Statistical distributions for the size of fatigue-initiating defects in Al-7%Si-0.3%Mg alloy castings : A comparative study

Statistical distributions used in the literature for size distributions of fatigue-initiating defects are reviewed. Seven distributions from the literature are fitted to two datasets for the fatigue-initiating defects in A356 aluminum alloy castings, reported previously by Yi et al. [J.Z. Yi, P.D. Lee, T.C. Lindley, T. Fukui, Mater. Sci. Eng. A, A432 (2006) 59]. The results of the goodness-of-fit tests indicate that only lognormal, Gumbel and General Extreme Value distributions provide acceptable fits to both datasets. Weibull, Frechet and Generalized Pareto distributions do not provide good fits to the two datasets. Based on mathematical statistics, however, it is recommended that only Gumbel or General Extreme Value distributions be used for the size of fatigue-initiating defects. The effect of using the correct statistical distribution for the size of defects on the accuracy of the fatigue life estimates is demonstrated.

[1]  F. Longin.  The Asymptotic Distribution of Extreme Stock Market Returns , 1996 .

[2]  Helen V. Atkinson,et al.  Application of the generalized pareto distribution to the estimation of the size of the maximum inclusion in clean steels , 1999 .

[3]  D. Darling,et al.  A Test of Goodness of Fit , 1954 .

[4]  John L. Campbell,et al.  Statistical distributions of fracture strengths of cast Al7SiMg alloy , 1993 .

[5]  D. Casellas,et al.  Fatigue variability in Al–Si cast alloys , 2005 .

[6]  B. M. Hillberry,et al.  Probabilistic Approach to Predicting Fatigue Lives of Corroded 2024-T3 , 1999 .

[7]  R. D'Agostino,et al.  Goodness-of-Fit-Techniques , 1987 .

[8]  S. Coles,et al.  An Introduction to Statistical Modeling of Extreme Values , 2001 .

[9]  H. R. Dvorak,et al.  Statistical distribution of flaw sizes , 1972 .

[10]  P. C. Paris,et al.  A Critical Analysis of Crack Propagation Laws , 1963 .

[11]  B. Gnedenko.  Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire , 1943 .

[12]  Yukitaka Murakami,et al.  Instructions for a New Method of Inclusion Rating and Correlations with the Fatigue Limit , 1994 .

[13]  M. A. Przystupa,et al.  Microstructure based fatigue life predictions for thick plate 7050-T7451 airframe alloys , 1997 .

[14]  F. Samuel,et al.  Statistical analysis of porosity in Al-9 wt% Si-3 wt% Cu-X alloy systems , 1996, Journal of Materials Science.

[15]  K. Trustrum,et al.  Applicability of Weibull analysis for brittle materials , 1983 .

[16]  Y. Murakami,et al.  Effects of defects, inclusions and inhomogeneities on fatigue strength , 1994 .

[17]  Stefano Beretta,et al.  STATISTICAL ANALYSIS OF DEFECTS FOR FATIGUE STRENGTH PREDICTION AND QUALITY CONTROL OF MATERIALS , 1998 .

[18]  N. R. Green,et al.  Influence of casting technique and hot isostatic pressing on the fatigue of an Al-7Si-Mg alloy , 2001 .

[19]  J. Knott,et al.  Fatigue performance of a cast aluminium alloy Al-7Si-Mg with surface defects , 1999 .

[20]  Vartan Choulakian,et al.  Goodness-of-Fit Tests for the Generalized Pareto Distribution , 2001, Technometrics.

[21]  Simon Barter,et al.  Interpreting fatigue test results using a probabilistic fracture approach , 2005 .

[22]  M. Stephens.  EDF Statistics for Goodness of Fit and Some Comparisons , 1974 .

[23]  Lorrie Molent,et al.  An experimental evaluation of fatigue crack growth , 2005 .

[24]  S. Spence,et al.  The EIFS distribution for anodized and pre-corroded 7010-T7651 under constant amplitude loading , 2005 .

[25]  M. Tiryakioğlu.  On the size distribution of fracture-initiating defects in Al-and Mg-alloy castings , 2008 .

[26]  John L. Campbell,et al.  The influence of structural integrity on the tensile deformation of cast Al-7wt.%Si-0.6wt.%Mg alloys , 2003 .

[27]  B. Zettl,et al.  Endurance limit and threshold stress intensity of die cast magnesium and aluminium alloys at elevated temperatures , 2005 .

[28]  Helen V. Atkinson,et al.  Characterization of inclusions in clean steels: a review including the statistics of extremes methods , 2003 .

[29]  M. Tiryakioğlu.  Pore size distributions in AM50 Mg alloy die castings , 2007 .

[30]  E. J. Gumbel,et al.  Statistics of Extremes. , 1960 .

[31]  Y. X. Gao,et al.  A micro-cell model of the effect of microstructure and defects on fatigue resistance in cast aluminum alloys , 2004 .

[32]  Peter J. Laz,et al.  Fatigue life prediction from inclusion initiated cracks , 1998 .

[33]  Nozer D. Singpurwalla,et al.  Extreme Values from a Lognormal Law With Applications to Air Pollution Problems , 1972 .

[34]  Peter D. Lee,et al.  Scatter in fatigue life due to effects of porosity in cast A356-T6 aluminum-silicon alloys , 2003 .

[35]  C. Davidson,et al.  Oxide films, pores and the fatigue lives of cast aluminum alloys , 2006 .

[36]  A. S. Machin,et al.  The effect of solution heat-treatment time on the fatigue properties of an Al-Si-Mg casting alloy , 2002 .

[37]  John L. Campbell,et al.  Effects of runner system design on the mechanical strength of Al-7Si-Mg alloy castings , 2003 .

[38]  Y. Murakami,et al.  Small Defects and Inhomogeneities in Fatigue Strength: Experiments, Models and Statistical Implications , 1999 .

[39]  Benjamin Epstein,et al.  Elements of the Theory of Extreme Values , 1960 .

[40]  Bjørn Skallerud,et al.  Fatigue life assessment of aluminum alloys with casting defects , 1993 .

[41]  Bruce A. Craig,et al.  Probabilistic method for predicting the variability in fatigue behavior of 7075-T6 aluminum , 1999 .

[42]  S. Stanzl-Tschegg,et al.  Influence of porosity on the fatigue limit of die cast magnesium and aluminium alloys , 2003 .

[43]  Trevor C. Lindley,et al.  Statistical modeling of microstructure and defect population effects on the fatigue performance of cast A356-T6 automotive components , 2006 .