applied fracture mechanics

Fracture Mechanics Based Models of Structural and Contact FatigueFracture Mechanics Based Models of Structural and Contact Fatigue 311756. ClosureThe chapter presents a detailed analysis of a number of plane crack mechanics problems forloaded elastic half-plane weakened by a system of cracks. Surface and subsurface cracks areconsidered. All cracks are considered to be straight cuts. The problems are analyzed by theregular asymptotic method and numerical methods. Solutions of the problems include thestress intensity factors. The regular asymptotic method is applied under the assumption thatcracks are far from each other and from the boundary of the elastic solid. It is shown thatthe results obtained for subsurface cracks based on asymptotic expansions and numericalsolutions are in very good agreement. The influence of the normal and tangential contactstresses applied to the boundary of a half-plane as well as the residual stress on the stressintensity factors for subsurface cracks is analyzed. It is determined that the frictional andresidual stresses provide a significant if not the predominant contribution to the problemsolution. Based on the numerical solution of the problem for surface cracks in the presenceof lubricant the physical nature of the "wedge effect" (when lubricant under a sufficientlylarge pressure penetrates a surface crack and ruptures it) is considered. Solution of thisproblem also provides the basis for the understanding of fatigue crack origination site (surfaceversus subsurface) and the difference of fatigue lives of drivers and followers. New twoandthree-dimensional models of contact and structural fatigue are developed. These modelstake into account the initial crack distribution, fatigue properties of the solids, and growth offatigue cracks under the properly determined combination of normal and tangential contactand residual stresses. The formula for fatigue life based on these models can be reduced to asimple formula which takes into account most of the significant parameters affecting contactand structural fatigue. The properties of these contact fatigue models are analyzed and theresults based on them are compared to the experimentally obtained results on contact fatiguefor tapered bearings.7. References[1] Kudish, I.I. and Covitch, M.J., 2010. Modeling and Analytical Methods in Tribology. BocaRaton, London, New York: CRC Press, Taylor & Francis Group.[2] Kudish, I.I. 2007. Fatigue Modeling for Elastic Materials with Statistically DistributedDefects. ASME J. Appl. Mech. 74:1125-1133.[3] Bokman, M.A., Pshenichnov, Yu.P., and Pershtein, E.M. 1984. The Microcrack andNon-metallic Inclusion Distribution in Alloy D16 after a Plastic Strain. Plant Laboratory,Moscow, 11:71-74.[4] Cherepanov, G.P. 1979. Mechanics o f Brittle Fracture. New York: McGraw–Hill.[5] Kudish, I.I. 1987. Contact Problem of the Theory of Elasticity for Pre-stressed Bodies withCracks. J. Appl. Mech. and Techn. Phys. 28, 2:295-303.[6] Yarema, S.Ya. 1981. Methodology of Determining the Characteristics of theResistance to Crack Development (Crack Resistance) of Materials in Cyclic Loading.J. Soviet Material Sci. 17, No. 4:371-380.[7] Tallian, T., Hoeprich, M., and Kudish, I. 2001. Author’s Closure. STLE Tribology Trans.44, No. 2:153-155.[8] Handbook o f Mathematical Functions with Formulas, Graphs and Mathematical Tables,Eds. M. Abramowitz and I.A. Stegun, National Bureau of Standards, 55, 1964.[9] Stover, J.D., Kolarik II, R.V., and Keener, D.M. 1989. The Detection of Aluminum OxideStringers in Steel Using an Ultrasonic Measuring Method. Mechanical Working and Steel