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Open Access 10.04.2024 | Full Research Article

Influence of part temperature on in-situ monitoring of powder bed fusion of metals using eddy current testing

verfasst von: Marvin A. Spurek, Adriaan B. Spierings, Marc Lany, Bernard Revaz, Gilles Santi, Jonatan Wicht, Konrad Wegener

Erschienen in: Progress in Additive Manufacturing

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Abstract

Powder bed fusion of metals (PBF-LB/M) is currently the most widely adopted additive manufacturing technology for the fabrication of metal parts. However, the inconsistent quality of PBF-LB/M-manufactured parts and high costs for part certification are impeding wider industrial adoption. In-situ monitoring technologies are expected to enable process control in order to ensure consistent quality, and to replace some of the post-process inspection steps, therefore, reducing part certification costs. Eddy current testing (ECT) is a standardized nondestructive testing technique, which can be used as an in-situ monitoring technology to measure the part quality during the PBF-LB/M build cycle. However, the process-induced complex temperature fields in PBF-LB/M parts during the build cycle are among the most relevant disturbances due to the temperature dependence of the electrical conductivity. This study investigates the process-induced temperature influence on in-situ monitoring of relative density using ECT. Parts made from AlSi10Mg were manufactured on a PBF-LB/M machine and the build cycle was monitored using ECT and an infrared camera, which was used to extract the part surface temperature right before the ECT measurement. The results demonstrate that the temperature increase of the parts during the build cycle decreases the electrical conductivity independently of the relative part density, which was measured via micro-computed tomography. Therefore, a temperature compensation method was proposed and applied demonstrating that a layer-to-layer difference of 0.15 % relative density can be detected via ECT. Consequently, it has been demonstrated that ECT is an effective in-situ monitoring technology for PBF-LB/M, even in the presence of temperature disparities within parts.

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1 Introduction

Powder bed fusion of metals (PBF-LB/M) is currently the most widely adopted additive manufacturing technology for fabricating metal parts [1]. Among the most important industries adopting PBF-LB/M are medical [2] and aerospace [3], where PBF-LB/M enables the manufacturing of individualized and complex-shaped parts, and parts with superior material performance relative to their weight, respectively. These industries require consistent and high part quality ensured by rigorous quality standards and, respectively, required part certificates owing to their safety-critical applications. According to Wei et al. [4], there is a large time lag between the design and certification of PBF-LB/M-manufactured parts as reproducible manufacturing of defect-free and structurally sound parts is still challenging. Determining suitable process conditions to obtain process qualification and part certification, therefore, requires extensive trial and error testing including destructive and nondestructive testing (NDT) of PBF-LB/M-manufactured parts during post-processing. Not only are these tests costly, but depending on the region of interest within the part volume and the alloy used, it can be very challenging to reliably detect the required defect types and characteristics due to the limitations of the respective testing methods. For example, reliably detecting small defects in the center of large parts made from dense metals via X-ray micro-computed tomography ($\upmu$CT) is difficult owing to the absorption of X-rays [5]. Consequently, a brute-force approach to qualify the PBF-LB/M process and to certify PBF-LB/M-manufactured parts typically has to be conducted per machine, feedstock material, and part geometry ultimately accounting for a significant proportion of the overall manufacturing costs per part which still impede the wider industrial adoption of PBF-LB/M [6].

In the future, in-situ monitoring technologies are expected to enable process control contributing to higher reproducibility of part quality, and to support or even replace some of the post-process inspection steps as discussed by Debroy et al. [6]. Therefore, tremendous effort was put into research and development of in-situ monitoring technologies in recent years reflected by the increase in related papers published pointed out by Grasso et al. [7]. While the majority of in-situ monitoring technologies are indirect techniques primarily focused on extracting process signatures and detecting anomalies within these signatures [7], there is a growing number of studies on developing established NDT technologies for in-situ inspection during the PBF-LB/M process. The benefits of employing these technologies as in-situ inspection techniques include their extensive industrial adoption for post-process inspection, their acceptance among users in the industry, and the availability of established standards and methodologies for generating part certificates during post-processing, which can be utilized for this purpose. One of these promising NDT technologies is eddy current testing (ECT) as the hardware is relatively inexpensive, and according to ASTM E3166-20 [8] it can be used to detect several relevant discontinuity classes in PBF-LB/M-manufactured parts: surface features, porosity, cracking, lack of fusion, inclusions and residual stress. The majority of research on the adoption of ECT to PBF-LB/M is focused on evaluating the ability to detect different designed defects in the near-surface region of PBF-LB/M parts after the build cycle has been completed and the respective parts have been removed from the PBF-LB/M machine. The studies primarily use parts with designed cavities of different sizes and shapes as exemplified in [9‐17], and porosity triggered by intentional degradation of process parameters as demonstrated in [18‐20]. However, there are only few studies on the adoption of ECT as an in-situ technique measuring the layerwise solidified material during the PBF-LB/M build cycle where the ECT system is mounted on the recoater of the PBF-LB/M machine [21‐23]. This approach enables to extend the testable area from the near-surface region of the part as described in ASTM E3166-20 [8] to the full part volume. However, it requires sophisticated signal processing methods to layerwise segment the ECT data and subsequently spatially match the layerwise segmented data with post-process $\upmu$CT data in order to establish defect detection algorithms as demonstrated by Spurek et al. [22].

Although ECT can generally be used in harsh environments and the aforementioned studies demonstrate the capability of in-situ monitoring of PBF-LB/M using ECT, the physics of the PBF-LB/M process impose several challenges among which the complex temperature fields in PBF-LB/M parts during the build cycle are expected to be one of the most critical ones as discussed by John et al. [24]. According to Wei et al. [4] and Mukherjee et al. [25], the temperature fields, cooling rates, and temperature gradients in PBF-LB/M highly depend on the alloy, process parameters, and part geometry used. Furthermore, Williams et al. [26] demonstrated that the inter-layer cooling time, i.e., the time between the laser illumination of two subsequent layers, affects the evolution of the part surface temperature during the build cycle. In addition, independent of the inter-layer cooling time, a significant increase of the part surface temperature as a function of the build height was demonstrated. This is owing to the cold start of the PBF-LB/M build cycle and the layer-to-layer heat input by the laser beam until an equilibrium with the heat loss, i.e., predominantly heat conduction to the build plate [4], is established throughout the build cycle as pointed out by Williams et al. [26]. Hence, the part geometry, process parameters, build height, build cycle details, i.e., number of parts, support structures, nesting, and sequence of part illumination, among others, will possibly lead to spatial temperature differences in the solidified material while the in-situ ECT measurement is conducted. The adoption of ECT for in-situ monitoring of PBF-LB/M relies on measuring the electrical conductivity of predominantly paramagnetic alloys and utilizing calibration models leveraging correlations between the measured electrical conductivity and defect characteristics within the corresponding material volume in space as demonstrated by Spurek et al. [22]. Since the electrical conductivity of metals is inversely related to their temperature [27], the aforementioned spatial temperature differences within parts and between parts disturb the ECT measurement as spatial differences in temperature affect the electrical conductivity and can, therefore, be misinterpreted as defect signatures. The influence of sample temperature variation on the electrical conductivity measurement via ECT is well known in the literature [27] and the corresponding change in electrical conductivity is calculated using a linear approximation according to

$$\begin{aligned} \sigma (T) = \sigma (T_0)~[1+\alpha ~\Delta T] \end{aligned}$$

(1)

$\sigma (T)$, $\sigma (T_0)$, $\alpha$ and $\Delta T$ denote the corrected electrical conductivity at temperature T, the electrical conductivity at reference temperature $T_0$, the temperature coefficient of the electrical conductivity of the alloy, and the temperature difference $\Delta T = T-T_0$, respectively. Given $\sigma (T_0)$, $\alpha$ and $\Delta T$, the temperature-induced measurement error can, therefore, be reduced using Eq. (1). However, when it comes to PBF-LB/M, it should be noted that, for the majority of the alloys, both $\alpha$ and $\sigma$ values are typically not known. The alpha value is usually established empirically, whereas the $\sigma$ value can be influenced by various process parameters as well as build orientation, as demonstrated by Silbernagel et al. [28]. Furthermore, it is not straightforward to obtain $\Delta T$ as determining the actual part surface temperature during the build cycle usually requires a sophisticated calibration of the, respectively, used temperature sensors as demonstrated by Williams et al. [29].

This study investigates the impact of process-induced part temperature differences on in-situ monitoring of PBF-LB/M using eddy current testing and proposes a suitable temperature compensation method. Therefore, high cuboid parts made from AlSi10Mg are manufactured on a PBF-LB/M machine to trigger the aforementioned part surface temperature increase as a function of the build height demonstrated by Williams et al. [26]. The parts are in-situ monitored during the build cycle by an ECT system and a calibrated infrared camera. The layerwise relative electrical conductivity per part is then extracted from the ECT data and compared to the corresponding layer-to-layer relative density determined via post-process $\upmu$CT analysis. Subsequently, the layer-to-layer part surface temperature at the moment of the ECT measurement is extracted from the infrared camera data. Based on these data, a temperature compensation method is developed and the performance is evaluated by comparing the resulting accuracy of the layerwise relative density measurement via ECT to the case without temperature compensation.

2 Materials and methods

2.1 Experimental setup and build cycle

The experiments were carried out on an AconityMIDI+ PBF-LB/M machine (Aconity3D GmbH, Herzogenrath, Germany) equipped with an Nd–YAG fiber laser with a maximum continuous laser power of 400 W. The recoater was modified as presented in Fig. 1a. The ECT measurement equipment was mounted on the opposite side of the brush holder on the recoater enabling to layerwise measure manufactured parts during the normal powder recoating process without modification of the build cycle. The ECT measurement was carried out adopting an Ultra-Portable Eddy Current (UPEC) instrument to which the ECT sensor, a ferrite pot core coil ($L=80~\mu$H) with an outer diameter of $d_c=5.8~mm$ (both Sensima Inspection Sarl, Gland, Switzerland), was connected in a bridge configuration. Further details on the system and machine integration are described by Spurek et al. [22]. The ECT sensor was positioned at a distance of $500~\mu m$ to the build plate surface before starting the build cycle as shown in Fig. 1b. The distance increases to the nominal lift-off $L_n$ due to the layer-to-layer increase of the solidified layer thickness at the start of the build cycle until the nominal solidified layer thickness is reached after $10-12$ layers as demonstrated by Spurek et al. [22].

An Optris PI 640i infrared camera (Optris GmbH, Berlin, Germany) with a resolution of 640 $\times$ 480 pixels, a field of view of 33$^\circ$ $\times$ 25$^\circ$ and a sampling rate of 32 Hz was mounted into the build chamber of the AconityMIDI+ PBF-LB/M machine as illustrated in Fig. 1a. To protect the camera from process by-products such as fumes, it was mounted within a customized housing and views the build area through a zinc sulfide window (Edmund Optics, Inc., Barrington, NJ, USA), which allows transmission within the wavelength range of 400–10,000 nm. The integration ensured that the majority of the build area was within the field of view. The camera focus was adjusted to ensure the center of the manufactured samples was in the focal plane of the camera albeit the distortion owing to the viewing angle of about 45$^\circ$ due to the mounting position of the infrared camera. The camera was connected to an acquisition computer outside of the build chamber on which the acquisition software Optris PI Connect (Optris GmbH, Berlin, Germany) was running, and the acquired data were stored.

Five parts with dimensions $10\times 10\times 60~mm^3$ were positioned according to Fig. 1a and manufactured with the process parameters presented in Table 1. Gas atomized AlSi10Mg powder (Carpenter Technology Corp., Philadelphia, PA, USA) with a particle size distribution of $10-60~\mu m$ was used as feedstock material, which was dried for 24 h under vacuum at 60 $^\circ$C prior to processing. All parts were fabricated without support structures onto an AlSi1MgMn build plate and afterwards removed by wire cutting.

Table 1

PBF-LB/M process parameters

Parameter
Scan speed (P1–P5)	$v_s$	[mm/s]	1500, 1800, 1915, 2015, 2100
Hatch distance	$h_s$	[$\upmu$m]	100
Laser power	$P_L$	[W]	380
Layer thickness	$t_{l,n}$	[$\upmu$m]	60
Laser spot diameter	$d_s$	[$\upmu$m]	105
Scan pattern		–	90$^\circ$ alternating
Recoater type		–	Silicone-reinforced carbon fiber brush
Recoating speed	$v_r$	[mm/s]	100
Shielding gas		–	Nitrogen
Chamber oxygen content		[ppm]	< 1000
Chamber overpressure		[mbar]	60

2.2 In-situ eddy current testing

The eddy current measurement principle is explained exhaustively by Bowler [27]. Furthermore, Spurek et al. [22] explain the aspects that are important when adopting ECT as an in-situ monitoring technique for PBF-LB/M. In principle, ECT utilizes the induction of eddy currents in testable metal samples owing to a time-varying primary magnetic field triggered by an alternating current, which runs through a coil brought in close proximity to the sample. The induced eddy currents generate a secondary magnetic field opposing the primary one, triggering a change in coil impedance, which is measured by the ECT instrument. The inspection depth in the sample is defined as the standard penetration depth [30], which is calculated according to

$$\begin{aligned} \delta = \frac{1}{\sqrt{\pi f \sigma \mu }} \end{aligned}$$

(2)

where f, $\sigma$, $\mu =~\mu _{0} \mu _{r}$ denote the excitation frequency, the electrical conductivity and the magnetic permeability of the material, respectively, and where $\mu _{r}$ is the relative magnetic permeability and $\mu _0=~1.256\cdot 10^{6}~H/m$ is the magnetic permeability in vacuum [27]. According to Eq. (2), the penetration depth of the eddy currents can be adjusted by setting a suitable excitation frequency f. Within this study, an excitation frequency of $f=200~kHz$ was selected yielding $\delta =313~\mu m$ in AlSi10Mg, given $\sigma =12.85~MSm^{-1}$ [28] and $\mu _{r}=1.00$ [27].

The ECT signals were continuously acquired during the PBF-LB/M build cycle using a sampling rate of $f_s = 375~Hz$ yielding a point spacing of $\Delta x = v_{r}/f_{s} = 0.26~mm$ given the recoating speed of $v_r=100~mm/s$ (see Table 1). The ECT signals were then layerwise segmented, i.e., the respective fraction of the time series was matched with the corresponding layer index of the PBF-LB/M build cycle. Subsequently, the recoater position information provided by the axis encoder was used to extract the ECT signals when moving across the center region of each part, specified by the encoder range $\Delta x_p = 3~mm$, to exclude a potential influence by the part edges. The resulting part- and layerwise segmented ECT signals were then transformed according to the method developed by Spurek et al. [22], which allows to calculate the relative electrical conductivity $\sigma _r$. Hereby, $\sigma _r$ corresponds to the electrical conductivity relative to the electrical conductivity of the final layer of part P1 where $\sigma _r$ = 100 %. Finally, the means and standard deviations of $\sigma _r$ per part and layer were calculated.

Before conducting in-situ measurements, the level of uncertainty in $\sigma _r$ arising from the ECT instrument noise was quantified according to the principle of the expanded uncertainty explained in [31] as $U_I = k\cdot \sigma _n\cdot n^{-0.5} = 0.03~\%$, expressed in units of $\sigma _r$. Hereby, $k=3$, $\sigma _n=0.0321~\%$ (expressed in units of $\sigma _r$), $n=11$ denote the coverage factor referring to a confidence level of $99.7~\%$, the standard deviation of the ECT instrument noise and the sample size per layer acquired within $\Delta x_p$, respectively.

2.3 In-situ full-field infrared monitoring

In order to measure the part temperature during the build cycle, the infrared camera requires calibration. Although the commonly adopted calibrating method using blackbody sources at known temperatures accounts for the camera sensor’s non-linear response, it does not consider the actual emissivity of the target object as discussed by Williams et al. [26]. The emissivity $\epsilon$ is the efficiency of a body to emit thermal radiation and is defined as the ratio of energy radiated from a material’s surface to that radiated from a blackbody [32]. The emissivity is a dimensionless number between 0 and 1, where 0 is considered a perfect reflector and 1 a perfect emitter. According to Williams et al. [26], the emissivity of a metal part will depend on the alloy used, the temperature, the surface roughness, the oxidation of the surface, and the view angle, among others.

The build scenario used in this study (see Sect. 2.2) contains 5 parts manufactured with different process parameters at different locations on the build plate. The different locations on the build plate translate to different camera view angles, and the different process parameters have an effect on the surface roughness according to Debroy et al. [6] both affecting the emissivity as previously discussed. Thus, in contrast to the build scenario of Williams et al. [26], each part with its unique location and process parameter must be calibrated independently in this study. Therefore, 5 geometrically identical calibration parts with the dimensions $10\times 10\times 10~mm^3$ (C1–5, see Fig. 2a)) were manufactured at the same build location using the same machine, feedstock material, and process parameters yielding similar surface roughness, therefore, similar emissivity as the parts to be investigated. After finishing the build cycle, the excess powder was removed and 5TC-GG-KI-30-1M K-type thermocouples (Omega Engineering Inc., Norwalk, CT, USA) were attached to a designed notch with dimensions $4\times 1.5\times 1.5~mm^3$ on the top surface of each calibration part using thermal paste as shown in Fig. 2a). The thermocouples were connected to USB-TC01 thermocouple measurement devices (National Instruments Corp., Austin, TX, USA) placed outside of the build chamber which were connected to an acquisition computer to log the temperature during calibration. During the calibration procedure, the build plate piston position was kept constant, hence the top surfaces of the calibration parts still lie in the PBF-LB/M process plane. The build chamber was then flooded with Nitrogen until an oxygen content of $<1000$ ppm was reached, which is similar to the oxygen content during the PBF-LB/M process (see Table 1).

The calibration parts were then heated up using an inductive heating unit (Aconity GmbH, Herzogenrath, Germany), which was sequentially set to the following heating temperatures: $T_h = \{35,~70,~100,~150,~250,~350,~500\}$ [$^\circ$C] as shown in Fig. 2b). After the temperature reading of the thermocouples stabilized at each temperature level, the temperature was recorded using the infrared camera, and the data was logged from the thermocouples for a measurement duration $t_m = 60\,s$, respectively. The infrared camera reading is performed on a $8\times 8$ pixels area on each part as depicted in Fig. 2b) and the temperature within the area averaged to mitigate pixel-to-pixel variations owing to local variation in surface roughness on each part surface. As the Optris PI Connect acquisition software requires setting an emissivity value, it was set to 1 for all parts, i.e., reported uncalibrated temperatures measured by the infrared camera correspond to the emissions of a blackbody source. Subsequently, the measurement data acquired via the thermocouples and the infrared camera at each temperature level $T_h$ were, respectively, averaged and the results plotted against each other as presented in Fig. 2c). Unique calibration curves per calibration part, i.e., per PBF-LB/M process parameter and part location, were then obtained by fitting 3rd-order polynomial functions (all $R^2 > 0.99$). These calibration functions allow to translate the respective part temperature recorded by the infrared camera to the actual part temperature measured by the thermocouples. Hence, the empirically obtained calibration functions enable to account for the non-linearity of the emissivity as a function of temperature, and the differences in emissivity owing to different PBF-LB/M process parameters and locations on the build plate.

2.4 X-ray micro-computed tomography

X-ray micro-computed tomography ($\upmu$CT) scans of the parts were obtained using a Zeiss Metrotom 1500 G3 system (Carl Zeiss AG, Jena, Germany) which was operated at 177 kV and 69 $\upmu$A yielding a voxel size of 12 $\upmu$m. According to Du Plessis et al. [5] the smallest detectable pore has a size of approximately $3\times 3\times 3=27$ voxels. Therefore, the smallest detected pore diameter is approximately 36 $\upmu$m. The porosity analysis was carried out using the VGDefX algorithm of the software VGSTUDIO MAX 3.5 (Volume Graphics GmbH, Heidelberg, Germany). The resulting porosity matrices per part containing the sphericity, location, and equivalent spherical pore diameter, i.e., the diameter of a sphere with the defect volume, were exported and subsequently analyzed. Hereby, the sphericity $\Phi$ is calculated according to $\Phi = A_{s}\cdot A_{d}^{-1}$ where $A_{d}$ and $A_{s}$ denote the surface area of the defect and the surface area of a sphere with equivalent volume, respectively.

Subsequently, image stacks per part with an image-to-image distance in the z-direction of $d_{im}=10~\mu m$ were exported. In order to layerwise compare the ECT signals with the relative density of the corresponding material volume obtained via $\upmu$CT, the method developed by Spurek et al. [22] was adopted, where each slice corresponds to the material volume that was layerwise measured by ECT during the PBF-LB/M build cycle $V_s = w_s \cdot l_s \cdot \delta ^{*} = d_c \cdot (\Delta x_p + d_c) \cdot \delta ^{*}$. As shown in Fig. 3, $w_s$, $l_s$, $\delta ^{*}$, $d_c$, $\Delta x_p$ denote the slice width, the slice length, the ECT standard penetration depth (rounded to the nearest tenth), the nominal layer thickness, the outer coil diameter and the selected encoder range at the center region of the part, respectively. Given $\delta ^{*} = 310~\mu m$ and $t_{l,n} = 60~\mu m$, the relative density per slice $\rho _{s,i}$ was determined according to

$$\begin{aligned} \rho _{s,i} = 1-\left( \frac{d_{im}}{\delta ^*} \sum _{j=d_{im}^{-1}(it_{l,n}-\delta ^*)}^{it_{l,n}d_{im}^{-1}}\frac{A_{d,j}}{A_s}\right) = 1-\left( \frac{1}{31} \sum _{j=6i-31}^{6i}\frac{A_{d,j}}{A_s}\right) \end{aligned}$$

(3)

$\{i \in \mathbb {N}~|~50 \le i \le 1000\}$, j, $A_{d,j}$, $A_s$ denote the layer index, the image index in the image stack, the pore area of image j and the total area of the respective region of interest of image j where $A_{d,j}$ and $A_s$ were determined using an ImageJ algorithm.

3 Results and discussion

3.1 $\upmu$CT analysis

The resulting 3D images of P1–5 obtained after applying the porosity detection algorithm (see Sect. 2.4) on the $\upmu$CT data are depicted in Fig. 4a). The defect-free volume is hereby shown in transparent gray whereas the detected pores are colored according to their equivalent spherical pore diameter. The porosity is homogeneously distributed within the respective part volumes and it increases from P1 to P5 as expected owing to the variation in scan speed (see Table 1) intentionally introducing an increasing amount of lack of fusion porosity from P1 to P5 as the volumetric energy density $E_v=P_L\cdot (v_s\cdot h\cdot t_{l,n})^{-1}$ defined by Stoffregen et al. [33] decreases with increasing scan speed.

The relative densities of P1–5 were calculated by dividing the total pore volume by the total part volume and are visualized as a function of the scan speed in Fig. 4b). The results confirm that the relative part density decreases as the scan speed increases, i.e., from P1 to P5, which is in agreement with several studies [34‐36]. The relative part densities of P1–5 cover a range of 99.0$-$99.9 %, i.e., the most interesting region of PBF-LB/M process window for structural applications, as porosity is typically minimized to avoid fatigue crack initiation [36, 37]. In Fig. 4c, d) the probability density functions of the equivalent spherical pore volume and the pore sphericity per part are visualized confirming that as the scan speed increases, the pore size increases and the pore sphericity decreases. This is due to the increased formation of larger lack of fusion pores which are typically larger and irregularly shaped compared to gas pores and keyhole pores [36, 38‐41].

The layer-to-layer relative density $\rho _s$ of each part P1–5 extracted from the $\upmu$CT data according to the procedure described in Sect. 2.4 is plotted in Fig. 5. Hereby, $\rho _s$ corresponds to the relative density of the material volume that was layerwise measured via ECT as discussed in Sect. 2.4.

The layer-to-layer relative densities $\rho _s$ of P1–5 demonstrate that P1 has the highest relative density over the given layer range and the relative density decreases towards P4–5 as expected given the overall relative densities of the parts and the homogeneous distribution of pores within the parts (see Fig. 4a, b). The layer-to-layer gradient of the relative density is relatively constant for P1–3, but slightly positive for P4–5, i.e., the relative density increases with the layer number of these parts. Hence, the relative density of P4–5 is slightly higher at the top of the parts compared to the bottom of the parts. Furthermore, the layer-to-layer fluctuation of the relative density is very small for P1 and increases in direction to P5. This is partially owing to a narrower pore size distribution with a smaller average equivalent pore size for P1 which increases towards P5 (see Fig. 4c). Thus, porosity is most homogeneously distributed in P1 and the homogeneity decreases towards P5.

3.2 In-situ full-field IR monitoring

The part surfaces of P1–5 were monitored for the duration of the build cycle according to the procedure outlined in Sect. 2.1. Figure 6 depicts raw infrared camera images of the build scenario after the laser melting of the respective layers denoted in the images.

The images qualitatively demonstrate the heat up of the parts during the build cycle as the layer index increases which is in agreement with the findings of Williams et al. [26] for 316L stainless steel. Additionally, there is a region of the powder bed around each part which exhibits a considerably higher infrared radiation which is most pronounced at layer 1000. This is caused by ejected spatter particles during laser melting which are predominantly moved away from the part surface by the gas flow and land on the surrounding powder bed as shown in Fig. 7. Although the parts were molten by the laser sequentially in ascending order by part number, i.e., P1 first and P5 last, and the images were extracted after the melting of the respective layer of P5 was finished, and spatter ejected during the melting of P1 had the most time to cool, there is the considerably largest and hottest area with landed spatter particles in proximity to P1. This is probably owing to the relatively higher energy input owing to the lowest scan speed used to melt P1 (see Table 1) triggering an increased amount of spatter, which is in agreement with several studies on the influence process parameters on spatter formation mechanisms [42‐44].

The part-wise temperature time series over the entire duration of the build cycle containing the average temperature of the regions illustrated by white squares in Fig. 6 were then extracted and converted to actual part surface temperatures adopting the calibration functions according to Sect. 2.3. The time fraction of processing one layer of P1 is exemplarily shown in Fig. 8 where different events can be identified: the rapid temperature increase (1) occurs when the laser is melting the material followed by a rapid cool down which is characteristic for PBF-LB/M [4]. Subsequently, the recoater moves towards the powder piston obscuring the view of the camera coinciding with a small temperature peak (2) which is primarily owing to a change in emissivity as the recoater is made from different material, lies out of the focal plane of the infrared camera, among others. Then, the powder piston moves upwards and the recoater moves in the opposite direction to create the next powder layer. During this movement, the eddy current sensor moves ahead of the powder sequentially measuring P1–5 before they are covered by powder. Thus, the part surface temperature (3) is extracted right before the eddy current sensor mounted on the recoater obscures the camera view a second time indicated by the next small peak (4). Therefore, the temperature was extracted during 3 s before this peak occurs as indicated in red, and the part surface temperature $T_S$ computed by averaging the temperature during the 3 s interval. After the powder recoating is completed, the parts are covered with powder (5) before the next layer cycle starts. An algorithm implemented in Python 3.9 was used to extract $T_S$ accordingly for each layer and part, respectively.

The resulting part surface temperature $T_S$ as a function of the layer index per part is plotted in Fig. 9. Notably, the periodicity, which is exemplarily shown in the zoomed window in the top left corner, coincides with the periodicity of the laser scan vector direction due to the adopted 90$^\circ$ alternating scan pattern (see Table 1). The scan vector direction influences the part surface profile and, therefore, the emissivity and the measured temperature as discussed in Sect. 2.3. Thus, the data were filtered with a moving average filter with a window size of 4 significantly reducing the noise; hence, the filtered data is used in the following analyses. $T_S$ of all parts increases as a function of the layer index from about 55 $^\circ$C to about 75 $^\circ$C. This is due to the cold start of the PBF-LB/M build cycle, i.e., initially the build plate is at room temperature and the layer-to-layer heat input by the laser beam as discussed by Williams et al. [26] triggering the layer-to-layer increase of the part surface temperature as the material underneath is increasingly preheated. In comparison to the layer-to-layer increase of $T_S$, the part-to-part differences over the layer range are small, but significant (ANOVA, $F(4,4995)=42.12,~p<0.001$). Potential reasons for these differences are discussed in the following sections.

In order to compare the part-to-part differences, the mean temperature per part across the layer range $\bar{T}_S$ was calculated the resulting values are reported in Table 2, among others. The largest difference was found between P1 and P5 with $\Delta \bar{T}_S = 3.4~^\circ C$, which corresponds to the mean vertical offset between P1 and P5 in Fig. 9. Notably, the maximum part-to-part differences estimated by $\Delta \bar{T}_S$ are small compared to the maximum layer-to-layer difference in $T_S$ of approximately 20 $^\circ$C.

Table 2

Volumetric energy density $E_v$, relative part density $\rho _r$, time delay $\Delta t_c$, and mean part surface temperature $\bar{T}_S$ per part

Part	$E_v~[\nicefrac {J}{mm^3}]$	$\rho _r~[\%]$	$\Delta t_c~[s]$	$\bar{T}_S~[^{\circ } C]$
P1	42.2	99.94	25.8	63.9
P2	35.2	99.67	24.8	65.7
P3	33.1	99.49	23.9	65.3
P4	31.4	99.09	22.8	66.7
P5	30.2	98.99	21.9	67.3

In general, part-to-part differences in $\bar{T}_S$ can be caused by different time delays $\Delta t_c$ between the laser illumination and the ECT measurement, and different energy inputs expressed by $E_v$ as a function of the process parameters. The extraction of $\Delta t_c$ is exemplarily shown in Fig. 8 and the results presented in Table 2 demonstrating that there are differences of up to about 4 s in $\Delta t_c$ among the parts owing to the illumination sequence of the parts. The parts are cooling down during $\Delta t_c$, thus the larger $\Delta t_c$, the longer the parts cool down until the ECT measurement is taken. This is in agreement with $\bar{T}_S$, which increases as $\Delta t_c$ decreases; hence, the small differences in $\bar{T}_S$ could be caused by the difference in $\Delta t_c$ owing to the illumination sequence of the parts.

The energy input as a function of the process parameters expressed by $E_v$ is expected to be positively correlated to $\bar{T}_S$. However, the data presented in Table 2 demonstrates that $\bar{T}_S$ decreases as $E_v$ increases; therefore, differences in $E_v$ owing to process parameter variation obviously do not contribute to the differences in $\bar{T}_S$ among the parts. However, there are differences in thermal conductivity $\kappa$ between the parts owing to the different relative densities triggered by the process parameters [45]. According to Butler et al. [45], porosity is inversely correlated with the thermal conductivity, i.e., the relative densities reported in Table 2 yield $\kappa _{P1}> \kappa _{P2}> \kappa _{P3}> \kappa _{P4} > \kappa _{P5}$. Thus, the differences in $\kappa$ among the parts yield differences in the efficiency of the heat conduction from the part surface to the build plate influencing the part cooling during $\Delta t_c$ potentially contributing to the differences in $\bar{T}_S$ among the parts.

Generally, the process parameters and illumination sequence only slightly affect $T_S$ given the small part-to-part differences in $T_S$ of maximum $\Delta \bar{T}_S = 3.4~^{\circ } C$. Layer-to-layer differences in $T_S$ are, therefore, by far the more relevant regarding the disturbing influence of $T_S$ on the in-situ ECT measurement.

3.3 Relative density monitoring via in-situ ECT

The layer-to-layer relative electrical conductivity $\sigma _r$ of P1–5 obtained after processing the ECT data according to Sect. 2.2 is plotted in Fig. 10. The overall relative electrical conductivity $\sigma _r$ per part reveals differences in electrical conductivity where P1 has the highest and P5 has the lowest electrical conductivity. According to Spurek et al. [18, 22], the relative electrical conductivity and the relative density are correlated. Although there are significant differences in $\sigma _r$ between the parts at a given layer index as expected due to the difference in relative density (see Fig. 4b)), the layer-to-layer $\sigma _r$ actually decreases with increasing layer number. This downward drift of $\sigma _r$ is independent of the actual relative density because there is no drift in the layer-to-layer relative density as shown in Fig. 5. According to Bowler [27], the electrical conductivity of metals is inversely related to the part temperature, i.e., higher part temperatures at higher layer index yield lower electrical conductivities measured via ECT. Thus, the drift in $\sigma _r$ is actually due to the increase in part surface temperature shown in Fig. 9 which decreases the actual layer-to-layer electrical conductivity of the near-surface fraction of the part volume at the moment the ECT measurement is conducted.

The strong correlation between the relative electrical conductivity and the relative density demonstrated by Spurek et al. [18, 22] allowed to establish a linear regression model to calibrate the ECT system to be able to measure the layer-to-layer relative density with high accuracy. In this context, the additional influence of the part temperature on the relative electrical conductivity acts as a disturbance: the linear regression predicting the relative density from the relative electrical conductivity is shown in Fig. 12a) indicating that there is a large fraction of the variance of $\sigma _r$ over the layer range which is not explained by the corresponding relative density. The goodness of fit $R^2=0.548$ supports this observation demonstrating that in fact only about 55 % of the variance in $\rho _s$ is explained by $\sigma _r$. The resulting regression function allows to predict $\hat{\rho }_s$ [%] from $\sigma _r$ [%] according to

$$\begin{aligned} \hat{\rho }_s(\sigma _{r}) = 0.9737\cdot \sigma _{r} + 2.3563 \end{aligned}$$

(4)

The prediction accuracy is quantified by the mean absolute error (MAE) which is calculated according to

$$\begin{aligned} MAE = \frac{1}{n}\sum _{i=1}^n|\hat{\rho }_{i}-\rho _{i}| = 0.223~\% \end{aligned}$$

(5)

The MAE is defined as the average error between predicted value $\hat{\rho }$ and true value $\rho$ in units of the predicted value, i.e., relative density $[\%]$. Thus, the MAE demonstrates that the layer-to-layer relative density can be measured via ECT after calibration adopting the regression model according to Eq. (4) with an average error of 0.22 %. In comparison to Spurek et al. [22] where $MAE=0.126~\%$, the MAE obtained in this study is larger owing to the temperature drift in the ECT data caused by a layer-to-layer increase of $T_S$, where the total range of $T_S$ is considerably larger owing to the part design.

Figure 11a–e depicts both the predicted layer-to-layer relative densities $\hat{\rho }_s(\sigma _r)$ for P1–5, obtained from Eq. (4), and the actual relative density $\rho _s$ measured using $\upmu$CT. As expected, the agreement between the predicted relative density $\hat{\rho }_s$ and the actual relative density $\rho _s$ is not consistent across the layer range for all parts. This is due to the influence of the part temperature on the relative electrical conductivity of the parts which is not considered in the regression model according to Eq. (4) and, therefore, acts as a model disturbance. Neglecting the part temperature, therefore, leads to under- and overestimation of $\rho _s$ for most of the layer range leading to the false conclusion that the drift in $\sigma _r$ as a function of the layer index is caused by an actual vertical gradient in the relative density $\rho _s$, which is not the case as shown in Fig. 11.

3.4 Temperature compensation

Temperature compensation methods adopted to reduce the temperature drift in electrical conductivity measurements conducted via ECT typically utilize the linear approximation of the temperature dependency of the electrical conductivity according to Eq. (1). In general, the linear approximation only holds for small changes in temperature as the temperature coefficient of the electrical conductivity changes as a function of temperature [46]. The relative electrical conductivity $\sigma _r$ as a function of the part surface temperature $T_S$ per part is shown in Fig. 12c). Given the small variation of relative density across the layer range (see Fig. 5), the corresponding influence of the relative density on the relative electrical conductivity is neglected. Thus, the good fit of the linear models to the respective data per part ($R^2 > 0.7$ for all parts) demonstrates that the linear approximation holds for the observed range of $T_S$.

In-situ monitoring of the relative part density via ECT requires the calibration of the specific ECT system for the alloy used adopting a linear model as demonstrated by Spurek et al. [18, 22]. These linear models are ideally experimentally obtained by in-situ monitoring of build cycles via ECT wherein test samples covering the region of interest in terms of relative density are fabricated and the relative density is subsequently measured via $\upmu$CT. Due to the demonstrated linear relationship of the part temperature and the relative electrical conductivity, the temperature compensation is included in the linear model used for calibrating the ECT system, i.e., the relative density $\hat{\rho }_s$ [%] is predicted from the relative electrical conductivity $\sigma _r$ [%] and the part surface temperature $T_S$ [$^\circ$C] according to

$$\begin{aligned} \hat{\rho }_{s}(\sigma _{r}, T_s) = 0.0507\cdot T_s + 1.6024 \cdot \sigma _{r} - 63.6758 \end{aligned}$$

(6)

Hereby, the linear regression model defined in Eq. (4) is extended to a multiple linear regression model according to Eq. (6) where the model is a least-square fitted plane in the 3D space defined by $\rho _s$, $\sigma _r$ and $T_S$. In comparison to the model according to Eq. (4), the multiple linear regression model fits the data significantly better with $R^2=0.797$, i.e., about 80 % of the variance of $\rho _s$ is explained by $\sigma _r$ and $T_S$, which is similar to the results obtained by Spurek et al. [22]. To quantify the model accuracy, the MAE is calculated according to

$$\begin{aligned} MAE = \frac{1}{n}\sum _{i=1}^n|\hat{\rho }_{i}-\rho _{i}| = 0.15~\% \end{aligned}$$

(7)

The MAE is significantly improved compared to the model without temperature compensation where MAE = 0.223 % (see Eq. (5)), i.e., the accuracy of measuring the relative density via ECT expressed by the MAE is reduced by 32.7 % to 0.15 % relative density by means of the temperature compensation. The comparison of the model residuals expressed in relative density [%] of the model without temperature compensation $\hat{\rho }_s(\sigma _r)$ and with temperature compensation $\hat{\rho }_s(\sigma _r,~T_S)$ is shown in Fig. 12d). Given the improvement of the accuracy expressed by the MAE, the distribution of the residuals of $\hat{\rho }_s(\sigma _r,~T_S)$ is significantly narrower compared to $\hat{\rho }_s(\sigma _r)$ accordingly.

Figure 13a–e presents the predicted relative densities $\hat{\rho }_s(\sigma _r,T_S)$ for P1–5, obtained using Eq. (6), along with the actual density $\rho _s$ that was measured using $\upmu$CT. In comparison to Fig. 11 where the temperature drift was visible for all parts, there are no downward temperature drifts visible demonstrating the effectiveness of temperature compensation. For P2-5 shown in Fig. 13b–e, the agreement between $\hat{\rho }_s$ and $\rho _s$ is very good, demonstrated by the small offset between the curves and similar layer-to-layer variation over the layer range which is most pronounced for P5 shown in Fig. 13e. Although the agreement for P1 depicted in Fig. 13a is good across the majority of the layer range, the model slightly overestimates the relative density at the lower end of the layer. Nevertheless, the presented method effectively compensates the temperature-induced drift in $\sigma _r$ yielding a detection accuracy of 0.15 % relative density expressed by the MAE.

3.5 Implications for industrial use

In industry, in-situ ECT can be adopted for monitoring of co-built test specimens, which are manufactured alongside the actual parts, where the measured relative density is used to approve the batch of parts manufactured within the build cycle as part of quality control, e.g., in accordance with ASTM 52920 [47]. Hereby, the overall relative density of the co-built test specimen is relevant and is typically determined by conventional methods, such as the Archimedes method, microscopic analysis of cross-sections, or $\upmu$CT. Table 3 presents the relative part density measured via $\upmu$CT alongside the relative part density measured via ECT with and without temperature compensation, respectively. Notably, although the model with temperature compensation is slightly more accurate, it is not required in this case as the model without temperature compensation also allows to determine the relative part density with high accuracy.

Table 3

Relative density of the parts determined via $\upmu$CT ($\rho _r$) and via in-situ ECT without temperature compensation ($\bar{\rho }_s(\sigma _r)$) and with temperature compensation ($\bar{\rho }_s(\sigma _r,~T_S)$) where $\bar{\rho }_s$ was determined by averaging the layerwise acquired signals shown in Fig. 13

Part	$\rho _r~[\%]$	$\bar{\rho }_s(\sigma _r)~[\%]$	$\Delta \rho _r~[\%]$	$\bar{\rho }_s(\sigma _r,~T_S)~[\%]$	$\Delta \rho _r~[\%]$
P1	99.94	99.80 ± 0.24	0.14	99.95 ± 0.16	0.01
P2	99.67	99.46 ± 0.14	0.21	99.51 ± 0.11	0.16
P3	99.49	99.31 ± 0.17	0.18	99.25 ± 0.12	0.24
P4	99.09	99.20 ± 0.16	0.11	99.14 ± 0.12	0.05
P5	98.99	99.12 ± 0.16	0.13	99.04 ± 0.13	0.05

In use cases where in-situ ECT is used to layerwise monitor the relative density, the risk of false interpretation of the measurement data owing to the temperature drift can lead to false alarms as $\hat{\rho }_s$ can fall below a defined quality threshold whereas the actual relative part density of the respective layer $\rho _s$ is actually above the quality threshold. However, the temperature compensation method fed with experimental or simulated temperature data can effectively remove the temperature drift. Alternatively, a reference build cycle with the same configuration, where the required part quality was achieved, can be used to detect deviations.

Given the small temperature differences within the same layer as discussed in Sect. 3.2, the in-situ nondestructive inspection of parts with ECT is probably not significantly influenced by the temperature effect as in this case, the goal is to detect individual defects within otherwise mostly pore-free material of the same layer. Furthermore, the influence of the layer-to-layer temperature increase is probably small compared to the contrast between defects and the surrounding material and should, therefore, be easily distinguishable.

4 Conclusions

In this paper, the effect of temperature of PBF-LB/M-manufactured metallic parts on the determination of the relative part density through its response to an electromagnetic excitation triggered by an ECT sensor was studied. It is of particular importance as the effective electromagnetic material properties, i.e., mainly the electrical conductivity for the non-magnetic material AlSi10Mg considered here, measured by the ECT sensor are affected both by the relative part density and part temperature, and part temperature variations are inherently occurring in PBF-LB/M. Therefore, the part temperatures were measured during the PBF-LB/M build cycle at the time of the in-situ ECT measurement, i.e., at each recoater crossing between layers, with a calibrated infrared camera. For the part temperature range observed within this study, it is confirmed that, as expected, the ECT response varies linearly with the part temperature. By applying a linear temperature compensation to the ECT signal, the mean average error of the layerwise measured relative density, which indicates the accuracy of determining the whole part relative density, is reduced by a third: from 0.22% to 0.15%. The improvement is valuable for a better discrimination between different part qualities, and especially for the layer-by-layer evaluation of the relative density as it removes the temperature drift in the ECT signal triggered by the observed layer-by-layer increase of part temperature. The temperature effect on the measured ECT signal is not correlated with the part density, allowing for the simple compensation scheme proposed in this study.

Another important finding is that the volumetric energy density, herein varied by selecting different scan speeds, and the illumination sequence, i.e., the order in which the laser illuminates the different parts on the build plate, have a negligible impact on the part temperature during the recoater crossing when an in-situ ECT measurement is conducted, the final part temperature, as well as the overall temperature variation during the build job. To be precise, the time delay between the laser illumination and the in-situ ECT measurement has a perceptible but small effect on the part surface temperature. For the experiments conducted in this study, the by far most relevant temperature variation is the layer-by-layer part temperatures increase from about 55$^{\circ }$C to 75$^{\circ }$C irrespective of the part position on the build plate and the applied process parameters. It means that, for a given part geometry, the temperature compensation parameters could be established once from a good fabrication without requiring the installation of any temperature sensors. For an additional level of sophistication, the routinely performed thermal simulations, i.e., for the evaluation of residual-stress-induced part deformations, could be used to give an input to the temperature compensation algorithm. Nevertheless, if a temperature sensor is available on the PBF-LB/M machine, its output can be used but the results demonstrate that this should not be necessary in most industrial use cases.

Declarations

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this article.

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Titel: Influence of part temperature on in-situ monitoring of powder bed fusion of metals using eddy current testing
verfasst von: Marvin A. Spurek
Adriaan B. Spierings
Marc Lany
Bernard Revaz
Gilles Santi
Jonatan Wicht
Konrad Wegener
Publikationsdatum: 10.04.2024
Verlag: Springer International Publishing
Erschienen in: Progress in Additive Manufacturing
Print ISSN: 2363-9512
Elektronische ISSN: 2363-9520
DOI: https://doi.org/10.1007/s40964-024-00600-5

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Influence of part temperature on in-situ monitoring of powder bed fusion of metals using eddy current testing

Abstract

Publisher's Note

1 Introduction

2 Materials and methods

2.1 Experimental setup and build cycle

2.2 In-situ eddy current testing

2.3 In-situ full-field infrared monitoring

2.4 X-ray micro-computed tomography

3 Results and discussion

3.1 \(\upmu\)CT analysis

3.2 In-situ full-field IR monitoring

3.3 Relative density monitoring via in-situ ECT

3.4 Temperature compensation

3.5 Implications for industrial use

4 Conclusions

Declarations

Conflict of interest

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Parameter
Scan speed (P1–P5)	\(v_s\)	[mm/s]	1500, 1800, 1915, 2015, 2100
Hatch distance	\(h_s\)	[\(\upmu\)m]	100
Laser power	\(P_L\)	[W]	380
Layer thickness	\(t_{l,n}\)	[\(\upmu\)m]	60
Laser spot diameter	\(d_s\)	[\(\upmu\)m]	105
Scan pattern		–	90\(^\circ\) alternating
Recoater type		–	Silicone-reinforced carbon fiber brush
Recoating speed	\(v_r\)	[mm/s]	100
Shielding gas		–	Nitrogen
Chamber oxygen content		[ppm]	< 1000
Chamber overpressure		[mbar]	60