The role of uncertainty in creep mechanics

The development of constitutive models for the analysis of the creep (and fatigue) of structures at high temperature has a long history. Nevertheless, with a few exceptions, it is common in engineering practice to use relatively simple models, typically based on time- or strain-hardening coupled with a simple power-law derived from steady-state behavior. The use of simple constitutive models is usually adopted even when advanced finite element simulation of complex structures is undertaken. An inherent feature of the use of such simple models is that the presence of scatter in the original creep data is ignored – the parameters in the material models are obtained from a ‘best-fit’ to the raw scattered data. In practice creep design is often carried through using ‘worst-case’ property values, although these can also be difficult to accurately define. This is quite problematic for design: the assessment of the stress, strain, and possibly failure, of complex structures at high temperature must then be carried out in the context of major uncertainties about the fundamental materials modeling – and usually by analysts whose experience of stress analysis could be principally based on low temperature behavior where elastic properties such as Young’s Modulus and, to some extent, time independent inelastic properties such as uniaxial yield stress and post-yield hardening are fairly certain, showing little variation. This situation in high temperature design leads to the identification of both types of known uncertainties in creep modeling and analysis: aleatory – scatter and randomness, that is stochastic uncertainty, and epistemic – lack of knowledge. The former has been studied in the literature, but to no great extent and has scarcely been embraced in design with the exception of the estimation of creep lifetime. The latter, to the writer’s knowledge, has hardly been studied for high temperature design. Epistemic uncertainty in the present context extends not only to lack of experience/knowledge on the part of the designer or analyst, but also to the use of simplified constitutive models based on limited, and scattered, creep tests. The latter can be reduced, for example, by using more detailed material models and conducting more tests. A significant feature of epistemic uncertainty is that much of what we do know about creep scatter has been gained from carefully conducted laboratory tests: how this relates to real components under actual service conditions is largely unknown. The aim of this paper is to review available work on aleatory uncertainty in creep mechanics related to the effect of scatter in stress analysis, to examine the consequences for modeling and design and to propose a way forward