. Marcus, Edge Effects on Fatigue Crack Closure of Aluminum Alloys, Scripta Metallurgica 3 (1979) 867–880.CrossRefGoogle Scholar
  12. A.F. Blom and D.K. Holm, An Experimental and Numerical Study of Crack Closure, Engineering Fracture Mechanics 22:6 (1985) 997–1011.CrossRefGoogle Scholar
  13. K. Ogura, Y. Miyoshi and I. Nishikawa, Fatigue Crack Growth and Closure of Small Cracks at the Notch Root, Current Research on Fatigue Cracks, MRS Vol. 1, Society of Materials Science, Japan (1985) 67–91.Google Scholar
  14. W.N. Sharpe and X. Su, Closure Measurements of Naturally Initiating Small Cracks, Engineering Fracture Mechanics 30:3 (1988) 275–294.CrossRefGoogle Scholar
  15. H. Nisitani, and K. Takao, Significance of Initiation Propagation and Closure of Microcracks in High Cycle Fatigue of Ductile Metals, Engineering Fracture Mechanics 15:3–4 (1981) 445–446.Google Scholar
  16. H. Sehitoglu, Crack Opening and Closure in Fatigue, Engineering Fracture Mechanics 21:2 (1985) 329–339.CrossRefGoogle Scholar
  17. J.E. Allison, R.C. Ku and M.A. Pompetzki, A Comparison of Measurement Methods and Numerical Procedures for the Experimental Characterization of Fatigue Crack Closure, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (1988) 171–185.Google Scholar
  18. J.A. Vazquez, A. Morrone and H. Ernst, Experimental Results on Fatigue Crack Closure for Two Aluminum Alloys, Engineering Fracture Mechanics 12 (1979) 231–140.CrossRefGoogle Scholar
  19. J.A. Vazquez, A. Morrone and J.C. Gasco, A comparative Experimental Study on the Fatigue Crack Closure Behavior Under Cyclic Loading for Steels and Aluminum Alloys, in Fracture Mechanics, ASTM STP 677 (1979) 187–197.Google Scholar
  20. J.M. Larsen, The Effects of Slip Character and Crack Closure on the Growth of Small Fatigue Cracks in Titanium-Aluminum Alloys, Ph.D. thesis, Materials Science Department, Carnegie Mellon University, 1988.Google Scholar
  21. P. Lalor and H. Sehitoglu, Crack Closure Outside Small Scale Yielding Regime, in ASTM STP 982 (1988) 342–360.Google Scholar
  22. R.C. McClung and H. Sehitoglu, Finite Element Analysis of Fatigue Crack Closure 1. Basic Modelling Issues, Engineering Fracture Mechanics 33:2 (1989) 237–252.CrossRefGoogle Scholar
  23. R.C. McClung and H. Sehitoglu, Finite Element Analysis of Fatigue Crack Closure 1. Basic Modelling Issues, Engineering Fracture Mechanics 33:2 (1989) 253–272.CrossRefGoogle Scholar
  24. R.C. McClung and H. Sehitoglu, Closure and Growth of Fatigue Cracks at Notches, ASME JEMT 114 (1992) 1–7.Google Scholar
  25. N. Fleck, Finite Element Analysis of Plasticity Induced Crack Closure under Plane Strain Conditions, Engineering Fracture Mechanics 25 (1986) 441–449.CrossRefGoogle Scholar
  26. J. Llorca and V.S. Galvez, Modelling Plasticity-Induced Fatigue Crack Closure, Engineering Fracture Mechanics 37:1 (1990) 185–196.CrossRefGoogle Scholar
  27. M. Nakagaki and S.N. Atluri, Fatigue Crack Closure and Delay Effects Under Mode I Spectrum Loading: An Efficient Elastic-Plastic Analysis Procedure, Fatigue of Engineering Materials and Structures 1 (1979) 421–429.CrossRefGoogle Scholar
  28. J.C. Newman, Jr., A Finite-Element Analysis of Fatigue Crack Closure, in Mechanics of Crack Growth, ASTM STP 590 (1976) 281–301.Google Scholar
  29. M. Shiratori, T. Miyoshi, H. Miyamoto and T. Mori, A Computer Simulation of Fatigue Crack Propagation Based on the Crack Closure Concept, Advances in Research on the Strength and Fracture of Materials, Fourth International Conference on Fracture, Waterloo, Canada, 2B, June (1977) 1091–1098.Google Scholar
  30. H. Sehitoglu and W. Sun, Residual Stress Fields During Fatigue Crack Growth, Fatigue and Fracture of Engineering Materials and Structures 15:2 (1992), 115–128.CrossRefGoogle Scholar
  31. B. Budiansky and J. Hutchinson, Analysis of Closure in Fatigue Crack Growth, Journal of Applied Mechanics, Transaction of ASME 45 (1978) 267–276.CrossRefGoogle Scholar
  32. J.C. NewmanJr. and H. ArmenJr., Elastic-Plastic Analysis of Propagating Crack Under Cyclic Loading, AIAA Journal 13:8 (1975) 1017–1023.CrossRefGoogle Scholar
  33. N. Fleck and J.C. Newman, Analysis of Crack Closure under Plane Strain Conditions, ASTM STP 982 (1988) 319–341.Google Scholar
  34. R.O. Ritchie, W. Yu, A.F. Blom and D.K. Holm, Response to a Discussion by A.J. McEvily, Fatigue and Fracture of Engineering Materials and Structures 12:1 (1989) 73–75.CrossRefGoogle Scholar
  35. H. Sehitoglu and W. Sun, Mechanisms of Crack Closure in Plane Strain and Plane Stress, Fatigue under Biaxial/Multiaxial, ESIS10, K. Kussmaul (ed.), Mechanical Engineering Publications, London (1991).Google Scholar
  36. R.C. McClung, Crack Closure and Plastic Zone Sizes In Fatigue, Fatigue and Fracture of Engineering Materials and Structures 14 (1991) 455–468.CrossRefGoogle Scholar
  37. T.C. Lindley and C.E. Richards, The Relevance of Crack Closure to Fatigue Crack Propagation, Materials Science and Engineering 14 (1974) 281–293.CrossRefGoogle Scholar
  38. A.J. McEvily, Discussion, Fatigue and Fracture of Engineering Materials and Structures 12:1, (1989) 71–72.CrossRefGoogle Scholar
  39. N.A. Fleck and R.A. Smith, Crack Closure—Is It Just a Surface Phenomenon, International Journal of Fatigue 4 (1982) 157–160.CrossRefGoogle Scholar
  40. H.R. Shercliff and N.A. Fleck, Effect of Specimen Geometry on Fatigue Crack Growth in Plane Strain—I. Constant Amplitude Response, II. Overload Response, Fatigue and Fracture of Engineering Materials and Structures 13:3 (1996) 287–310.CrossRefGoogle Scholar
  41. H. Sehitoglu and W. Sun, Modelling of Plane Strain Fatigue Crack Closure, ASME Journal of Engineering Materials and Technology 113 (1990) 31–40.CrossRefGoogle Scholar
  42. K. Gall, H. Sehitoglu and Y. Kadioglu, F.E.M. Study of Fatigue Crack Closure Under Double Slip, Metallurgica (1995) to be published.Google Scholar
  43. H. Sehitoglu, K. Gall and Y. Kadioglu, Microstructure Effects on Crack Closure, ASTM Workshop on Advances in Fatigue Crack Closure (1995).Google Scholar
  44. K. Gall, Huseyin Sehitoglu and Yavuz Kadioglu, Plastic Zones and Fatigue Crack Closure Under Plane Strain Double Slip, Metallurgical Transactions, to be published.Google Scholar
  45. A. Garcia and H. Sehitoglu, A Model for Roughness induced Crack Closure, to be submitted (1995).Google Scholar
  46. W.L. Morris and M.R. James, Statistical Aspects of Fatigue Failure Due to Alloy Microstructure in ASTM STP 811 (1983) 179–206.Google Scholar
  47. P. Neumann, Coarse Slip Model of Fatigue, Acta Metallurgica 17 (1969) 1219.CrossRefGoogle Scholar
  48. R.C. McClung and H. Sehitoglu, Constraint Effects in Fatigue Crack Growth, Proceedings 3rd International Conference on Fatigue and Fatigue Thresholds, Charlottesville, Va. 3 (1987) 1401–1410.Google Scholar
  49. R.C. McClung, Closure and Growth of Mode I Cracks in Biaxial Fatigue, Fatigue and Fracture of Engineering Materials and Structures 12:5 (1989) 447–460.CrossRefGoogle Scholar
  50. H. Sehitoglu and W. Wei, The Significance of Crack Closure Under High Temperature Fatigue Crack Growth with Hold Periods, Engineering Fracture Mechanics 33:3 (1989) 371–388.CrossRefGoogle Scholar
  51. K. Tanaka and Y. Nakai, Propagation and Non-Propagation of Short Fatigue Cracks at a Sharp Notch, Fatigue of Engineering Materials and Structures 6:4 (1983) 315–327.CrossRefGoogle Scholar
  52. S. Usami, Short Crack Fatigue Properties and Component Life Estimation, Current Research on Fatigue Cracks, MRS Vol. 1, Society of Materials Science, Japan (1985).Google Scholar
  53. C.S. Shin and R.A. Smith, Fatigue Crack Growth from Sharp Notches, International Journal of Fatigue 7:2 (1985) 87–93.CrossRefGoogle Scholar
  54. C.S. Shin and R.A. Smith, Fatigue Crack Growth at Stress Concentrations—The Role of Notch Plasticity and Crack Closure, Engineering Fracture Mechanics 29:3 (1988) 301–315.CrossRefGoogle Scholar
  55. H. Sehitoglu, Characterization of Crack Closure, Fracture Mechanics: Sixteenth Symposium, ASTM STP 868 (1985) 361–380.Google Scholar
  56. S. Suresh and R.O. Ritchie, Propagation of Short Fatigue Cracks, International Metals Reviews 29:6 (1984) 445–476.Google Scholar
  57. H. Sehitoglu, Crack Opening and Closure in Fatigue, Engineering Fracture Mechanics 21:2 (1985) 329–339.CrossRefGoogle Scholar
  58. B.N. Leis and T.P. Forte, Fatigue Growth of Initially Physically Short Cracks in Notched Aluminum and Steel Plates, Fracture Mechanics: Thirteenth Conference, ASTM STP 743 (1981) 100–124.Google Scholar
  59. K. Tanaka and Y. Nakai, Propagation and Non-Propagation of Short Fatigue Cracks at a Sharp Notch, Fatigue of Engineering Materials and Structures 6:4 (1983) 315–327.CrossRefGoogle Scholar
  60. M.M. Hammouda and K.J. Miller, Elastic Plastic Fracture Mechanics Analysis of Notches, Elastic-Plastic Fracture, ASTM STP 668 (1979) 703–719.Google Scholar
  61. M.M. Hammouda, R.A. Smith and K.J. Miller, Elastic-Plastic Fracture Mechanics for Initiation and Propagation of Notch Fatigue Cracks, Fatigue of Engineering Materials and Structure 2 (1979) 139–154.CrossRefGoogle Scholar
  62. S. Usami, Short Crack Fatigue Properties and Component Life Estimation, Current Research on Fatigue Cracks, MRS Vol. 1, Society of Materials Science, Japan (1985)Google Scholar
  63. C.S. Shin and R.A. Smith, Fatigue Crack Growth from Sharp Notches, International Journal of Fatigue 7:2 (1985) 87–93.CrossRefGoogle Scholar
  64. C.S. Shin and R.A. Smith, Fatigue Crack Growth at Stress Concentrations—The Role of Notch Plasticity and Crack Closure, Engineering Fracture Mechanics 29:3 (1988) 301–315.CrossRefGoogle Scholar
  65. H. Sehitoglu, Fatigue Life Prediction of Notched Members Based on Local Strain and Elastic-Plastic Fracture Mechanics Concepts, Engineering Fracture Mechanics 18:3 (1983) 609–621.CrossRefGoogle Scholar
  66. R.C. McClung and H. Sehitoglu, Characterization of Fatigue Crack Growth in Intermediate and Large Scale Yielding, JEMT 113 (1991) 15–22.Google Scholar
  67. R.C. McClung, Finite Element Modeling of Fatigue Crack Growth, International Conference on Theoretical Concepts and Numerical Analysis of Fatigue, UK (1992).Google Scholar
  68. H.L. Ewalds and R.T. Furnee, Crack Closure Measurement Along the Fatigue Crack Front of Center Cracked Specimens, International Journal of Fracture 14 (1978) R53-R55.Google Scholar
  69. D.S. Mahulikar, W.P. Slagle and H.L. Marcus, Edge Effects on Fatigue Crack Closure of Aluminum Alloys, Scripta Matallurgica 13 (1979) 867–880.CrossRefGoogle Scholar
  70. T.C. Lindley and C.E. Richards, The Relevance of Crack Closure to Fatigue Crack Propagation, Materials Science and Engineering 14 (1974) 281–293.CrossRefGoogle Scholar
  71. W.J. Mills and R.W. Hertzberg, The Effect of Sheet Thickness on Fatigue Crack Retardation in 2024-T3 Aluminum Alloy, Engineering Fracture Mechanics 7 (1975) 705–711.CrossRefGoogle Scholar
  72. K. Minakawa, G. Levan and A.J. McEvily, The Influence of Load Ration on Fatigue Crack Growth in 7090-T6 and IN9021-T4 P/M Aluminum Alloys, Metallurgical Transactions A, 17A (October 1986) 1787–1795.CrossRefGoogle Scholar
  73. A.J. McEvily, Discussion, Fatigue and Fracture of Engineering Materials and Structures 12:1 (1989) 71–72.CrossRefGoogle Scholar
  74. H. Sehitoglu, Unpublished research.Google Scholar
  75. R.J. Asaro, Micromechanics of Crystals and Polycrystals, Advances in Applied Mechanics, John W. Hutchinson (ed.) 23 (1983) 1–115.Google Scholar
  76. J.R. Rice, D.E. Hawk and R.J. Asaro, Crack Tip Fields in Ductile Crystals, International Journal of Fracture 42 (1990) 301–321.CrossRefGoogle Scholar
  77. W.T. Koiter, Stress-strain relations, uniqueness and variational theorems for elastic plastic materials with a singular yield surface. Quarterly of Applied Mathematics 11 (1953) 350.Google Scholar
  78. A.J. McEvily and R.C. Boettner, On Fatigue Crack Propagation in F.C.C. Metals, Acta Metallurgica 11 (1963) 725–742.CrossRefGoogle Scholar
  79. R.M.N. Pelloux, Mechanisms of Formation of Ductile Fatigue Striations, Transactions of the ASME 62 (1969) 281–285.Google Scholar
  80. N.J.I. Adams, Fatigue Crack Closure at Positive Stresses, Engineering Fracture Mechanics 4 (1972) 543–554.CrossRefGoogle Scholar
  81. V.W. Trebules, R. RobertsJr. and R.W. Hertzberg, ASTM STP 536 (1973) 115.Google Scholar
  82. R.W. Hertzberg and W.J. Mills, ASTM STP 600 (1976) 220.Google Scholar
  83. G.T. GrayIII, J.C. Williams and A.W. Thompson, Roughness-Induced Crack Closure: An Explanation for Microstructurally Sensitive Fatigue Crack Growth, Metallurgical Transactions 14A (1983) 421–433.CrossRefGoogle Scholar
  84. S.J. Balsone, J.M. Larsen, D.C. Maxwell and W.J. Jones, Effects of Microstructure and Temperature on Fatigue Crack Growth in the TiAl Alloy Ti-46.5A1–3Nb-2Cr-0.2W, Materials Science and Engineering A 192/193 (1995) 457–464.CrossRefGoogle Scholar
  85. J. Llorca, Roughness Induced Fatigue Crack Closure: A Numerical Study, Fatigue and Fracture of Engineering Materials and Structures 15:7 (1992) 655–669.CrossRefGoogle Scholar
  86. S. Suresh, Fatigue Crack Deflection and Fracture Surface Contact: Micromechanical Models, Metallurgical Transactions 15A (1984) 249–260.Google Scholar
  87. K.S. Ravichandran, Fatigue Crack Growth Behavior of Small and Long Cracks in Titanium Alloys and Intermetallics, WL-TR-94–4030 (1994).Google Scholar
  88. J.A. Greenwood and J.B.P. Williamson, Contact of Nominally Flat Surfaces, Proceedings Royal Society London A295 (1966) 300–19.CrossRefGoogle Scholar
  89. K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, UK (1985).CrossRefGoogle Scholar
  90. K.L. Johnson and H.R. Shercliff, Shakedown of 2-Dimensional Asperities in Sliding Contact, International Journal of Mechanical Science 34:5 (1992) 375–394.CrossRefGoogle Scholar
  91. A. Kapoor and K.L. Johnson, Steady State Topography of Surfaces in Repeated Boundary Lubricated Sliding, Thin Films in Tribology, Leeds-Lyon Symposium on Tribology (1993) 81–90.Google Scholar
  92. J.A. Vazquez, A. Morrone and H. Ernst, Experimental Results on Fatigue Crack Closure for Two Aluminum Alloys, Engineering Fracture Mechanics 12 (1979) 231–140.CrossRefGoogle Scholar
  93. J.A. Vazquez, A. Morrone and J.C. Gasco, A comparative Experimental Study on the Fatigue Crack Closure Behavior Under Cyclic Loading for Steels and Aluminum Alloys, Fracture Mechanics, ASTM STP 677 (1979) 187–197.Google Scholar
  94. R.C. McClung, The Influence of Applied Stress, Crack Length, and Stress Intensity Factor on Crack Closure, Metallurgical Transactions 22A (1991) 1559–1571.CrossRefGoogle Scholar
  95. H.U. Staal and J.D. Elen, Crack Closure and Influence of Cycle Ratio R on Fatigue Crack Growth in Type 304 Stainless Steel at Room Temperature, Engineering Fracture Mechanics 11 (1979) 275–283.CrossRefGoogle Scholar
  96. M.W. Brown and K.J. Miller, Mode I Fatigue Crack Growth under Biaxial Stress at Room and Elevated Temperature, Multiaxial Fatigue, ASTM STP 853 (1985) 135–152.Google Scholar