A Stochastic and Local Theory of Fatigue for Aging Pressure Vessels and Piping

Published

November 4, 2012

Author(s)

Jeffrey T. Fong, Nathanael A. Heckert, James J. Filliben

Abstract

We begin with a review of the fatigue design methodology for new pressure vessels and piping, based on both deterministic and stochastic approaches. We will then prove that the same methodology for estimating the remaining life of aging pressure vessels and piping (APVP) using a deterministic approach fails, unless nondestructive evaluation (NDE) data of crack growth from periodic inspection is available. This leads to the introduction of a stochastic and local theory of fatigue life of APVP using NDE data of the growth of a single crack in engineering materials (Ref.: Fong, Marcal, Hedden, Chao, and Lam, Proc.ASME 2009 PVP Conf., Paper PVP2009-77827), in which the standard deviation of the estimated fatigue life was derived in terms of the means and standard deviations of the initial crack length, final crack length, fracture toughness, and other material property parameters. We then introduce a more general theory of the remaining life of APVP using NDE data of the growth of multiple cracks. This general stochastic theory will be known as the APVP MULTI-CRACK GROWTH THEORY. To illustrate the methodology for estimating the remaining life of APVP with multiple cracks, we introduce an open-source Bayesian statistical analysis software named WinBUGS, and a Markov Chain Monte Carlo (MCMC) algorithm to calculate the mean and standard deviation of both the initial crack length and the initial crack growth rate from a set of NDE-measured multiple crack length data over many inspection intervals. A numerical example using synthetic NDE and fracture toughness data for high strength steels is included. Significance and limitations of this Bayesian approach to estimating the uncertainty of fatigue life prediction for aging pressure vessels and piping in nuclear industry applications are also presented.

Proceedings Title

3rd International Symposium on Structural Integrity

Conference Dates

October 31-November 4, 2012

Conference Location

Jinan, Shandong

Pub Type

Conferences

Keywords

Aging pressure vessels and piping (APVP), crack growth theory, fatigue design, fracture mechanics, nondestructive evaluation (NDE), remaining life, stochastic theory of crack growth, uncertainty quantification.

Citation

Fong, J. , Heckert, N. and Filliben, J. (2012), A Stochastic and Local Theory of Fatigue for Aging Pressure Vessels and Piping, 3rd International Symposium on Structural Integrity, Jinan, Shandong, -1 (Accessed April 19, 2024)