Abstract
Using only readily available material properties and the concept of dislocation density evolution ahead of the crack tip, the fatigue damage map attends to develop a virtual tool able to predict the limits and the corresponding crack tip propagation rates characterising each of the fatigue stages, namely crack arrest, microstructurally and physically short crack (Stage I), long crack growth (Stage II), and Stage III growth.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
According to the Schmid’s law (τ c = σ cos θ cos ঁ, where for θ and ঁ equal to 45°, τ c is a maximum), plastic deformation occurs when, the applied tensile stress σ, resolved as τ c on a particular slip plane, exceeds a determined shear stress τ y .τ y = σ y/2 if the material observes the Tresca’s principles, where σ y is the corresponding yield stress.
References
A.A. Griffith, “The Phenomenon of Rupture and Flow in Solids,” Philos. Trans. R. Soc. Lond. A, Vol. 221, 1921, pp. 163–197.
P.C. Paris and F.A. Erdogan, “Critical Analysis of Crack Propagation Laws,” J. Basic Eng. TRANS ASME, Vol. 85(Series D), 1963, pp. 528–534.
N.E. Frost and D.S. Dugdale, “The Propagation of Fatigue Cracks in Test Specimens,” J. Mech. Phys. Solids, Vol. 6, 1958, 92–110.
J. Schijve, Fatigue of Structures and Materials, Kluwer Academic Publishers, The Netherlands, 2001.
Fatigue Design Handbook AE-10, Society of Automotive Engineers, USA, 1988.
S.R. Swanson, Handbook of Fatigue Testing, ASTM STOP 566, 1974.
S. Suresh, Fatigue of Materials, 2nd edition, Cambridge, University Press, Cambrige, 1998.
P. Lukáš, “Fatigue Crack Nucleation and Microstructure,” ASM Handbook Volume 19: Fatigue and Fracture, ASM International, Materials Park, Ohio, 1996, pp. 96–109.
J.R. Yates, “Fatigue of Engineering Materials. MSc in Structural Integrity (MPE603), course notes,” Department of Mechanical Engineering, The University of Sheffiel, Sheffield, U.K., 1999.
K.J. Miller, “Fundamentals of Deformation and Fracture,” In: Proc. Eshelby Memorial Symposium, Cambridge, U.K., B.A. Bilby, Cambridge University Press, 1985, pp. 477–500.
D.W. Hoeppener, “Model for Prediction of Fatigue Lives Based upon a Pitting Corrosion Fatigue Process. Fatigue Mechanisms,” In: Proc. of an ASTM-NBS-NSF Symposium, Kansas, City, Mo., J.T. Fong, Ed., ASTM STP 675, 1978, pp. 841–870.
R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd edition New York, USA, John Wiley & Sons, 1989.
F. Guiu, R. Dulniak, and B.C. Edwards, “On the Nucleation of Fatigue Cracks in Pure Polycrystalline a-iron,” Fatigue Fract. Eng. Mater. Struct., Vol. 5, 1982, pp. 311–321.
K.J. Miller, “Materials Science Perspective of Metals Fatigue Resistance,” Mater. Sci. Technol., Vol. 9, 1993, pp. 453–462.
P.J.E. Forsyth, “A two stage process of fatigue crack growth, in crack propagation,” In: Proceedings of Cranfield Symposium, London, Her Majesty’s Stationery Office, 1962, pp. 76–94.
V.M. Radhakrishnan and Y. Mutoh, “On Fatigue Crack Growth in Stage I,” In: The Behaviour of Short Fatigue Cracks, EGP Pub. 1. Great Britain, K.J. Miller and E.R. de.los.Rios, Eds., Mechanical Engineering Publications Limited, 1986, pp. 87–99.
M.W. Brown, “Interfaces Between Short, Long and Non-Propagatig Cracks,” In: The Behaviour of Short Fatigue Cracks, EGF Pub. Sheffield, U.K., K.J. Miller and E.R. delosRios, Eds., Mechanical Engineering Publications, London, 1986, pp. 423–439.
Y. Mutoh and V.M. Radhakrishnan, “An Analysis of Grain Size and Yield Stress Effects on Stress at Fatigue Limit and Threshold Stress Intensity Factor,” J. Eng. Mater. Technol., Vol. 103, 1986, pp. 229–233.
E. Hay and M.W. Brown, “Initiation and Early Growth of Fatigue Cracks from a Circunferential Notch Loaded in Torsion,” In: The Behaviour of Short Fatigue Cracks, EGF Pub. Sheffield, U.K., K.J. Miller and E.R. delosRios, Eds., Mechanical Engineering Publications, London, 1986, pp. 309–321.
R.O. Ritchie, F.A. McClintock, H. Nayeb-hashemi, and M.A. Ritter, “Mode III Fatigue Crack Propagation in Low Alloy Steel,” Metall. Trans., Vol. 13A, 1982, pp. 101–110.
P.C. Paris and F.J. Erdogan, “A Critical Analysis of Crack Propagation Law,” J. Basic Eng. Trans. ASME, Series D, Vol. 85, No. 4, 1963, pp. 528–535.
P.C. Paris, “Fracture Mechanics and Fatigue: A Historical Perspective,” Fatigue Fract. Eng. Mater. Struct., Vol. 21, 1998, pp. 535–540.
J.F. Knott, Fundamentals of Fracture Mechanics, Butterworths, London, 1973.
W. Elber, “Fatigue Crack Closure Under Cyclic Tension,” Eng. Fract. Mech., Vol. 2, 1970, pp. 37–45.
S. Suresh and R.O. Ritchie, “The Propagation of Short Fatigue Cracks,” Int. Met. Rev., Vol. 29, No. 6, 1984, pp. 445–501.
N. Louat, K. Sadananda, M. Duesbery, and A.K. Vasudevan, “A Theoretical Evaluation of Crack Closure,” Metall. Trans., Vol. 24-A, 1993, pp. 2225–2232.
R.O. Ritchie, S. Suresh, and C.M. Moss, “Near Threshold Fatigue Crack Growth in 21/4 Cr 1Mo Pressure Vessel Steel in Air and Hydrogen,” J. Eng. Mater. Technol. (Trans. ASME), Vol. 102, 1980, pp. 293--299.
S. Suresh and R.O. Ritchie, “A Geometric Model for Fatigue Crack Closure Induced by Fracture Surface Roughness,” Metall. Trans. A, Vol. 13A, 1982, pp. 1627–1631.
S. Pearson, “Initiation of Fatigue Cracks in Commercial Aluminium Alloys and the Subsequent Propagation of Very Short Cracks,” Eng. Fract. Mech., Vol. 7, 1975, pp. 235–247.
J. Lankford, “The Growth of Small Fatigue Cracks in 7075-T6 Aluminium,” Fatigue Fract. Eng. Mater. Struct., Vol. 5, No. 3, 1982, pp. 233–248.
D. Kujawski and F. Ellyin, “A Microstructurally Motivated Model for Short Crack Growth Rate,” Short Fatigue Cracks, ESIS 13, K.J. Miller and E.R. de los Rios, Eds., Mechanical Engineering Publications, London, 1992.
D. Taylor and J.F. Knott, “Fatigue Crack Propagation Behaviour of Short Cracks: The Effect of Microstructure,” Fatigue Fract. Eng. Mater. Struct., Vol. 4, No. 2, 1981, pp. 147–155.
K.J. Miller, “The Behaviour of Short Fatigue Cracks and their Initiation. Part I – A Review of Two Recent Books,” Fatigue Fract. Eng. Mater. Struct., Vol. 10, No. 1, 1987, pp. 75–91.
K.J. Miller, “The Behaviour of Short Fatigue Cracks and their Initiation. Part II – A General Summary,” Fatigue Fract. Eng. Mater. Struct., Vol. 10, No. 1, 1987, pp. 75–91.
K. Tokaji and T. Ogawa, “The Growth Behaviour of Microstructurally Small Fatigue Cracks in Metals,” Short Fatigue Cracks, ESIS 13, K.J. Miller and E.R. de los Rios, Eds., Mechanical Engineering Publications, London, 1992, pp. 85–99.
S. Suresh and R.O. Ritchie, “The Propagation of Short Fatigue Cracks,” Int. Met. Rev., Vol. 29, No. 6, 1984, p. 445.
H. Kitagawa and S. Takahashi, “Applicability of Fracture Mechanics to Very Small Cracks or the Cracks in the Early Stage,” In: 2nd International Conference on Mechanical Behaviour of Materials (ICM2), Boston, USA. American Society of Metals, Metal park, Ohio, 1976, pp. 627–631.
K.J. Miller, “The Behaviour of Short Fatigue Cracks and their Initiation. Part I – A Review of Two Recent Books,” Fatigue Fract. Eng. Mater. Struct., Vol. 10, No. 1, 1987, pp. 75–91.
D. Taylor, “Fatigue of Short Cracks: The Limitations of Fracture Mechanics,” In: The Behaviour of Short Fatigue Cracks, EGF Pub. Sheffield, U.K., K.J. Miller and E.R. delosRios, Eds., Mechanical Engineering Publications, London, 1986, pp. 479–490.
J.M. Kendall, M.N. James, and J.F. Knott, “The Behaviour of Physically Short Fatigue Cracks in Steels,” In: The Behaviour of Short Fatigue Cracks, EGF Pub. Sheffield, U.K., K.J. Miller and E.R. delosRios, Eds., Mechanical Engineering Publications, London, 1986, pp. 241–258.
E.R. de.los.Rios, P. Mercier, and B.M. El-Sehily, “Short Crack Growth Behaviour Under Variable Amplitude Loading of Shot Peened Surfaces,” Fatigue Fract. Eng. Mater. Struct., Vol. 19, No. 2/3, 1996, pp. 175–184.
R.C. Boettner, C. Laird, and A.J. McEvily, “Crack Nucleation and Growth in High Strain-Low Cycle Fatigue,” Trans. Metall. Soc. AIME, Vol. 233, 1965, pp. 379–385.
K.S. Chan and J. Lankford, “A Crack Tip Model for the Growth of Small Fatigue Cracks,” Scr. Metall., Vol. 17, 1983, pp. 529–538.
K. Tanaka, “Modelling of Propagation and Non-Propagation of Small Cracks,” In: Small Fatigue Cracks, R.O. Ritchie and J. Lankford, Eds., Metallurgycal Society Inc. 1986, pp. 343–362.
P.D. Hobson, “The Formulation of a Crack Growth Equation for Short Cracks,” Fatigue Fract. Eng. Mater. Struct., Vol. 5, No. 4, 1982, pp. 323–327.
P.D. Hobson, M.W. Brown, and E.R. de.los.Rios, “Two Phases of Short Crack Growth in a Medium Carbon Steel,” In: The Behaviour of Short Fatigue Cracks, EGF Pub. Sheffield, U.K., K.J. Miller and E.R. delosRios, Eds., Mechanical Engineering Publications, London, 1986, pp. 441–459.
D. Angelova and R. Akid, “A Note on Modelling Short Fatigue Crack Behaviour,” Fatigue Fract. Eng. Mater. Struct., Vol. 21, 1998, pp. 771–779.
J.R. Rice, The Mechanics of Fracture, ASME AMD, Vol. 19, 1976, pp. 23–53.
R.M. McMeeking, “Finite Deformation Analysis of Crack Tip Opening in Elastic-Plastic Materials and Implications for Fracture,” J. Mech. Phys. Solids, Vol. 25, 1977, pp. 357–381.
J.F. Knot, “Microscopic Aspects of Crack Extension,” In: Advances in Elasto-Plastic Fracture Mechanics, L.H. Larsson, Ed., Applied Science Publishers, Essex, England, 1980.
B.A. Bilby, A.H. Cottrell, and K.H. Swinden, “The Spread of Plastic Yielding from a Notch,” Proc. R. Soc. Lond. A, Vol. 272, 1963, pp. 304–314.
A. Navarro and E.R. de.los.Rios, “A Model for Short Fatigue Crack Propagation with an Interpretation of the Short-Long Crack Transition,” Fatigue Fract. Eng. Mater. Struct., Vol. 10, No. 2, 1987, pp. 169–186.
A. Navarro and E.R. de.los.Rios, “Compact Solution for a Multizone Bcs Crack Model with Bounded or Unbounded End Conditions,” Philos. Mag. A, Vol. 57, No. 1, 1988, pp. 43–50.
A. Navarro and E.R. de.los.Rios, “Fatigue Crack Growth Modelling by Successive Blocking of Dislocations,” Proc. R. Soc. Lond. A, Vol. 437, 1992, pp. 375–390.
A.H. Cottrell and D. Hull, “Extrusion and Intrusion by Cyclic Slip in Copper,” Proc. R. Soc. Lond. A, Vol. 242, 1957, pp. 211–213.
P.J.E. Forsyth, “Slip Band Damage and Extrusion,” Proc. R. Soc. Lond. A, Vol. 242, 1957, pp. 198–202.
E.R. de los Rios, M.W. Brown, K.J. Miller, and H.X. Pei, “Fatigue damage accumulation during cycles of non-proportional straining,” In Basic questions in fatigue, Vol. 1, ASTM STP 924: 1988, pp. 194–213, ASTM, Philadelphia.
N.J. Petch, “The Cleavage Strength of Polycrystals,” J. Iron Steel Inst., Vol. 174, 1953, pp. 25–28.
E.R. de los Rios, “Dislocation Modelling of Fatigue Crack Growth in Polycrystals,” Eng. Mech., Vol. 5, No. 6, 1998, pp. 363–368.
D. Kujawski, “A Fatigue Crack Driving Force Parameter with Load Ratio Effects,” Inter. J. Fatigue, Vol. 23, 2001, pp. S236–S246.
A. Navarro, C. Vallellano, E.R. de los Rios, and X.J. Xin, Notch Sensitivity and Size Effects Described by a Short Crack Propagation Model,” In: Engineering Against Fatigue, J.H. Beynon, M.W. Brown, T.C. Lindley, R.A. Smith and B. Tomkins, Eds., Balkema, Netherlands, 1999.
E.R. de los Rios and A. Navarro, “Considerations of Grain Orientation and Work Hardening on Short-Fatigue Crack Modelling,” Phil. Mag. A, Vol. 61, No. 3, 1990, pp. 435–449.
C.A. Rodopoulos, “Predicting the Evolution of Fatigue Damage Using the Fatigue Damage Map Method,” Theor. Appl. Fract. Mech., Vol. 45, 2006, pp. 252–265.
M.W. Brown, “Interfaces Between Short, Long and Non-Propagating Cracks,” In: The Behaviour of Short Fatigue Cracks, K.J. Miller and E.R. de los Rios, Eds., Mechanical Engineering Publications, London, 1986, pp. 423–439.
A.T. Winter, “Cyclic Deformation: the Two Phase Model,” Proceedings of the Eshelby Memorial Symposium, International Union of Theoretical and Applied Mechanics, B.A. Bilby, K.J. Miller and J.R. Willis, Eds., Cambridge University Press, Cambridge, 1984, pp. 573–582.
S. Taira, K. Tanaka, and Y. Nakai, “A Model of Crack Tip Slip Band Blocked by Grain Boundary,” Mech. Res. Comm., Vol. 5, 1978, pp. 375–381.
C.A. Rodopoulos and Al.Th. Kermanidis, “Understanding the Effect of Block Overloading on the Fatigue Behaviour of 2024-T351 Aluminium Alloy Using the Fatigue Damage Map,” Inter. J. Fatigue, Vol. 29, No. 2, 2006, pp. 276–288.
G.R. Yoder, L.A. Cooley, and T.W. Crooker, “On Microstructural Control of Near-Threshold Fatigue Crack Growth in 7000-Series Aluminium Alloys,” Scr. Metall., Vol. 16, 1982, pp. 1021–1025.
C.A. Rodopoulos, E.R. de los Rios, J.R. Yates, and A. Levers, “A Fatigue Damage Map for the 2024-T3 Aluminium Alloy,” Fatigue Fract. Eng. Mater. Struc., Vol. 26, No. 7, 2003, pp. 569–576.
E.R. de los Rios, Z. Tang, and K.J. Miller, “Short Crack Fatigue Behaviour in a Medium Carbon Steel,” Fatigue Fract. Eng. Mater. Struct., Vol. 7, No. 2, 1984, pp. 97–108.
R.M. Pelloux, “Crack Extension by Alternating Shear,” Eng. Fract. Mech., Vol. 1, 1970, pp. 697–704.
F.A. McClintock, “Considerations for Fatigue Crack Growth Relative to Crack Tip Displacement,” In: Engineering Against Fatigue, J.H. Beynon, M.W. Brown, T.C. Lindley, R.A. Smith and B. Tomkins, Eds., A.A. Balkema Publishers, Rotterdam, Netherlands, 1999.
J.N. Eastbrook, “A Dislocation Model for the Rate of Initial Growth of Stage I Fatigue Cracks,” Inter. J. Fract., Vol. 24, 1984, pp. R43–R49.
D.J. Nicholls, “The Relation Between Crack Blunting and Fatigue Crack Growth Rates,” Fatigue Fract. Eng. Mater. Struct., Vol. 17, No. 4, 1994, pp. 459–467.
A.A. Wells, “Application of Fracture Mechanics at and Beyond General Yielding,” Br. Weld. J., Vol. 10, 1963, pp. 563–570.
Author information
Authors and Affiliations
Corresponding author
Editor information
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Rodopoulos, C.A. (2009). Fatigue Damage Map as a Virtual Tool for Fatigue Damage Tolerance. In: Farahmand, B. (eds) Virtual Testing and Predictive Modeling. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-95924-5_4
Download citation
DOI: https://doi.org/10.1007/978-0-387-95924-5_4
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-95923-8
Online ISBN: 978-0-387-95924-5
eBook Packages: EngineeringEngineering (R0)