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Design and Analysis

The Effect of Material Models on Elastic Follow-Up

[+] Author and Article Information
James T. Boyle

Department of Mechanical & Aerospace
Engineering,
University of Strathclyde,
Montrose Street,
Glasgow G1 1XJ, UK
e-mail: jim.boyle@strath.ac.uk

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received November 1, 2011; final manuscript received February 1, 2012; published online November 6, 2012. Assoc. Editor: Dennis K. Williams.

J. Pressure Vessel Technol 134(6), 061210 (Nov 06, 2012) (7 pages) doi:10.1115/1.4006127 History: Received November 01, 2011; Revised February 01, 2012

The phenomenon of elastic follow-up in high temperature piping has a long history and rules to limit its significance in design are well established. However, most design rules, and numerous associated supporting studies, have been limited to a simple power-law of creep, with variations to account for time- or strain-hardening in primary creep. A common feature of the most studies of elastic follow-up in structures subject to power-law creep is that a plot of (maximum) stress against strain—a so-called isochronous stress– strain trajectory—is almost insensitive to the creep law (in particular, the stress exponent in the power-law) and is almost linear (until perhaps the later stages of stress relaxation). A limitation of the power-law is that it assumes to be valid across all stress ranges, from low through moderate to high, yet it is well known that this is not generally the case. This paper aims to investigate the effect of stress-range dependent material models on the nature of elastic follow-up: both a simple two-bar structure (common in studies of elastic follow-up) and a detailed finite element analysis of a piping elbow are examined. It is found that stress-range dependent material models can have a significant effect on the accepted characteristics of elastic follow-up.

FIGURES IN THIS ARTICLE
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Copyright © 2012 by ASME
Topics: Creep , Stress , Pipes , Design
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Figures

Grahic Jump Location
Fig. 1

Steady creep of austenitic AISI 316 L(N) 550–650 °C (after Evans et al. [28])

Grahic Jump Location
Fig. 2

Steady creep of austenitic AISI 316 L(N) 550–650 °C (after Evans et al. [28]): comparison of secondary creep models

Grahic Jump Location
Fig. 3

Simple two-bar structure subject to a fixed axial displacement, δ

Grahic Jump Location
Fig. 4

Two-bar structure: isochronous stress–strain curve for a power-law model

Grahic Jump Location
Fig. 5

Two-bar structure: isochronous stress–strain curve for (a) Soderberg model, (b) Prandtl model, (c) CSM model, (d) Naumenko model, n = 5, (e) Garofalo model, n = 3, (f) Garofalo model, n = 5, (g) Lemaitre–Chaboche model, n = 3, and (h) Lemaitre–Chaboche model, n = 5

Grahic Jump Location
Fig. 6

ansys finite element model of a simple piping elbow, geometry from Ref. [30]

Grahic Jump Location
Fig. 7

Piping elbow: isochronous stress–strain curve for power-law

Grahic Jump Location
Fig. 8

Piping elbow: isochronous stress–strain curve for Prandtl law

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