1 Introduction

Laser powder bed fusion (L-PBF) technology has emerged as a new manufacturing candidate to produce critical parts in the automotive, aerospace and biomedical sectors. The advantages of this technology are well-known: weight reduction, geometric complexity for functionalised products and near net-shape production. However, the path towards a complete maturity of this technology is still challenged by internal defects, which appear to be typical of the process [1, 2].

Limiting the presence of defects in L-PBF parts is essential to ensure high mechanical properties. The mechanism of defect formation has been widely investigated in the literature. Simulation and analytical models [3, 4] as well as experimental campaigns [5, 6] were carried out to determine in which condition it is possible to obtain fully dense parts. For this purpose, process maps have been developed to identify the optimal process parameters (usually laser power and laser speed) with respect to the porosity content [7,8,9,10], even if defects can also occur when optimal process conditions are assumed [11].

The concept of a process map linking porosity to process parameters can be further simplified considering a synthetic index known as energy density, which is used to summarise the energy level per unit volume considered during layer melting. In particular, the volumetric energy density VED (J/mm3) for a pulsed laser is defined as:

$$E_{d} = \frac{P \cdot t}{{d_{p} \cdot d_{h} \cdot z}}$$
(1)

where P (W) is the laser power, t (μs) is the exposure time, dp (μm) is the point distance, dh (μm) is the hatch distance and z (μm) is the layer thickness.

Low-energy values result in a lack of fusion (LOF) porosity, which means that the energy is not sufficient to melt the powder fully, resulting in large irregular porosities spread all across the part [12]. High-energy density values result in over-melting, usually referred to as keyhole porosity [13]. At high-laser power and scan speed, the balling effect takes place [14, 15]. In this condition, the molten track breaks into droplets and it does not solidify uniformly, generating defects in the final part. In the region between these energy density limits, the steady region is used to denote the range of values ensuring the complete melting of the track and bonding between adjacent layers.

Different authors [16, 17] showed that parts with the same static properties can be printed using a small range of process parameters (± 10%) and values of the energy densities in the steady region. Furthermore, according to these papers, the energy density alone can be used successfully to predict the mechanical properties of the parts despite changes in the process parameter settings determining the same energy density. In conclusion, it is a standard practice to assume that the mechanical properties of L-PBF parts can be predicted easily considering the energy density value only, without the need to specify the specific parameter setting.

This work investigates how tensile properties, namely UTS, YS and elongation, vary when a large range of energy densities are used, and different process parameter combinations are used to obtain the same level of energy density. The experimental results show that while the energy density can predict UTS and YS, the porosity structure, defined as the distribution of volume, position and shape of the porosity inside the sample, plays an important role in predicting the elongation.

The porosity structure can be detected using XCT. The use of XCT to characterise the influence of the internal structure of L-PBF parts is well established in the literature [18,19,20,21], and [22]. Porosity in L-PBF can be divided into two main categories according to Snow et al. in [11]: the first is made of systematic flaws due to the suboptimal selection of process parameters. In contrast, the second class is represented by random flaws, which can be ascribed to random and unpredictable fluctuations in the quality of materials and processes, such as the natural variability of the powder feedstock, the irregular layering of particles and the random occurrence of atmospheric changes. The former group of defects can be avoided by selecting the appropriate energy density region, i.e., the steady region (Fig. 1), so as to avoid keyhole porosity, balling and a lack of fusion conditions. On the other hand, random flaws cannot be predicted and can occur even when optimal process parameters are used.

Fig. 1
figure 1

Relationship between part density and energy density

Full size image

Kim et al. [23] studied the porosity structure of Co-Cr disks produced via L-PBF using different combinations of process parameters, with different process settings determining the same energy density. In this work, speed and hatch distance were varied and, as a result, two energy density levels (30.5 and 60.9 J/mm3) were obtained with two different combinations of process parameters each. According to this study, the mean density of samples sharing the same energy density was similar even if characterised by a different porosity structure measured via XCT.

The influence of porosity on the static properties of manufactured parts was also investigated in two recent papers. Yang et al. [24] studied the influence of linear energy density (evaluated as laser power divided by laser speed) and the VED on AlSi10Mg samples produced via L-PBF, showing that the number of pores decreased as both the power and the scanning speed decreased. In their study, the authors provide information about the resulting tensile properties, but no statistical analysis of the correlation between pore structure and the mechanical performances was shown. In Salarian et al. [25], the pore structure of L-PBF specimens is correlated to their tensile behaviour using Inconel 625. The experiment entailed varying the laser power and keeping the other parameters fixed. They found that the pore morphology influenced strain to failure, but no statistical evidence is provided.

Zhang et al. [26] studied the relationship between porosity and the ductility of magnesium alloy in high-pressure die casting. The result showed that local porosity played a primary role in determining the elongation of the samples. Erickson et al. [27] used a finite element modelling method to simulate different porosity networks based on real data from additive manufacturing experiments. Tensile specimens were tested virtually, and the relationship between porosity and tensile properties was investigated using a descriptor function that considered the volume and the position of pores. A summary of the literature on the influence of porosity structure on final part properties is reported in Table 1.

Table 1 Summary of the literature review
Full size table

This paper explores the use of the VED as a unique indicator to predict UTS, YS and elongation of 316L stainless steel parts produced via L-PBF. A specific experimental campaign is carried out to show that the porosity structure can also be relevant to predict mechanical properties. In particular, the paper presents a new model, combining the VED with a few indicators representing the porosity structure as a viable solution to represent the tensile properties completely.

The paper is organised as follows. In Sect. 2, the experimental design and procedures are described. In Sect. 3.1, the results of the apparent density and tensile properties for all samples are described and discussed. A regression equation that predicts UTS based on the energy density is estimated. In Sect. 3.2, a fractographic and microstructural analysis of selected samples at a specific energy density value is carried out. In Sect. 4, the porosity structure is analysed qualitatively and quantitatively. In conclusion, a model predicting elongation based on the porosity index is presented.

2 Experimental procedures

2.1 L-PBF machine and material

Tensile test samples were produced using a L-PBF Renishaw AM250 system. The industrial machine is equipped with a Nd:YAG laser working in pulsed mode; the maximum power is 200 W and the laser spot diameter is 70 μm at the focal position. The material used in this study was stainless steel powder 316L (LPW Technology Inc.), with a size range between 15 and 45 μm, produced with the gas atomisation process (Fig. 2).

Fig. 2
figure 2

SEM image of AISI 316L powder

Full size image

The chemical composition provided by the manufacturer is shown in Table 1, and it is compliant with AM standard ASTM F3184-16.

2.2 Process parameters

Process parameters were selected following the procedure described in [16]. The idea is to select different combinations of process parameters resulting in predefined values of energy density values. For the present work, samples were built at three levels of energy density: 59, 103 and 180 J/mm3. The smaller value, 59.2 J/mm3, belongs to the steady region of energy density as defined in Fig. 1, and it was selected based on our experience with the machine and a preliminary experimental campaign not reported here. The higher value, 180 J/mm3, is beyond the limit between the steady region and the balling/keyhole region.

The process parameter ranges considered for the generation of the different conditions (called ‘treatments’ in Table 2) were large compared with previous works [16, 17] because the objective is to study the influence of a large variation of process parameters. In this work, the range considered for the individual parameters is ± 50–100%:

  • Exposure time m, 75 ≤ t ≤ 280 µs.

  • Point distance 35 ≤ dp ≤ 85 µm.

  • Hatch distance 75 ≤ dh ≤ 124 µm.

Table 2 Chemical composition of AISI 316L powder in wt%
Full size table

Power was varied at two values only: 150 W and 200 W. Power values lower than 150 W did not ensure full powder melting even when varying all the other parameters. On the other hand, 200 W is the maximum power available in the industrial system.

Two samples were produced for each treatment. The experimental design could not be a standard 2 k factorial design because of the constraint on the energy density value. The treatments in Table 2 do not result in the exact value of energy density, but a slight variation of ± 2 J/mm3 was deemed acceptable.

The meander scanning strategy was applied to all samples. In this configuration, the laser moves in a straight line vector from each side of the border. The scanning lines’ direction is rotated by 67° at each layer. Hatch lines were scanned first, followed by two contour lines. All samples were built in the vertical position (90°) and no preheating was applied.

2.3 Mechanical properties

Samples were characterised in terms of apparent density, cross sections and tensile properties. Archimedes’ method was used to evaluate the apparent density of each sample. An electronic scale with a kit for density measurement was used (Sartorius YDK 01). The apparent density ρA was evaluated according to the following formula:

$$\rho_{A} = \frac{{W_{a} \cdot \rho_{fl} }}{{W_{a} - W_{fl} }} [{g/cm}^3],$$

where \(W_{a}\) [g] is the weight of the specimen in the air, \(W_{fl}\) [g] is the weight of the specimen in water and \(\rho_{fl}\)[g/cm3] is the density of the water. Measurements both in water and air were repeated three times. A suitable measurement method should be identified to analyse the porosity structure. There are typically three methods to measure part porosity content: Archimedes method, metallurgical sections and XCT [28]. Archimedes method is considered reliable and accurate but provides only a macroscopic result, as specific information on the position, shape and size of pores cannot be derived. On the contrary, metallurgical sections can provide location and size information on pores but only on predefined planes, and a large amount of cross-sectional analysis is required to obtain statistically representative data on part density. Moreover, the pores detected in 2D images can provide only a general indication of the size and shape of the actual 3-dimensional volume, as shown in Fig. 3. While a spherical pore can be easily observed in different cross-sections resulting in several circular shaped 2D voids (see Fig. 3a), a single lack of fusion pore might appear as a set of small pores in different sections (see Fig. 3b). Therefore, detecting irregular pores with metallurgical sections might generate large variability and less accuracy than Archimedes method, as results strongly depend on the analysed sections. X Ray-CT allows full 3D information on the pores’ size, shape and position to be obtained, so that a complete characterisation of the porosity structure can be ascertained.

Fig. 3
figure 3

D reconstruction of pores produced by the L-PBF process

Full size image

Tensile properties were computed according to standard ASTM E8/E8M-16a, considering a geometry of the tensile specimens shown in Fig. 4. The machine used for the tensile test was an MTS Alliance RF/150. Samples were tested in the ‘as-built’ condition, without any post-processing.

Fig. 4
figure 4

Tensile specimen dimension and coordinate system, dimensions are in mm

Full size image

Samples were prepared by grinding and polishing, and V2A etching was used to perform the microstructural analysis.

2.4 XCT measurement

The tensile test samples were analysed by X-ray Computed Tomography. Scans were performed using a Nikon XT H 225 machine. Considering only the gauge length as the region of interest, samples were positioned close to the X-ray gun to obtain a high resolution, with a voxel size of 14.8 × 14.8 × 14.8 μm3. During all scans, the scanning parameters were kept constant. 10 W of power and an acceleration voltage of 150 kV were used. A 1.25 mm Cu filter was used throughout all the measurements to reduce the beam hardening effect. The scan parameters are reported in Tables 3, 4.

Table 3 Process parameters used in the experimentation
Full size table
Table 4 XCT scanning parameters
Full size table

The power of the XCT was kept below 10 W, with a standard focus setting. Above this power, the auto-defocus setting was used to avoid damage to the detector. Each sample was positioned in the XCT using a fixture, which allowed us to obtain the XCT measurements of the same portion of the sample.

Reconstruction was performed using Nikon CTPro 3D, and surface determination was performed using VGStudio MAX 3.0. The local iterative surface determination algorithm was used to create the STL file with a search distance of 4 voxels. The region of interest (i.e., the part and the pores) was converted to mesh using the VGStudio MAX ‘Precise’ setting. The threshold was selected manually, and it is the starting point for the iterative surface reconstruction.

The surface was divided into the individual pores using Matlab and the geom3d package [29]. The procedure allows the properties of each pore to be measured, i.e., the volume V; the position of the centroid described using a cylindrical coordinate system in which the radial position is indicated with ρ; the surface area, A and the bounding box. The bounding box refers to the elongation of each sample along the X, Y and Z planes (see Fig. 5) where ΔX = Xmax – Xmin, ΔY = Ymax – Ymin, and ΔZ = Zmax – Zmin represent the elongation of each pore along the three different directions.

Fig. 5
figure 5

Example of Bounding Box

Full size image

Eventually, the sphericity of the pore was evaluated as [30]:

$$\psi = \left( {\frac{{36 \cdot \pi \cdot V^{2} }}{{A^{3} }}} \right)^{1/3}$$

where V represents the pore volume and A the surface area. A sphericity index close to 1 means that the shape of a pore is similar to a sphere. As the sphericity index decreases, the shape of the pore becomes more irregular.

All pores with less than 23 voxels were considered ‘noise’ and eliminated from the analysis.

2.4.1 Porosity indexes

Several metrics have been proposed in the literature to characterise pore networks. The most commonly used are the pore with the maximum volume, total pore count, average equivalent pore diameter and maximum equivalent pore diameter [27]. For the present work, two indexes were used based on the information obtained in the literature. The objective was to identify two indexes that could consider the amount of porosity and the distribution of the pore location within a sample. These two aspects (volume and position) are considered the most important features affecting the mechanical properties [26, 31], and [32]. Chawla and Deng [31] investigated the effect of the pore structure on porous sintered steel materials, and they found that pore clustering acts as stress concentration, reducing the tensile and fatigue properties of the parts. Biswal et al. [32] investigated the effect of the pore structure on the fatigue properties of additively manufactured Ti6Al4V alloy. Their results showed that a critical aspect is the location of the pores: pores close to the surface significantly decrease the mechanical performance. The results obtained by Zhang et al. [26] were discussed in the introduction. In conclusion, two indexes of porosity are considered in this paper to study the influence of the pores’ volume and position on the mechanical properties of the parts:

Maximum Volume Reduction along the building direction, Π, an index proposed by [26] for high-pressure die casting processes. The index is computed by dividing the scanning region of each sample in a set of layers, considering the Z-axis (i.e., the building direction) as reference. In our case, a set of 150 layers was considered with a height of 0.05 mm each, which corresponds to the layer thickness of the L-PBF process. In other words, the first layer is the one between 0 mm and 0.05 mm, the second layer is constrained by 0.051 and 0.100 mm and so on. The pores with the centroid belonging to each layer are then extracted and their volumes summed up. For each sample j, the worst layer (i.e., the layer with the highest porosity) is then selected as well as the corresponding value of total pore volume indicated with Πj. Πj combines the effects of pore volume and spatial correlation as high values of Πj indicate the presence of pores concentrated in a small region of the sample.

Radial Equivalent Distance, RED. The radial equivalent distance is an index that weighs the pores’ volume based on their distance from the centre of the sample in the XY plane. This index is based on the concept that the most critical pores are large pores near the edge of the sample; the less critical ones are small pores near the centre [32]. The RED index is based on the porosity index defined in [27], where it was found to correlate with the tensile properties. More specifically, the RED index is given by:

$${\text{RED}}_{j} = \frac{1}{{V_{{{\text{tot}}}} }}\sum\limits_{i = 1}^{{N_{j} }} {V_{i} e^{{\frac{{ - \left| {g - \rho_{i} - r_{eq,i} } \right|}}{g\gamma }}} }$$
(2)

where Vtot is the total volume of the gauge length, Nj is the number of pores in the j-th sample, g is the nominal radius of the sample in the gage, ρi is the radial position of the i-th pore in the XY plane, req,i is the equivalent radius of the i-th pore and γ is a smoothing parameter. The weight function selected is exponential with smoothing parameter γ. A small value of γ results in less weight imposed on the pores far away from the centre, a larger value of γ results in a slower decay of the weight function, therefore reducing the effect of the distance of the pores on the value of the index. In our case, γ was set equal to 0.2 [27].

3 Tensile tests results and discussion

In this section, the results of the tensile tests along with the fractographic analysis are discussed. A regression model is finally proposed to predict UTS based on the VED.

3.1 Static mechanical properties

The results of the mechanical properties of the samples are listed in the Appendix. The density of all samples is higher than 94% (considering 7.98 g/cm3 as the reference value). The apparent density changes with the VED as expected. The scatterplot in Fig. 6a also shows that as the VED increases, the variability of the apparent density increases as well and high-density samples can sometimes also be obtained with large values of VED. Similar results were obtained in [33]. The two samples at 180 J/mm3 resulting in low apparent density were produced with different settings of process parameters, therefore their low performances cannot be ascribed to the processing conditions but to the inevitable variability of the process.

Fig. 6
figure 6

Mechanical properties of 316L samples during the different treatments (Table 2) b UTS, c Yield strength, d Elongation El %. Bars represent ± 1 standard deviation

Full size image

The range of energy density between 59 and 103 J/mm3 belongs to the steady region as identified in Fig. 1,

while at 180 J/mm3, the apparent density is lower, indicating keyhole and balling phenomena. Tensile test results are illustrated in Fig. 6b–d. UTS and YS show a linear reduction in energy density, as expected based on the apparent density data. Dotted horizontal lines were added in correspondence to the reference values of AISI 316L processed via L-PBF according to standard ASTM F3184-16 (UTS = 530 MPa, YS = 240 MPa, and El = 30% for the annealed condition). UTS and YS are also highly correlated in the range of energy density considered, as shown in

Figure 7, showing a Pearson’s correlation coefficient equal to 0.808 (with a 95% confidence interval of [0.652;0.898]).

Fig. 7
figure 7

Correlation between UTS and YS

Full size image

The variability observed on the elongation is much larger than the one observed on UTS and YS and appears to be more severe when the optimal VED (59 J/mm3) is assumed. Moreover, the elongation seems to be driven by other factors than process parameters and VED as different values of elongation can be observed both on different treatments at the same VED and on different replicates during the same treatment.

Table 5 shows a synthetic summary of mechanical properties observed in our study along with the ones reported in the literature.

Table 5 Mechanical properties of 316L processed with L-PBF
Full size table

In summary, the macroscopic characterisation of our experimental study showed that:

  • UTS and YS decrease as the VED increases. Despite the reduction in UTS and YS, the resulting properties are coherent with the reference values for the material. In general, it appears that even a considerable variation of process parameters (and VED) does not cause a considerable variation in UTS and YS. UTS and YS are highly correlated in the process window considered.

  • Elongation varies significantly among the treatments and among replicates in the treatments.

Based on these results, a linear model can be fitted to describe UTS as a function of the energy density VED (note that YS cannot be included as a regressor, as it is highly correlated with UTS).

The estimated model \(\widehat{UTS}({\text{VED}})\) is given by:

$$\widehat{UTS} = 574.64 - 39.13 \cdot VED (\text{adj-R}^{2}=73.04\%).$$

The regression equation indicates a statistically significant decrease in UTS as energy density VED increases; this result is expected because of the considerable variation of energy density and process parameters considered in the experiment. Nevertheless, all the samples sharing the same energy density value show similar UTS values (as visible in Fig. 6b). This finding was unexpected because the large variation of individual process parameters was supposed to influence UTS (and YS); the result shows that using the same energy density does not influence UTS and YS even when a large variability of process parameters is considered.

On the contrary, it is not possible to derive a relationship between the elongation and the energy density, and therefore a different approach should be considered. The analysis of the elongation data will focus on the samples produced at the lowest energy density value only. In fact, this value belongs to the steady region of the parameters (apparent density > 99%) and low-energy density results in high build rates, too. Therefore, these parameters are the most likely to be used in all industrial environments.

First, a fractographic analysis is performed to investigate the different fracture surfaces obtained in the tests, and later, a more detailed analysis of the XCT data is carried out. The objective is to find an equation to predict the elongation values with the porosity indexes defined in Sect. 2.4.1.

3.2 Fractographic analysis

The fractographic analysis focuses on samples produced at energy density level 59 J/mm3. The detailed elongation results at 59 J/mm3 are illustrated in Fig. 8, where elongation data are visualised for each treatment level (1–6, as stated in Table 3).

Fig. 8
figure 8

Elongation values at treatment level for Ed = 59 J/mm3. Bars represent ± 1 standard deviation

Full size image

Samples produced at P = 150 W are characterised by a lower elongation than samples at P = 200 W. Furthermore, sample S12 (treatment 6) printed at P = 200 W presents a low elongation value, while its replicate (sample S11) shows standard properties.

The effect of changing power at a fixed energy density on tensile properties of L-PBF parts was already investigated in the literature [24]. Using AlSi10Mg powder, the authors found that the power influences the UTS, while also showing a limited effect on the elongation. However, results obtained in [24] for aluminum alloy cannot be transferred to our case as the material used in our study is different.

An interesting result observed in our experiments is the variability of elongation values observed on specimens produced with the same parameters (same treatment). To better study this variance, SEM images of fracture surfaces and cross sections on four reference samples were analysed. The reference samples are selected as replicated conditions of two treatments, namely treatments 3 and 6; in these two conditions, the replicated samples show a large variability of elongation values.

The samples considered for the SEM analysis are reported in Table 6.

Table 6 Reference samples used for SEM analysis
Full size table

In Fig. 9, the SEM fracture surfaces of two samples produced using treatment 3 are illustrated. Sample S5 in Fig. 9a obtained an elongation of 44%, while sample S6 in b resulted in low elongation (18.5%). In the first sample, the fracture surface shows unmelted particles, especially at the centre of the surface. In addition, the upper edge contains a pronounced shear lip. In the latter case, several unmelted particles are visible on the surface, which explains the low elongation. The fracture surface is homogeneous, and the shear lip is not visibly different from the previous case.

Fig. 9
figure 9

SEM images of the fracture surface of replicated samples produced using treatment 3 and P = 150 W a Sample S5, b Sample S6

Full size image

In Fig. 10, fracture surfaces of samples produced using treatment 6 are shown. Sample S11 in Fig. 10a obtained an elongation of 55%. The fracture surface has a homogenous structure and no visible defects are detected. The dimples are visible only at high magnification. Sample S12 in Fig. 10b is characterised by a low elongation (27%). The fracture surface is entirely different from its replicate in Fig. 10a. Dimples are visible at lower magnification, and the shear lip is present in the upper part of the specimens as it was for the sample in Fig. 9a. Cavities and minor porosity are found on the surface.

Fig. 10
figure 10

SEM images of the fracture surfaces of replicate samples using treatment 6 and P = 200 W a Sample S11, b Sample S12

Full size image

Samples were cross-sectioned and polished to obtain SEM images of defects. The porosity found for the reference samples is shown in Fig. 11. Samples S5 and S6 are characterised by large and irregular porosity, probably due to a lack of fusion. The detected defects have a size of around 100 μm and are scattered along the entire surface. In samples S11 and S12, a few defects are found, mainly with a regular shape. However, irregular pores are also detected for sample S12. Compared with the low-power samples, the irregular pores found at P = 200 W have a smaller size (around 50 μm).

Fig. 11
figure 11

SEM cross-sectional images for reference samples. a Treatment 3, elongation 44% (Sample S5), b treatment 3 (Sample S6) elongation 18.5% and c treatment 6, elongation 27% (Sample S12)

Full size image

Generally, pores detected for P = 150 W are large and irregular, while at P = 200 W, spherical pores are mostly found. The irregular porosity at P = 200 W has a smaller size than the ones at P = 150 W. A deeper analysis of the pore structure is required to understand the effect of the pore structure on the elongation of the samples.

The microstructure on the XY plane of reference samples during the different treatments was analysed using an optical microscope. The optical micrographs illustrated in Fig. 12 show identical features for all samples produced at 59 J/mm3; the laser scans are visible with well-defined melt pool boundaries. The microstructure does not vary despite changing the process parameters using the same volumetric energy density.

Fig. 12
figure 12

Cross-sectional views on the XY plane of samples at different treatments a treatment 1, b treatment 2, c treatment 3, d treatment 4, e treatment 5 and f treatment 6

Full size image

In conclusion, the investigation of the cross-sections and the fracture surfaces of selected specimens did not help identify a possible explanation for the considerable variation in elongation.

4 XCT analysis

For the qualitative XCT analysis, the focus is on the reference samples in Table 6. Then, a correlation between elongation and the porosity indexes for all samples produced at 59 J/mm3 is carried out.

4.1 Porosity structures

This section focuses on the porosity structure of the samples produced with the combination of parameters that resulted in different elongation values. The objective is to understand what difference in porosity structure between these samples caused the premature failure.

Box plots showing the logarithmic transformation of the volume distribution are shown in Fig. 13. The median values of the volume distribution do not vary among the considered samples. Samples S6 and S11 are characterised by a skewed distribution with an increased presence of larger pores. The low limit for all volume distribution is similar because data are cut off, as explained in Sect. 2.3. The volumes' distributions do not differ significantly, as expected from the mean density measurements performed using Archimedes method.

Fig. 13
figure 13

Volume distribution for the reference samples. Volume data were transformed with a natural log transformation

Full size image

In all four cases, the pores are elongated along the XY direction rather than on the Z direction, as shown by the histograms in Fig. 14. This result is coherent with the literature [38] and [23]. Samples S6 and S12 present the largest values of ΔX, ΔY and ΔZ compared with their respective replicates. Smaller pores characterise the samples produced at P = 200 W (Treatment 6) in all directions.

Fig. 14
figure 14

Elongation of the pores along the X-, Y- and Z-axis. a Samples S5 and S6, b samples S11 and S12

Full size image

The relationship between the pores’ size and shape is shown in Fig. 15, where each dot represents a pore. The shape distributions of the pores do not change among the different samples in Fig. 15 so it cannot explain elongation differences, as suggested in the literature [25]. Interestingly, high spherical pores are also found for large pores (ΔZ between 0.08 and 0.10 mm), independent of the power used. In addition, irregular pores are also found in samples S11 and S12 (Fig. 15b), indicating that occasionally a lack of fusion defects can be generated even when optimal energy density and high power are used. Samples S5 and S6 in Fig. 15a are characterised by a more irregular shape of the pores as the minimum value of the sphericity index is close to 0.3. The presence of highly irregular pores is expected at low-power values.

Fig. 15
figure 15

Relationship between the pores’ size (ΔZ) and sphericity for the four samples a Sample S5, b sample S6, c sample S11 and d sample S12

Full size image

The position of the pores inside the sample is also investigated. The histograms shown in Fig. 16 represent the distribution of pore position along the radial direction. Pores are mainly positioned near the sample edge, 500–200 μm from the edge. These pores are usually formed at the interface between the end of the melt track and the contour lines [11]. The distribution of pore location is similar in all the considered samples.

Fig. 16
figure 16

Distribution of the pores along the radial position ρ

Full size image

From this qualitative analysis, it can be concluded that:

Pores are more elongated along the XY plane than the Z plane for all samples. This result was also found in [21, 23, 38].

The morphology of the pores is similar for all samples.

The position of the pores is similar for all samples, with a peak of porosity at the hatch-contour interface.

The qualitative analysis shows that the porosity structure is different among the samples even if the apparent density is similar; this result is coherent with Kim et al. [23]. The samples with the lowest elongation show the largest pores.

4.2 Relationship between porosity structure and elongation

The relationship between elongation and the porosity index defined in Sect. 2.4.1 is presented in Fig. 17.

Fig. 17
figure 17

Correlation between a elongation and volume-based index Π b elongation and position-based index RED

Full size image

The trend between elongation and Π is clear for energy density 59 J/mm3: a substantial decrease in elongation as the cross-sectional area is reduced. The same index was used in [26] for the high-pressure die casting process, and a statistical correlation between porosity and elongation was found.

The position-based index (RED) proposed in the literature [27] for L-PBF processes does not show any correlation with the elongation. At Ed = 59 J/mm3, similar values of RED result in an extensive range of elongation, indicating a low correlation between pore position and elongation: the correlation coefficient is 0.460 (95% confidence interval for the correlation coefficient is [− 0.818; − 0.154]).

In conclusion, the elongation is highly correlated with a volume-based index rather than a position-based index. The clustering of pores is detrimental to the mechanical properties, especially elongation, while UTS and YS were not affected by the porosity structure. Based on the result of the analysis, the position of the pores (RED index) does not influence the mechanical properties.

It is possible to estimate a regression equation in the form \(\widehat{El}_{\% } = \widehat{El}_{\% } \left( {\Pi \left| {VED = 59\;{\text{J/mm}}^{{3}} } \right.} \right)\). The equation is given in Table 7 and it is shown Fig. 18.

Table 7 Regression equations for elongation as a function of porosity index Π at a fixed energy density, VED = 59 J/mm3
Full size table
Fig. 18
figure 18

Relationship between the highest volume reduction (Π) and elongation. Dotted lines represent the prediction interval

Full size image

5 Conclusion

This work investigates the influence of a wide variation of process parameters on the tensile properties of AISI 316L processed via L-PBF. Three levels of energy density were selected, ranging from the optimal region (59 J/mm3) to the keyhole region (180 J/mm3), and each level was obtained using different combinations of individual process parameters, namely power, point distance, hatch distance and exposure time.

Specimens were analysed in terms of the average apparent density, XCT scan and tensile properties. The results showed that the UTS and YS varied according to energy density: as the energy density decreases towards non-optimal values, UTS and YS reduce. Interestingly, even with a significant variation of process parameters, energy density is still a good predictor for tensile strength (adj-R2 = 73%), while UTS and YS are shown to be highly correlated.

Elongation was found to vary quite significantly even considering samples produced at the same energy density, which contrasts with the results of UTS and YS. By considering only the optimal level of energy density, XCT data were used to find a statistical correlation between specific features of the observed porosity and the final value of elongation observed, as suggested by the literature. Two indexes were proposed to characterise the distribution of the pores: a layer-wise volume-based index (Π) and a position-based index (RED). Π index was able to predict the sample elongation with a very good statistical fit (adj-R2 = 91%), while the RED index did not show a good correlation with elongation. In conclusion, the clustering of the pores influences the elongation rather than the position of the pores inside the sample.

Further studies will focus on extending the experimental investigation to consolidate our results and better investigate the effect of process parameters. Additional models will also be investigated to increase the prediction ability of porosity indicators in terms of final mechanical performances, particularly for fatigue properties.