Constraints Imposed by the Wilshire Methodology on Creep Rupture Data and Procedures for Testing the Validity of Such Co
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I.
INTRODUCTION
IN general, when selecting alloy steels for large-scale components used in power and petrochemical plants, decisions are based on the ‘‘allowable creep strengths,’’ normally calculated from the tensile stresses causing failure in 100,000 hours at the relevant service temperatures.[1] However, creep life measurements for structural steels show considerable batch to batch variability so, in Europe, tests up to 30,000 h have often been completed for five melts of each steel grade.[2] The development of a parametric approach, termed the Wilshire equations,[3,4] offers the realistic potential of being able to accurately life materials operating at in service conditions from accelerated test results lasting no more than 5000 h. A plethora of recent publications have applied these equations to a range of different materials[5–8] and have provided evidence to suggest that data extrapolation from accelerated tests using these Wilshire equations is a realistic and attractive alternative to expensive long-term testing. This opportunity is particularly exciting when considering the development of new materials for high temperature applications. Indeed a reduction in the development cycle for new steels was identified as the No. 1 priority in the 2007 UK Strategic Research Agenda.[9] The Wilshire equations[3,4] seem to avoid the unpredictable n value variations that are well known to exist when using the following power law expression for
MARK EVANS, is with the College of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, U.K. Contact e-mail: [email protected] Manuscript submitted June 12, 2014. Article published online November 18, 2014 METALLURGICAL AND MATERIALS TRANSACTIONS A
modeling creep properties as a function of stress and temperature e_ m ¼ A ðr=rTS Þn expðQc =RTÞ;
½1
where T is the absolute temperature, r the stress, rTS the ultimate tensile strength, R the universal gas constant and Q*c the activation energy for self-diffusion. A* and n are further parameters of the model. Q*c is normally estimated from the temperature dependency of e_ m at constant r/rTS, whilst n is normally estimated from the normalized stress dependency of e_ m at constant T (often this power law model is expressed in a format that excludes the tensile strength). In the Wilshire model, the unpredictable n variation is overcome by describing the stress and temperature dependencies of the minimum creep rate e_ m as v ; ½2 ðr=rTS Þ ¼ exp k2 e_ m exp Qc =RT where k2 and v are further model parameters. This equation provides a sigmoidal data presentation such that e_ m fi ¥ as (r/rTS) fi 1 (provided v < 0), whereas e_ m fi 0 as (r/rTS) fi 0. Wilshire and Battenbough[3] proposed a very similar expression to Eq. [2] for the stress and temperature dependencies of the time to failure, tf u ; ½3 ðr=rTS Þ ¼ exp k1 tf exp qQc =RT where q is often taken to be equal to unity and is the exponent in the Monkman–Grant relation.[10] To link this Wilshire expression to that for the minimum creep r
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