Fatigue Life Prediction for Porosity-Containing Cast 319-T7 Aluminum Alloy
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¼ CðDKeff Þm
INTRODUCTION
ALUMINUM casting technology has been greatly improved over the years, and cast aluminum products have become viable alternatives in structural applications for aerospace and automotive industries.[1] The cast aluminum alloys, even with similar processing and testing conditions, show a wide range of fatigue lives, with the presence of casting defects such as porosity or oxide inclusions with various sizes and shapes acting as easy crack-initiation sites.[2–8] Figure 1, for example, shows the stress vs number of cycles to failure (S-N) curves for the cast E319-T7 aluminum alloy with porosity,[9] demonstrating that the fatigue limit varies up to 40 pct with different porosity levels. Linear elastic fracture mechanics (LEFM) has been used to predict the fatigue life of a structural component containing a flaw, including damage-tolerant flaws,[10,11] corrosion pits,[12] constituent particles,[13,14] or casting defects[5,7,8,15] in metals. The fatigue crack growth rate in region II was first proposed by Paris and Erdogan,[16] as follows: da=dN ¼ CDKm
½1
where C and m are Paris’s constant and exponent, respectively. The Paris equation was later modified by Elber[17] to account for the effect of crack closure:
YOUNGHWAN JANG and YOUIN JEONG, Research Engineers, and CHONGHO YOON, Airframe Design Section Leader, are with the Research & Development Division, Korea Aerospace Industries, Ltd., Sachon 664-942, Korea. SANGSHIK KIM, Professor, is with the School of Nano and Advanced Materials Engineering, Engineering Research Center, i-Cube Center, Gyeongsang National University, Chinju 660-701, Korea. Contact e-mail: [email protected] Manuscript submitted August 27, 2008. Article published online February 26, 2009 1090—VOLUME 40A, MAY 2009
½2
where DKeff is the effective stress intensity factor range, DKeff = Kmax Kcl, Kmax is the maximum stress intensity factor, and Kcl is the stress intensity factor at which the crack closure occurs. For the prediction of the entire da/dN-DK curve, it was expanded as a more complicated equation by Newman:[18] 2 m 1 DKth;eff =DKeff da=dN ¼ CðDKÞ ½3 1 ðKmax =KIc Þ2 where DKth,eff is the effective threshold stress intensity factor range and KIc is the fracture toughness. For porosity-containing aluminum alloys, several models have been proposed to predict fatigue life on the basis of the LEFM concept.[4–6,8,15] Buffie`re et al., for example, proposed the fatigue life prediction modeling method for cast Al-Si7-Mg0.3 aluminum, based on the conventional LEFM concept, using da/dN-DK data.[4] They reported that the LEFM-based fatigue life prediction was reasonable at high stresses; at low stress levels, it was a very conservative prediction. Couper et al.[5] proposed that the fatigue life of the cast CP601 aluminum alloy could be estimated by integrating the expanded Paris law. In this analysis, the DKeff was defined as DKeff = UR(a)Y(a)Dr(pa)1/2, where UR(a) is the crack closure factor, Y(a) is the geometry factor, and the equivalent initial flaw size (EIFS) was determined as t
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