Mathematical analysis of stress criteria in the interior of a heated translating work piece

Abstract

If metal work piece is heated non-uniformly as in surface heat treatment or welding, it experiences a stress distribution in its interior. If this reaches a high level fracture may occur, as is the case with concrete or stone. In materials such as metals under normal circumstances, the stress may be such that the elastic limit is passed and plastic deformation of the material occurs. It will depend on the nature of the application whether such behaviour is welcome or not. Fracture is desirable in laser scabbling of concrete, in which it is desired to remove the surface layer. Similarly, plastic deformation is central to the process of laser forming. It is not normally desirable however when the primary function of heating is to facilitate surface treatment of a work piece, or to weld two parts of an assembly together. A simple method of estimating the stress distribution in a translating, heated work piece is developed and the manner in which constraints on the processing parameters can be deduced is outlined. The method is based on an extension of point and line sources for the thermal part of the problem and the corresponding point solutions in the theory of linear elasticity.If metal work piece is heated non-uniformly as in surface heat treatment or welding, it experiences a stress distribution in its interior. If this reaches a high level fracture may occur, as is the case with concrete or stone. In materials such as metals under normal circumstances, the stress may be such that the elastic limit is passed and plastic deformation of the material occurs. It will depend on the nature of the application whether such behaviour is welcome or not. Fracture is desirable in laser scabbling of concrete, in which it is desired to remove the surface layer. Similarly, plastic deformation is central to the process of laser forming. It is not normally desirable however when the primary function of heating is to facilitate surface treatment of a work piece, or to weld two parts of an assembly together. A simple method of estimating the stress distribution in a translating, heated work piece is developed and the manner in which constraints on the processing parameters can be deduced is outl...