Estimating quench residual stresses in cylindrical steels bars: Excluding the effects of phase transformation

Uncoupled thermo-mechanical finite element analyses, using ABAQUS, are conducted to determine residual stresses created by quenching of 316 stainless steel and AISI 1020 low-carbon steel cylindrical bars. It is found that the magnitude of the residual stresses can be determined from an estimate of the thermal strain difference created in the bars during quenching. It is shown that the strain difference is a function of the Biot and Fourier numbers and the initial and final quench temperatures. The results of the analyses are used to create a diagram with non-dimensional axes with residual stress as a function of maximum thermal strain. The residual stresses are normalised with respect to the room temperature yield strength and the thermal strain normalised with respect to the room temperature yield strain. It is proposed that quench residual stresses can be estimated using this diagram irrespective of the quench conditions and bar diameter for steels. This is provided if there is no phase transformation during quenching. It is shown that if the normalised thermal strain is greater than about 3.6, the surface residual hoop and axial stresses are equal to the compressive room temperature yield strength, while the interior tensile stresses linearly increase (approximately) with thermal strain.