Elementary mathematical theory of thermal stresses and fracture during welding and cutting

In many technological processes involving the cutting or welding of thin plates there is local thermal heating or cooling at the tip of the cut. Under particular conditions the cut may be considered as a semi-infinite crack and the thermal source as a point heat source. For cutting processes the cut is behind the moving thermal source and for welding the cut is ahead of the moving thermal source. For most processes the value of the thermal source is positive (e.g. lasers, electron beam cutting, welding and others). In this paper the authors investigate analytically the stress distribution induced by a point thermal source moving with a constant velocity in an infinite plate. The stress intensity factor due to the point thermal source at the tip of the cut is calculated. It is shown that for both welding and cutting in the case of a thermal heat source the stress intensity factors will be negative, which means that the thermal field induced by the point thermal heat source will tend to close the surfaces of the cut in the vicinity of the tip. The opposite situation occurs when the cut tip is cooled by the thermal source. In this case there are positive values for the stress intensity factors and the thermal stresses may lead to brittle fracture ahead of the cut. As an example, the applications of the theory under development to the uncontrolled fracture phenomenon during the thermal beam cutting of brittle material is considered in detail. A fracture criterion for this process is obtained, which enables choosing the manufacturing parameters of the process in order to avoid the possibility of uncontrolled fracture