PSI - Issue 8

412 P. Conti et al. / Procedia Structural Integrity 8 (2018) 410–421 Author name / Structural Integrity Procedia 00 (2017) 000–000 characterization activity. The model also allows to choose the most promising combination of technological parameters (scan speed, laser power, path overlapping). The work is based on FE modeling of a thin stack of layers realized with SLM technique, the material considered is stainless steel AISI316L, a material often used in industrial applications; the bulk characteristics of AISI316L can be found in K.C. Mills (2002). The more relevant simplified hypotheses adopted in the work are:  The thermal characteristics are assumed to be piecewise linearly dependent from temperature as shown below,  The powder characteristics are assumed to be linearly dependent from porosity,  Absorbance is assumed constant for powder and bulk material,  Latent melting energy is not explicitly considered but its effect is simulated by a steep rise of the specific heat capacity. In order to model the selective laser process, many physical aspects must be taken into account. During the creation of a component a laser beam scans a thin layer of metal powder and heats up a small cell until the melting temperature is reached; afterwards the cell cools down again as the laser spot moves away. In this process, the material undergoes many state transformations (powder  liquid  solid) accompanied by shrinkage, density change, material structure changes. Moreover, the same cell will be cyclically heated up and cooled down as the laser beam impinges neighboring regions of the same layer or the corresponding region of the next layer. A model of the process must consider all these aspects (Y. Li et al. 2014) which depend on temperature history; the main problem to be addressed is therefore the mathematical formulation of the thermal process. A balance of heat input and heat output in a single cell must be established. During the SLM process, the heat input is represented by the laser beam energy absorbed by the layer surface and the heat outputs are represented by heat losses from the cell due to conduction, radiation and convention, I.A. Roberts et al. (2009). The balance between input and output heats up the cell and supplies the latent heat to melt the powder. The governing equation of the thermal balance is, J.C. Heigel et al. (2015), K. Dai (2005): � � � � = ��� � �(�) �(�) · � � (�) · ∇�� + �(� � ) ( · � � )� � (�) (1) Eq. (1) must be completed with boundary conditions on the free edges represented by the radiation losses and convection losses, respectively � ��� = ��(� � � − � �� ) and � ���� = ℎ(� � − � � ) where � � represents the surface temperature and � � the fabrication room temperature. All the parameters are temperature dependent, L. Papadakis et al. (2014). Moreover, during the phase change, a further term should be added to the right side of Eq. (1) to take into account the latent heat. In this paper - as illustrated below - the influence of the latent heat was simulated by a sudden rise of the specific heat at the melting temperature, A. Hussein et al. (2013). 2.2 Model of the laser beam spot The incident energy flux from the laser beam is assumed to have an axisymmetric Gaussian distribution. With this hypothesis, �(�, �, �) - the energy flux - is related to the laser power through the following relation, K. Dai (2005): �(�, �, �) = 2 � � � � �� � �� � � �� � � �� (2) 2. Model description 2.1. Thermal balance