Inductions from Monte Carlo simulations of small fatigue cracks

Abstract The relationship between random microstructure and the statistics of small fatigue crack growth is illuminated by Monte Carlo simulations whose formulation has been described in previous work by the author. In this paper, more detailed analysis is presented of fluctuations in crack shape and the observed surface crack velocity, d c d N , using empirical laws of growth proposed elsewhere for Al 2219-T851 and Al 7075-T6. Unusually large values of d c d N are shown to follow retardation or arrest of the surface crack tips while the subsurface crack front has continued to advance. This relation implies that a physically based model of the statistics of d c d N must account for irregular crack shape to predict the distribution of d c d N and remaining lifetime accurately. The value of even rough measurements of surface crack depth in estimating remaining lifetime from nondestructive evaluation of a small crack is demonstrated. It is concluded that the statistics of d c d N require at least two independent random variables for their description. It is also proposed that experimental observations of the degree of irregularity of cracks of various sizes provide the most direct means to date of comparing the mechanics of the growth of surface and subsurface segments of the crack front.

[1]  F. Kozin,et al.  Probabilistic models of fatigue crack growth—II , 1984 .

[2]  Subra Suresh,et al.  Fatigue crack deflection and fracture surface contact: Micromechanical models , 1985 .

[3]  Two-stage microplastic surface deformation in Al 2219-T851 , 1987 .

[4]  W. Morris,et al.  MODEL-BASED STATISTICAL ANALYSIS OF SHORT FATIGUE CRACK GROWTH IN Ti 6Al-2Sn-4Zr-6Mo , 1987 .

[5]  J. Newman,et al.  Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads , 1984 .

[6]  James C. Newman,et al.  Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates , 1979 .

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

[8]  James C. Newman,et al.  An empirical stress-intensity factor equation for the surface crack , 1981 .

[9]  W. Morris,et al.  The Effect of Grain Size on Fatigue Growth of Short Cracks , 1983 .

[10]  F. Kozin,et al.  Probabilistic models of fatigue crack growth: Results and speculations , 1989 .

[11]  James Lankford,et al.  THE GROWTH OF SMALL FATIGUE CRACKS IN 7075–T6 ALUMINUM , 1982 .

[12]  B. N. Cox,et al.  Monte Carlo simulations of the growth of small fatigue cracks , 1988 .

[13]  W. Morris,et al.  Growth rate models for short surface cracks in AI 2219-T851 , 1981 .

[14]  B. N. Cox,et al.  A probabilistic model of short fatigue crack growth , 1987 .

[15]  Robert O. Ritchie,et al.  AN ANALYSIS OF CRACK TIP SHIELDING IN ALUMINUM ALLOY 2124: A COMPARISON OF LARGE, SMALL, THROUGH‐THICKNESS AND SURFACE FATIGUE CRACKS , 1987 .

[16]  Anthony G. Evans,et al.  Crack deflection processes—I. Theory , 1983 .

[17]  J. Rice,et al.  Slightly curved or kinked cracks , 1980 .

[18]  A. Pineau,et al.  SHORT CRACK BEHAVIOUR IN NODULAR CAST IRON , 1984 .

[19]  W. Morris,et al.  Effect of Fracture Surface Roughness on Growth of Short Fatigue Cracks , 1983 .

[20]  J. Yang,et al.  On statistical moments of fatigue crack propagation , 1983 .

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

[22]  J. Lankford.  Initiation and early growth of fatigue cracks in high strength steel , 1977 .

[23]  Subra Suresh,et al.  Crack deflection: Implications for the growth of long and short fatigue cracks , 1983 .

[24]  W. Morris.  The noncontinuum crack tip deformation behavior of surface microcracks , 1980 .

[25]  Takeshi Ogawa,et al.  LIMITATIONS OF LINEAR ELASTIC FRACTURE MECHANICS IN RESPECT OF SMALL FATIGUE CRACKS AND MICROSTRUCTURE , 1986 .

[26]  W. Morris,et al.  Microplastic surface deformation of A12219-T851 , 1987 .