Numerical Simulation of Steel Quenching B. Smoljan (Submitted 22 May 2001) The algorithm and computer program are completed to simulate the quenching of complex cylinders, cones, spheres, etc. Numerical simulation of steel quenching is a complex problem, dealing with estimation of microstructure and hardness distribution, and also dealing with evaluation of residual stresses and distortions after quenching. The nonlinear finite volume method has been used in numerical simulation. By the established computer program, mechanical properties and residual stresses and strains distributions in the quenched specimen can be given at every moment of quenching. Keywords hardenability, hardness, modeling, quenching, simu- lation, steel properties 1. Introduction Steel quenching can be defined as “cooling of steel work- pieces at a rate faster than still air.” [1] Although very simple on first sight, quenching is physically one of the most complex processes in engineering and very difficult to understand. Quenching used to be called the black hole of heat treatment processes. [2] Computer simulation of quenching includes several differ- ent analyses: (1) heat transfer analysis for computation of cool- ing curves, (2) material properties analysis for computation of microstructure composition and mechanical properties, (3) thermoplastic analysis for computation of stresses and strains, and (4) fracture mechanics analysis for computation of damage tolerance. [1] Generally, in simulation of steel quenching, two essential problems have to be solved. The first problem is to develop a mathematical model of cooling and prediction of the mechani- cal properties, stresses and strains. The second problem is to establish the proper method for real heat data evaluation. Simulation of any one process can be made successfully only if all mechanisms of the process are well known and if the appropriate mathematical methods are used. For steel quench- ing, it means that the essential characteristics of the phase transformation and mechanisms of stress and strain generation during the quenching should be known. In steel quenching stress-strain analysis, both strains due to thermal strain and strains due to phase changes have to be taken into account. [1] Physical and mechanical materials properties, as functions of structure and temperature, should be known in each moment during the quenching. From these reasons it is understandable that computer simulation of steel quenching is of interest to engineers from a wide range of disciplines, i.e., material sci- ence, thermodynamics, mechanics, manufacturing, mathemat- ics, chemistry, etc. Detailed theoretical and quantitative analysis of the process that can be applied to a wide range of different types of quench- ing remains unavailable. Although many attempts have been made to develop theoretical models to describe steel quench- ing, all the earlier work relied on simplifications that rendered the analysis unrealistic. In particular, successful description of steel quenching is not possible without a good theoretical ex- planation of all physical processes involved in the mathemati- cal model. Second, the real complexities of plasticity have to be introduced into the model, but it is known that the theory of plasticity is not sufficiently developed. Moreover, change of physical and mechanical properties by temperature change have to be involved in the mathematical model. In the past three decades the Finite Element Method (FEM) has enjoyed an undivided popularity as the method for solid body stress analysis. On the other hand, the Finite Volume Method (FVM) has been established as a very efficient way of solving heat transfer problems. Recently, FVM was used as a simple and effective tool for the solution of a large range of problems in the thermoplastic analysis. [3] 2. Temperature Field Change Temperature field change in an isotropic rigid body with heat conductivity , density , and specific heat capacity c, can be described by Fourier’s law of heat conduction: cT t = divgradT (Eq 1) The heat sources that can exist during steel quenching are neglected in Eq 1. Axially symmetrical bodies, such as com- plex cylinders, cones, and spheres, can be described as 2-D problems in cylindrical coordinates r, z, and   1. To solve Eq 1, the finite volume scheme is used. The time domain is divided into a number of discrete time steps, t, whereas the space domain is divided into a number of rectan- gular cells. Each cell is bounded by four faces with areas S i(j,j+n) and S (i,i+n)j, (i  1,2 . . . i max ;j  1,2 . . . j max ;n  ±1), and it contains one computational nodal point at its center (Fig. 1). Linear distribution of the temperature T between neighboring points is assumed. The discretization equation system was es- tablished by integrating the differential Eq 1 over each control volume, taking into account initial and boundary conditions. B. Smoljan, University of Rijeka Faculty of Engineering, Rijeka, Vukovarska 58, HR5100 Rijeka, Croatia. Contact e-mail: bozo. smoljan@ri.hinet.hr. JMEPEG (2002) 11:75-79 ©ASM International Journal of Materials Engineering and Performance Volume 11(1) February 2002—75