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The International Journal of Advanced Manufacturing Technology (2018) 97:3761–3775 https://doi.org/10.1007/s00170-018-2168-6 ORIGINAL ARTICLE Rheological characterization of process parameters influence on surface quality of Ti-6Al-4V parts manufactured by selective laser melting Amir Mahyar Khorasani 1 & Ian Gibson 1 & Ali Reza Ghaderi 2 Received: 13 February 2018 / Accepted: 10 May 2018 / Published online: 31 May 2018 # Springer-Verlag London Ltd., part of Springer Nature 2018 Abstract Additive manufacturing is one of the promising production processes, which has the ability to manufacture final shape directly from computer-aided designs. In this research, the thermal effect of process parameters on the average surface of selective laser melting (SLM) Ti-6Al-4V is discussed and mathematically characterized. Based on Taguchi L25, the experiment was designed, and laser power, scan speed, hatch spacing, laser increment pattern angle, and heat treatment in five levels were selected as input parameters. Interfacial forces including surface tension, Marangoni’s effect, pressure in droplet, capillarity force, work adhesion, wetting, recoil pressure, drag forces (due to solid-liquid transition) and interaction of surface tension, hydrostatic and vapor pressures have been characterized mathematically to analyze their effect on surface quality. Results showed higher energy density and temperature cause lower surface tension and capillary force, generating unstable and lower surface quality. In addition, higher energy density and temperature increase droplet pressure, internal pressure, recoil pressure, and thermal stress and change the balance of forces on the surface of the melting pool and reduce surface quality. Keywords Selective laser melting . Rheology . Thermal gradient . Surface roughness Nomenclature C1, C2 dA dV1 E1 E2 g h H Hs Iimp Planck distribution constants Increase the surface area Decrease of internal volume Melting pool energy Energy of solidified layer Gravity acceleration Height of meniscus Enthalpy Hatch space Impregnation criteria for surface energy * Amir Mahyar Khorasani [email protected] Ian Gibson [email protected] Ali Reza Ghaderi [email protected] 1 School of Engineering, Deakin University, Waurn Ponds, Victoria, Australia 2 Institute for Frontier Materials, Deakin University, 75, Pigdons Road, Waurn Ponds, Victoria, Australia Lp n P0 Pch Precoil Q R2 Rbub Rcur Rdrop Rg Sc Scontact Ss T0 Tc Tmp U Uf Ufb V0 Vliquid Laser power Katayama-Guggenheim factor Reference value for pressure Chamber pressure Recoil pressure Internal heat Second radius of meniscus Bubble radius Curvature radius Radius of droplet Universal gas constant Contact area of melting pool with solidified layer Contact surface of droplet and base Scan speed Reference value for temperature Critical temperature Titanium melting point temperature Cohesive energy Fluid speed Speed of melted particles at the end of melting pool Reference value for volume Volume of liquid in the melting pool 3762 Wa We Wi Ws Wsu Wt Z Zb αL αv γ0 γSL,γSG,γLG γ∗ δ λ ρ Int J Adv Manuf Technol (2018) 97:3761–3775 Work of adhesion Required work correspond to pull out external fluid Initial work to increase the pressure of droplet Required work correspond to increase internal area Other works Total work Axial length toward the end of keyholes Distance of keyhole from top to the bed Linear coefficient of expansion Volumetric coefficient of expansion Reference value for surface tension Surface tension for solid-liquid, solid-gas and liquid-gas Constant surface tension for each liquid Molecular dimension Wave length Density 1 Introduction Generally, the surface roughness is low in powder bed systems such as selective laser melting (SLM) and electron beam melting (EBM), but the surface quality in EBM is lower due to excessive Marangoni’s convection, unstable melting pool, and falling powder particle on the unstable melting pool [1–4]. It is reported that surface roughness varies between 1 and 20 μm depending on process parameters such as layer thickness, hatch spacing, laser power, scan speed, and particle size [5–9]. Few investigations were found in the literature which purely analyzed the surface quality of as-built parts on SLM. Reducing scanning speed and increasing layer thickness lead to formation of irregular tracks and lower surface quality. Also, use of finer powder and layer thickness improve the surface roughness [10]. The width of melting pool is associated with hatch spacing and is a critical factor in the formation of Marangoni’s effect and surface quality [11]. Using full factorial design of experiment to analyze the effect of process parameters on the surface quality of CoCrMo showed that laser power, hatch spacing and scan speed are the most influential parameters. The surface roughness using contactable profilometry for single layer printing was obtained as 8 μm. However, the reported value is based on the cutoff length of the profilometer needle [11]. Thermal phenomena and scanning strategy were found to be effective factors on the surface roughness of Hastelloy for up-skin and down-skin surfaces. The effect of laser power, scan speed, layer thickness, and sloping angle on surface roughness showed that due to lack of wettability and Rayleigh instability, if the scan speed exceeds the original equipment manufacturer recommendations, higher balling effect and lower surface quality results [12]. A Gaussian process-based model has been used for learning and prediction of the porosity in SLM of 17-4 PH stainless steels as a function of process parameters. Cross-validation for all eight test samples proved the accuracy of this approach to predict the value of porosity and surface defects is acceptable [13]. It is reported that [5] to obtain better surface quality, maximum hatch distance should not exceed the average width of the continuous track. The value of temperature, thermal gradient, and subsequently surface quality in SLM is also associated with scan length. Particle size distribution has a major influence on the density and surface quality of the printed parts. Spierings et al. [14] investigated the effect of three different particle sizes and two layer thicknesses on surface quality and density of AM parts. The results showed that using optimum powder particle size and post-processing such as blasting improves the quality of the surface in AM and granulation improves the surface quality but is changed due to the spatter nature of the process. The size of particle diameter and layer thickness should be proportional to improve adhesion along the step edge and to fill gaps between consecutive layers and improve surface quality [15]. Various post-processings such as re-melting, milling, turning, grinding shot peening, or sand blasting have been suggested to improve the quality of as-built samples. For instance, laser re-melting improved the surface roughness Ra from 15 to 1.4 μm [16] or milling improved it to 6 μm depending on cutting strategy and parameters [17–20]. However, these methods increase the cost and manufacturing lead-time in the production process. Most of the investigations theoretically mentioned the effect of process parameters on surface quality. However, there is a lack of rheological characterization literature on thermal phenomena of the surface of as-built parts. In this research based on Taguchi L25, Ti-6Al-4V parts were printed and thermal effect of process parameters such as laser power, scan speed, and hatch space on melting pool and interface-related phenomena were scrutinized to clarify their effect on the surface of the printed parts. Different phenomena such as surface tension and Marangoni’s effect, capillary force, the pressure in droplet, wetting, work adhesion, recoil pressure, drag force/ contraction forces, and interaction of surface tension, hydrodynamic and vapor pressure are discussed in depth. 2 Materials and methods 2.1 Powder material and SLM process Due to its high strength, good corrosion resistance and lowdensity Ti-6Al-4V is highly suited for production parts in the biomedical, aerospace, and automotive industries. In this work, spherical Ti-6Al-4V powder was used as a feed in the Int J Adv Manuf Technol (2018) 97:3761–3775 printing process. SLM Solutions 125HL equipped with Yttrium laser and maximum power of 200 W and minimum spot size 5 μm was used. 2.2 Surface roughness measurement Samples were printed based on ASM standard E8 for further analysis on tensile properties. Surface roughness measurement has been carried out using an Alicona Infinite Focus optical profilometer that is equipped with 5 to 100× zoom. The measurement was performed on asbuilt samples and not post-polishing was implemented on the samples to keep the original surfaces. To have consistency in the obtained results and regions of 5 × 3 mm (about 3000 points) and five times in different areas of the top surface on the samples were scanned to achieve the value of the surface roughness. Normalized value of surface parameters was calculated by this device. Based on ISO 4288 and ISO 11056 standards, a high pass Gaussian filter was used. Then, Ra values converted to Sa to have a more general and consistency in results. 2.3 Design of experiment The important feature in the characterization of different aspects such as mechanical properties, surface quality, and dimensional deviations of SLM parts is low repeatability (while is good repeatability for DMD parts [21, 22]) due to the complex interactions between various process parameters. Therefore, to increase the accuracy and generality of this research, Taguchi L25 orthogonal design of experiment (DOE) has been used, and laser power, scan speed, hatch space, and laser pattern incrementing angle were selected for input parameters. Our previous research showed that due to high cooling rate (103–108 K/s) as-built samples have low ductility, therefore, according to ASM standards different annealing processes such as stress relieving, mill annealing, recrystallization and beta annealing have been carried out to improve mechanical properties for further research [23–25]. Thus, annealing temperature was added to the DOE as an independent parameter to analyze the effect of heat treatment on surface quality and to increase generality of the experiment for each factor five levels were chosen (Tables 1 and 2). 2.4 Analyzing the effect of process parameters on the surface Based on our previous investigations laser power, scan speed and hatch space affect melting pool and subsequently surface characteristics of printed parts. Therefore, the effect of the mentioned parameters is characterized in this section 3763 Table 1 SLM Constant process parameters System parameters Value Min. scan line/wall thickness 120 μm Operational beam focus variable 100 μm Layer thickness Laser spot diameter 30 μm 0.2 mm [24–26]. The surface roughness of as-built parts is highly associated with thermal phenomena and behavior of melting pool which is discussed based on rheological science and phenomena [12]. To analyze the effect of process parameters on the average surface, artificial neural networks (ANN) was used. Multi-layer perceptron ANN has been used with 5 inputs according to Table 2 and output was average roughness. The number of training, validation, and test samples was 17, 3 and 5 respectively. To analyze the generality of the proposed ANN, five cross validations have been performed; therefore, all samples were tested and results are illustrated in Table 3 and Fig. 1. As shown in Table 3 and Fig. 1, a high accuracy of the proposed model is proven. To analyze the effect of process parameters on average roughness, the interaction of effective process parameters on melting pool including laser power, scan speed, and hatch space has been drawn. 3 Results and discussions For analyzing the effective process parameters on melting pool, the simplifications are: (I) Molten material is assumed to be incompressible, (II) the interface has no thickness, (III) the interface is smooth, (IV) the chamber has constant working pressure, (V) heat capacitance and thermal conductivity of the melted materials were constant [21, 22], and (VI) layer thickness was constant for all 25 samples and therefore neglected. 3.1 Surface tension and Marangoni’s effect In this research SLM Solutions, 125HL equipped with Yttrium laser was used. We simplified the laser with black body, therefore, the radiation energy in temperature “T” by using Planck distribution is [27–29]: E ðb;λÞ ðλ; T Þ ¼ C 1 C2 −1 λ5 exp λT ð1Þ 3764 Int J Adv Manuf Technol (2018) 97:3761–3775 Table 2 Process parameters and levels Laser Power (W) Scan Speed (mm/min) Hatch spacing (μm) Scanning pattern incrementing angle (°) 90 95 600 650 65 70 36 40 20 600 100 105 700 750 75 80 45 60 750 925 110 800 85 75 1050 It should be noted that not all of the laser energy will be used in melting the powder due to reflection, etc. Importing process parameters in the Planck distribution and by substitution of energy density in SLM with the radiation energy, we have [26, 29, 30]: T mp ¼ C2 C1 SS H S λln þ1 LP λ5 ð2Þ In the bulk of the melt pool, molecules have interaction with surrounding molecules due to Van der Waals forces. In interfaces, molecules have half space for interactions with neighboring molecules. Surface tension is obtained by cohesive energy “U” according to Eq. 3 [30]. γ¼ U 2δ2 ð3Þ The power of 2 for δ relate to the surface of the molecule. The developed Eotvos equation for surface tension is called Katayama-Guggenheim and shows that surface tension is a direct function of temperature [31, 32]. 1 0 B γ ¼ γ*B @1− C C 2 C A C1SS H S T C λln þ 1 LP λ5 ð4Þ A critical point in thermodynamics is the end of phase equilibrium. This is the point of coexistence of liquid and its vapor at the end of liquid in the phase equilibrium curve. By determining reference values (γ0, T0), the surface tension is: T C −T 0 ð5Þ γ ¼ γ* TC Combining Eqs. 1–3 shows that for linear changes of temperature in relation to surface tension, Eq. 6 is obtained: γ¼γ * 2 2 33 n T C −T 0 4 4 C2 T C 55 − 1− TC ðT C −T 0 Þλln CL1 S SλH5 S þ 1 T C −T 0 P ð6Þ Heat treatment temperature C° Equation 4 is thermocapillary or Marangoni’s effect (Marangoni’s convection). Temperature distribution was highly influenced by the energy density and in the case of higher laser power and lower scan speed (higher energy density), the interface of melting pool is locally heated and according to Eq. 6 surface tension reduced (Fig. 2). The gradient of surface tension induced at the interface from the hotter to the cooler area then propagates toward the bed of the melting pool. The higher the temperature, the higher the motion of melting pool resulting in greater irregularity on the surface of the pool. Since the cooling rate is high in AM, surfaces form quickly and irregularities in the solidified process are maintained [11, 33–35]. Moreover, high energy density enhances densification but induces fine spherical pores and thermal micro-cracks by increasing liquid lifetimes and thermal process [36]. If scan speed increases or laser power decreases, the value of energy density decreases and less heat generated in the process thus less micro-fluid flow and instability occurs in the melting pool forming better surface quality. This trend was proved by the literature [10, 37–39]. Analyzing hatch space on the surface quality shows with lower hatch space, higher overlap occurs. This creates a mush area and the gradient of micro-fluid motion (due to higher viscosity) is zero and no Marangoni’s convection happens and energy density increases and the chance of formation of keyholes and defects also increases [34]. Moreover, the higher cooling rate on the surface of the melt pool and reduced overlap leads to higher heat penetration and increases the chance of the formation of keyholes and lower surface quality. 3.2 Capillarity force Capillary force is important in the characterization of melting pool behavior in micro-scale. To explain the melting pool behavior, we assume the previous hatch and surrounding unmelted powder act as two plates for the melting pool (Fig. 3). We can simplify the melting pool in terms of fluid between two parallel plates. Due to low hatch space in our experiment (60–80 μm), a liquid film tends to be Int J Adv Manuf Technol (2018) 97:3761–3775 Table 3 3765 Results of the cross-validation Cross validation Std. dev. Max error Correlation Cross validation Std. dev. Max error Correlation 1st 2nd 3rd Train Test Recall Train Test Recall Train Test 0.01063 0.03022 100 2.11326 3.51448 99.709 2.159 3.482 96.228 0.00557 0.01632 100 2.86936 4.19455 93.884 1.855 2.871 97.061 0.00075 0.002 100 3.10811 3.87853 96.116 3rd 4th 5th Recall Train Test Recall Train Test 1.46058 2.29187 95.276 0.0007 0.00165 100 3.60215 6.15992 99.29 1.56434 2.28229 99.6 0.00095 0.00249 100 2.41102 3.04171 96.897 generated between two parallel plates and is considered to be adhesive. Capillary force is predominant in microfluids and to minimize free energy a meniscus with round shape is created. Using Laplace’s law at free interface and by supposing the first radius of curvature “Rcur,” the second radius of meniscus is “R2” is calculated by: π Hs sin θ− ⇒H s ¼ ð−2R2 cosθÞ ð7Þ ¼ 2R2 2 The minus sign in Eq. 7 shows that the liquid moves down due to the interaction of capillary and Van der Waals forces. The pressure in the melting pool is related to hatch spacing, and therefore, Eq. 8 by applying Laplace’s law is derived [30, 40]: 8 1 1 1 2cosθ > > ΔP ¼ P −P ¼ γ − ¼ γ þ 0 1 > > Rcur R2 R Hs > > > > > < if curvature is concave > > 1 1 1 ð2cosθÞ > > −P ¼ γ þ ¼ γ − ΔP ¼ P > 0 1 > > Rcur R2 R Hs > > : if curvature is convex ð8Þ Due to higher Van der Walls forces in melted metals and formation of a convex shape, Eq. 8 is dominant. The value of hatch space is much less than vertical radius and the capillary pressure in the surface of melting pool by Laplace’s law is obtained based on Eq. 9 (Fig. 4). 8 −2γcosθ < ΔP ¼ ð9Þ HS :π =2 ≪θ≪π The value of contact angle is in the second quarter of trigonometric circle and therefore the value of melting pool pressure is positive. The capillary force for melting pool between two parallel plates, including a solidified layer on one side and powder particle on the other, and considering the hatch space as the distance between the plates is [30, 40]: 2 2 33n 2cosθ 2 * T C −T 0 4 4 C2 T C 55 − 1− F≈ πR γ TC HS ðT C −T 0 Þλln CL1 S SλH5 S þ 1 T C −T 0 P ð10Þ By increasing laser power and decreasing scanning speed (higher energy density), the surface of melting pool has a higher temperature and due to Marangoni’s convection, the value of surface tension in Eqs. 4 and 10 decreases. The capillary force reduces therefore the surface of the melt pool has weaker adhesion to the sidewalls and considering the convex shape of melted metals the horizontal radius of curvature decreases and rougher surfaces in the staircase are obtained. In this situation, fast solidification forms surfaces with more distortion and less quality [30, 34]. In lower laser power and higher scanning speed (lower energy density), the temperature of the surface on the melt pool is lower and based on Eq. 10, the capillary force increases and the interaction of intermolecular forces versus wall adhesion move toward equilibrium and surface becomes smoother. Decreasing contact angle in Fig. 4 is another reason for decreasing cosθ (from π to π/2) in the numerator of Eq. 10 and reduction of capillary force. Using principle of minimum energy, metal liquid moves downwards in tinner tubes which shows surface energy in dry walls is lower than wet walls. The impregnation criterion is Iimp = γSG − γSL. The liquid goes down when γSL > γSG and using Young’s law and equations A1 and A-2 in appendix the height of the meniscus between two parallel plates separated by distance hatch space is h¼ 2γcosθ ρgH S ð11Þ 3766 Int J Adv Manuf Technol (2018) 97:3761–3775 Fig. 1 a–c Interaction of laser power, scan speed, and hatch spacing on average roughness. d Samples Equation 11 shows that increasing hatch space leads to decreasing contact angle and decreasing value of “h.” Therefore, the roughness on the surface of melt pool tends to disappear and smother surfaces were obtained. radius Rdrop to Rdrop + dRdrop due to increasing internal volume is [30, 40]: δwi ¼ −P0 dV 0 ð12Þ dV 0 ¼ 4πR2drop dRdrop 3.3 Pressure in droplet The necessary work to pull out the external fluid and the work corresponding to increase in interfacial area “ws” are: During SLM process, on account of fully melting of particles, two types of droplets including gas and melted powder particles exist which can affect the quality of the surface. In this research, a spherical powder particle was used and by supposing the melted particle to be surrounded by liquid, the necessary work to increase Fig. 2 Marangoni’s effect and surface quality δwe ¼ −P1 dV 1 ð13Þ dws ¼ γdA; dA ¼ 8πRdrop dRdrop ð14Þ where dV1 is the decrease of external volume proportion to dV0. At mechanical equilibrium on the surface and bulk Int J Adv Manuf Technol (2018) 97:3761–3775 3767 Fig. 3 Horizontal curvature in capillarity (optical image) of the melting pool, the total introduced work has zero value. P1 ¼ P0 − 2 Rdrop γ* 2 2 33n T C −T 0 4 4 C2 T C 55 − 1− TC ðT C −T 0 Þλln CL1 S SλH5 S þ 1 T C −T 0 P δwt ¼ δwi þ δwe þ δws ¼ 0 ð15Þ ð18Þ By combining Eqs. 12–14, the pressure in droplet for bulk and surface of the melting pool is derived from Eq. 16. ΔP ¼ P0 −P1 ¼ γ dA dV ð16Þ The shape of droplet for melted powder particle is spherical and therefore the internal pressure of a droplet is [30, 38–40]: ΔP ¼ 2γ Rdrop ð17Þ In the case of higher laser power and lower scanning speed, the accumulated heat in melting pool increases, so the pressure of droplet according to Eq. 18 also increases: Fig. 4 Different capillary effects on melting pool In addition, higher energy density and temperature leads to a reduction of surface tension and increasing melted particle radius and subsequently the pressure of the droplet increases and leads to bursting droplets from the melting pool, which is illustrated by Fig. 5. As it can be seen, the abovementioned mechanism generates some large dents on the surface of the samples and decreases surface quality. In the case of increasing hatch spacing and decreasing overlap area, Marangoni’s convection reduces surface temperature and decreases droplet pressure. In lower hatch space and wider overlap area, the gradient of fluid flow is zero and accumulated heat results in higher temperature and 3768 Int J Adv Manuf Technol (2018) 97:3761–3775 pressure in droplets. This mechanism leads to bursting droplets from the melting pool in the overlap area and reduction of surface quality (Fig. 5). 3.4 Wetting Lower surface quality was obtained in lower scan speed and higher laser power (higher energy density and temperature) because a liquid spreads in a film if the surface energy is lowered. Figure 6 shows Young’s law has been derived for triple line regardless of determining the interactions near the contact line. Close to triple line, the molecules have different interaction compared to those in the interfaces. When we increased the scan speed in the range of standard values the laser track becomes continuous and tends to remove recoil pressure marks on the topmost surface due to higher gradient of momentum and smaller size of the droplets. Therefore, a line tension term is added to Young’s law according to Eq. 19 [30, 38–41]: γ SG ¼ γ SL þ γ LG cosθ þ γ SLG Rdrop ð19Þ By increasing scan speed the value of “Rdrop” becomes smaller and with respect to very small “θ” cosθ = 1 then according to Eq. 20 the value of γSG increases: γ lim SLG ∼∞ γ SLG ≠0 ð20Þ Rdrop →0 Rdrop The wettability of melting pool is defined by the spreading parameter “S.” According to Eq. 21, the type of spreading can be film or droplet [30, 38–40]: 8 < S ¼ γ SG −ðγ SL þ γ LG Þ ð21Þ If S > 0⇒Film appears : If S < 0⇒Droplet appears Equation 19 shows that by reduction of droplet size the value of γSG increases and S > 0 so the film of melted titanium appears on the surface. Lower surface tension and higher wetting results in lower viscosity by taking into account the number of laser pulses and instability of the melting pool. Waves are generated on the top surface and fast cooling procedure leads to decreasing surface quality. Moreover, in the melting pool, bubbles often form along contact surfaces. The pressure of the bubbles is obtained from Laplace’s law according to Eq. 22: P¼ γ Rcur ð22Þ When laser power increases and scan speed decreases, the temperature of the surface on account of higher energy density raises and, based on Eq. 21, spreading factor increases S > 0 and the film is formed on the melting pool. In this situation, Eq. 6 shows that surface tension decreases due to Marangoni’s effect. Based on the Katayama-Guggenheim relation (Eq. 4) in critical temperature (boiling temperature), the value of surface tension is zero. However, surface tension has non-zero value in SLM process since the working temperature will not go higher than 2250 °C and boiling temperature for Ti-6Al-4V is around 3560 °C [42]. Increasing wettability from Eqs. 21 and 22 leads to: lim Lp →Lphigh γ ∼∞ Rcur →0 Rcur ðPÞ ¼ lim ð23Þ Therefore, the value of the internal pressures increases radically and the bubbles burst during the process and throw some particles above solidified surfaces and reduce the surface quality. Figure 7 shows the thrown particles due to hydrophilic contact with the melting pool. In other words, the interaction of higher internal pressure for bubbles and lower surface tension due to higher energy density leads to a volcano effect on the top of the samples. Small balling was found at low scan speeds and high scan powers due to longer liquid lifetimes, increased melt volumes, and decreased melt viscosities [12, 43]. Decreasing hatch space leads to increase in the value of overlap area. When the second hatch is scanned by the laser in the overlap area, partial melting happens and based on Katayama-Guggenheim theory, surface tension in solidliquid and liquid-gas increases. The material phase in the overlap area is mush and the gradient of fluid flow in this area is zero: * ∇ uf ¼ ∂u f ^ ∂u f ^ ∂u f ^ jþ iþ k¼0 ∂x ∂y ∂z ð24Þ Therefore, no Marangoni’s convection happens in the overlap area and surface tension in liquid phase increases: γ SG < ðγ SL þ γ LG Þ⇒S < 0 ð25Þ Based on Eq. 25, partial wetting happens which causes more waviness and rougher surfaces are formed during solidification [9, 34]. 3.5 Work of adhesion In this section, the effect of laser power, scan speed, and hatch space on work adhesion and surface quality has been analyzed parametrically. The work of adhesion is defined for solid/liquid or immiscible liquids. In solid, liquid interfaces such as melting pool/solidified layer the combination of work adhesion and Young’s law produces Young-Dupre’s equations. These relations are used to Int J Adv Manuf Technol (2018) 97:3761–3775 3769 Fig. 5 Bursting droplet in the surface of the melting pool: (A) colored map and (B) normal map characterize the effect of laser power, scan speed, and hatch space on the surface quality. If the contact of melting pool with the solidified layer is “SC,” then surface energy is obtained from Eq. 26: E SL ¼ γ SL S C ð26Þ The work that is required to separate the melting pool and solidified layer is work of adhesion and after separation, the energy is: E t ¼ E 1 þ E2 ¼ ðγ 1 þ γ 2 ÞS C ð27Þ Now the work of adhesion is obtained according to Eq. 28 [30, 38, 40]. W a ¼ γ 1 þ γ 2 −γ 12 ⟹W a ¼ γ LG þ γ SG −γ SL γ 1 ¼ γ LG ; γ 2 ¼ γ SG ; γ 12 ¼ γ SL ð28Þ By drawing different forces exerted on triple line (topmost surface/melting pool) at equilibrium, the forces must be zero and along scan direction, the following equation is derived [1, 2] (Fig. 8). γ LG cosθ ¼ γ SG −γ SL ð29Þ The work adhesion for melted and solidified layers from Eqs. 26 and 27 is obtained by [30, 40]: Fig. 6 Partial melting in the surface: (a) more droplet and (b) more film shape W a ¼ γ ð1 þ cosθÞ ð30Þ In the case of higher laser power and lower scan speed due to generation and accumulation of higher heat, the value of γLG decreases and melting pool becomes a film and from Eq. 30 work adhesion decreases. This phenomenon leads to reduction of initial adhesion of melting pool with solidified layer and due to the movement of laser and instability of melting pool, melted material flows and the gradient of fluid flow has non-zero value specifically at the bottom of the melt pool [12]. * ∇ ufb ¼ ∂ufb ^ ∂ufb ^ ∂ufb ^ jþ k≠0 iþ ∂x ∂y ∂z ð31Þ Due to this motion, larger waves occur and unmelted powder particles drop to the melting pool even when top surface of the melt pool has small movement/fluctuation, which increases the value of average roughness during fast solidification. In the case of lower laser power and higher scanning speed, lower energy density and temperature leads to increase in surface tension and work adhesion. As a result, more adhesion and higher stability in melting pool generate better surface quality. Increasing hatch space leads to increasing contact surface between the melting pool and solidified layers. Therefore, the surface energy increases according to Eqs. 26 and 27. Work of adhesion is a function of surface energy thus, by increasing 3770 Int J Adv Manuf Technol (2018) 97:3761–3775 Fig. 7 a Hydrophilic surface and small bubbles. b Hydrophobic and larger bubbles. c The effect of bursting of small bubbles on surface quality surface energy this factor increases and melting pool becomes more stable and consequently smaller waves and better surface quality were obtained. 3.6 Recoil pressure The recoil/snapback movement of melted fluid is a common rheological phenomenon in laser-based production processes [44]. The source of snapback movement is related to laser pressure and viscous and elastic characteristics of fluid under deformation forces. The effect of recoil pressure is quite obvious on the top surface of SLM parts and is obtained according to the following Eq. [44]: ΔH V 1 1 ð32Þ − Precoil ¼ P0 exp Rg T V T mp Recoil pressure in SLM is defined based on process parameters by substituting titanium melting temperature from Planck dispersion and using Eqs. 2 and 32 and 33: 13 C1SS H S λln þ 1 6 ðδQ þ VdPch −δW SU Þ B 1 C7 LP λ5 C7 B − ¼ P0 exp6 4 A5 @T V Rg C2 2 Precoil 0 ð33Þ Fig. 8 Triple contact line on the surface of the printed part In SLM by increasing laser power and decreasing scanning speed (increasing energy density), the argument of a logarithmic function in Eqs. 32 and 33 decreases. In SLM, the surface pressure from the chamber is constant and by assuming no additional work goes on inside the chamber “Wsu” the recoil pressure increases (Eq. 34). Increasing recoil pressure leads to a more pronounced step effect on the surface of the samples and decreasing surface quality as shown in Fig. 9. 13 C1SS H S λln þ 1 C7 6 δQ B 1 LP λ5 B C7 ¼ P0 exp6 A5 4 Rg @ T V − C2 2 Precoil 0 ð34Þ In addition, enthalpy is a function of heat dh = δQ; therefore, according to Eq. 2, increasing energy density leads to increasing temperature and generated heat on the surface of melting pool and subsequently recoil pressure increases and higher stair effect was observed on top of the melting pool. Also, according to Fig. 10, the volume of displaced material piled up around the edges of the melt pool increased and lower surface was observed. Increasing hatch space generates a greater log term in Eq. 34 and as a result, lower recoil pressure and step effect are observed in the top surface of the samples. Int J Adv Manuf Technol (2018) 97:3761–3775 3771 Another reason for increasing the average roughness for smaller hatch space is associated with the promotion of particle attachment in the overlap of two subsequent hatches. Larger overlap leads to enabling the previously fabricated track to absorb more energy and increase the temperature. This effect is stronger than the cooling of overlap area due to the heat sink effect. The wider heat affected zone and more partially melted powder attached to a solid interface is the result of this phenomenon and increased average roughness [5, 12]. 3.7 Drag force/contraction forces In powder bed, additive manufacturing the build substrate is welded to the sample to prevent primary movement and acts as a temporary base and reduces the degree of freedom. The linear expansion coefficient of Ti at melting pool at 1600 °C grows about seven times compared to the ambient temperature (Fig. 10), so the increase in volume is significant and the following equation is drawn: T ΔV mp ¼ exp ∫T 0 aV ðT ÞdT ð35Þ V For isotropic materials aV = 3aL, however for printed Ti6Al-4V due to anisotropic behavior of the material, the volumetric expansion due to increasing the temperature in melting pool by combining Eqs. 2 and 35 is: 8 0 C2 1 > > C1 SS H S > > B λln LP λ5 þ1 C < ΔV ¼ expB ðξaL ðT ÞÞdT C @∫ T 0 A V > > > > : ξ>1 ð36Þ Increasing the laser power and decreasing scan speed tend to increase the upper interval of integral and change of volume. Also, in higher temperature such as melting pool, the thermal expansion coefficient is aL(T0) = 7aL(Tmp); therefore, the volumetric change within the process increase 7ξ. In this situation, the volume of melted material expand and becomes bigger. In addition, thermal stress for anisotropic material such as SLM Ti-6Al-4V is obtained from Eqs. 36 and 37 [46]. σth ¼ σth ¼ Eξα T mp −T 0 1−ν Eξα C1SS H S ð1−ν Þ λln þ1 LP λ5 ð37Þ C S H C 2 −T 0 λln 1 S 5 S þ 1 LP λ ð38Þ From Eq. 38, it can be observed that when the higher energy density is selected (increasing laser power and decreasing scanning speed and hatch spacing), the value of the argument in the log term increases and therefore the numerator of the fraction becomes bigger and denominator gets the smaller value. As a result, thermal stress greatly increases and with respect to Eqs. 35 and 37, the higher thermal stress and larger volumetric expansion on the surface generate a larger rippling effect on the top surface (Fig. 10b). In solidification, the initial cooled part of the material is granular followed by boundary regions (which floated in the melting volume). By carrying out a cooling process, grain boundaries are converted to semisolid/mush. When higher laser power and lower scan speed and hatch spacing are selected, higher energy and thermal stress exerted to the material according to Eq. 38. Under higher stress and forces, high thermal gradient in liquid phase [47] and destabilization of the solidification cause a transition from a planar to cellular or dendritic solidification. Therefore, grain size becomes smaller and tensile strength improves up to 25% compared to wrought materials [24, 25, 42]. Grain boundaries reduce the thermal and electrical conductivity of the material and this is more obvious for Ti-6Al-4V due to low thermal conductivity (21.9 W m−1 K−1). Thus, a combination of these four factors comprising low thermal conductivity, small grain size, low elongation, and high volumetric expansion for Ti-6Al4V, generates higher distortion on the surface and formation of micro-cracks and cracks in bulk of the material. According to Eq. 37, increasing energy density (laser power and decreasing hatch space and scan speed) increases the value of thermal stress, so due to high thermal expansion the interaction of contraction forces and substrate resistance may result in cracks and reduce the surface quality. 3.8 Interaction of surface tension, hydrostatic and vapor pressures In SLM of metals, keyholes are one of the defects appearing on whole surface and bulk. In the melting pool, a vapor pressure acts versus hydrostatic force and surface tension on the interface of liquid/solid so in keyhole walls the vapor pressure increases by increasing depth of the keyhole and decreasing the radius [1, 48]. Gasses trapped in the balling region form a classical keyhole shaped void (Fig. 11). Hydrostatic pressure and surface tension tend to close the walls of keyholes, while, vapor pressure acts in opposite and tends to keep the walls open (Fig. 9). Hydrostatic and vapor pressures are derived based on Eqs. 39 and 40 [1, 2]: Phydro ¼ P0 þ ρgzSinθ Pvapor ¼ P0 þ γ ðT Þ þ ρgz RðzÞ ð39Þ ð40Þ It is known that the working temperature for Ti-6Al-4V is less than boiling (critical temperature); therefore, the surface tension has non-zero value and based on Eq. 41, high pressure is observed at the end of the keyhole: 3772 Int J Adv Manuf Technol (2018) 97:3761–3775 Fig. 9 The effect of recoil pressure on the step effect of SLM parts 8 > > γ ðT Þ > > > lim ∼∞ > < z→zb RðzÞ C2 > ≠T c ⇒ γ ðTÞ≠0 > > > C S 1 SHS > > þ 1 : λln LP λ5 ð41Þ Then by considering non-equilibrium equations in the X direction (normal to build plane): ∑Px ¼ P0 þ 2 γ ðT Þ þ ρgh RðzÞ 3 2 2 33n C2 T C 55 * T C −T 0 4 4 4 − 1− − γ −P0 þ ρghSinθ5 TC ðT C −T 0 Þλln CL1 S SλH5 S þ 1 T C −T 0 P ð42Þ Vapor pressure is higher than hydrostatic and surface tension (Eq. 42); therefore, according to Eqs. 41–43, we have: Pvapor ≫Phydro þ γ⇒∑Px ≠0 ð43Þ By decreasing scanning speed and increasing laser power according to Eqs. 42–44, the value of "Γ” and the chance of formation of keyholes increase. This phenomenon shows the head of keyholes stays open and surface quality decrease. 2 2 2 33n 3 γ ðT Þ 4 * T C −T 0 4 4 C2 T C 55 5 1− Γ¼ − γ − TC RðzÞ ðT C −T 0 Þλln CL1 S SλH5 S þ 1 T C −T 0 P ð44Þ Increasing hatch spacing also leads to generation of a lower overlap area and is noted that in overlap area the value of Ra is five to seven times higher than the center of the track [34]. Higher hatch space also leads to increase in the radial acceleration and speed of melting flow. Therefore, the speed of melting flow is not zero and higher conduction occurs on melting pool, while in overlap area, lower contact and conduction are happening. Consequently, the size of the melt pool increases and average surface improves [34]. Also, higher hatch space leads to higher Marangoni’s convection and carrying the heat from the keyhole bottom to the surface then radially outward and the results are increasing weld pool width near the top surfaces [34]. The higher hatch spacing, the smaller “Γ" and the chance of formation of keyholes and lower surface roughness reduces. In another word, lower hatch space and higher overlap area increase the region with no velocity vectors that is a fertile ground for the formation of keyholes (Appendix) [1, 2]. Also, the remaining liquid films in the keyhole in the Fig. 10 a Thermal expansion coefficient versus increasing temperature [45]. b Rippling effect Int J Adv Manuf Technol (2018) 97:3761–3775 3773 Fig. 11 SEM image for the interaction of hydrostatic pressure, surface tension, and vapor pressure on formation of keyholes final stage of solidification are critical to solidification cracking as it forms a region of extremely low shear strength [49]. 4 Conclusion One significant aspect of AM is the fact that metal-based AM is characterized by low repeatability due to the complex and various physical transformations and non-linear interaction of different process parameters and thermophysical properties of different materials. In the current work, according to Taguchi L25 SLM Ti-6Al-4V parts were printed and thermal effect of the process parameters comprising laser power, scan speed and hatch space on melting pool, interfaces and average surface were characterized. The effect of different rheological phenomena like surface tension and Marangoni’s effect, capillary force, the pressure in droplet, wetting, work adhesion, recoil pressure, drag force/contraction forces and interaction of surface tension, hydrodynamic and vapor pressure on average surface analyzed and the following conclusion were drawn. Higher temperature leads to lower surface tension and irregularity on the top surface and decreases surface quality. In higher laser power and lower scan speed, the value of surface tension decreased and subsequently capillary force reduced; therefore, horizontal radius of curvature decreases and a rougher surface is generated. Higher energy density and temperature increase droplet pressure and therefore, higher pressure in droplets acts as boiling effect and splashing particles out of the melting pool and increases surface roughness. Higher internal pressure in bubbles and low surface tension result in a volcano effect on the surface of the samples. In low laser power and high scan speed, the work adhesion becomes smaller and the surface of melting pool becomes unstable and rough. Recoil pressure is a direct function of energy density. Higher energy density leads to higher recoil pressure and step effect on the surface and reduces the surface quality. Higher energy density increases thermal stresses and due to higher thermal expansion of Ti-6Al-4V in higher temperature the interaction of contraction forces and substrate resistance generates crack and distortion on the surface of the printed parts. Increasing laser power and decreasing scanning speed tend to increase non-equilibrium forces on the surface of melting pool and increase the chance of formation of keyholes and reduction of surface quality. Better surface quality leads to better layering between each two subsequent layers and can provide higher density followed by better tensile strength. Appendix When liquid moves down to the tube, the system gains potential energy due to hydrostatic force. The balance is: 1 1 ρghV liquid −S contact I ¼ ρghπR2 h−2πRhI 2 2 1 ¼ ρgπR2 h2 −2πRhγcosθ 2 E¼ ðA1Þ The equilibrium evolution of the liquid is derived by: ∂E 2γcosθ ¼ 0⇒h ¼ ∂h ρgH S ðA2Þ 3774 Int J Adv Manuf Technol (2018) 97:3761–3775 Table 4 Surface roughness values Laser power (W) Scan speed (mm/s) Hatch space (μm) Pattern angle (Deg) Heat treatment Average temperature (C) surface μm 90 600 65 36 20 12.24 90 650 70 40 600 12.24 90 90 700 750 75 80 45 60 750 925 13.10 16.92 90 95 800 600 85 70 72 45 1050 925 19.51 17.14 95 650 75 60 1050 23.31 95 95 700 750 80 85 72 36 20 600 10.93 11.13 95 800 65 40 750 10.86 100 100 600 650 75 80 72 36 600 750 8.61 10.51 100 100 100 700 750 800 85 65 70 40 45 60 925 1050 20 14.27 22.32 11.89 105 105 105 105 105 110 600 650 700 750 800 600 80 85 65 70 75 85 40 45 60 72 36 60 1050 20 600 750 925 750 22.91 10.60 9.21 7.73 15.08 10.05 110 110 110 110 650 700 750 800 65 70 75 80 72 36 40 45 925 1050 20 600 17.45 21.47 12.54 10.16 7. 8. 9. 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