Modeling and simulation of micro-plasma transferred arc deposition process for additive manufacturing

Abstract

Additive manufacturing (AM) is a bottom-up manufacturing approach possessing ability to (i) manufacture complex geometries; (ii) to add delicate features to an existing product; (iii) remanufacture or repair or refurbish of a slightly defective and/or worn but usable product; and (iv) customize a product. Consequently, AM has been attracting interest of manufacturing research community and manufacturing industries. Researchers at various national laboratories and renowned universities are engaged in (i) developing new AM processes for different materials particularly for metallic materials; (ii) enhancing material and shape applicability of the developed processes; (iii) improving the process performance through modeling, simulation and optimization.High energy beams such as laser beam, electron beams, and electric arc are the most commonly used heat sources for AM of the metallic materials. Laser and electron beam-based AM processes have low deposition rate (2-10 g/min.), higher heat transfer efficiency and yield very good quality of deposition but they are very costly and suitable for miniature sized AM of metallic materials. Arc-based AM processes give higher deposition rate (50-130 g/min.), low to medium heat transfer efficiency but gives poor quality of deposition. Though they are cheaper, but they yield undesirable post-deposition effects such as higher dilution, thermal distortion, and heat affected zone (HAZ), and are suitable for only macro-sized AM of metallic materials. Consequently, these two types of AM processes force the AM user to compromise between volume and quality of deposition of metallic materials. Therefore, efforts have been made to improve the performance of AM such as (i) combining two different energy sources to achieve their benefits simultaneously for example combining laser beam with tungsten inert gas arc (Baufeld et al., 2011), or (ii) to develop new processes to bridge the gap between process capabilities of high energy beam-based and arc-based AM processes. Continuing in this direction, a novel process named as micro-plasma transferred arc (μ-PTA) deposition process has been developed at IIT Indore for AM of the metallic materials with capability to feed thedeposition material either in wire or powder form. This process has been confirmed to be cost-effective, material efficient and environmental friendly alternative to the existing AM processes with capability to generate fully dense structures for tool steel (Jhavar et al., 2014). Information presented in Table 1 shows that the capabilities of μ-PTA deposition process significantly bridges the gap in capabilities of high energy beam-based and arc-based deposition processes.Table 1: Comparison of process capabilities of deposition processes used for metallic deposition (Sawant and Jain, 2017; Hoefer, 2017; Liu et al., 2016; Jhavar et al., 2014a; Gharbi et al., 2013 and Zhao et al., 2012). Criteria Laser-based deposition process Arc-based deposition process μ-PTA deposition process Applicable form of the deposition material Powder and powder both Powder and wire both Powder and wire both Deposition material consumption rate 900 mm/min (for wire form) 2 g/min (for powder form) 2880 mm/min (for wire form) 250 g/min (for powder form) 1275 mm/min (for wire form) 3.5 g/min. (for powder form) Energy consumption per unit travel length of substrate material 48-75 J/mm 1490 J/mm 270 J/mm Power consumption per unit deposition material consumption 30-48 J/mm 50 J/mm 20 J/mm Equipment cost Very high Medium Low The bonding strength between successive layers and dimensional accuracy of an additive manufactured components are influenced by size and shape of each deposited layer. Figure 1 depicts geometry of a typical single-track deposition. It is characterized as deposition width ‘w’, deposition height ‘h’, bead root angle ‘𝛳’, aspect ratio (ratio of deposition width ‘w’ to deposition height ‘h’) and percentage dilution (relative amount of substrate material mixed with the deposition material and expressed as percentage of ratio of area of diluted material ‘A2’ to sum of area of deposited material ‘A1’ and area of diluted material ‘A2’ i.e. = A2/[A1 + A2]).Modeling, simulation, prediction and optimization of the deposition geometry characteristics (i.e. width, height, aspect ratio, dilution, heat affected zone, thermal distortion and residual stresses) is essential to understand the influence of AM processparameters (i.e. micro-plasma power, travel speed of worktable and wire/powder feed rate) and substrate/deposition material properties (i.e. density, specific heat and thermal conductivity) on them. Pinkerton and Li (2004) have developed a mathematical model for laser direct metal deposition (LDMD) process. They used one-dimensional heat conduction equation to model geometry of the molten pool using concepts of energy and mass balances. Lalas et al. (2005) developed analytical model as a function of torch travel speed and powder feed rate and considering effect of surface tension of the melt pool to predict geometry of cladding by laser-based deposition. Liu and Li (2006) proposed a theoretical model as a function of scanning velocity, powder flow rate and power input to predict width of multi-layer deposition by laser cladding process. Finite element simulation (FES) of the melt pool in any AM process greatly helps in improving the accuracy of the thermal models. Some researchers have used different types of simulations to predict and simulate the influence of temperature distribution, thermal cycles and residual stresses generated during multi-layer and multi-track deposition process. Peyre et al. (2008) did numerical and analytical simulation to predict the dimensions of the melt-pool for laser-based direct metal deposition process. Vasquez et al. (2012) used FES topredict the shape and size of the melt pool. Gan et al. (2004) used FE based thermo-mechanical analysis to predict residual stresses generated by plasma spray coating. While Zaho et al. (2012) carried out FE-based analysis to predict the residual stresses produced in single pass multi-layer deposition by gas metal arc (GMA) based deposition process. Research gaps identified from review of the past work done on modeling and simulation of various AM processes for the metallic materials are: (i) no work has been reported on development of a generic thermal model (which can be used for any combination and form of deposition and substrate materials) and 3D-FES to predict deposition geometry characteristics of single-layer single-track deposition by arc-based processes and their micro-versions; (ii) no work has been reported for development 3D-FES of temperature distribution, thermal cycles and residual stress analysis of single-layer multi-track and multi-layer single-track deposition by micro-version of arc-based deposition process; and (iii) no work has been reported on optimization of the AM process parameters using the generic thermal model.Therefore, the research objectives identified for the present research work are: (i) thermal modeling of single-layer single-track deposition width and height by micro-plasma transferred arc (μ-PTA) deposition process; (ii) 3D-FES of the temperature distribution in the melt pool of single-layer single-track deposition by μ-PTA depositionprocess using micro-plasma power, feed rate of the deposition material, travel speed of worktable, and temperature dependent properties of the substrate material; (iii) prediction of the melt pool dimensions using image processing; (iv) temperature distribution and thermal cycle analysis of multi-layer single-track deposition by μ-PTA deposition process using 3D-FES; (v) prediction and analysis of residual stresses in single-layer multi-track deposition by μ-PTA deposition process using 3D-FES; and (vi) optimization of μ-PTA deposition process parameters using real-coded genetic algorithms. A generic thermal model was developed in the terms of μ-PTA process parameters and substrate and deposition material properties to predict width ‘w’ (Eq. 1) and height ‘h’ (Eq. 2) of single-layer single-track deposition using the concepts of energy balance and heat transfer.𝑤≈𝑤𝑚=2𝑅𝑚=2[ ƞ𝑃−𝑉𝑑𝜌𝑑𝐶𝑝𝑑 (𝑇𝑚𝑑−𝑇𝑖) 17.8𝜌𝑠𝐶𝑝𝑠∗(𝑇𝑚𝑠 − 𝑇𝑖)√𝛼𝑠𝑣[erfc(1)− 1𝑒𝑥𝑝√𝜋+ 1√𝜋]] 23 (1) ℎ=4(1−𝐷)𝑉𝑑 𝜋 𝑣 𝑤 (2) Where,wm is width of the melt pool (mm); ƞ is thermal efficiency of micro-plasma transferred arc (%); P is micro-plasma power (W); Vd is volumetric deposition rate (mm3/s); ρd and ρs are densities of the deposition and substrate material respectively (Kg/mm3); Cpd and Cps* are specific heat and modified specific heat of the deposition and substrate material respectively (J/kg K); Tmd and Tms are melting temperatures of the deposition and substrate material respectively (K); αs is thermal diffusivity of the substrate material (mm2/min); v is travel speed of worktable (mm/min); D is dilution (%); and Ti is ambient temperature (K). The results predicted by the developed model were validated using the experimental results of Jhavar et al. (2014) obtained using 0.3 mm diameter wire of P20 tool steel as deposition material on 100 mm x 180 mm x 9 mm size substrate of P20 tool steel in μ-PTA wire deposition process on the developed experimental apparatus. This gave error between the predicted and experimental width (Fig. 2a) in a range from -15 to 18% and error between predicted and experimental height (Fig. 2b) in a range from -18 to 22%. Subsequently, 3D-FES of melt pool in the substrate material was done using heat conduction equation (Eq. 3) as governing equation and below-mentioned boundary conditions with an objective to reduce the error between predicted and experimental width and height of single-layer single-track deposition by μ-PTA wire deposition processFig. 2: Comparison of theoretical and experimental values of (a) deposition width and (b) deposition height, for single-layer single-track deposition of P20 tool steel by μ-PTAWD. process. 𝜌𝑠𝐶𝑝𝑠(𝜕𝑇𝜕𝑡)=𝑞+𝐾𝑠∗[𝜕2𝑇𝜕𝑥2+𝜕2𝑇𝜕𝑦2+𝜕2𝑇𝜕𝑧2] (3) Where, T is temperature of the molten pool (K); t is the time at which micro-plasma arc strikes the substrate material (s); q is the actual volumetric heat flux density (W/m3); ρs, Cps and Ks* are density (Kg/m3), specific heat (J/Kg K) and the modified thermal conductivity considering effect of Marangoni flow for the substrate material. Boundary conditions used in 3D-FES were as follows: (i) Initial temperature: At the start of deposition process, the substrate material is at ambient temperature Ti, i.e., 𝑇= 𝑇𝑖 (=298 𝐾) at 𝑡=0 (ii) Equation 4 for actual volumetric heat flux density ‘q’ was obtained for the micro-plasma heat source considering thermal efficiency ‘ƞ’ of the micro-plasma arc and theoretical volumetric heat flux density q(X, Y, Z) (W/m3) at a point having coordinates ‘X, ‘Y’ and ‘Z’ with respect to centre of the micro-plasma arc of radius ‘ro’ (m) as shown in Fig. 3. .............