PSI - Issue 17

Eduardo A. Lima et al. / Procedia Structural Integrity 17 (2019) 246–253 Eduardo A. Lima/ Structural Integrity Procedia 00 (2019) 000 – 000

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2.1. Thermal Treatment Model

In this model, the wheel was subjected to transient analysis using the ABAQUS/standard type coupled-temperature displacement that began with all FEM nodes in the wheel at a temperature of 860°C (austenitizing zone). The quench is applied as a heat flow ( ɸ = -588000 W/m²) in the tread surface and a heat transfer coefficient (h = 15 W/m² ºC) on all external surface for 345 seconds. Next, all wheel surfaces enter the drawing back process during 13320 seconds with heat transfer coefficient (h = 10 W/m² ºC) at 550°C. In the final step, all external surface of the wheel was subjected to slow cooling until room temperature (25°C). In this process, the time was 50400 seconds and the heat transfer coefficient was the same as the drawing back step. All thermal treatment process follows the procedures and the information given by Gordon (1998) and Santos et al. (2009) . The ABAQUS  use the element type C3D8T (eight nodes linear hexahedral) for the 3D model in coupled temperature-displacement analysis to solve simultaneously the heat transfer problem and the structural problem, (Abaqus, 2017). The boundary conditions of the structural analysis were adopted as shown in Fig. (1). The temperature distribution obtained in the thermal analysis was used as loads in the structural analysis. The stress field comes from the coefficient of thermal expansion (°C -1 ) given by Eq. (1) . The AAR − American Association of Railroads ( Railroads, 2007) has a standard that lists the properties which should be used in temperature-dependent thermal simulations, as the specific heat (J/kg °C), Eq. (2), and thermal conductivity (W/m °C), Eq. (3). Moreover, the AAR specifies that the radiation boundary condition must be disregarded in thermal simulation. The density of the wheel material was 7833,4 kg/m³ and the hardening model used in ABAQUS  was kinematic (bilinear model). The mechanical properties of the class C railway wheel for the simulation are shown in Fig. (2).

(1) (2) (3)

5 9 6.448.10 ( ) 1.065.10 − − + = T 

0.3919( ) 434.02 + = T C 1.87.10 ( ) 48.3 2 + = − − T k

Fig. 1. Boundary conditions used during structural analysis of thermal treatment process in the railway wheel.

Fig. 2. Temperature-dependent stress-strain data used in thermal treatment process in the railway wheel ( Santos et al., 2009) .