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Research Papers: Design and Analysis

# Stress Intensity Factors of Various Surface Cracks Inside a Hollow Cylinder Under Steady State Thermal Striping

[+] Author and Article Information
Toshiyuki Meshii

Graduate School of Engineering, University of Fukui, 3-9-1 Bunkyo, Fukui, Fukui 910-8507, Japan

Kentaro Shibata

University of Fukui, 3-9-1 Bunkyo, Fukui, Fukui, Japan

J. Pressure Vessel Technol 131(3), 031208 (Apr 17, 2009) (6 pages) doi:10.1115/1.3109978 History: Received December 28, 2007; Revised August 10, 2008; Published April 17, 2009

## Abstract

A thermal stress problem of a long hollow cylinder was considered in this paper. The outer surface of the cylinder was adiabatically insulated, and the inner surface was heated axisymmetrically by a fluid with sinusoidal temperature fluctuations (hereafter called as thermal striping), whose temperature amplitude $(ΔT)$ and angular velocity $(ω)$ were constant. The heat transfer coefficient $h$ was also assumed to be constant. The stress intensity factor (SIF) due to the thermal stress for a given cylinder configuration varies not only with these three parameters $ΔT$, $ω$, and $h$, but also with time. The temperature and, as a result, SIF fluctuation amplitude soon became constant (Meshii, T., and Watanabe, K., 2004, “Stress Intensity Factor of a Circumferential Crack in a Thick-Walled Cylinder Under Thermal Striping,” ASME J. Pressure Vessel Technol., 126(2), pp. 157–162), which hereafter is called as steady state. If one is interested in fatigue crack growth (assuming Paris law) under this thermal stress, because the SIF range soon converges to a constant, it seemed important to know the maximum value of the steady state SIF range for a given cylinder configuration, for all possible combinations of $ΔT$, $ω$, and $h$. This maximum SIF evaluation is time consuming. Thus in this paper, this maximum steady state SIF range for four typical surface cracks’ deepest point, inside a hollow cylinder for all possible combinations of $ΔT$, $ω$, and $h$ were presented as a first step. Thin-to thick-walled cylinders in the range of mean radius to wall thickness parameter $rm/W=10.5–1$ were considered. Crack configurations considered were 360 deg continuous circumferential, radial, semi-elliptical in the circumferential and radial directions. Normalized crack depth for all cases was in the range of $a/W=0.1–0.5$. In case of semi-elliptical crack, the normalized crack length $a/c$ was all in the range of 0.063–1.

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## Figures

Figure 7

Normalized upper limit SIF range of a radial crack in a long cylinder under thermal striping (ν=0.3)

Figure 8

Normalized upper limit SIF range of the deepest point of circumferential semi-elliptical crack in a long cyclinder under thermal striping (ν=0.3)

Figure 9

Normalized upper limit SIF range of the deepest point of radial semi-elliptical crack in a long cylinder under thermal striping (ν=0.3)

Figure 6

Normalized upper limit SIF range of a circumferential crack in a long cylinder under thermal striping (ν=0.3)

Figure 5

Cylinder with a radial semi-elliptical crack under thermal striping

Figure 4

Cylinder with a circumferential semi-elliptical crack under thermal striping

Figure 3

Cylinder with a radial crack under thermal striping

Figure 2

Circumferentially cracked cylinder under thermal striping

Figure 1

Thermal striping at flow joined area (left) and simplified model for analysis (right)

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