RELIABILITY-BASED MICROMECHANICAL SMALL CRACK GROWTH MODEL

A probabilistic small crack growth fatigue model is proposed in which a small crack is defined as a crack of size comparable to the microstructure. The model relates the microstructural material heterogeneities to the statistical scatter in the macrostructural response. The microstructure is explicitly modeled with microelements that represent the grains of a single phase alloy. The properties of the grain such as size, orientation, and frictional strength are modeled as random variables. The macrostructure is modeled as an ensemble of microelements. A cracktip opening displacement model based on the assumption of continuously distributed dislocations is used to determine the small crack growth rate. The models are combined in a Monte Carlo simulation to determine the statistical distribution of short crack growth fatigue response of the macrostructure. The modeled response is compared to the trends in experimental observations from the literature. The purpose of the study is to investigate only the microstructural effects. Variations in the applied loading, stress concentrations! residual stresses, and global geometry are not consrdered.

[1]  G. Smith,et al.  Crack propagation in high stress fatigue , 1962 .

[2]  A. Cottrell,et al.  The spread of plastic yield from a notch , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  Fatigue crack nucleation at intermetallic particles in alloys — A dislocation pile-up model , 1979 .

[4]  W. Hackbusch.  Singular Integral Equations , 1995 .

[5]  T. A. Cruse,et al.  Probabilistic Mesomechanical Fatigue Crack Nucleation Model , 1997 .

[6]  Computer simulation of fatigue crack initiation , 1980 .

[7]  J. C. Newman,et al.  Impact of small-crack effects on designlife calculations , 1989 .

[8]  S. Antolovich,et al.  A study of fatigue damage mechanisms in Waspaloy from 25 to 800 C , 1984 .

[9]  Peter Joseph Edward Forsyth,et al.  The physical basis of metal fatigue , 1969 .

[10]  Nisitani Hironobu,et al.  Significance of initiation, propagation and closure of microcracks in high cycle fatigue of ductile metals , 1981 .

[11]  J. Lankford,et al.  A crack-tip strain model for the growth of small fatigue cracks , 1983 .

[12]  K. J. Miller,et al.  MODELLING SMALL FATIGUE CRACKS INTERACTING WITH GRAIN BOUNDARIES , 1991 .

[13]  P. D. Hobson.  THE FORMULATION OF A CRACK GROWTH EQUATION FOR SHORT CRACKS , 1982 .

[14]  W. Gerberich,et al.  A Review of Fatigue Fracture Topology Effects on Threshold and Growth Mechanisms , 1979 .

[15]  K. J. Miller,et al.  Short crack fatigue behaviour in a medium carbon steel , 1984 .

[16]  J. Lankford,et al.  The role of microstructural dissimilitude in fatigue and fracture of small cracks , 1988 .

[17]  D. S. Dugdale.  Yielding of steel sheets containing slits , 1960 .

[18]  Keisuke Tanaka,et al.  A model of crack-tip slip band blocked by grain boundary , 1978 .

[19]  A. Bataille,et al.  Surface damage accumulation in low-cycle fatigue: Physical analysis and numerical modelling , 1994 .

[20]  J. Weertman.  Crack tip stress intensity factor of the double slip plane crack model: Short cracks and short short-cracks , 1984 .

[21]  Robert P. Wei,et al.  Modelling of small fatigue crack growth interacting with grain boundary , 1986 .

[22]  A. Navarro,et al.  A MICROSTRUCTURALLY-SHORT FATIGUE CRACK GROWTH EQUATION , 1988 .

[23]  K. J. Miller,et al.  THE BEHAVIOUR OF SHORT FATIGUE CRACKS AND THEIR INITIATION PART II‐A GENERAL SUMMARY , 1987 .

[24]  R. Miner,et al.  The effect of microstructure on 650 °C fatigue crack growth in P/M astroloy , 1983 .

[25]  N. Louat,et al.  The Distribution of Dislocations in Linear Arrays , 1955 .

[26]  W. Morris,et al.  A simple model of stress intensity range threshold and crack closure stress , 1983 .

[27]  M. Newby.  Markov models for fatigue crack growth , 1987 .

[28]  B. N. Cox,et al.  A STATISTICAL MODEL OF INTERMITTENT SHORT FATIGUE CRACK GROWTH , 1987 .

[29]  A. J. Mcevily,et al.  Crack opening displacement and the rate of fatigue crack growth , 1972 .

[30]  D. Davidson.  Small and large fatigue cracks in aluminum alloys , 1988 .