STAU - a general-purpose tool for probabilistic reliability assessment of ceramic components under multiaxial loading

Lack of appropriate design tools is one of the facts that hinders ceramics from being widely applied as structural material with high strength, good resistance against wear and corrosion, strong high temperature durability and favourable thermal properties. Ceramics design methods differ completely from design methods for metals as they are based on fracture statistics rather than on maximum tolerable stresses. During the past few years, the post-processing tool STAU (STatistical A n lysis of ceramic components U nder various loading conditions) has been developed. As a back-end to the general-purpose Finite Element code ABAQUS, STAU is able to generate failure probabilities from stress analysis results. Additionally, a local risk of fracture is calculated. From this it is possible to identify critical regions and to modify the component design accordingly. In its basic form, STAU deals with fracture due to unstable crack extension under static loading. Several additional modules are available to deal with more general situations, e.g. STAULE for subcritical crack growth and time-dependent loading and STAUB for the analysis of proof tests. The capabilities of the code are illustrated by several examples taken from applications of ceramics materials in gas turbines operating at very high temperatures. INTRODUCTION The failure behaviour of monolithic ceramic materials can be well described by the multiaxial Weibull theory [1-4] and its extensions [5,6]. The lifetime distribution can be predicted for components on the basis of test results obtained with laboratory specimens of very simple shape such as four-point bend bars. In this sense, ceramics are very well understood. Design of ceramics is always reliability based due to the inherent scatter of the fracture strength caused by the presence of natural flaws. Codes are currently available which allow a probabilistic design under constant [7] or general time-dependent loading [8]. Temperature-dependent material properties can also be taken into account [8,12]. REVIEW OF MULTIAXIAL WEIBULL THEORY In the multiaxial Weibull theory it is assumed that failure of ceramic materials is caused by the unstable extension of natural flaws of random size, random location, and random orientation with respect to the principal stress axes. The worst flaw, i.e. the flaw with the worst combination of size, orientation, and stress determines the maximum tolerable load. Spontaneous failure The probability that the size a of a given flaw exceeds its critical size ac is given by