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The Analytical Computation of Residual Thermal Stresses


Lassen, Herbert Arthur (1951) The Analytical Computation of Residual Thermal Stresses. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XH09-8359.


An analytical method is developed in detail whereby it is possible to calculate, with arbitrary accuracy, the temperature, the stresses, and the residual strains as a function of the radial position and time induced in an infinitely long solid isotropic cylinder by a quench in a large body of fluid, assuming that all of the pertinent parameters are known (graphical) functions of the temperature.

In the course of this development, a general theory is presented whereby it is theoretically possible to predict the stresses and the residual strains in an isotropic body at any time during a thermal and mechanical history if the following very general assumptions are satisfied.

1) The temperature and the boundary conditions are known functions of the position and time and the free thermal expansion is a known function of the temperature.

2) There are values of E, G and v which are known functions of the temperature and which relate, through Hooke's Law, the changes in the stresses with the changes in the strains which occur if the stresses are removed from an infinitesmal element of the body.

3) There is a theory of strength available which either predicts the maximum stresses which the material can sustain, as a function of the temperature and the past history, or which predicts the plastic strain rates as a function of the stresses, the temperature and the past history.

Selecting the values of the pertinent parameters from the literature, a numerical calculation of the residual stresses is made for a specific case of a quenched solid cylinder. The results axe compared with experimental values for the same case determined by other investigators.

The developments for a solid cylinder are extended to a hollow cylinder and a flat plate. Various suitable theories of strength are considered. The modifications to the general theory and the additional information required if a phase change is involved are briefly indicated.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mechanical Engineering and Electrical Engineering)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Minor Option:Electrical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Housner, George W.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1951
Record Number:CaltechTHESIS:02072012-112201922
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6814
Deposited By: Benjamin Perez
Deposited On:07 Feb 2012 19:45
Last Modified:03 May 2023 21:00

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