Prediction of thermal stress and strain generated during the quenching of low-alloy steel.

The free edge of a quenched plate is subject to zero stress in a direction perpendicular to this edge. Therefore the thermal stresses set up in such a component must be modified in the vicinity of the edge in order to allow the required stress configuration to be produced. This is referred to as the 'edge effect' and its magnitude is conventionally estimated by the well-known Saint Venant Principle. However a detailed understanding of the variation in stress in such a specimen is not well understood and it has been the objective of the present programme to make a detailed elastic/plastic analysis of the stress generation process using a finite element method. To this end a disc specimen has been considered, so that both experimental and theoretical estimates of the stress fields are not influenced by the presence of sharp corners, which lead to a very complex stress system. The stress generation process has been followed by a finite element axisymmetric model. The use of such a plane strain representation has been checked by comparison with a full 3 dimensional elastic analysis, at a very early stage in the process when plastic flow was not present. The results obtained by the two methods of calculation were in good agreement and justify the use of the plane strain model. The finite element programme calculated the thermal history of the specimen by the Crank-Nicholson method, and the weighted mean technique was selected as the best method of smoothing the results. The effects of different element stress functions, and element size, as well as time and load steps have been studied and the optimum combination selected. Considerable difficulty had been experienced with the stability of the results, which was found to be due to limitations in the BERSAFE finite element package. The elimination of this problem led to a situation where successive stages in the stress generation process were calculated and examined with confidence, although great care was required to balance the time step with the thermal loading step.The results from this model in the central region of the plate were ingood agreement with those results reported by earlier workers. The complex variation of stress distribution predicted by the model asthe free edge is approached has been examined and justified against theclassical governing equations. This includes non-linear decay of in-plane stresses and the development of axial and shear stresses near the edge of the plate. A further product of this work has been an evaluation of the development of plastic zones during the quench process.Although the effect of the edge on the inplane stresses differs with axial position in the plate, the derivation of an overall edge correction factor (which is a mean ratio of average stress to the stress on the axis) provides a value which is consistent with the Saint Venant Principle. Therefore, it is concluded that the use of edge correction factors based on the linear decay of in-plane stresses from a position that is one plate's thickness from the edge is satisfactory for determining "real" body stresses from a finite difference model.