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Research Papers: Design and Analysis

# Residual Thermal Stresses Induced by Local Heat Treatment on Spherical Vessels and Their Influential Factors

[+] Author and Article Information
Wang Ze-jun

School of Materials Science and Engineering, Tianjin University, Tianjin 300072, P.R.C.; Tianjin Special Equipment Supervision Inspection and Technology Research Institute, Tianjin 300192, P.R.C.

Jing Hong-yang

School of Materials Science and Engineering, Tianjin University, Tianjin 300072, P.R.C.

J. Pressure Vessel Technol 130(1), 011208 (Jan 23, 2008) (8 pages) doi:10.1115/1.2826435 History: Received April 13, 2006; Revised December 01, 2006; Published January 23, 2008

## Abstract

For the purpose of finding a way to control effectively the residual thermal stresses induced by local heat treatment on spherical vessels, a thermal tracing program is developed successfully based on the transient thermal analysis and controlling method of average temperature of nodes located in an “observed region.” Typical calculation cases reveal that the local heat treatment process itself does cause obvious residual thermal stress that is high enough to cause yield when concentrated heating on small region is adopted, but decentralized heating on a larger region can lower effectively the residual thermal stresses to a rather desirable level. It can be found through a one by one analysis of ten factors, which are possibly influential on residual thermal stress: arc radius of heated region, holding temperature, volume, and wall thickness of the vessel are primary effective factors. The bandwidth of the annular insulated region, the heating rate, and the size of the observed region are secondary factors. Heating pattern, holding time, and cooling rate can hardly affect the residual thermal stress. Considering the primary factors except holding temperature, and taking 30% of yield stress as the expected residual thermal stress level, the recommended arc radius of heated region should be 2.2$Rt$ in minimum.

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## Figures

Figure 1

Model schematic

Figure 2

Temperature dependent properties of 16MnR

Figure 3

Typical results from the tracing program

Figure 4

Distortions and equivalent stresses at various times (distortions are enlarged by 15 times). (a) Heating up to 220°C, time=7200s, maximum stress=245MPa. (b) End of heating, time=21,600s, maximum stress=273MPa. (c) End of holding, time=28,800s, maximum stress=255MPa. (d) End of controlled cooling, time=54,000s, maximum stress=221MPa. (e) Residual stress and residual distortion, time=225,900s, maximum stress=307MPa.

Figure 5

Residual thermal stress on inner and outer surfaces of heated and annular insulated regions (arc radius of heated region=300mm)

Figure 6

Residual thermal stress on inner and outer surfaces of heated and annular insulated regions (arc radius of heated region=1000mm)

Figure 7

The effect of the arc radius of the heated region on residual thermal stress

Figure 8

The effect of volume on residual thermal stress

Figure 9

The effect of wall thickness on residual thermal stress

Figure 10

The effect of the bandwidth of the annular insulated region on residual thermal stress

Figure 11

The effect of heating rate on residual thermal stress

Figure 12

The effect of holding temperature on residual thermal stress

Figure 13

Variation of thermal stress with time under different holding times

Figure 14

The formation process of residual thermal stress under different controlled cooling rates

Figure 15

Comparison of heat treatment curves

Figure 16

Comparison of thermal stress curves

Figure 17

The effect of heating pattern

Figure 18

The effect of observed region

Figure 19

Selection of optimized heated region

## Errata

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