A novel 2-D mathematical modeling to determine LHP to protect the industrial transient heat treatment quenched low carbon steels bar

2-dimensional mathematical model of axisymmetric transient industrial quenched low carbon steel bar, to examine the influence of process history on metallurgical and material characteristics, a water-cooled model based on the finite element technique was adopted. A 2-dimensional axisymmetric mathematical model was utilized to predict temperature history and, as a result, the hardness of the quenched steel bar at any node (point). The LHP (lowest hardness point) is evaluated. In this paper, specimen points hardness was evaluated by the transformation of determined characteristic cooling time for phase conversion t8/5 to hardness. The model can be used as a guideline to design cooling approach to attain the desired microstructure and mechanical properties, for example, hardness. The mathematical model was verified and validated by comparing its hardness results to the results of commercial finite element software. The comparison demonstrates that the proposed model is reliable.