The Application of the Battelle “Short Formula” to the Determination of Ductile Fracture Arrest Toughness in Gas Pipelines

Many models and formulae have been put forward, over the years, for the determination of the toughness necessary for the arrest of propagating ductile fracture in gas pipelines. One of the first, and most prominent, was that developed by Battelle Columbus Laboratories for the Pipeline Research Committee of the American Gas Association. As originally embodied, the model involved the comparison of curves expressing the variation of fracture velocity and of decompression wave velocity with pressure (the “two-curve model” — TCM). To aid in analysis, at a time long before a computer was available on every desk, a “short formula” (SF) was developed that provided a good fit to the results of the TCM for a substantial matrix of conditions. This SF has subsequently been adopted by several standards bodies and used widely in the analysis of the results of full-scale burst tests. Since the original description of the derivation of the SF is to be found only in a report to the PRC dating back to the Seventies, many in the pipeline industry today are left without a full appreciation of its range of validity. The present paper briefly discusses the original intent of the SF as a substitute for the TCM, and presents the results of extensive calculations comparing the results of the two. It can be concluded that the SF provides an excellent estimate of the results of the TCM over a very wide range of design and operating parameters, within the limitations inherent in the method.