PSI - Issue 68

Ema Kukuljan et al. / Procedia Structural Integrity 68 (2025) 822–827 E. Kukuljan et al. / Structural Integrity Procedia 00 (2025) 000–000

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An axisymmetric 8-node thermal 2D finite element (PLANE77) with a single degree of freedom, temperature was used. A parametrically defined APDL code, Ansys Inc. (2010) was created with the aim that the numerical analysis can be adapted to different specimen geometries and different materials. During model development, three distinct geometries/meshes were used which correspond to reference specimens having diameters of 95 mm, 48 mm and 28 mm and for which experimental data and cooling curves were available. A convergence check dependent on model dimensions was performed. Boundary conditions in the form of thermal loading were defined as convection on exposed borders of the model denoting heat transfer between the steel specimen’s surface and quenchant. As initial condition prior to quenching, uniform temperature distribution throughout the specimen is assumed and is set to 800°C in every node of the model, according to reference cooling curves. 5. Calibration of a numerical model based on reference cooling curves The challenge in developing a numerical model for oil quenching simulation lies in the non-stationarity of cooling and related parameters. Since their values and temperature dependence are unknown, an iterative calibration of heat transfer and conduction coefficients was performed using reference experimentally determined cooling curves. The numerically obtained cooling curves are compared with the reference ones and calibrated in the cooling range from 800°C to 500°C, as this range determines the t 8/5 value, which is ultimately the most relevant for hardness assessment. Values of other parameters relevant for reference steel 34Cr4 quenched in oil were taken as ρ = 7870 kg/m³ and c = 561 J/kgK. The coefficients of heat conductivity λ and heat transfer α were considered as temperature dependent and their values in relation to the temperature were determined through iterative calibration. Figure 4 presents comparison of reference cooling curves digitized from literature, Max Planck Institute (1954), and curves obtained numerically for 34 Cr 4 steel specimens of three different diameters, 28 mm, 48 mm and 95 mm.

Reference - SURFACE

Calibrated - SURFACE

Reference - CORE

Calibrated - CORE

Fig. 4. Reference curves, Max Planck Inst. (1954) and calibrated cooling curves for surface and core of 34 Cr 4 steel specimens quenched in oil

While there is still room for improvement, particularly good agreement is present between reference curves and those obtained with the calibrated numerical model in the region marked in yellow which is most relevant for the determination of cooling times from 800°C do 500°C, i.e. t 8/5 .