Theoretical study on residual thermal stresses caused by the brazing process in annular and bilayer structures

It is well-known that residual thermal stress poses a significant threat to the stability and reliability of brazed structures. However, theoretical studies focusing on the effects of residual thermal stress on even simple brazed structures remain largely absent from the literature. In this paper, we use complex variable methods to derive theoretical solutions characterizing residual stress fields for annular and bilayer structures. In addition, using a series of numerical examples, we investigate the main factors determining residual thermal stress in brazing. Our results show that both radial and hoop stress are present in the annular structure while the stress component parallel to the interface is the unique principal stress in the bilayer structure. In an annular structure in which the total thickness of materials coincides with the length of the inner radius, the residual thermal stress in the outer base material is four times higher than that of the inner base material. This is attributed to the fact that the two materials have different curvatures. In the case of a thin-wall structure in which the inner radius is ten times that of the total thickness of materials, the corresponding residual thermal stress has no more than 15% error when compared to that from the bilayer structure. Since the distortion of brazed structures is due mainly to the effects of residual thermal stress within the corresponding base materials, it would seem practical to minimize the thickness of the solder used in the brazing process.