Structured porous 17-PH stainless steel layer fabrication through laser powder bed fusion

ABSTRACT

This study aimed to fabricate thin, porous layers of 17-4 PH stainless steel with a defined porosity using laser powder bed fusion (LPBF). The central composite design (CCD) approach was utilized to examine the effect of process parameters on porosity. Three different methods were employed to measure the porosity of 17-4 PH stainless steel samples, i.e. theoretical analysis, buoyancy, and X-ray computed tomography (X-CT). A statistical quadratic regression model is generated that correlates with LPBF parameters to forecast porosity with high prediction accuracy. The maximum obtained porosity is 51.25% ± 0.33% with a laser power of 60 W, a scanning speed of 1800 mm/s, and a hatch spacing of 0.115 mm, which resulted in an average pore size of 24.8 ± 0.38 µm. Permeability was also analysed, as the volume energy density decrease ranges from 19.30 to 14.22 J/mm³, the permeability coefficient increases from 1.39 to 9.41 × 10⁻¹¹ m². In addition, it is observed that the minimum energy density to fabricate the 17-4 PH SS with the highest porosity and free of defects and fragmentation is 14.2 J/mm³.

KEYWORDS:

• Porous layer
• LPBF
• permeability
• porosity

1. Introduction

Additive manufacturing (AM) is a technique of layer-by-layer fabrication of products using 3D geometric models created by computers (Dhanesh, Dhanawade, and Bhatwadekar 2017; Piedra-Cascón et al. 2021; Sun et al. 2021; Tamez and Taha 2021; Vaezi, Seitz, and Yang 2013; Ziaee and Crane 2019). AM techniques offer several advantages over traditional manufacturing methods. One notable benefit is the reduction in energy consumption achieved by minimising material waste and eliminating machining processes. Additionally, AM allows for manufacturing complex parts, opening significant opportunities for innovation and technological advancements in various industries (Dhanesh, Dhanawade, and Bhatwadekar 2017; Sun et al. 2021; Tamez and Taha 2021; Verhoef et al. 2018). The utilisation of AM techniques enables the production of an extensive variety of materials, including ceramics, glass, metals, polymers, and composite materials. Two common power sources utilised in AM techniques are laser- and electron-beam-based (Sun et al. 2021). AM technologies are categorised into seven groups (Piedra-Cascón et al. 2021; Tamez and Taha 2021): vat-polymerisation (Tamez and Taha 2021), material extrusion, material jetting (Gülcan, Günaydın, and Tamer 2021), binder jetting (Ziaee and Crane 2019), powder-based fusion (Bhavar et al. 2017), sheet lamination (Zhang et al. 2018), and direct energy deposition (Dass and Moridi 2019).

In the powder bed fusion process, heat energy (a laser or electron beam) precisely fuses selected areas on the powder layer together to generate solid 3D structures (Bhavar et al. 2017; Sun et al. 2021; Verhoef et al. 2018). The powder bed fusion process comprises the subsequent prevalent printing techniques, including electron beam melting (EBM), selective heat sintering (SHS), laser powder bed fusion (LPBF) a.k.a. ‘selective laser melting (SLM)’, and selective laser sintering (SLS) (Dev Singh, Mahender, and Raji Reddy 2021; Dhanesh, Dhanawade, and Bhatwadekar 2017; R. Singh et al. 2019; Verhoef et al. 2018).

The LPBF process uses a high-power laser as a heat source to create layer-by-layer metal components by fully melting a selective area on the powder bed (Bhavar et al. 2017; R. Singh et al. 2019). In LPBF, a laser with a series of lenses focuses on the powdered material is mounted on top to consolidate the layer. The building platform descends once a layer is fused, and the coater arm creates a new layer on the bed. This procedure is repeated until the whole component is formed (R. Singh et al. 2019). Faster cooling rates, compared to traditional production methods, provide higher-quality structures. Therefore, LPBF has been extensively employed in aerospace, automotive, medical treatment, and industrial applications because of the excellent mechanical properties of LPBF-produced parts (Dev Singh, Mahender, and Raji Reddy 2021; Dhanesh, Dhanawade, and Bhatwadekar 2017).

When using LPBF, one of the key factors determining how much powder particles are melted is the laser energy density, which indicates the average energy exerted per unit of volume in a material. The energy density per unit volume, $E_v$ (J/mm³), is given by (Gotoh et al. 2022)

(1) $E_v=\frac{P}{\mathit{V}\times \mathit{\delta }\times \mathit{H}},$(1)

where P represents the laser power (W), V denotes the scanning speed (mm/s), H represents the hatch spacing (mm), and δ denotes layer thickness (mm) (Arısoy et al. 2017; Gotoh et al. 2022; Gu et al. 2013; Zheng, Peng, and Wang 2021). These key process parameters of LPBF are usually optimized to achieve the highest feasible density and to decrease porosity and surface roughness (Gotoh et al. 2022; Liu, Li, and Li 2019; Mahmoudi et al. 2017; Oliveira, LaLonde, and Ma 2020). Mahmoudi et al. (2017) found that a key element in obtaining desired component qualities is LPBF process parameter adjustment.

The 17-4 PH stainless steel (SS) is a commonly used metallic material (Mahmoudi, Elwany, Yadollahi, Thompson, Bian, and Shamsaei 2017) in various industries such as aerospace (Raj et al. 2007), marine (Arisoy, Başman, and Şeşen 2003; Raj et al. 2007), nuclear (Bhaduri et al. 1999; Lin et al. 2012), chemical (Lin et al. 2012), and medical (Garcia-Cabezon et al. 2023) due to its exceptional mechanical properties, including high tensile strength, impact strength, fracture toughness, and corrosion resistance (Kazior et al. 2013; Lin et al. 2012; Wu and Lin 2002; Zai et al. 2020). This study utilized the 17-4 PH SS powder to conduct the investigations due to its remarkable mechanical properties and cost-effectiveness.

Previous research on LPBF-manufactured 17-4 PH SS parts has focused on manufacturing parts with minimal porosity. The study conducted by Ponnusamy et al. (2020) examined the influence of laser power, laser defocus distance, layer thickness, and build orientation on the mechanical properties of 17-4 PH SS structures manufactured using LPBF. These four process parameters were optimized using a fractional factorial design to achieve the minimum porosity. (L. Huang et al. 2022) reported that a laser power of 220 W, a scanning speed of 0.416 mm/min, and hatch spacing of 0.011 mm, resulted in 17-4 PH SS parts with the appropriate density of 99.4%. Lee et al. (2020) examined the impact of process variables on produced 17-4 PH SS parts and estimated that a specific energy density level of 64.29 J/mm³ and a scanning speed of more than 1884 mm/s could achieve the fewest possible defects. The study conducted by Hu et al. (2017) aimed to explore the effect of scanning speed (ranging from 166.66 to 1666.67 mm/s), hatch spacing (ranging from 90 to 130 μm), and layer thickness (ranging from 20 to 40 μm) on the density, defect, and microhardness of LPBF manufactured 17-4 PH SS parts. They discovered that once the scanning speed is increased, the relative density first increases and subsequently drops. Furthermore, the influence of hatch spacing is less when the velocity is low and more pronounced when the velocity is high, within the specified range.

There are several applications where it is essential to make components with the highest possible density, as was noted in the review of previous research (Hu et al. 2017; L. Huang et al. 2022; Lee et al. 2020; Ponnusamy et al. 2020). However, there are several significant technical applications where the possibility to regulate and alter the degree of porosity is crucial. These include advancements in tissue engineering, lightweight structures, capillary structures, aeration or filtration components, medical implants, electrochemical components, implants that encourage bone fixation, and other uses (Abele et al. 2015; Faghri 2014; Gotoh et al. 2022; Stamp et al. 2009).

Fuel cells require highly porous surfaces for transport, and previously, these surfaces and components were made through another manufacturing process, which is time-consuming. On the other hand, LPBF offers a faster, cheaper, and easier method than conventional technologies and could be a promising manufacturing method for creating thin-walled porous structures that meet the necessary specifications. 17-4 PH is currently being investigated as a possible candidate for developing specific fuel cell components. Fuel cells can contribute to carbon capture and sustainability by providing efficient and low-emission electricity generation method and enabling the use of renewable fuels like green hydrogen. Electrodes in new fuel cell designs must be thin, mechanically strong, electrically conductive, and have a specific porosity to enable mass transport (Abele et al. 2015; Faghri 2014; Gotoh et al. 2022; Stamp et al. 2009). Therefore, to fulfill the needs of fuel cell applications, this study aimed to create thin-walled samples with controlled porosity percentages suitable for energy storage applications.

To the best of the authors’ knowledge, only two studies concentrate on developing porosity in 17-4 PH SS materials by varying LPBF process parameters. (Spierings, Wegener, and Levy 2014) maximised 17-4 PH SS material properties by optimising layer thickness, scanning speed, build orientation, and laser power using a full-factorial experimental design while generating parts with a defined degree of porosity. They found a strong relationship between the material’s density and the energy density that was delivered to the material. The Archimedes method was used in this study to measure the porosity range between <0.1% (with a 190 W laser power, an 800 mm/s scanning speed, and a 30 μm layer thickness) and 26.1% (105 W, 1300 mm/s, 50 μm). Abele et al. (2015) also manufactured 17-4 PH SS thin, porous structures by also varying and optimising LPBF process parameters, i.e. laser power (160–190 W), scanning speed (1000–1400 mm/s), and hatch distance (100–200 μm) using a central composite design. In this experiment, after the fabrication of the samples by an EOS M270 LPBF machine with a 200 W Yb-fibre laser, a theoretical approach was employed to assess porosity, which contains interconnected and isolated pores between 0.99% and a maximum of 17.35%. None of these studies produced thin materials with high porosity, which is desirable for porous transport layers (PTLs) and mass transport applications. This study aims to manufacture a 17-4 PH SS thin, porous transport layer with a higher range of porosities using LPBF. The influences of LPBF process variables, i.e. laser power, scanning speed, and hatch spacing, are investigated to generate porosity in as-built 17-4 PH SS layers. This work compares three approaches i.e. X-ray computed tomography (X-CT), buoyancy, and theoretical for measuring the porosity of additively built 17-4 PH SS components, and a statistical regression model was developed to predict porosity. Then, ten parameter sets were fabricated to optimise and validate the determined regression model. A gas permeability experimental setup is then used for measuring the through-plane permeability of three porous layers with the highest porosity levels.

2. Methodology

2.1. Material and equipment

Argon-gas-atomised 17-4 PH SS powder from Oerlikon was used for this research study. The chemical composition is listed in Table 1. The Morphologi G3 particle analysis system was used for powder characterisation and the average particle size was 25.67 ± 13.72 µm which were mostly spherical with a circularity average of 90.2 ± 12.4%.

Table 1. Composition of chemicals in 17-4 PH SS powder.

Chemical composition	Fe	Cr	Ni	Cu	Nb+Ta	C	Other
Value (wt.%)	73	17	4.5	4	0.3	0.07	<1.0

The LPBF of 17-4 PH SS was performed with the ORLAS Coherent CREATOR 3D metal printer (Coherent, Inc., California, USA), which is equipped with an internal fibre having a maximal laser power of about 250 W at the build platform that offers superior beam quality with a diameter of 40 µm. The LPBF process was conducted under a high-purity argon gas (99%) in the building chamber to maintain an oxygen level below 0.01% during the process. The temperature in the building chamber was maintained at 25–40°C. The scan strategy in which the scan vectors are disposed to the previous layer by 90° is applied to all fabricated samples. The standard manufacturing processing parameters for a fully dense optimised build are summarised in Table 2.

Table 2. Qualified manufacturing processing parameters of CREATOR 3D metal printer for fabrication of dense 17-4PH SS samples.

Parameters	Laser power (W), P	Scan speed (mm/s), V	Layer thickness (mm), δ	Hatch spacing (mm), H	Scan strategy (Shift angle), S
17-4 PH	110	1000	0.025	0.055	45° rotation between layers

2.2. Response surface methodology

The purpose of this study is to manufacture highly porous 17-4 PH SS samples. First, Minitab v19 (Minitab Inc., State College, PA, USA) was used to set up a design of experiments (DoE) to investigate the porosity of 5 mm cubic samples (Figure 1) by examining the LPBF process factors individually and their interaction effect. The main approach to determine the ranges of the parameters is derived from an analysis of the manufacturer’s recommended parameters as well as the literature review to understand the energy levels and their corresponding parameters resulting in the fully dense builds. Starting from these parameters as shown in Table 2, corresponding volumetric energy density is determined as the upper bound. Based on this upper bound, a central composite design is created that investigates the lower volumetric energy dose for the build while also investigating the effect of the individual parameters (power, scanning speed, hatch spacing, and layer thickness), with an aim to investigate the porosity and permeability as response.

Figure 1. 17-4 PH stainless steel cubic sample.

To account for non-linear effects, central composite design (CCD) was employed involving three variables (laser power, scanning speed, hatch spacing) and the extension factor of α = 1.6818. The extension factor is the distance between each star point from the centre point. The main advantage of using a CCD over a full factorial design is that it requires less experimental runs (20 vs. 125 runs) while providing more information about the response surface (Hinkelmann 2012; Ravichander et al. 2021). Twenty trials contain 8 factorial points, 6-star points placed at the distance of α from the centre point and 1 centre points which investigate the variability of the experiment. The factor levels and CCD can be seen in Table 3. Every numeric variable was assigned five levels: factorial points (−1, 1), star points (-α, α), and the centre point.

Table 3. The ranges of effective parameters.

Factor	Laser power (W), P	Scanning speed (mm/s), V	Hatch spacing (mm), H
−α	53.18	1263.64	0.061
−1	60	1400	0.075
0	70	1600	0.095
1	80	1800	0.115
+α	86.82	1936.36	0.129

According to the set of defined ranges shown in Table 3, a total of 20 trials of laser power, scanning speed, and hatch spacing were generated, as summarised in Table 4. The layer thickness, which is usually used for increasing the production rate, was kept constant at 0.025 mm for all samples to reflect the default setting for the selected material and LPBF machine. A scan strategy with 90° rotation between the successive layer was used for all samples to maximise the porosity of the as-built parts, as suggested by (Shi et al. 2022). To ensure repeatability, three replicas for each possible combination were produced, i.e. 60 cubes with a size of 5 mm for each. The porosity of the samples was evaluated (the method will be discussed in the section 2.3). A second-order regression equation was used to acquire a mathematical model for the estimation of porosity from the process variables using Minitab v19, i.e.

Table 4. Experimental design and its responses.

Run	Laser power (W)	Scanning speed (mm/s)	Hatch spacing (mm)	Laser energy density (J/mm^3)	X-CT Porosity (%)	Theoretical Porosity (%)	Buoyancy Porosity (%)	Mean ferret diameter (μm)
1	70	1600	0.095	18.42	38.70 ± 2.50	34.73 ± 0.87	32.80	27.44 ± 0.45
2	53	1600	0.095	14	Defect	Defect	Defect	Defect
3	80	1800	0.075	23.7	31.45 ± 1.18	28.15 ± 0.83	24.99	30.39 ± 0.779
4	70	1600	0.129	13.6	44.25 ± 2.76	40.47 ± 0.61	39.28	24.7 ± 0.69
5	80	1400	0.115	19.88	36.69 ± 2.26	30.20 ± 0.60	27.82	29.74 ± 1.36
6	60	1400	0.075	22.86	35.96 ± 2.96	30.32 ± 0.36	28.39	28.61 ± 1.18
7	70	1600	0.095	18.42	37.25 ± 1.33	33.89 ± 1.99	24.73	26.99 ± 0.71
8	60	1800	0.075	17.78	40.87 ± 4.57	37.58 ± 1.10	33.65	26.37 ± 0.48
9	70	1936	0.095	15.22	44.90 ± 4.14	39.15 ± 0.54	37.38	26.046 ± 0.54
10	60	1400	0.115	14.91	47.01 ± 1.72	38.25 ± 1.49	42.76	24.89 ± 0.36
11	87	1600	0.095	22.85	30.96 ± 5.26	28.15 ± 0.93	25.51	32.81 ± 1.68
12	70	1600	0.061	28.52	25.08 ± 0.59	25.84 ± 0.41	20.96	33.95 ± 0.33
13	80	1400	0.075	30.48	23.60 ± 1.42	22.58 ± 0.10	25.97	37.093 ± 2.6
14	70	1264	0.095	23.32	28.03 ± 0.66	28.41 ± 0.49	25.61	32.12 ± 0.91
15	70	1600	0.095	18.42	36.48 ± 2.63	33.43 ± 1.25	23.44	28.023 ± 1.07
16	70	1600	0.095	18.42	37.63 ± 1.44	34.70 ± 1.09	32.29	27.72 ± 0.66
17	70	1600	0.095	18.42	37.54 ± 0.69	31.58 ± 0.61	21.66	28.43 ± 0.19
18	70	1600	0.095	18.42	36.60 ± 1.46	33.63 ± 6.91	35.64	28.82 ± 0.28
19	80	1800	0.115	15.46	40.38 ± 3.41	36.28 ± 1.49	34.05	25.76 ± 0.85
20	60	1800	0.115	11.59	52.81 ± 3.85	51.25 ± 0.33	53.03	24.8 ± 0.38

(2) $\mathit{Y}=b_0+{\sum }_{i=1}^n{b}_i{x}_i+{\sum }_{i=1}^n{b}_{\mathit{ii}}{x}_i^2+{\sum }_{i=1}^{n-1}{\sum }_{j=i+1}^n{b}_{\mathit{ij}}{x}_i{x}_j+\mathit{e}$(2)

where Y is the response value, $b_i$ is the invariant coefficient of the model, $\mathit{e}$ is a random error, $x_i$, $x_i^2$ and $x_i{x}_j$ are the coefficients for the individual, squared, and combined terms in the equation, respectively (Shim 2021; G. Singh et al. 2021; Vilanova et al. 2020). ANOVA table and normal residual plots were examined to ensure the adequacy of the model. Response surface method(RSM) is used to optimise the input factors to get defined Y values (i.e. porosity) according to the required applications.

2.3. Porosity measurement techniques

Porosity is one of the most critical parameters to evaluate permeability, and therefore, multiple methods are used in this work to estimate the porosity accurately. In this case, porosity is measured based on the overall geometry and density of the sample (theoretical method), computer micro-X-ray tomography (µCT), and Archimedes principle. The first two methods are able to compute open and closed pores, while the last method is only able to estimate open pores. Open and closed pores are defined as pores that are interconnected with the external environment, and completely isolated from the outside surface, respectively (Li, Rong, and Li 2001).

2.3.1. Theoretical method

The theoretical method is used to estimate open and closed porosity. The calculation of porosity is determined by (Abele et al. 2015)

(3) $\mathit{Porosity}=\left(1-\frac{\mathit{m}/{\mathit{\rho }}_{\mathit{mat}}}{\mathit{V}}\right)\times 100$(3)

where V represents the volume of the sample, m denotes its measured weight, and ${\rho }_{\mathit{mat}}$ denotes the density of the material. The sample weight is obtained using an analytical balance (Denver Instruments, p-114, ±0.1 mg) and the sample volume is estimated by measuring the sample’s dimension using a digital micrometer (Mitutoyo Japan, ±2 μm).

2.3.2. X-ray computed microtomography (X-CT)

X-CT is a non-destructive method that takes X-ray images of samples at varying angles and uses them to create a three-dimensional reconstruction (Spierings, Schneider, and Eggenberger 2011). In this study, an X-ray computer tomography instrument (ZEISS Xradia Versa X-ray Microscopes, Germany) is used to acquire the images and create the three-dimensional reconstructions of the LPBF as-built samples. A voltage of 140 kV, a power of 21 W, and an exposure time of 2 seconds were used for all cubic samples. The voxel resolution was 13.6 µm. To reduce the data acquisition time, eight samples were stacked together during a single scan. The DragonFly Pro software (Object Research Systems, Montreal, Canada) was employed for analysis. DragonFly Pro’s manual segmentation method was employed to label regions of interest as either matrix or pore space, as shown in Figure 2. It should be noted that Ostu method was first used for segmentation but resulted in large difference of 21.47–38.60% between its outcomes and theoretical values (see Appendix A). Therefore, manual segmentation was used.

Figure 2. Segmentation of matrix and voids using ORS DragonFly pro (yellow and red colors are used to define the matrix and voids, respectively). (a) Original image. (b) Segmented image.

This approach measures open and closed pores with a significant investment of time, specialised equipment, and restricted accuracy of outcomes due to the methodology employed for image segmentation and image resolution (Shukla et al. 2019).

2.3.3. Buoyancy method

In the buoyancy approach, the porosity of the examined porous media is computed as follows (Shukla et al. 2019):

(4) $\mathit{Porosity}=1-\frac{{\mathit{V}}_{\mathit{solid}}}{V_{\mathit{bulk}}},$(4)

where V_bulk is the total volume of the sample and V_solid is the solid volume only. The total volume of the sample (V_bulk) is obtained from geometric measurements. Then, the volume of the solid (V_solid) is obtained by weighting the sample in air (S_a)and a fully wetting fluid of known density (ρ_IPA), in this case 2-propanol (S_IPA) (which is presumed to occupy all open pores of the sample). Archimedes principle is used, i.e (Shukla et al. 2019; Zou and Malzbender 2016),

(5) $V_{\mathit{solid}}=\frac{S_a-S_{\mathit{IPA}}}{{\rho }_{\mathit{IPA}}},$(5)

The schematic of the measurement setup is depicted in Figure 3. An analytical balance (Denver Instrument, p-112, ±0.1 mg) is employed for weight measurement. The Buoyancy method is a quick, repeatable, chemical-free, reliable, low-cost approach for characterizing porous material (Shukla et al. 2019).

Figure 3. The schematic shows the measurement of the sample’s mass in air and IPA.

2.4. Determination of permeability

Permeability determines the rate at which gases can pass through the porous material under certain pressure differentials. To measure the permeability of thin, porous samples, the pressure drops across the sample at varying gas flow rates were measured using the setup and methodology described in Carrigy et al. (2013); Pant, Mitra, and Secanell (2012). Briefly, a 2.5 × 1.4 cm² sample was manufactured and laminated between two 3 mm lamination sheets with an 8 mm diameter hole in the centre, and sandwiched between two acrylic plates that act as the pressure channels, using appropriate gaskets to prevent any leakage. The two acrylic plates contain a channel of 150 mm in length and a 15 × 2 mm² cross-sectional area, which contains an inlet/outlet and a port to measure the pressure.

Table 7 shows the process parameters of the porous media used for experimentation. Three samples were manufactured with varying process parameters to estimate permeability. Three pieces of each sample were tested to ensure the repeatability of the test.

As previously mentioned in Carrigy et al. (2013); Pant, Mitra, and Secanell (2012), nitrogen gas (PRAXAIR, UHP 5.0) is injected into the inlet channel by means of a mass flow controller (Cole-Parmer, Serial Number: 62704, Range: 0–5 SLPM), while the second channel remains open to the surrounding atmosphere. One port, in each channel, is connected to a differential pressure transducer (OMEGA, Serial Number: 422542, Range: 0–70 mbar). The data is recorded for a duration of 125 seconds, with a total of 25 measurements taken for each flow rate, and the average pressure differential from the last 20 readings is used as the final value. Figure 4 shows a schematic of the permeability measuring setup based on Carrigy et al. (2013); Pant, Mitra, and Secanell (2012).

Figure 4. An experimental equipment schematic which was used to measure permeability in the through-plane direction.

The evaluation of permeability involves measuring the pressure differential at 10 equally spaced nitrogen gas flow rates within a range of 0–2 standard litres per minute (slpm). To calculate the offset of the pressure transducer, a ‘zeroth period’, where the flow rate is set to zero, is run for 125 s and the measured differential pressure is recorded. At non-zero flow rates, the offset differential pressure is removed from the average data. The experiment was conducted three times to enhance the reliability of the obtained results. Pressure readings had an average standard deviation of less than 3.0% of the average value.

Darcy’s law governs fluid transport through a porous media at very low flow velocities (Re <1), and it is given by (Gostick et al. 2006; Mangal et al. 2015)

(6) $\mathrm{\nabla p}=-\frac{\eta }{B_v}\mathit{v}\to \mathit{\hspace{0.17em}}\frac{\mathrm{\Delta P}}{L}=\frac{p_2-p_1}{\mathit{L}}=-\frac{\eta }{B_v}\mathit{v},$(6)

where p is the gas pressure, η is the gas dynamic viscosity, B_v is the material permeability, v is the gas velocity with magnitude v, L is the sample thickness, and $p_1$ and $p_2$ are the high and low pressures across the porous media, respectively. The velocity in the porous medium is calculated by dividing the volumetric flow rate by the cross-section of the aperture across the porous media, i.e (Pant, Mitra, and Secanell 2012)

(7) $\mathit{v}=\frac{\dot{Q}}{\mathit{\pi }{D}^2/4},$(7)

where $\dot{Q}$ represents the volumetric flow rate measured by the mass flow controller, and D represents the aperture’s diameter in the porous material (i.e. 8 mm).

Combining and recombining Equations (6)(6) $\mathrm{\nabla p}=-\frac{\eta }{B_v}\mathit{v}\to \mathit{\hspace{0.17em}}\frac{\mathrm{\Delta P}}{L}=\frac{p_2-p_1}{\mathit{L}}=-\frac{\eta }{B_v}\mathit{v},$(6) and (7(7) $\mathit{v}=\frac{\dot{Q}}{\mathit{\pi }{D}^2/4},$(7) ), the permeability can be obtained by plotting the measured pressure drop vs flow rate and fitting the slope of the equation using MATLAB (Pant, Mitra, and Secanell 2012), i.e.

(8) $\mathrm{\Delta P}=\frac{4\mathit{\eta }}{\pi }\frac{L}{B_v{D}^2}\dot{Q}=\frac{4\mathit{\eta }}{\pi }\frac{L}{B_v{D}^2}\frac{\mathit{RT}}{\mathit{p}1}\dot{n},$(8)

Where $\dot{n}$ is the molar flow rate which is sometimes used for convenience.

3. Results and discussions

3.1. Comparison of porosity measurement methods

Table 4 summarises the mean porosity percentage and pore size outputs corresponding to three approaches with different laser power, scanning speed, hatch spacing, and standard deviation between the three replicates. In addition, Figure 5 shows the mean porosity percentage of the three approaches for each run. The maximum porosity is obtained in test number 20, corresponding to 60 W laser power, 1800 mm/s scanning speed, and 0.115 mm hatch spacing. Run 13 shows the lowest porosity, obtained with a laser power of 80 W, a scanning speed of 1400 mm/s, and a hatch spacing of 0.075 mm. Therefore, low laser power, high scanning speed, and large hatch spacing are beneficial for increasing sample porosity. In terms of managing porosity, as indicated in Table 4, the porosity values for each parameter set across three replicates fall within an acceptable range of standard deviation. This demonstrates effective control over the process parameters, ensuring the targeted porosity percentage is achieved. Furthermore, the method described in the manuscript yielded a ferret diameter range of 24.7–37.093 µm for pore size, which falls within the necessary range for applications such as fuel cells.

Figure 5. Comparing mean porosity of each run.

Figure 6 compares the three methods used to measure porosity in this study. All three methods gave similar results and clearly demonstrate that the porosity of the samples increases as the energy density decreases, ranging from 30.48 to 11.59 J/mm³. Furthermore, considering the similarities between the theoretical and the buoyancy method, the volume of closed pores is relatively small compared to the number of open pores which would contribute to transport.

Figure 6. Comparison of three porosity measurement methods.

3.2. Response surface analysis

Least-square fitting (Minitab software v19) is used to develop a regression model to represent the correlation between the porosity and the LPBF parameter, i.e. laser power, scanning speed, and hatch spacing. The obtained regression model is given by,

(9) $\mathrm{Porosity}\mathrm{\%}\left(\mathrm{Theoretical}\right)=6.2-0.622\left(\mathrm{P}\right)+0.036\left(\mathrm{V}\right)\text{break}+262\left(\mathrm{H}\right)+0.00952\left(P^2\right)-491\left(H^2\right)-0.000539\left(\mathit{P}.\mathit{V}\right)-3.65\left(\mathit{P}.\mathit{H}\right)+0.1952\left(\mathit{V}.\mathit{H}\right)$(9)

The mean absolute error (MAE), root mean squared error (RMSE), and $R^2$ are 0.58, 0.72, and 96.24%, respectively. These values demonstrate the good capability of the regression model in predicting porosity (L. S. Huang and Che 2008; Lu and Shi 2022). The normal probability plot in Figure 7(a) shows that the hypothesis of normality is met since the residuals are rather close to the red diagonal line. The residual plot in Figure 7(b) shows a random distribution of the residuals, and no obvious trend indicates that there is a constant variance between the residuals. Both plots (Figure 7(a-b)) confirm that the model meets the requirement of constant variance.

Figure 7. The plot of (a) normal probability, and (b) residual.

The analysis of variance (ANOVA) is shown in Table 5, which assesses the significance of each component within the regression model. The main effects of hatch spacing, laser power, and scanning speed are of great significance because they have a very small p-value of less than 0.05. Regarding quadratic effects, $p^2$ which represents laser power’s quadratic effects, is also significant. There is an interaction effect between laser power and scanning speed (P.V), laser power and hatch spacing (P.H), and scanning speed and hatch spacing (V.H) interaction is likewise significant (has small P-values).

Table 5. ANOVA results for the porosity percentage.

Source	DF	Adj SS	Adj MS	F-Value	P-Value	Comments
Model	9	2154.45	239.384	133.73	0.000
Linear	3	2056.58	685.527	382.96	0.000
Laser power, P (W)	1	665.42	665.416	371.72	0.000	Significant
Scanning speed, V (mm/s)	1	548.66	548.661	306.5	0.000	Significant
Hatch spacing, H (mm)	1	842.5	842.504	470.65	0.000	Significant
Square	3	24.22	8.072	4.51	0.007
$P^2$	1	22.89	22.89	12.79	0.001	Significant
$V^2$	1	0.01	0.013	0.01	0.933	Insignificant
$H^2$	1	1.65	1.647	0.92	0.342	Insignificant
2-Way Interaction	3	55.31	18.438	10.3	0.000
P.V	1	27.86	27.857	15.56	0.000	Significant
P.H	1	12.82	12.82	7.16	0.010	Significant
V.H	1	14.64	14.637	8.18	0.006	Significant
Error	47	84.13	1.79
Lack-of-Fit	4	18.34	4.585
Pure Error	43	65.79	1.53
Total	56	2238.59

The main effects of parameters on porosity are plotted in Figure 8(a). The impact of scanning speed and hatch spacing is positive; however, the laser power impact porosity negatively. The power of the laser determines how much heat is required to melt the powder layer and create an appropriate melt pool. However, reduced laser power may not melt the powder fully, or it may not penetrate deeply enough into the powder layer to fuse the successive layers together. Regarding the laser power impact, Figure 8(a) shows that decreasing the laser power value increases the porosity percentage from 43.43% to 61.40%. Yang et al. reported a similar observation that decreased the laser power for 17-4 PH SS, decreased the density by 2.2% (Yang et al. 2021).

Figure 8. (a) Parameter effect and (b) percentage contribution on porosity.

The scanning speed, or how fast the laser scans the powder layer to melt it, is crucial for increasing porosity while producing an LPBF part. Since the laser time on the metal powder is reduced when a higher scanning speed is used, the surrounding powder particles in the molten pool do not have enough time to melt fully before solidifying, leading to non-fusion and porosity. A similar trend was obtained since the scanning speed increased from 1263.64 mm/s to 1936.36 mm/s, and the porosity increased from 43.81% to 58.34% (Figure 8(a)). Chen et al. (2022). also claimed that when the scanning speed is too fast, defects like unmelted powder appear, and the relative density is reduced.

Hatch spacing refers to the distance between consecutive laser tracks made by a laser beam as it passes through a powder layer. Increasing hatch spacing may prevent the laser from overlapping enough, leading to inadequate particle melting and increased porosity. The effect of hatch spacing plays an important role in forming porosity, which increased from 37.88% to 61.77% with the increase of hatch spacing. This effect was also detected by Dong et al. for 316 L SS (Dong et al. 2018).

Additionally, Figure 8(b) provides the percentage contribution of the main factors and their interactions. Based on this data, it seems that the hatch spacing, laser power, and scanning speed have a dominant impact on the porosity, respectively. As seen in the bar chart, all interactions have a negligible impact on porosity.

Figure 9 shows contour plots and surface plots to investigate how the process parameters relate to the porosity of the sample based on the regression model. Two factors are varied, while a third is fixed to study their interactive influence on porosity. Figure 9(a–b) show the impact of laser power, and scanning speed when the hatch spacing is held constant (0.095 mm). The porosity shows an upward trend as laser power decreases and scanning speed rises. It indicates that increasing the porosity through the LPBF method requires employing a low laser power along high scanning speed. From Figure 9(c–d), it is observed that with the increase of hatch spacing at lower laser power, the porosity is increased. From Figure (e) and (f), it is seen that at 70 W laser power, porosity increases with the increase of either scanning speed or hatch spacing.

Figure 9. Response surface and contour plot for porosity percentage: (a) surface plot, (b) contour plot for the interaction between laser power and scanning speed, (c) surface plot, (d) contour plot for the interaction between laser power and hatch spacing, (e) surface plot and (f) contour plot for the interaction between scanning speed and hatch spacing.

3.3. Optimization

In the last part of our experimental research, we conducted validation tests using information from regression model. We adjusted the laser power, scanning speed, and hatch spacing settings to find the best combination to help us achieve the desired porosity range of 30–50% in the samples according to the achieved regression model. To increase the accuracy of our predictions, the insignificant terms ($V^2$ and $H^2$) were removed from the equation because they did not significantly impact the results. As a result, the fitted refined quadratic porosity model is obtained as Equation 10(10) $\mathit{Porosity}\%=8.6-0.602\left(\mathit{P}\right)+0.0375\left(\mathit{V}\right)+169\left(\mathit{H}\right)+0.00940\left(P^2\right)-0.000539\left(\mathit{P}.\mathit{V}\right)-3.65\left(\mathit{P}.\mathit{H}\right)+0.1952\left(\mathit{V}.\mathit{H}\right)$(10) :

(10) $\mathit{Porosity}\%=8.6-0.602\left(\mathit{P}\right)+0.0375\left(\mathit{V}\right)+169\left(\mathit{H}\right)+0.00940\left(P^2\right)-0.000539\left(\mathit{P}.\mathit{V}\right)-3.65\left(\mathit{P}.\mathit{H}\right)+0.1952\left(\mathit{V}.\mathit{H}\right)$(10)

Furthermore, the quadratic regression model was subjected to a process called ‘normalisation’ to analyse how various process factors and their combinations affect the final product (Equation 11). The process involves utilising Max-Min scaling, a technique that standardises the values in the model to ensure they fall within a uniform and comparable range. Therefore, terms with larger absolute coefficients have a greater impact on response than terms with smaller coefficients.

(11) $\mathit{Porosity}\%=30.29-10.047\hat{P}+7.92\hat{V}+8.9312\hat{H}+3.76{\hat{P}}^2+4.312\left(\widehat{\mathit{P}.}\hat{V}\right)-2.92\left(\hat{P}.\hat{H}\right)+3.1232(\hat{V}.\hat{H})$(11)

For optimisation, 10 combinations of factors and two replicas of each combination were created (Figure 10). The porosity values of these replicated samples were measured to confirm our predictions’ accuracy. Table 6 and Figure 11 display the results of a comparison between the estimated and the measured experimental outcomes of the optimal samples. The standard deviation between the regression model prediction interval and experimental results increases as energy density decreases. The maximum difference between the regression model’s 95% prediction interval and experimental results occurs at the minimum energy density, 11.2 J/mm³, which equals 25.71% as the energy density of 11.2 J/mm³ may not provide enough energy to fully melt the powder particles, leading to defect formation in the sample. While the energy density is above 14.2 J/mm³, the experimental results fall within the regression model’s 95% prediction interval, indicating that predictions and experimental findings agree. It means that 14.2 J/mm³ is the minimum energy density needed for 17-4 PH SS to fabricate fully porous samples without any defect failure. At insufficient laser energy density, energy is not enough to melt the powder particles effectively. As a result, the particles may not fuse together, leading to a lack of solidification and incomplete sample fabrication. This was observed in the cases where the sample fabrication failed several times repeatedly at the energy density of lower than 11.2 J/mm³. Regarding three samples with energy densities of 11.2 to 14.2 J/mm^3, which fall out of the regression model’s 95% prediction for two reasons. Firstly, it can be seen in the CT images (Figure 12), there are defects inside samples 3, 5, and 6. Secondly, a micrometer was used to measure the dimensions as the micrometer is typically used for measuring flat surfaces and because the cube samples have a significant defect on the surfaces and have a curvature, and the spindle diameter of the micrometer is bigger than the cross-section of the samples so leading to excess volume and inaccuracy in volume measurement as well. As a result, defects lead to over predicting porosity measurement. So, in order to produce porous samples, the minimum required energy density should be considered.

Figure 10. 17-4 PH SS optimized specimens.

Figure 11. Mean porosity vs. Laser energy density of optimized 17-4 PH SS results.

Figure 12. X-CT images of failed samples.

Table 6. Optimal setting and predicted porosity.

Run	Laser power (W)	Scanning speed (mm/s)	Hatch spacing (mm)	Laser energy density (J/mm^3)	Experimental porosity (%)	95% prediction interval (PI)
1	60	1936.36	0.129	9.64	Not fabricated	_
2	53.18	1936.36	0.108	10.15	Not fabricated	_
3	70	1936.36	0.129	11.24	66.72 ± 0.05	(45.59, 52.75)
4	70	1934.05	0.129	11.25	61.72	(45.55, 52.68)
5	65.28	1867.43	0.099	14.15	52.93 ± 1.41	(40.095, 45.806)
6	70	1600	0.123	14.22	41.40 ± 0.20	(36.713, 42.408)
7	70	1600	0.105	16.63	36.32 ± 0.36	(33.071, 38.596)
8	82.21	1568.61	0.129	16.30	36.01 ± 0.30	(30.752, 37.214)
9	66.67	1859.49	0.072	19.95	34.59 ± 0.21	(30.721, 36.714)
10	70	1600	0.091	19.30	32.37 ± 1.68	(29.950, 35.479)

3.4. Permeability measurements

Permeability experiments and the R-squared of the results are shown in Table 7. Three samples of the same run were measured to assess repeatability, named samples a, b and c. Furthermore, for each test three experiments were performed. Figure 13 shows the pressure drop vs. flow rate for all three repeated tests for sample #1-piece a (41.40% porosity). All three experiments provide similar results, and the predicted permeability had a standard deviation of only 0.34% of the average (The MFC and PT values for the actual and average flow rate and pressure gradient of sample 1-piece a are shown in Appendix B.1).

Figure 13. Test repeatability for sample #1-piece a.

Table 7. Through-plane permeability for each sample.

Sample	Laser power (W)	Scanning speed (mm/s)	Hatch spacing (mm)	Laser energy density (J/mm^3)		${\mathit{B}}_{\mathit{v}}\left({10}^{-11}\mathit{\hspace{0.17em}}{\mathrm{m}}^2\right)$	${\mathit{R}}^2$
1	70	1600	0.123	14.22	Piece a	9.00 ± 0.031	(0.9979–0.9985)
					Piece b	6.07 ± 0.015	(0.9992–0.9994)
					Piece c	9.41 ± 0.039	(0.9971–0.9981)
2	82.21	1568.61	0.129	16.30	Piece a	4.45 ± 0.020	(0.9972–0.9979)
					Piece b	4.73 ± 0.011	(0.9987–0.9991)
					Piece c	4.47 ± 0.023	(0.9979–0.9984)
3	70	1600	0.091	19.30	Piece a	1.39 ± 0.004	(0.9990–0.9993)
					Piece b	1.72 ± 0.002	(0.9970–0.9974)
					Piece c	1.44 ± 0.001	(0.9972–0.9976)

Figure 14 shows the pressure drop vs. flow rate curves for samples 1, 2, and 3 with porosities of 41.40, 36.01 and 32.37%, respectively. The permeability is inversely proportional to the slope of the lines and the summarised data are presented in Table 7. Permeability increases with porosity as expected based on Kozeny–Carman equation.

Figure 14. Pressure drop vs. flow rate for samples#1,2 and 3.

4. Conclusion

In this study, a response surface methodology is employed to optimise LPBF process parameters to increase the porosity of 17-4 PH SS samples for applications requiring a certain degree of porosity. A laser power of 53.18–86.82 W, scanning speed of 1263.64–1936.36 mm/s, and hatch distance of 0.061–0.129 mm were chosen for producing porous structures. The sample porosity was estimated using X-CT, theoretical analysis, and buoyancy analysis, and a predictive regression model was developed using the RSM to predict the impact of LPBF process parameters on material porosity. Thin-wall samples of varying porosity were manufactured and analysed to evaluate the permeability of porous samples. The results are summarised as follows:

• The porosity of the 17-4 PH SS samples exhibits an upward trend as the energy density drops. It is feasible to produce theoretical porosity values ranging from 51.25 ± 0.33 to 22.58 ± 0.10% with an energy density between 11.59 and 30.48 J/mm³.

• It has been shown that the development of porosity in 17-4 PH SS depends on hatch spacing, laser power, and scanning speed, respectively.

• Through the optimisation process, it is found that when the energy density exceeds 14.2 J/mm³, it is feasible to use 17-4 PH stainless steel to produce porous samples, without significant occurrence of fragmented samples.

• The results of the permeability evaluation demonstrate a clear pattern: when the volumetric energy density decreases within the range of 19.30–14.22 J/mm³, there is a corresponding rise in the permeability coefficient, ranging from 1.39 to 9.41 ×${10}^{-11}$ m².

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author [A.J.Q], upon reasonable request.

Additional information

Funding

Funding provided by the Future Energy Systems (FES) grant number FES-T06-Q05 is highly appreciated.

Notes on contributors

S. Sardarian

S. Sardarian is a graduate student in the Mechanical Engineering department at the University of Alberta, Canada, pursuing an MSc. Specializing in additive manufacturing. She completed her Meng (2014) in Biomedical Engineering from the University of Birmingham, United Kingdom. Her research interests focus on the fabrication and characterization of additive manufacturing products, and optimizing additive manufacturing processes.

S. Dehgahi

S. Dehgahi is a PhD in Mechanical Engineering with extensive experience in metal additive manufacturing, material science and corrosion engineering. Her current research interest includes laser powder bed, wire arc and fused deposition modeling techniques. Currently, she is a postdoctoral researcher at university of Alberta.

F. Wei

F. Wei is a PhD in Mechanical Engineering with extensive experience in experimental analysis of mass transport in low platinum loading polymer electrolyte membrane fuel cells, with special attention to water transport. His research interests include fuel cells and water electrolysis.

M. Secanell

M. Secanell is a Professor in the Department of Mechanical Engineering at the University of Alberta, Canada, and the director of the Energy Systems Design Laboratory. He received his Ph.D. (2008) and M.Sc. (2004) in Mechanical Engineering from the University of Victoria and a B.Eng. degree (2002) from the Universitat Politècnica de Catalunya (BarcelonaTech). His research interests are in the areas of: a) analysis and computational design of electrochemical energy technologies, such as polymer electrolyte fuel cells, polymer electrolyzers and flywheels, b) fabrication and characterization of polymer electrolyte fuel cells and electrolyzers, c) finite element analysis, and d) multidisciplinary design optimization.

A.J. Qureshi

A.J. Qureshi is an associate professor at the University of Alberta and leads the Additive Design and Manufacturing Systems (ADaMS) Laboratory in the Mechanical Engineering Department. His work includes developing advanced AM systems and materials, such as plasma-transferred arc systems for metal-ceramic parts, robotic wire arc additive manufacturing, and 4D ferromagnetic polymer-metal composites for printing magnets. He also focuses on the quality control of 3D printed parts with in-situ non-contact metrology. His contributions extend to digital design, robotic additive manufacturing, engineering design processes, and manufacturing systems engineering and industry 4.0.

Appendices

Appendix A

Comparison of X-CT results based on the Ostu method with theoretical and Buoyancy results

Figure A1. Comparison of three porosity measurement methods.

Appendix

B

During the experiment, readings are taken of the pressure drop and gas flow rate vs. time for each sample type. The MFC and pressure transducer values for the actual and average flow rate, and pressure gradient of sample 1(a) are shown here. At each set point, the steady state is clearly obvious, with fluctuations being negligible in comparison to the overall changes.

Figure A2. Oscillatory and average volume flow rate, and pressure gradient readings for sample#1(a).