MODELING THE EFFECT OF RADIUS ON TEMPERATURE HISTORY OF TRANSIENT QUENCHED BORON STEEL

One-dimensional (1D) model of an axisymmetric unste ady state industrial quenched boron steel 50B46H bar based on finite element method (FEM) has been applied to investigate the influence of process history on its material properties. The eff ct of four different radii on its temperature history is determined. The model can be employed as a guideline to design cooling approach to achieve desired microstructure and mechanical prope rties such as hardness. A computer program of the model is developed, which can be used indepe ndently or incorporated into a temperature history software named (LHP)-software to continuous ly calculate and display temperature history of the boron steel bar and thereby to study the effect of radius on temperature history. The developed program based on (1D) FEM model has b een verified by comparing its results with commercial finite element software results. Th e comparison indicates its validity and reliability.


Introduction
Mathematical models are used particularly in the natural sciences and engineering disciplines (such as thermal engineering, heat treatment of unsteady state industrial quenched steel bar as in this work).A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system.A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour; in this paper modelling the effect of radius on temperature history of transient quenched boron steel as shown in Fig. 1 is studied.Models allow us to predict behaviours or results that are as yet unseen or unmeasured such as LHP is unseen and unmeasured before as shown in Fig. 1.
The key steps in modelling process are shown in Fig. 1.Mathematical modelling is a method of simulating real-life situations with mathematical equations to forecast their behaviour.In this manuscript the heat transfer analysis is carried out in three dimensions (3D).The (3D) analysis is reduced to a 1-D axisymmetric analysis to save cost and computer time.This is achievable because in axisymmetric conditions, the temperature deviations are only along radius (R) while there is no temperature variation in the (Ɵ) and (Z) directions.The Galerkin weighted residual technique is used to derive the verified mathematical model [1][2][3][4][5][6].DOI

Mathematical model verification
The same data input for the steel properties and boundary condition used in the mathematical model when the radius equal 12.5 mm is applied to the ANSYS software to verify the temperature simulation results.The temperature distribution from the ANSYS analysis is depicted figuratively as shown in Fig. 6 and Fig. 7.  From the graphs, it can be clearly seen that the temperature history of the quenched steel bar have the same pattern.The heat transfer across the steel bar is uniform.As known during quenching, there are two important temperatures [800°C and 500°C] to calculate the cooling time [7,[8][9][10].Because the characteristic cooling time, relevant for structure transformation for most structural steels, is the time of cooling from 800 to 500°C (time t8/5) [7,[11][12][13][14][15][16][17].Then important mechanical properties such as hardness can be computed.In the mathematical model for the node W5 in the surface when the radius equal 12.5 mm, we found that it takes 2. during quenching from 850oC to 800oC and it takes 7.8 sec during quenching from 850°C to 500°C then the cooling time t c = 5.5 sec.While in ANSYS for the same node M55, we found that the cooling time t c = 2.294191 sec.And for the nodes on the centres W1 and M11, it was found that t c = 9.8 sec and 14.202646 sec for the mathematical model and ANSYS respectively.From the cooling time (t c ) the hardness of the boron steel-50B46H determined as in reference [2], it was found that by mathematical model when t c = 5.5 sec the hardness = 52.808and when tc = 9.8 sec the hardness = 44.953,while by Ansys when t c = 2.294191 sec the hardness = 57.215and when t c = 14.202646 sec the hardness = 43.623.From the above, it can be seen that there is a strong agreement between both results.
The difference between all the results of the mathematical model and the ANSYS simulations can be accounted due to the fact that the ANSYS software is for commercial purpose, and thereby has some automated input data.On the other hand the developed mathematical model is precisely for a circular steel bar axisymmetric cross section.However, there is strong agreement between both results and thereby the result is validated where, the comparison indicated reliability of the proposed model.

Conclusions
It is clear from our results that the node on the surfaces cools faster than the nodes at half the length at the centre; this means that the mechanical properties such as hardness will be different.
Where the hardness on the surface nodes will be higher than the hardness on the center nodes The results showed that the node on the surface will be the 1st to be completely cooled after quenching because it is in the contact with the cooling medium then the other points (nodes) on the radial axis to the centre respectively while the last point that will be completely cooled after quenching will be at centre of half length.Hence, lowest hardness point will be at half the length at the centre of the quenched industrial boron steel bar.Experimental calculation of lowest hardness point is an almost impossible task using manual calculation techniques.Also the earlier methods only used hardness calculated at the surface, which is higher than lowest hardness point, which has negative consequence and can result in the deformation and failure of the component.
) DOI 10.12776/ams.v19i2.94p-ISSN 1335-1532 e-ISSN 1338-1156 { } ( ) { } ( ) the input data and boundary conditions provided, a sensitivity analysis is carried out with the developed program to obtain the temperature distribution at any point (node) of the quenched boron steel bar.

Fig. 2
Fig. 2 Temperature history along WW cross-section when the radius equal 12.5 mm.

Fig. 3 Fig. 4
Fig. 3 Temperature history of the selected nodes when the radius equal 25 mm

Fig. 5
Fig. 5 Temperature history of the selected nodes when the radius equal 100 mm.