key: cord-0429185-bz5atkcx authors: Kamaraj, Abishek B.; Sundaram, Murali title: A mathematical model to predict the porosity of nickel pillars manufactured by localized electrochemical deposition under pulsed voltage conditions date: 2020-12-31 journal: Procedia Manufacturing DOI: 10.1016/j.promfg.2020.05.036 sha: ed850258ee57088fa0f129d0795056f3b1644a70 doc_id: 429185 cord_uid: bz5atkcx Abstract Metal parts manufactured with engineered porosity offer advantages over traditional parts as they have excellent specific mechanical properties at a lower weight. This is especially of interest in the aerospace and automobile industries. Additive manufacturing allows for creating parts with computer aided design (CAD) modeled lattice structures that offer lightweight parts. However, there is a need for porous structures at the micron scale (<50 µm) which cannot be achieved in a controlled manner using traditional powder-bed based metal additive manufacturing processes. Electrochemical Additive Manufacturing (ECAM) is a novel non-thermal metal additive manufacturing process capable of producing metal 3D parts with engineered porosity at the micron scale. There is a lack of understanding of the cause of porosity and controlling the porosity generated in the parts created using this process. In this paper, the effects of the electrical parameters of deposition, such as the pulse duty cycle and pulse frequency during electrodeposition, on the porosity of the manufactured parts were mathematically modeled. The model predicts that higher frequency electrodeposition leads to more porous structures. The model developed in this study can be used to predict the process parameters needed to deposit nickel microstructures with desired levels of porosity between 20 and 55 %. These model predictions were also validated by experiments. Two mechanisms for the cause of porosity in the deposits were identified. The diffusion-limited deposition phenomenon causing a lack of availability of cations results in larger sized pores and hollow structures to form on the part. The crystal growth and the nucleation process cause micron-scale pores. Localized electrochemical deposition is an electrochemical process where metal ions are deposited onto a substrate locally near the vicinity of a microelectrode tool anode. By combining the principles of additive manufacturing (AM) and localized electrochemical deposition (LECD), Electrochemical Additive Manufacturing (ECAM) a novel process is developed [1] that is capable of producing 3D parts layer by layer. Since it is a non-thermal process, ECAM is capable of producing parts with low residual stresses and is able to overcome some challenges of traditional AM processes, such as the need for support structures [2] . The LECD process depends on several electrical input factors that determine the quality of the deposit. Porous lightweight metal parts are increasingly being used in industrial applications such as energy, environment, metallurgy, chemical, and biomedical industries. The porous part not only inherits the intrinsic metal characteristics such as weldability, plasticity, thermal conductivity, and electric conductivity, but also displays many new properties such as lower specific weight, controlled permeability, large specific surface area, and high energy absorption as explained by [3] . Some of the methods used in the manufacturing of porous metal parts include injection molding, e-beam melting, and powder sintering [4] [5] [6] . The recent advances in additive manufacturing have made engineering-controlled porosity in the part possible. Localized electrochemical deposition is an electrochemical process where metal ions are deposited onto a substrate locally near the vicinity of a microelectrode tool anode. By combining the principles of additive manufacturing (AM) and localized electrochemical deposition (LECD), Electrochemical Additive Manufacturing (ECAM) a novel process is developed [1] that is capable of producing 3D parts layer by layer. Since it is a non-thermal process, ECAM is capable of producing parts with low residual stresses and is able to overcome some challenges of traditional AM processes, such as the need for support structures [2] . The LECD process depends on several electrical input factors that determine the quality of the deposit. Porous lightweight metal parts are increasingly being used in industrial applications such as energy, environment, metallurgy, chemical, and biomedical industries. The porous part not only inherits the intrinsic metal characteristics such as weldability, plasticity, thermal conductivity, and electric conductivity, but also displays many new properties such as lower specific weight, controlled permeability, large specific surface area, and high energy absorption as explained by [3] . Some of the methods used in the manufacturing of porous metal parts include injection molding, e-beam melting, and powder sintering [4] [5] [6] . The recent advances in additive manufacturing have made engineering-controlled porosity in the part possible. Localized electrochemical deposition is an electrochemical process where metal ions are deposited onto a substrate locally near the vicinity of a microelectrode tool anode. By combining the principles of additive manufacturing (AM) and localized electrochemical deposition (LECD), Electrochemical Additive Manufacturing (ECAM) a novel process is developed [1] that is capable of producing 3D parts layer by layer. Since it is a non-thermal process, ECAM is capable of producing parts with low residual stresses and is able to overcome some challenges of traditional AM processes, such as the need for support structures [2] . The LECD process depends on several electrical input factors that determine the quality of the deposit. Porous lightweight metal parts are increasingly being used in industrial applications such as energy, environment, metallurgy, chemical, and biomedical industries. The porous part not only inherits the intrinsic metal characteristics such as weldability, plasticity, thermal conductivity, and electric conductivity, but also displays many new properties such as lower specific weight, controlled permeability, large specific surface area, and high energy absorption as explained by [3] . Some of the methods used in the manufacturing of porous metal parts include injection molding, e-beam melting, and powder sintering [4] [5] [6] . The recent advances in additive manufacturing have made engineering-controlled porosity in the part possible. Localized electrochemical deposition is an electrochemical process where metal ions are deposited onto a substrate locally near the vicinity of a microelectrode tool anode. By combining the principles of additive manufacturing (AM) and localized electrochemical deposition (LECD), Electrochemical Additive Manufacturing (ECAM) a novel process is developed [1] that is capable of producing 3D parts layer by layer. Since it is a non-thermal process, ECAM is capable of producing parts with low residual stresses and is able to overcome some challenges of traditional AM processes, such as the need for support structures [2] . The LECD process depends on several electrical input factors that determine the quality of the deposit. Porous lightweight metal parts are increasingly being used in industrial applications such as energy, environment, metallurgy, chemical, and biomedical industries. The porous part not only inherits the intrinsic metal characteristics such as weldability, plasticity, thermal conductivity, and electric conductivity, but also displays many new properties such as lower specific weight, controlled permeability, large specific surface area, and high energy absorption as explained by [3] . Some of the methods used in the manufacturing of porous metal parts include injection molding, e-beam melting, and powder sintering [4] [5] [6] . The recent advances in additive manufacturing have made engineering-controlled porosity in the part possible. 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to Some of the metal additive manufacturing processes involved in manufacturing porous parts are selective laser melting (SLM), electron beam melting (EBM), laser engineered net shaping (LENS), and inkjet 3D printing [7] [8] [9] . These methods suffer from lower part quality because of thermal stress or are limited by the powder size, which determines the minimum feature size as shown by [10, 11] . The minimum pore size of the parts using these processes can be engineered only to about 20 µm. [12] showed that the controllability of the porosity of parts is an issue in Selective Laser Sintering (SLS). One parameter that porosity depends on in SLS is the alignment of the powder particles, thus the SLS process is dependent on the motions of the powder, which are both unpredictable and hard to control as described by [13] . In powder metallurgy, one study claimed that porosity is dependent on the pressure of the gas and the metal's tension and thus has no replicability, causing variability in the parts produced [14] . The same study also noted that for the sintering and dissolution process, there is randomness associated with the template placement, causing the porosity to be unpredictable. In this paper, a model predicting the porosity of the deposits made by LECD under varying process parameters was developed. As the LECD process adds material atom by atom through an electrochemical reaction, the porosity study also gives insights into the electrochemical deposition mechanisms. This increases the controllability of the porosity achievable in this process. The feasibility of the LECD was demonstrated more than two decades ago [15] . Most of the subsequent studies focused on investigating the effects of various process parameters on the characteristic of the deposited structures and the deposition rate [16] . It has been shown that while there is a minimum voltage required for deposition to occur, very high voltages cause porous or irregular deposition structures due to the depletion of ions at high currents and bubble formation [17] . The same study reported that there was no significant effect of the electrolyte concentration on the deposition rate, but lower concentrations affected the quality of the deposit (porous) [17] . This phenomenon is again explained due to the reduction of ions from the formation of the depletion layer at lower electrolyte concentrations. The choice of electrolyte for the electrodeposition process has been derived mostly from the electrolyte used for the electroplating of the same metal. Organic additives to the electrolyte produce smooth and finegrained microcrystalline deposits due to the altering of the reduction (deposition) mechanism with the addition of additives [18] . A study focussing on localization showed that the insulation of the micro tool electrode (anode) results in improved localization of the deposition [15] . However, insulation layer damage due to the formation of bubbles is an issue as it limits the life of the tool. Another study reported that the deposition rate increased toward the center of the cathode, which caused a more conical shape and the parts produced were found to be more porous toward the bottom of the pillar than the top [19] . Several studies focusing on the quality of the deposit during electrochemical deposition have been reported in the literature. It has been shown that several mechanisms and process parameters such as current density, gas bubbles, feeding mechanism, electrolyte flow, and pulse parameters influence the quality of the electrodeposited part, but these parameters are all related to the current density associated during the deposition. It has been reported that a high nucleation rate is promoted by the high pulse current density of the triangular waveform, leading to smaller grain size, and thus less porous deposits [20] . Another study concluded that lowering the current density will reduce the emission of hydrogen bubbles, thus improving the quality of the deposit [17] . Mechanical methods have also been used to enhance deposit characteristics and resolution. One such method included the utilization of a rotating electrode which created a uniform deposition field to overcome defects in the electrode tip [21] . Another method utilized ultrasonic vibrations during deposition to enable the regular removal of air bubbles which accumulate during deposition and often block deposition growth causing pores [22] . The duty cycle of the pulse power affects the surface finish of the deposited structure due to the mass transport of the ions during the off-time, resulting in the replenishment of the ions [23, 24] . These studies, however, did not consider nanosecond pulses which enable the localization of the deposits by reducing the stray current, because of the double-layer capacitance [25] . A recent experimental study also reported the localization effect of these high-frequency pulses [1] . From the above literature review, claims on the effect of process parameters such as current density and duty cycle on the quality of the deposits during LECD is inferred. Furthermore, none of the studies quantify the porosity of the produced deposits, as the aim of those studies was to improve deposit quality. In this paper, we aim to quantify the amount of porosity generated during the ECAM process by modeling it and study the effect of pulse power parameters on the porosity of the parts. Faraday's laws of electrodeposition give the volume of metal deposited with respect to the current and time of deposition as = Where is the molar mass of nickel (g/mol), is the nickel deposition efficiency, is the average deposition current (A), is the deposition time (s), is the density of nickel (Kg/m 3 ), is the valency of nickel, and is the Faraday's constant. Porosity can be defined as the ratio of the volume of voids inside the part to the total volume of the part as given below, The volume of pores ( ) is assumed to be caused by a part of hydrogen gas generation as well as the irregular packing of the growing nucleus of the deposit. This is expressed as shown below in Equation 3 where PF is the packing factor and 2 is the volume of hydrogen gas entrapped in the part calculated as given below. where 2 is the molar mass of hydrogen (g/mol) 2 is the hydrogen entrapment efficiency, is the average deposition current (A), is the deposition time (s), 2 is the density of H2 gas (Kg/m 3 ), 2 is the valency of hydrogen, and is the Faraday's constant. The packing factor is generally between 0.63