A Mathematical Model for the Prediction of the Scale Layer Formation on ASTM A510/A853 Cold-Drawn Hypoeutectoid Steel Wire After Batch Annealing

Abstract

Annealed hypoeutectoid ASTM A510/A853 steel wire is widely used in the construction industry due to its mechanical properties, which makes it a very versatile material to work with. This work concerns the prediction of the thickness of the scale layer of the hypoeutectoid steel wire once subjected to a batch annealing process. We propose a mathematical model to approach oxidation occurring during the process. The model treats this phenomenon as a non-isothermic instance; it takes as input a heating curve, a cooling curve, and a holding time that corresponds to the heating and cooling cycles and a heating holding cycle. We assume the temperature of material outer spiral segments as the furnace atmosphere temperature. With the aid of this model, it is possible to predict the oxide scale layer of the outer spirals segments of the annealed drawn wire coils after batch annealing with reasonable accuracy. We did not find visible evidence of decarburization; the steels of the study in this work do not decarburize. As an approximation, we assumed that the temperature of the outside of the drawn wire coils equals the furnace atmosphere.

Appendix A Model parameters summary

In order to make use of this model, parameters needed for it were gathered mainly from the bibliography. This section summarizes the required parameters; Table 4 provides them next.

Table 4 Oxidation model parameters

Note: Original values for $k_0$ and Ea from [9] are 8.8x10$^6$ and 140738 J/mol, respectively, for temperatures $T<1173 \text {K}$ whose mathematical model is $x[\mu m]=K \cdot \sqrt{t}$. These values were converted to be usable for the isothermal model $x^2[mm]=K \cdot t$, on which our model is based.