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Research Papers: Materials and Fabrication

# Assessment Procedure for Multiple Volumetric Flaws in $p-M$ Diagram

[+] Author and Article Information
Shinji Konosu

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

J. Pressure Vessel Technol 131(3), 031407 (Apr 22, 2009) (13 pages) doi:10.1115/1.3110036 History: Received May 01, 2008; Revised January 30, 2009; Published April 22, 2009

## Abstract

Assessment of multiple volumetric flaws is one of the most common problems relating to pressure vessels and piping components. Under the current fitness for service rules, such as ASME, BS, and so on, multiple volumetric flaws are usually recharacterized as an enveloping volumetric flaw (defined as a single larger volumetric flaw) as well as multiple cracklike flaws, following their assessment rules. However, the rules proposed in their codes will not often agree and their justification is unknown. Furthermore, they can provide unrealistic assessment in some cases. In this paper, the interaction between two differently sized nonaligned volumetric flaws such as local thin areas is clarified by applying the body force method. Unlike multiple cracklike flaws, the effect of biaxial stresses on the interaction is evident. Based on the interaction that indicates the magnification and shielding effects and reference stress solutions, a new procedure for multiple volumetric flaws is proposed for assessing the flaws in the $p-M$ (pressure-moment) diagram, which is a simple assessment procedure for vessels with volumetric flaws.

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## Figures

Figure 7

Assumed stress distribution in the cross section of a cylinder containing multiple partly through flaws

Figure 8

Flaw tip separation angle whereby interaction effect can be ignored under pure bending moment action versus average angle of two flaws

Figure 9

True stress-true strain curve used in FEA

Figure 12

p-M diagram in Ibaraki FFS rule (6,16-17)

Figure 13

(a) Flowchart for multiple nonaligned volumetric flaws’ assessment Level 1 in p-M diagram. (b) Flowchart for multiple nonaligned volumetric flaws’ assessment Level 2 in p-M diagram.

Figure 5

Extent of plastic deformation around multiple flaws at TES load (cylinder numbers V_I(2) mL38.62P and V_I(2)mL44.1C1.5P)

Figure 6

Crack tip separation whereby interaction effect can be ignored under pure pressure action versus average length of two flaws

Figure 10

Normalized limit pressure (the ratio of limit pressure for multiple flaws to that for the severest of the individual longitudinal flaws) versus longitudinal distance H0/(2c¯) of equivalent aligned flaws

Figure 11

Normalized limit moment (the ratio of limit moment for multiple flaws to that for the severest of the individual circumferential flaws) versus circumferential distance S0/(2cθ¯) of equivalent aligned flaws

Figure 1

Body force method (7)

Figure 2

Multiple nonaligned flaws of different sizes in a cylinder subjected to internal pressure or bending

Figure 3

Alignment rule from nonaligned volumetric flaws into equivalent aligned volumetric flaws

Figure 4

(a) Alignment rule for nonaligned flaws in the case of Y/(2c¯)=0.1. (b) Alignment rule for nonaligned flaws in the case of Y/(2c¯)=1.0.

## Errata

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