The Scientific Bulletin of VALAHIA University MATERIALS and MECHANICS –Vol. 15, No. 12 DOI 10.1515/bsmm-2017-0005 THE MATHEMATICAL MODEL APPLIED TO SOLIDIFY AND SEGREGATION OF LEDEBURITE TOOL STEEL INGOTS Vasile BRATU, Ileana Nicoleta POPESCU* Valahia University of Targoviste, Faculty of Materials Engineering and Mechanics, 13 Aleea Sinaia Street, Targoviste, Romania E-mail: v_bratu22@yahoo.com, * pinicoleta24@yahoo.com (author correspondent) Abstract. In order to determine the optimum geometry of the ingot mold format (the format of ingot mold with a diameter per height ratio H / D <3 and the conicity of minimum 7%) was analyzed by mathematical modeling of solidification and segregation of the carbon and sulfur in it. It was considered 205Cr115 steel type (according with , STAS 3611 - Romanian stardandization) and known also as X210Cr12 steel type (according with European standard). It has been considered an element of volume of coordinates x, y, z in the solidifying ingot and have made the following assumptions: (i) the equilibrium distribution ratio K, is applied to the solid-liquid interface; (ii) solid diffusion is negligible during solidification; and (iii) the solid density is constant during solidification. In carrying out the simulation of segregation mechanisms are resolved heat transfer equation, that simulating the solidification process and are are solved the interdendritic fluid equation of motion. Keywords: X210Cr12, solidification mathematical model, ledeburite tool steel ingots 1. INTRODUCTION Tool steels quality is evaluated by how the tool behaves under conditions of use. Tool steel should have those technical characterisitcs that assure maximum reliability, even if their production causes some difficulties in manufacturing technology. The main characteristics that determine the behavior of the service tool are hardness and toughness, both related to the chemical composition, size and distribution of carbides, depens also of grain size and degree of purity[1-4]. The steel purity is assured by the way of elaboration process (oxidation, deoxidation), steel evacuation and casting of steel. The quality of the carbides is based, first of all, on the chemical composition of steel and of a number of technological factors, such as: (a) the conditions of casting and solidification, (b) plastic deformation and (c) heat treatmen, which more or less influence the homogeneity. In the segregation process it has an important role the physico-chemical charactistics of policomponent system (the alloy tool steel). Each steel grade having its own solidification characteristics and even in the same type of steel are differences depending on the carbon content)[1, 2]. Thus, at the solidification process appear at a time the , H, phases, carbides, the areas of occurrence of each phase and their coexistence with the liquid being very different. Taking into account the starting pouring temperature and the early change starting solidification temperature (separation of carbides and the extent of different temperature areas on the different phases ) resulting importance of respecting the conditions of casting, for the quality of carbides: the temperature and speed casting, the characteristics of the mold, the cooling conditions. It is known that the casting temperature is increasing influence on the re-melting and, consequently, the removal, and the degree of segregation and the size of the primary carbides In the following table (Table 1) shows the dimensional characteristics of steel ingot mould used for casting of ledeburite tool steel ingots: Table 1. Dimensional characteristics of ingot mould Dimensional characteristics of ingot mould Steel Grade Pro- duct Diame ter Ingot Type Side [mm] Heigh t [mm] H/D Wall Thick ness [mm] < 80 mm 254 mm 30 0kg 310/ 225 710 2.52 65 /72 Lede- burite tool steel < 150m m 356 mm 1050 kg 425/ 314 1258 3.40 90/ 96 The size of the ingot has a great influence on the size of the network of carbides, in particular with respect to its homogeneity of the ingot section, as shown in Fig. 1. Studies on ingot less than 300 kg, used in ledeburite steel casting have shown that the best results on the ingot axial capacity is obtained when using ingots with H / D <3 and conicity less than 7% [1]. 28