1949 Volume 18 Issue 4 Pages 12-19
Everybody recognizes that the welding residual stress is due to the external and internal constraints. As to special test piecer extenally constrained, some theoretical calculations have been made by Dr. Tanka, Dr. Naka, etc ... However, there is no report t discussing internal constraint. It is a wellknown fact that the internal constraint is due to temperature distributed nonuniformly but itsmechanism and rate have not been subjected to close examinations. In this report we dealt withsuch problems and have been led to the following conclusions.
Inheret strain .aT (a. Coeft of expansion, T : temperature difference) do not always satisfy the condition of continuity. It goes without saying that the deformation which does not satisfy such a condition cannot occur. And this condition can be expressed by the compatibility equation of strain, which is the foundamental one in the theory-of elasticity. Therefore the rate of internal' constraint will be defined by the rate of aT which does nat satisfy that equation.
From such considerations we can obtain some impartant characteristics of a family of isotherms. The differential equation for the temperature distribution of a welded plate is given by Rasenthal (J. A. W. S, . May 1941) as follows,
whece ξ=x-vt, v : moving speed of electrode, k2 ;thermal diffusivity, t ; time. From the above equation, the constraining rate is expressed by
F*=-v/k2 ∂T/∂ξ+1/k ∂T/∂t
Apalysing the above, equation, we can get the following characteristics;
(1) Constraing rate in the tangential directin of the isotherms is the greatest and that in the normal onl is the minimum. Tnen we know that the maximum principal stress'acts in the tangential direction and thh minimum one in the normal direcion of the curves.
(2) Greater stress acts in the closer part of the isotherms than in the dispersed part.
Examination of the equation of F will show the relations between the welding stress and the family of isotherms, welding conditions, etc.,