Creep crack growth in the absence of grain boundary precipitates in UDIMET 520
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NTRODUCTION
CCGR ⫽ Ad 1⫺q K2
CRACK growth resistance under creep, fatigue, or combined loading conditions is required to improve damage tolerance of advanced gas turbine components. Creep crack growth (CCG) or hold time crack behavior of high-temperature materials has been widely studied in the past 2 decades either as part of creep-fatigue-environment interaction studies or from a fracture mechanics perspective.[1–7] A quantitative understanding of the CCG process and its dependence on microstructural features and environment is of considerable importance. Recently, a grain boundary sliding (GBS)–controlled creep crack growth rate (CCGR) model has been proposed by the authors,[8] which considers pure GBS (without other creep mechanism contributions including creep cavitation) to be the rate controlling factor in the CCG process. According to this model, the GBS-controlled CCGR is independent of the grain size (d ) in materials containing clean grain boundaries, i.e., without grain boundary precipitates, and is inversely proportional to d in the presence of a discrete grain boundary precipitate distribution. In the presence of continuous grain boundary precipitates, the CCGR is predicted to be inversely proportional to d 2. This model also predicts that GBS-controlled CCGR has a dependence on the stress intensity factor (K ) to the power of 2. The model is expressed in the following equation:
where A is a material constant and q is the grain-size-dependent index. This index takes a value of 1 for a grain boundary without grain boundary precipitates, a value of 2 for a discrete grain boundary precipitate distribution, and a value of 3 when a continuous grain boundary precipitate network is present. For creep-brittle materials, K is often employed to correlate CCGR. It has been shown that K is the appropriate loading parameter both for describing the deformation field around a crack tip and also for correlating with measured creep crack growth rates in superalloy IN-718 at 650 ⬚C.[9] If environmental effects are included, the K dependence of CCGR could change to a higher value. Typically, a relationship of the form
S. XU, formerly Graduate Student, Department of Engineering Physics and Materials Engineering, Ecole Polytechnique de Montreal, is now Research Scientist with CANMET-Materials Technology Laboratory, Ottawa, ON, Canada K1A 0G1. A.K. KOUL, formerly Senior Research Officer, NRC, Ottawa, is President, with Life Prediction Technologies Inc., Ottawa, ON, Canada K1J 8M0. J.I. DICKSON, Professor, is with the Department of Engineering Physics and Materials Engineering, Ecole Polytechnique de Montreal, Montreal, PQ, Canada H3C 3A7. Manuscript submitted February 22, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
CCGR ⫽ A⬘Km
[1]
[2]
is observed in many materials, where A⬘ and m are experimentally determined constants. The exponent m often lies in the range of 2 to 8. Any modeling approach must eventually stand the test of experimental results, and the primary objective of this article is to evaluate prediction
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