An intergranular creep crack growth model based on grain boundary sliding
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I. INTRODUCTION
FRACTURE mechanics analyses and experiments have shown that path-independent energy integrals C(t) and C* control the crack-tip stress fields under creep cracking conditions.[1,2] This is why creep crack growth rates (CCGRs) under steady-state conditions in highly creep-ductile materials are often related to C*.[1–4] The stress intensity factor K has also been successfully employed to correlate CCGRs, especially in the presence of environmental embrittlement effects. Relations based on K are commonly employed to characterize the CCG behavior of high strength heat resistant alloys, such as superalloys,[5–8] titanium aluminides,[9] and aluminum alloys.[10] Typically, a relationship of the form da 5 A8K m dt
[1]
is observed, where A8 and m are experimentally determined constants. The exponent m often lies in the range of 2 to 8 but differs from the power-law creep stress exponent for the same material. The proportional constant A8 is a temperaturedependent term, which is also dependent on microstructural features, especially the grain size (e.g., References 5 through 8) and grain boundary morphology.[5] Recent work on Ni-base superalloys has shown that grain boundary sliding (GBS) plays an important role during creep deformation and fracture in complex engineering alloys.[11,12,13] Since intergranular fracture also predominates in such alloys during creep crack growth, GBS coupled with
S. XU, formerly Ph.D. Student, Department of Metallurgy and Materials Engineering, Ecole Polytechnique de Montreal, is Research Scientist with Materials Technology Laboratory, CANMET, Natural Resources Canada, Ottawa, ON, Canada K1A 0G1. X.-J. WU, Research Officer, and A.K. KOUL, Senior Research Officer, are with the Structures, Materials and Propulsion Laboratory, Institute for Aerospace Research, National Research Council of Canada, Ottawa, ON, Canada K1A 0R6. J.I. DICKSON, Professor, is with the Department of Metallurgy and Materials Engineering, Ecole Polytechnique de Montreal, Montreal, PQ, Canada H3C 3A7. Manuscript submitted June 9, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
environmental effects is considered to control the creep crack growth process. It is the purpose of this article to develop a CCGR model where GBS is considered to be the ratecontrolling factor during the intergranular fracture process. II. THE PROPOSED INTERGRANULAR CRACK GROWTH MODEL The growth of an intergranular crack is considered in the presence of several competing deformation mechanisms in the crack-tip region. In this modeling approach, it is assumed that different deformation mechanisms dominate to modify the stress distribution in different regions ahead of the crack tip. But a creep crack always grows intergranularly as a result of GBS under the influence of the modified stress distribution. Therefore, the degree to which the stress distribution is modified by a particular deformation mechanism will only alter the magnitude of the driving force leading to intergranular fracture due to GBS.
A. Stress Distribution in the
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