A Mathematical Dimensional Model for Predicting Bulk Density of Inconel 718 Parts Produced by Selective Laser Melting

Abstract

In this work, dimensional analysis is used to develop a general mathematical model to predict bulk density of SLMed components taking volumetric energy density, scanning speed, powder’s thermal conductivity, specific heat capacity, and average grain diameter as independent variables. Strong relation between dependent and independent dimensionless products is observed. Inconel 718 samples were additively manufactured and a particular expression, in the form of a power-law polynomial, for its bulk density, in the working domain of the independent dimensionless product, was obtained. It is found that with longer laser exposure time, and lower scanning speed, better densification is attained. Likewise, volumetric energy density has a positive influence on bulk density. The negative effect of laser power in bulk density is attributed to improper process conditions leading to powder particle sublimation and ejection. A maximum error percentage between experimental and predicted bulk density of 3.7119% is achieved, which corroborates the accuracy of our proposed model. A general expression for determining the scanning speed, with respect to laser power, needed to achieve highly dense components, was derived. The model’s applicability was further validated considering SLMed samples produced by AlSi10Mg and Ti6Al4V alloys. This article elucidates how to tune relevant manufacturing parameters to produce highly dense SLM parts using mathematical expressions derived from Buckingham’s π- theorem.

Enhanced Mathematical Model for Producing Highly Dense Metallic Components through Selective Laser Melting

“…Figure 1 presents a schematic of the methodology followed in this work. The novelty of the work here presented, in relation to [13] upon which this is improving and expanding, is wide. First of all, the derived mathematical expressions are now of greater practical significance since they now incorporate laser power and hatch spacing, which are directly modifiable relevant manufacturing parameters.…”

“…The dimensional analysis of the selective laser melting process developed in [13] was revised, and it was decided to exclude the concept of volumetric energy density and incorporate relevant manufacturing parameters like laser power and hatch spacing. The enhanced mathematical model is presented in the following subsection.…”

“…Following the work presented by Estrada et al [13], a subtle modification to the set of independent variables is introduced. Volumetric energy density is no longer regarded as an independent physical quantity since it has been identified not to be a reliable design factor for the SLM process [14,15].…”

“…This line is drawn using Equation (5) by incorporating the independent dimensionless product (π 1 ), defined in Equation 3, alongside the respective C and α fitting parameters values for each work, presented in Table 2. Computed curves of dependent (π 0 ) versus independent (π 1 ) dimensionless products fitted for different materials used to produce metallic components with the selective laser melting (SLM) process: (a) Estrada et al [13] with In718, (b) Wang et al [16] with In718, (c) Bai et al [17] with AlSi10Mg, (d) Read et al [18] with AlSi10Mg, (e) Kempen et al [19] with AlSi10Mg, (f) Maamoun et al [20] with Al6061, (g) Spierings et al [21] with SS316L, (h) Cherry et al [22] with SS316L, (i) Tucho et al [23] with SS316L, (j) Milad et al [24] with SS304L, (k) Kasperovich et al [25] with Ti6Al4V, (l) Dilip et al [26] with Ti6Al4V, (m) Pal et al [27] with Ti6Al4V, (n) Fischer et al [28] with Ti26Nb, (o) Chen et al [29] with TiSiC, (p) Enneti et al [30] with W and (q) Jadhav et al [31] with Cu. A strong relation between dependent and independent dimensionless products is observed in all materials, evidencing the validity of the developed model.…”

“…Khan et al [12] made a connection between dimensional analysis and SLM in the modeling of the heat source as a function of laser parameters and powder properties. Estrada-Díaz et al [13] developed a mathematical model, through dimensional analysis, that was able to predict SLMed (produced via Selective Laser Melting) components' bulk density. Moreover, they developed expressions that enable the user to successfully calculate the needed scanning speed value, with respect to laser power, to achieve highly dense components.…”