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The modeling of an axisymmetric industrial quenched alloy steel SCM440 based on the finite element method (FEM) has been produced to investigate the impact of process history on material properties and metallurgical. Mathematical modeling of the 1-Dimensional element axisymmetric model has been adopted to determine the temperature history and consequently the hardness of the heat-treated steel bar at any node. The lowest hardness point (LHP) will be at the half-length at the center and the effect of radius on (LHP) is calculated. In this manuscript hardness (HRC) in specimen points was determined by the conversion of computed characteristic cooling time for phase transformation t8/5 which equal  (t5 - t8) to hardness. The model can be employed as a guideline to design a cooling approach to achieve desired mechanical properties such as hardness, toughness, and microstructure. The developed mathematical model was converted into a computer program. The computer program can be used independently or incorporated into a temperature history software named (E-LHP-software) to continuously determine and display the temperature history of the heat-treated quenched steel bar and thereby calculate the lowest hardness point and the effect of the radius in LHP can be analyzed and studied. The developed program from the mathematical model (MM) has been verified and validated by comparing its hardness results with experimental work results. The comparison indicates the reliability of the proposed model.

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