PSI - Issue 7

E. Vacchieri et al. / Procedia Structural Integrity 7 (2017) 182–189

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E. Vacchieri et al. / Structural Integrity Procedia 00 (2017) 000–000

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direction. Moreover, service-like TMF cycles have been defined on the basis of FE simulation of the blade and the experimental results have been exploited to assess the lifing procedure. In the present paper the experimental campaign is not discussed in details, but more information can be found in Vacchieri et al. (2016) and Vacchieri (2016). The field feedback for this blade derives from the analysis of the whole set of blades for 20 plants, that have operated in the complete range of service condition for GT, from base load to daily cycling, after a single life cycle of about 25 kEOH. The statistical approach that has been used to treat all the available information about operated blades is based on the Weibull distribution. The Weibull statistical distribution function is widely used throughout the engineering industry in order to approach statistical analysis of the field data, Salzman (2005). The probability density function (PDFW) designed by Weibull is described by a shape parameter β , a minimum life or location parameter γ , that specifies the failure free period below which there is a zero probability of failure, and a characteristic life η , Eq. 1. f ( x ) = β · X ( γ ) · ( ( x − γ ) β − 1 ( η − γ ) β ) · e − ( x − γ η − γ ) β (1) where 0 < x < ∞ . The cumulative distribution, F ( x ), Eq. 2, is calculated as the integral of f ( x ) in dx . F ( x ) = 1 − e − ( x − γ η − γ ) β (2) Generally a linear form of Eq. 2, as reported by Melis et al. (1999), is proposed in order to calculate the survivability level, S , of a statistical population, Eq. 3. where S ( x ) = 1 − F ( x ), L = x − γ and L β = η − γ . S means the fraction of samples that survives to a certain failure criteria that is considered in the statistical analysis, while x represents the life in cycles or hours for the (1 − S ) samples that fail. L β is known as the scale parameter of the distribution or adjusted characteristic life and it is the life for which 63.2% of the samples fail. Finally, the shape parameter β is the slope of the linear relation, which is an indicator of the scatter or distribution of the data: the larger is the slope, the smaller is the scatter. Weibull statistics have been applied to crack lengths measured on operated blades, considering di ff erent crack sizes. The statistical approach has been used in order to correlate the entity of the service damage to the number of cycles experienced by the di ff erent blade sets. Weibull statistics are used as a support to the creep-fatigue life prediction methodology so, they have been used only for the critical locations correctly identified by the calculation. In the present paper, the analysis allows the evaluation of the time or cycle number necessary to have at least one blade in the set with a defect / crack of the fixed size. The experimental data on which the analysis has been applied, are crack lengths measured during the visual inspection after the stripping process. Three crack length levels have been taken into account in order to evaluate not only the presence of the defect but to study its propagation. Considering l as the minimum length of an observable cracks, blades with at least a cracks of length l , 2 l and 2 . 5 l have been taken into account in the statistical analysis. The data for cracks longer than 2 . 5 l are not su ffi cient to be statically treated. Destructive analyses on seven operated blades have been conducted to map the cracks, measure their maximum penetration in the substrate and be able to determine the relationship between crack length and depth. ln ( ln ( 1 S ( x ) )) = β ln ( L L β ) (3)

3. Results and Discussions

In the following paragraphs, the developed creep-fatigue lifing procedure is described and applied to the selected case study, the first stage blade of Ansaldo F-class GT plant. The lifing results are verified through the available field feedback. Weibull statistics have been used to treat the service damage observed in the critical locations identified by the lifing procedure. This analysis allows the estimation of the operating life limit for repairability and structural integrity through the correlation between crack length and its penetration.

3.1. Creep-Fatigue Lifing Procedure

The developed creep-fatigue lifing strategy starts from an integrated procedure described in Holdsworth (2010, 2011) and depicted in Fig. 1.