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Research Papers: Materials and Fabrication

# Validity of Assessment Procedure in $p-M$ Method for Multiple Volumetric Flaws

[+] Author and Article Information
Shinji Konosu

Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japankonosu @ mx.ibaraki.ac.jp

Masato Kano

Sumitomo Metal Technology, Inc., 16-1 Sunayama, Kamisu, Ibaraki 314-0255, Japankano-mst@smt-co.com

Norihiko Mukaimachi

JGC Corporation, 2-3-1 Minatomirai, Nishiku, Yokohama 220-6001, Japanmukaimachi.norihiko@jgc.co.jp

Shinichiro Kanamaru

JGC Corporation, 2-3-1 Minatomirai, Nishiku, Yokohama 220-6001, Japankanamaru.shinichiro@jgc.co.jp

J. Pressure Vessel Technol 132(2), 021402 (Jan 29, 2010) (10 pages) doi:10.1115/1.4000507 History: Received April 10, 2009; Revised September 16, 2009; Published January 29, 2010; Online January 29, 2010

## Abstract

General components such as pressure vessels, piping, storage tanks, and so on are designed in accordance with the construction codes based on the assumption that there are no flaws in such components. There are, however, numerous instances in which in-service single or multiple volumetric flaws such as local thin areas are found in the equipment concerned. Therefore, it is necessary to establish a fitness for service rule, which is capable of evaluating these flaws. The procedure for a single flaw or multiple flaws has recently been proposed for assessing the flaws in the $p-M$ (pressure-moment) diagram, which is an easy way to visualize the status of the component with flaws simultaneously subjected to internal pressure $p$ and external bending moment $M$ due to earthquake, etc. If the assessment point $(Mr,pr)$ lies inside the $p-M$ line, the component with flaws is judged to be safe. In this paper, numerous experiments and finite element analysis for a cylinder with external multiple volumetric flaws were conducted under (1) pure internal pressure, (2) pure external bending moment, and (3) subjected simultaneously to both internal pressure and external bending moment, in order to determine the plastic collapse load at volumetric flaws by applying the twice-elastic slope (TES) as recommended by ASME. It has been clarified that the collapse (TES) loads are much the same as those calculated under the proposed $p-M$ line based on the measured yield stress.

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## Figures

Figure 1

Several definitions of term “limit load”

Figure 2

p-M diagram in Ibaraki FFS rule (6,11)

Figure 3

Flowchart for multiple nonaligned volumetric flaws assessment in p-M diagram (6)

Figure 4

Comparison of allowable wall thickness for a single longitudinal flaw between p-M procedure and Code Case N-597-2 procedure

Figure 5

Comparison of allowable wall thickness for multiple longitudinally aligned twin flaws between p-M procedure and Code Case N-597-2 procedure

Figure 6

True stress-true strain curve used in FEA

Figure 7

(a) Typical single and multiple rectangular volumetric flaw geometries for internal pressure load used for experimental test and FEA. (b) Typical multiple rectangular volumetric flaw geometries for bending moment load used for experimental test and FEA. (c) Typical multiple rectangular volumetric flaw geometries for combined internal pressure and bending moment load used for experimental test and FEA.

Figure 8

Schematic diagram of experimental apparatus

Figure 9

Typical FE mesh for a cylinder with multiple flaws

Figure 10

TES load for multiple volumetric flaws plotted on p-M diagram based on σf=σysmean (mid of multiflaws: midpoint of volumetric flaws)

Figure 11

Plastic initiation (pl. init), TES, and plastic instability (max) loads for multiple volumetric flaws plotted on Ibaraki FFS p-M diagram based on σf=σysmin/1.5 (mid of multiflaws: midpoint of volumetric flaws)

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