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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 70

The Effects of Temperature Variation on the Creep Behaviour of Pressure Vessels using Theta Projection Data

M. Law, W. Payten and K. Snowden

Australian Nuclear Science and Technology Organisation, Menai, Australia

Full Bibliographic Reference for this paper
M. Law, W. Payten, K. Snowden, "The Effects of Temperature Variation on the Creep Behaviour of Pressure Vessels using Theta Projection Data", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 70, 2001. doi:10.4203/ccp.73.70
Keywords: creep, non-linear, pressure vessel, finite element.

Summary
The effect of thermal gradients on thick walled pressure vessels can be significant. Where thermal gradients occur, thermally induced stresses [1] will exist in addition to the pressure stresses. The creep response of the wall depends on the local stress, temperature, and previous creep history. The combination of the altered initial stress state and the altered creep response may lead to differing final stress states through time and a reduced creep life to that calculated for vessels without temperature variation using a constant secondary creep rate law.

The Theta projection method [2] is being more widely used as its advantages and flexibility become appreciated. The Theta projection equation is an attempt to both empirically fit the strain-time behaviour of a material during creep, and to provide an insight into the processes occurring during creep [3]. The equation is an expression of creep response over time:

(70.1)

where is the creep strain, is the time, and the terms are experimentally determined constants. Each Theta term is itself a function of temperature and stress, of the form;

(70.2)

where is the stress, is the temperature and . The parameters used in this work were obtained as part of an extensive vacuum creep testing program of ex-service Cr – 1 Mo steels.

Models were analysed of pressure vessels under a number of temperature gradients, and under a steady state temperature field. A comparison was made with a simpler Norton law analysis.

The stress redistributions show complex behaviour. In addition to the usual creep induced stress redistribution based on the initial thermal and pressure induced initial stress state, there are two linked factors which add to the complexity of the stress response. Firstly the temperature variation across the wall thickness alters the creep rates so that, at the same stress, the inner wall experiences faster creep rates than that of the outer. Thus the inner wall relaxes offloading stress onto the outer wall. At these higher stresses the outer wall then completes its strain redistribution, this then offloads stress the inner wall. Thus it is some time before the stresses stabilise. The difference in relative creep rates between the inner and outer walls is a function of temperature, local von–Mises stress and time.

Secondly, the temperature variation means the relative difference in the creep rates may vary through time. For example, the material in one part of the vessel may be entering its tertiary (accelerating) phase while in another part of the vessel the material may still be exhibiting a decreasing or constant creep rate (primary or secondary creep).

The redistribution of stresses by creep in a pressure vessel was modelled and compared to results predicted by the Norton equation. The differences found were attributed to the more versatile features of the Theta projection. The cases modelled included thermal variation across the wall of a pressure vessel. The stress evolution was similar to that found in previously published work. However, more complex interactions were noted as a result of coupled thermal variation of creep rates and thermally induced stresses.

References
1
Timoshenko S., Goodier J., "Theory of Elasticity", McGraw Hill, p. 413, 1951.
2
Evans R., Wilshire B., "Creep of Metals and Alloys", Inst. of Metals, London, 1985.
3
Ule B., Rodic T., Sustar T ., "Modification of projection creep law by introducing mean stress term", Materials Science & Technology, V13, p. 555-559, July 1997.

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