Stochastic aspects of creep cavitation in ceramics
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I.
INTRODUCTION
AT low
or intermediate temperatures ceramic materials typically fail in a brittle manner, with the failure emanating from preexisting flaws formed either during processing or surface finishing. Statistical models based on a weakest link approach have proven to be quite successful in predicting failure probabilities of ceramics in these temperature regimes. At elevated temperatures, however, failure of ceramic materials commonly occurs by the nucleation, growth, and coalescence of grain boundary cavities and/or microcracks, l This increase in damage with time precludes the use of the weakest link type models. An alternative approach is, therefore, needed for predicting the failure times or probabilities of ceramic materials at elevated temperatures. Lifetime prediction schemes based on an integration of one or more of the cavity nucleation and/or growth models have been proposed. 2-5 However, although these treatments have been somewhat successful, they fail to treat the statistical aspects of cavitation. It is the purpose of this paper to establish the importance of a viable statistical failure model by demonstrating the highly stochastic nature of grain boundary cavitation and then discussing the consequences of such stochastic cavitation. Recent small-angle neutron scattering measurements of cavity nucleation and growth rates ~-t~ and micromechanical models of the cavitation proc e s s 11-14 will be employed to reveal the stochastic nature of cavitation. In particular, it will be demonstrated that (1) the driving force for creep cavitation is stochastic grain boundary sliding, (2) grain boundary sliding events can be represented as an inhomogeneous Poisson process, and (3) the rate of cavity nucleation is directly proportional to the intensity function describing the stochastic grain boundary sliding process. Any discussion of cavitation in ceramics should give consideration to the various grain boundary microstructures available in ceramic systems and the effect that the microstructure has on the mechanisms involved in cavitation. For R.A. PAGE and K. S. CHAN are Senior Scientists, Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78284. This paper is based on a presentation made at the symposium "Stochastic Aspects of Fracture" held at the 1986 annual AIME meeting in New Orleans. LA, on March 2-6, 1986, under the auspices of the ASM/MSD Flow and Fracture Committee.
METALLURGICAL TRANSACTIONS A
simplicity, only two microstructural groups will be consid ered in this paper, one group being composed of material that contain no glassy second phase on the grain boundarie and the other group being composed of materials that con tain a continuous glassy phase on the grain boundarieL In the following sections experimental data and micro mechanical models representative of both microstructura groups will be used to illustrate the stochastic aspects o cavitation, and, despite the general consensus that the oper ative cavitation mechanism is different in the two micro structural groups,*
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