Use of weibull statistics to quantify property variability in TiAl alloys
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I. INTRODUCTION
THE TiAl alloys possess an attractive combination of strength, stiffness, oxidation resistance, and low density that make them candidates for intermediate temperature (⬍800 ⬚C) applications in gas-turbine engines where component weight is an issue.[1] However, these alloys exhibit limited ductility, compared to competing nickel-based superalloys and titanium alloys, coupled with considerable variability in this property. This trait must be considered in the design of components, particularly in regions containing stress concentrators.[2,3,4] The relatively low average ductility of cast ␥ -TiAl-based alloys (⬇ 2 pct) is less troubling than the rather large variation in that property (0.2 to over 3 pct) because even 0.8 pct ductility seems to be sufficient to blunt elastic-stress concentration factors as large as 2.4.[3] Although limited ductility in TiAl alloys has been given much attention in the literature, the greater concern for TiAl component designers is usually ductility variability. An understanding of the factors contributing to ductility variability could lead to substantially improved alloys and methods for processing them. Recent experiments[5,6] by the authors and coworkers have shown that cast titanium aluminides may be subject to substantial variability in both ductility and yield stress over the range of conditions likely to be encountered in industrial casting processes. Additionally, considerable variation in properties has been found in materials with the same composition and nominal heat treatment and even in specimens machined from a single cast plate. Other studies in which
NICHOLAS BIERY, Research Engineer, is with Exxon Mobile Upstream Research Co., Houston, TX. MARC DE GRAEF, Professor, Department of Materials Science and Engineering, and JACK BEUTH, Professor, Department of Mechanical Engineering, are with Carnegie Mellon University, Pittsburgh, PA 15213. RAFEL RABAN, Engineer, is with Pratt & Whitney, East Hartford, CT. ANDREW ELLIOTT, Graduate Research Assistant, and TRESA M. POLLOCK, Professor, are with the Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109. Contact e-mail: [email protected] CURT AUSTIN, Consultant, was formerly with GE Aircraft Engines, Cincinnati, OH 45215. Manuscript submitted November 22, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
multiple tension tests were conducted for a given alloy composition also reveal considerable variability in tensile ductility.[7,8] Because structural components are typically designed with consideration of minimum rather than average properties, quantification and control of property variability is critically important.[10] Limited tensile ductility coupled with the variability in this property and the mounting evidence for a dependence of the ductility of ␥ -titanium aluminides on strained volume[3,4,9,10] suggests that a probabilistic approach to the prediction of fracture strengths may be appropriate. Weibull statistical methods are often used when evaluating the pr
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