Numerical Simulation with Thorough Experimental Validation to Predict the Build-up of Residual Stresses during Quenching of Carbon and Low-Alloy Steels

Abstract

A mathematical model to calculate the build-up of residual stresses during quenching of carbon (AISI 1045) and low-alloy (AISI 4140 and 4340) cylindrical steel bars is proposed. The model is implemented as a combination of the commercial software AC3®, to simulate the microstructure evolution, and Abaqus®, to model the heat transfer and the elastic, plastic, thermal, and phase transformation strains/stresses by the finite element method. All steel properties required in the model are calculated as an average of the properties of individual microconstituents (austenite, pearlite, bainite, or martensite) weighted by their local volume fractions, enabling the model application to any type of carbon or low-alloy steel. To thoroughly verify the simulation results, experimental measurements were carried out in cylindrical bars quenched in stirred water and these measurements were compared with model results. The heat transfer coefficient between the bar and the water was calculated by an inverse solution technique, resulting in the constant value of 7200 W m–2 K–1 for the whole quenching period. For the low-alloy steels, measured and calculated volume fractions of martensite in the bar cross sections are in very good agreement, but for the carbon steel, large discrepancies are observed in the fractions of most constituents. Tangential and axial residual stresses were measured on the lateral surface of the quenched bars using the X-ray diffraction method. These stresses, which are compressive, agree well with those calculated by the present model, showing discrepancies generally lower than 10%.