Characterization of flexural fatigue behaviour of additively manufactured (PBF–LB) gyroid structures

Unit cells can be arranged in various configurations, leading to distinct geometries. In Fig. 1b, a non-conformal homogeneous cell arrangement is presented within a cylindrical block with a hole along its rotational axis. The cylinder's boundaries are independent of cell properties, resulting in an uneven shell surface. In contrast, Fig. 1c illustrates radially conformal unit cells that adapt to the cylindrical contour, varying in size across the cross section to maintain conformity. As a result, the relative density varies across the specimen's cross section. The specimens in this study feature an arrangement of radially conformal unit cells around a 1 mm diameter recess along the rotation axis.

The outer contour of the specimen geometry follows the specifications from DIN 503113:2018–12 [20] with the central portion being replaced by a cellular structure. This cellular structure gradually increases its wall thickness and diameter toward the 12.2 mm shafts, as shown in Fig. 2a. The selected cell geometry is the “Gyroid Schoen” form, initially described by Alan Schoen in 1970 [21], depicted in Fig. 1a.

The cells are arranged radially, as illustrated in Fig. 1c, causing the cell size and, consequently, the specimen's relative density to vary across the diameter. In the outermost row of the central part, samples consist of 4 mm × 4 mm unit cells with a 0.5 mm wall thickness. The wall thickness remains unaffected by the conformal arrangement, while the unit cell size diminishes toward the rotation axis of the specimen to facilitate conformity, resulting in a calculated relative porosity of 70% for the central part of the specimen under investigation. Additionally, the samples incorporate a 1 mm diameter recess along the rotation axis to ensure effective powder removal, as shown in the cross section in Fig. 2b. For precise geometrical specifications, refer to Fig. 2a.

The complex features of the sample geometry were calculated using field-driven design within the software nTopology (nTop Inc., USA). The continuous augmentation of the wall thickness and the diameter aims to avoid sudden jumps in Young’s modulus and the section modulus within the transition zone of the structure and shaft, allowing a targeted investigation of the cylindrical 8 mm × 8 mm cell structure in the gage length.

An SLM 280 HL PBF–LB system (SLM Solutions Group AG, Germany) was employed for fabricating the samples in this research. All samples were manufactured with a layer height of 30 μm under an argon inert gas atmosphere, using AlSi10Mg powder sourced from SLM Solutions Group AG, Germany with a relative humidity of less than 5%.

A total of 50 specimens were fabricated, with 25 printed using the standard parameters (Std.Par) for AlSi10Mg provided by SLM-Solutions AG, and 25 employing a modified parameter set (Mod.Par). The relevant parameters for each set are detailed in Table 1. Within the modified parameter set, changes were made to the beam compensation, the border distance as well as the scanning speed, the laser power and the build platform temperature. The beam compensation parameter governs the distance between the centre of the contour beam and the geometry’s border contour. The reduction of this parameter in combination with the reduced border distance, leads to two contour scan lines of the delicate 0.5 mm walls. This contrasts with the standard parameters, which utilize only one contour scan. This distinction is graphically depicted in Fig. 3, showcasing the calculated laser trajectories of both parameter sets on the same layer within the specimen's centre. The geometry outline is given in green, contour parameters are highlighted in red, while hatch parameters are represented in yellow. Notably, the modified parameter set accommodates two contour scans and a hatch on the slender wall geometry, whereas the standard parameters use a single contour scan to meet the geometry requirements. Both the standard parameter and the modified parameter scan from the inside to the outside. This means the following sequence: first the hatch, if present, is exposed, then the inner contour and finally the outer contour.

To manage energy input while executing multiple scans, the laser power of the contours was nearly halved, and the scan speed was notably increased in the modified parameter set. Despite this adjustment, the total energy input of the modified parameters was still increased on this specific geometry, due to the execution of two contours plus a hatch instead of a single contour. Achieving optimal parameters for thin-walled structures requires an extensive parameter study which falls out of the scope of this work (Table 2).

All samples were manufactured without incidents and exhibit no visual defects. It is noticeable that the surface of the specimens manufactured with the modified parameters exhibits a significantly rougher texture, but in return, they appear to have a higher level of detail resolution of the filigree walls, as can be seen in Fig. 4. Due to the complex thermal conditions during manufacturing, which can result in residual stresses within the fabricated component, there are geometric inaccuracies related to the concentricity of the shafts. To address this, the concentricity of the shafts was ensured through lathe machining, with both shafts being turned down to a diameter of 12.0 mm.

The rotating bending tests were conducted using a Italsigma 2 TM831 rotating bending machine (Italsigma s.r.l, Italy) with a stress ratio, R = − 1 and 20 Hz rotation frequency. Due to the intricate cell geometries present in the test specimens, employing the conventional method of calculating bending stress using data from attached strain gauges and theoretical bending stresses proves challenging. Consequently, an empirical approach is adopted, utilizing the deflection “f” of the specimen's centre as a measure rather than the bending stress. The adaptation of the rotating bending test was driven by practical considerations due to the complexity of the specimen’s geometry and allows for a comparative analysis of the porous specimens investigated in this work. The principle of displacement measurement is illustrated in Fig. 5. This approach enables the determination of cycle count based on the sample’s deflection. The deflection is measured using a dial gauge (Hahn & Kolb, Germany) positioned from the top at the specimen's centre. Different weights were applied, resulting in deflections ranging from 0.1 mm to 1 mm. Each deflection was tested five times for each parameter set, yielding two independent Woehler curves. The examined deflection horizons cover 0.1 mm, 0.15 mm, 0.25 mm, 0.5 mm, and 1 mm. To achieve the respective deflections, identical weights were applied to both set of specimens, indicating similar stiffness.

One sample from both the standard parameter set and the modified parameter set was cut in the centre, embedded in epoxy resin, and polished to a mirror-like finish, after which they were treated with Dix & Keller reagent. SEM images of the microstructure of the thin walls in the centre of the specimen were taken using a Zeiss Sigma 300VP (Carl Zeiss AG, Germany) at an acceleration voltage of 5 kV. Light microscope images were taken with a Zeiss Axioscope 7 (Carl Zeiss AG, Germany).

For each set of parameters, 5 roughness measurements were taken before turning at 3 randomly selected locations along the shafts orthogonal to the build direction using a Zygo NewView 8300 (Zygo Corporation, USA) white-light interferometer.

Optical porosity analysis was conducted using ImageJ software [22] with microscopic images capturing the entire cross section of a sample from each parameter set.

Exploratory hardness tests were conducted on two fractured specimens from different parameter sets. Vickers HV0.3 microhardness tests were performed following ISO 6507 [21] guidelines on two cross sections using an Emcotest Durascan (Emco GmbH, Austria) with a test force of 3 N and a dwell time of 10 s at each measuring point. Along the rotational axis of each sample geometry, 20 measuring heights were selected, spaced 5 mm apart from one another (refer to Fig. 8). Multiple measurements per height were taken near the fracture point, and a mean value with standard deviation was calculated.

The arithmetic surface roughness of the samples manufactured with the modified parameters is noticeably worse, with an Ra value of 28.4 ± 12.2 µm, compared to the samples with the standard parameters, which exhibit a surface roughness of 3.9 ± 1.6 µm. Also noteworthy is the large standard deviation in the modified parameter samples, indicating significant irregularities on the surface. These irregularities, visible in the white-light interferometry images in Fig. 6, appear to result from powder particles adhering to the specimen's surface.

These results are in line with the detailed studies conducted by Poncelet et al. [13], who examined various scan strategies and offsets on 0.6 mm AlSi10Mg walls and ultra-thin walls consisting of two scan lines, covering parameters similar to those presented in this study. The high surface roughness in the modified parameter samples can thus be attributed to significant protuberances formed by outward-flowing melt pools when the geometry's hatch is exposed first. The already solidified hatch disrupts the contour tracks and pushes them outward toward the unmelted powder [13], which can then partially sinter to the specimens surface. The thin walls of the standard parameter samples in the present work are exposed with a single contour scan, while the modified parameter samples are exposed from the inside out with a small hatch and two subsequent contour scans each. Poncelet et al. [13] report that the phenomenon did not occur in samples that exposed the outer contour first, suggesting that the resulting surface roughness of the modified parameters could be improved by swapping the scan order of the contours.

High surface roughness in AM parts is not necessarily linked to poor fatigue behaviour [14, 23]. Partially melted powder particles, spatters, and powder particles stuck to the surface are not considered sites of crack nucleation as long as they extend outward from the part profile [14]. Surface and sub-surface defects such as pores and sharp edges, however, are considered to have a large impact on the fatigue performance of build parts, as they act as crack initiation sites under cyclic loading [14, 23, 24]. Surface finishing techniques such as sandblasting and milling, however, do not consistently eliminate these defects and thus exhibit inconsistent improvements in the fatigue behaviour of PBF–LB specimens [15, 16]. Surface post-processing of cellular structures also proves to be a challenging endeavour due to inaccessible surfaces.

In the micrographs of the samples shown in Fig. 7, it can be observed that the modified parameter samples exhibit significantly fewer pores in the delicate structure region than the standard parameter samples. This is not the case in the shaft, which consists of a larger volume. The optical analysis using ImageJ reveals that the shafts of the modified parameter sample exhibit a relative density of 99.9%, while the shafts of the standard parameter sample are marginally lower at 99.87%. However, when focusing solely on the thin-walled structure area, the difference in relative density is drastic, with 99.90% for the modified parameter sample and only 99.17% for the standard parameter sample. As software was employed to measure the percentage porosity, it is conceivable that the resolution of the images may not permit the consideration of the finest pores present. The optical contrast between the porosities depicted in Fig. 7 appears to be significant, whereas the numerical difference only amounts to a delta of 0.73%.

With a few exceptions, all pores exhibit high sphericity, indicating they consist of entrapped gas. Given that the standard parameter operates with more than double the track energy density (TED) of the modified parameter and a slower scan speed, the material's liquefaction and solidification occur rapidly upon single exposure of the thin wall contour. This could potentially result in the entrapment of gas formed due to vaporization of material [25, 26], or due to the entrapment of shield gas because of surface turbulence in the melt pool [27]. The large pores in the standard parameters always formed at the centre of a weld track. Aboulkhair et al. [26] also reported increased gas pore formation in AlSi10Mg samples manufactured with slow scanning speeds at high energy densities. Pores have been shown to significantly influence the fatigue behaviour of PBF–LB AlSi10Mg parts, as they can act as internal crack initiation sites [28‐30].

The Vickers hardness test results are presented in Fig. 8. The central part of the graph displays the distance of the measuring points from the bottom of the sample, with corresponding hardness values on the left and right for each tested specimen. The fracture point is marked with a dashed line, and the build direction (BD) is indicated by an arrow. Within the shafts, the average hardness for the standard parameter sample is 103.5 ± 3.4 HV0.3, while for the modified parameter sample, it is 99.7 ± 3.6 HV0.3. Regarding the fine structures, the standard parameters yielded a hardness of 84.3 ± 7.9 HV0.3, whereas the modified parameters resulted in a hardness of 94.9 ± 5.9 HV0.3. Published literature reports a range of values between 95 and 135 HV [13, 31‐33] for as-built PBF–LB AlSi10Mg, positioning our specimens below the typical hardness of as-built PBF–LB AlSi10Mg. The AlSi10Mg powder from the manufacturer is specified to yield parts with a hardness of 124 ± 7 HV5, while the heat-treated condition is noted at 82 ± 1 HV5 [34]. Reduced hardness has been associated with a coarser microstructure in PBF–LB AlSi10Mg specimens [13, 35], suggesting microstructure coarsening in the specimens manufactured in this work, particularly within the thin wall sections. This effect seems to be more prominent in areas where the low build volume hampers heat dissipation through the build part, leading to slower cooling of the solidified material. A coarsening in microstructure is generally associated with an improved ductility. Another possible factor that can contribute to reduced hardness is the decreased supersaturation of aluminium crystals with silicon particles resulting from a slower cooling rate [36].

The wide range in reported hardness values indicates that both the geometry and process parameters have a significant impact on the resulting hardness. This can be attributed to the resulting thermal profile of the specimen during manufacture, which varies significantly based on energy density, exposure strategy, and available volume for heat dissipation. This variability is known to affect the microstructure and thus influences the hardness [31, 35].

The inhomogeneous microstructure of as-built PBF–LB AlSi10Mg usually consists of cellular α-Al dendrites with ultra-fine eutectic Si networks at their boundaries [17], with the Al dendrites growing epitaxially in the build direction. It is strongly influenced by the melt pool and can be divided into three zones: a fine cellular zone, a coarse cellular zone, and the heat-affected zone in the previously solidified layers [33]. Figure 9 displays comparative SEM images of the standard and modified parameter samples, taken at a random location below the fracture point in the thin-walled structure. Due to the microstructure's division into different regions depending on the melt pool, a quantitative comparison of grain size cannot be provided here. However, it is evident that the eutectic Si network in the modified parameter sample varies significantly at the observed location due to the repeated energy input resulting from the two contours, alternating between a fine cellular structure and a broken, coarser distributed Si phase, as is common for PBF–LB manufactured specimens [13, 33, 37]. In contrast, the SEM image of the sample with standard parameters displays a relatively uniform coarser cellular structure. The decrease in hardness observed in the thin walls of the standard parameters could suggest, that the fast energy input and higher platform temperature linked to these parameters may lead to grain coarsening due to prolonged exposure to elevated temperatures, a phenomenon documented by other researchers [13, 33]. This could potentially lead to a deterioration in mechanical behaviour following the Hall–Petch relationship.

All specimens exhibited consistent fracture behaviour, breaking near the centre of the sample with the fracture point slightly shifted upward in the direction of construction. Since all samples fractured at the same point, a qualitative comparison can be made. The results of the rotating bending tests for specimens manufactured using AlSi10Mg standard parameters and modified parameters are depicted in Fig. 10. The graph shows the deflection "f" at the centre of each sample on the y-axis and the corresponding number of cycles until failure on the x-axis, both on a logarithmic scale. Linear regressions were calculated for each dataset in accordance with the ASTM E739-23 standard [38], represented by two straight lines with a slope of -0.47 for the standard parameters and -0.54 for the modified parameters. The samples manufactured with the modified parameters exhibit improved fatigue resistance, evident from the rightward shift of the linear regression lines.

As discussed in the respective sections, two mechanisms could be responsible for these effects, both stemming from the reduced track energy density: Firstly, a high TED can lead to grain coarsening due to prolonged exposure to elevated temperatures, consequently diminishing the mechanical properties. Secondly, the high TED seems to contribute to the formation of numerous pores within the thin walls of the standard parameter specimens, negatively impacting their fatigue performance. While surface defects are considered a main contribution factor to the fatigue resistance of additively manufactured (AM) parts [39], in the tested specimens, the influence of build defects and microstructural changes seem to outweigh the impact of poor surface quality. This is evident as the modified parameter samples exhibit significantly improved performance in the high-cycle fatigue range.

The slightly reduced slope of the linear regression line for the standard parameter samples compared to the modified parameter samples suggests that microstructural effects as well as build defects become more significant at larger deflections. Conversely, this implies that the high surface roughness becomes more pronounced at higher cycle numbers, as the lines converge in the high cycle fatigue region. None of the deflection horizons appear to reach the knee point in the conducted tests, which usually indicates the transition to the endurance limit region, characterized by a wider scatter of results [12]. Beretta et al. [39] indicated that the knee point for PBF–LB as-built AlSi10Mg lies around 4 × 10^6 cycles in tension fatigue tests of solid samples with similar outer geometry, yet complexities in our structure might reduce fatigue strength.