A Review of Statistical Failure Time Models with Application of a Discrete Hazard Based Model to 1Cr1Mo-0.25V Steel for Turbine Rotors and Shafts.

Mark Evans

doi:10.3390/ma10101190

Abstract

Producing predictions of the probabilistic risks of operating materials for given lengths of time at stated operating conditions requires the assimilation of existing deterministic creep life prediction models (that only predict the average failure time) with statistical models that capture the random component of creep. To date, these approaches have rarely been combined to achieve this objective. The first half of this paper therefore provides a summary review of some statistical models to help bridge the gap between these two approaches. The second half of the paper illustrates one possible assimilation using 1Cr1Mo-0.25V steel. The Wilshire equation for creep life prediction is integrated into a discrete hazard based statistical model—the former being chosen because of its novelty and proven capability in accurately predicting average failure times and the latter being chosen because of its flexibility in modelling the failure time distribution. Using this model it was found that, for example, if this material had been in operation for around 15 years at 823 K and 130 MPa, the chances of failure in the next year is around 35%. However, if this material had been in operation for around 25 years, the chance of failure in the next year rises dramatically to around 80%.

Highlights

The prediction of long-term creep properties from short timescale experiments is rated as the most important challenge to the UK Energy Sector in a recent UK Energy Materials Review [1]
This paper has provided a summary review of some statistical failure time models with the aim of aiding thehas assimilation such models with existing creep life
This paper providedof a summary review of somepredictive statisticalmodels failure for time models withwill the aim enable anassimilation enrichment ofof prediction to be achieved with a predictive move awaymodels from predicting failure of aiding the such models with existing for creep life. times. This will onan theenrichment average towards predictingtothe life associated chance of failure. This was enable of prediction besafe achieved with a with movea minimum away from predicting failure times on followed by an illustration of one possible assimilation, namely—the deterministic Wilshire equation and the statistical discrete hazard model

Summary

Introduction

The prediction of long-term creep properties from short timescale experiments is rated as the most important challenge to the UK Energy Sector in a recent UK Energy Materials Review [1]. Creep strain (ε) is a function of stress (τ) and absolute temperature (T), and of time (t) ε = f1 (τ, T, t) (1a). Equation (1a) is often represented in differential form ε = f2 (τ, T, t) (1b). When it comes to extrapolating from short term accelerated test data, three very broad approaches can be identified. A single creep curve at steady uniaxial stress τ and absolute temperature T can be modelled using a general functional form ε = η t, Ψ1 , Ψ2 , .

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