PSI - Issue 8

P. Conti et al. / Procedia Structural Integrity 8 (2018) 410–421 Author name / Structural Integrity Procedia 00 (2017) 000–000 Where � � is the radius of the laser beam at which the heat flux is reduced by a factor 0.13 with respect to the flux at the center of the beam; �, � are the coordinates on the building plate ( � will be the growth direction) in a reference system centered in the laser beam center and � is the laser power. 2.3 Material characteristics As shown in Eq. (1), many thermal characteristics must be evaluated, moreover, the characteristics will differ between powder and bulk material, they will be temperature dependent and will switch from one to another during the melting process. Let’s first consider the powder characteristics dependence from porosity. Following the approach suggested by A. Hussein et al. (2013), porosity can be defined through the void fraction Φ corresponding to: Φ = � ���� − � ������ � ���� (3) We assume thermal conductivity to be linearly dependent from porosity, and, of course, also the density will obey to the same scheme. � ������ = � ���� (1 − Φ) (4a) � ������ = � ���� (1 − Φ) (4b) The dependence of the characteristics with the temperature must also be considered. The approach suggested by A. Hussein et al. (2013), was adopted. In K.C. Mills (2002) many data on variation of the thermal characteristics of AISI 316L steel with temperature are reported and the assumption in the present work are based on these data. The temperature range was divided in three intervals bounded by the ambient temperature (293 °K) and the transition melting range bounds (1670 °K and 1723 °K respectively). A linear variation was assumed inside every temperature span in accordance with the model of A. Hussein et al. (2013). The specific heat of the powder is not directly dependent from the temperature as in Eq. (1) the dependence is introduced by the variation of the density according to Eq. 4b. Thermal expansion was assumed to be zero in the powder at room temperature and steeply increasing up to bulk material at melting temperature. 413

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Fig. 2. Specific heat vs. temperature

Fig. 1. Density vs. temperature