Time and Crack Length Dependent Stochastic Models of Fatigue Crack Growth. State-of-the-Art Review
Random character of fatigue crack growth observed in experiments inspires many researchers to apply the methods of probability theory and theory of stochastic processes in modeling of the phenomenon. Among many proposals the continuous stochastic models seen to be very promising both in theoretical consideration and engineering applications. In the paper two concepts of this kind of modeling are presented: the time and crack length dependent models. Some advantages and objections concerning both approaches are extensively discussed. It allows us to draw some more general conclusions on the necessary improvements which should be accounted for in the stochastic modeling of the fatigue crack growth.
References
Z.W.BIRNBAUM, S.C.SAUNDERS, A new family of life distributions, J. Appl. Prob., 6, 319-327, 1969.
O.DITLEVSEN, Random fatigue crack growth – a first passage problem, Engng. Fract, Mechanics, 23, 2, 467-477, 1986.
O.DITLEVSEN, R.OLESEN, Statistical analysis of the Virkler data of fatigue crack growth, Engng. Fract. Mechanics, 25, 177-195, 1986.
K.DOLIŃSKI, Stochastic loading and material inhomogeneity in fatigue crack propagation, Engng. Fract. Mechanics, 25, 5/6, 809-818, 1986.
K.DOLIŃSKI, Stochastic modeling and statistical verification of the crack growth under constant amplitude loading, Engng. Fract. Mechanics, [in print].
W.FELLER, An introduction to probability and its applications, Wiley, New York 1966,
H.GHONEM, S.DORE, Probabilistic description of fatigue crack growth in aluminum alloys under constant amplitude loading, Report AFOSR-83-0322, Univ. of Rhode Island 1986.
H.GHONEM, S.DORE, Experimental study of the constant-probability crack growth curves under constant amplitude loading, Engng. Fract. Mechanics, 27, 1, 1-25, 1987.
R.Z.KHASMINSKII, A limit theorem for the solution of differential equations with random right hand sides, Theory of Probability and Application, 111 390-405, 1966.
F.KOZIN, J.L.BOGDAN0FF, A critical analysis of some probabilistic models of fatigue crack growth, Engng. Fract. Mechanics, 14, 58-89, 1981.
Y.K.LIN, J.N.YANG, On statistical moments of fatigue crack propagation, Engng. Fract. Mechanics, 18, 2, 243-256, 1983.
H.O.MADSEN, Stochastic modeling of fatigue crack growth, Lecture Notes for Advanced Seminar on Structural Reliability, ISPRA Course, lspra, Italy.
K.ORTIZ, A.KIREMIDJIAN, Time series analysis of fatigue crack growth data, Engng. Fract. Mecl1anics, 24, 5, 657-675, 1986.
K.ORTIZ, A.KIREMIDJIAN, Stochastic modeling of crack growth, Engng. Fract. Mechanics, 29, 3, 317-334, 1988.
P.PARIS, F.ERDOGAN, A critical analysis of crack propagation laws, J. Basic Engng., Trans, ASME, 85, 528-534, 1982.
K.SOBCZYK, On the Markovian models for fatigue accumulation, J. Mécanique Théorique et Appliquée, Numéro special, 147-160, 1982.
K.SOBCZYK, Modeling of random fatigue crack growth, Engng. Fract. Mechanics, 24, 4, 609-623, 1986.
B.F.SPENCER Jr., J.TANG, Markov process model for fatigue crack growth, J. Engng. Mech., ASCE, 114, 12, 2134-2157, 1988.
E.SCHRÖDINGER, Zur Theorie der Fall- und Steigversuche an Teilchen mit Brownscher Bewegung, Physikalische Zeitschrift, 10, 289-295, 1915.
J.TANG, B.F.SPENCER Jr., Reliability solution for the stochastic fatigue crack growth problem, Engng. Fract. Mechanics, 34, 2, 419-433, 1989.
A.TSURUI, H.ISHIKAWA, Application of the Fokker-Planck equation to a stochastic fatigue crack propagation, Structural Safety, 4, 15-29i 1986.
D.A.VIRKLER, B.M.HILLBERRY, P.K.GOEL, The statistical nature of fatigue crack propagation, Technical Report AFDL-TR-78-43, Wright-Patterson Air Force Base, Ohio, 1978.
D.A.VIRIKLER, B.M.HILLBERRY, P.K.GOEL, The statistical nature of fatigue crack propagation, J. Engng. Materials and Technology, 101, 2, 148-152, 1979.
J.N.YANG, G.C.SALIVAR, C.G.ANNIS, Statistics of crack growth in engine materials, vol. I. Constant amplitude fatigue crack growth at elevated temperatures; vol.2. Spectrum loading and advanced techniques, Technical Report AFWAL-TR-82-4040, Wright-Patterson Air Force Base.