On the Influence of Cross-Section Size on Measured Strength of SLM-Produced AlSi10Mg-Alloy

The freedom in choice of geometries in additive manufacturing (AM) favors the use of structures with large surface and small cross-section such as lattice structures and thin-walled hollow profiles. On the other hand, the practices of strength testing of metals require a certain bulk of the material to be printed to be able to produce a sample and test material properties. The size of the sample cross section might influence the strength and up to 30% decrease in strength for small struts was reported in the literature. Understanding the influence of the cross-section size on the strength of SLM-produced metal is crucial to be able to relate the strength determined through tensile testing and the strength of an SLM-produced component with complex geometry. This article deals with effect of cross-section size on the measured strength of the SLM-produced AlSi10Mg-alloy. It is demonstrated how the decrease in strength can be explained by the difference between measured and actual cross-section area induced by surface roughness rather than by the difference in microstructure between the samples of different sizes.


Introduction
As the additive manufacturing (AM) technology develops beyond its initial niche of rapid prototyping towards the use of additively manufactured components as load bearing parts, the material testing engineers are faced with the need to characterize the strength and other mechanical properties of the AM-produced materials. Selective Laser Melting is a type of (AM) technology that allows to produce fully dense metal parts. This paper focuses on mechanical properties of AlSi10Mg, which is one of the most used SLM-processed aluminium alloys along with AlSi12 and AlSi7Mg.
Although, the mechanical properties of SLM-produced aluminum are extensively studied, lack of research based universally accepted guidelines and standards makes it is difficult to benchmark or compare the properties of the same material printed using different SLM-machines and/or different specimen geometries, as noted by [1]. ASTM F3122-14 [2] only provide some general guidelines on use of existing material testing standards on AM-products, but the existing standards are not fully adopted for additive manufacturing. E.g., when it comes to SLM produced aluminum, it is not clear how the rough surfaces produced by SLM-process should be handled, hence most researchers tend to machine their tensile samples, as Table 1 indicates. Studies that make direct comparison between different SLM-printers are scarce, among reviewed papers in Table 1, only one [3] makes a direct comparison of mechanical AlSi10Mg-alloy produced by different SLM-printers and a similar comparison was done by [4] for 316L austenitic steel. The comparison of different sample sizes and geometries also seems not to have received enough attention in the literature yet. In our earlier work we reported a comparison of strength of SLM-produced AlSi10Mg samples of different diameters [5]. Similar, but more focused study was reported by [6] who compared the strength, the microstructure and the porosity of AlSi10Mg samples of different diameters and reported up to 30% decrease in strength for small struts. [7] also studied size effect and made a comparison of microstructure of SLM-produced AlSi10Mg plates of different thickness, but no tensile properties were tested.  [3], [30]- [35] Flat cross-section samples cut out of a plate or thin-walled profile [36]- [39] Net shape rectangular cross-section samples that were sandblasted [40] Net shape cylindrical [6], [41]- [43] Mass-produced net shape rectangular samples [44] Understanding the influence of the sample cross-section size on the measured strength is crucial to be able to compare the values of strength reported using different sample geometries. In this article we complement our previous results from [5] with additional study of material microstructure and make a comparison with the results of [6] in order to gain a deeper understanding on how the measured strength and microstructure of SLM-produced AlSi10Mg are affected by the size of printed cross-section.

Materials and Methods
The experimental work reported in [5] and [45] includes 15 sets of uniaxial tension test samples printed in two rounds sets #1-6 in the first round and sets #7-15 in the second round. The samples were printed by SLM®280 metal printer with 400 W laser using 50 μm printing layer thickness and argon gas as protective atmosphere. AlSi10Mg powder for printing was acquired from TEKNA advanced material [46].  This article aims at better understanding the effect of the sample size on measured strength of net shape samples; therefore, we concentrate on further analysis of series ID#3, ID#6, ID#11, ID#13, and ID#15 reported in Table 2. The samples in these series were oriented vertically i.e., in the build direction, which allows to 3D-print samples without the need for support structure. Overview of the all 15 series can be found in [5].
Cylindrical samples were used. Fig. 1a illustrates the geometry for d=5.0 mm sample; as can be seen, the parallel length Lc=35 mm, which allows for gauge length L0=25 mm. Sample geometry is in accordance with [47]. Net shape samples were printed directly while the machined samples were printed with 1 mm surplus that was later machined away. Fig. 1c shows samples of different diameters; samples of 2.5 mm, 4.0 mm and 6.0 mm diameter were produced by scaling the original 5.0 mm diameter sample geometry.
The additional microstructure investigation reported in this article was performed using the Scanning Electron Microscope Jeol JSM-7200F. The samples for microstructure investigation were cut out of the gauge length section of the sample after the testing and from the grip part of the sample as Fig. 1a indicates.

Microstructure
The SLM-produced AlSi10Mg obtains a unique cellular microstructure shown in Fig. 1b, which forms due to rapid cooling and remelting during SLM-process. The microstructure is sub-granular i.e., the cells are substantially smaller that the individual grains (see e.g. [48] for EBSD images) and the cell walls consist of small particles of Si. The heat treatment or prolonged exposure to the heat under the printing process leads to formation of bigger spherical particles of Si in Al matrix and reduction of strength combined with increase of ductility.
[6] reported comparison of net shape AlSi10Mg samples with diameter in the gauge part d=5.0 mm, d=4.0 mm, d=3.0 mm, d=2.0 mm, and d=1.0 mm; they measured strength, microstructure, and porosity. [6] reported that sample strength decreases with diameter; porosity increases with diameter and the microstructure of the material varies in such a way that the silicon cell size decreases with diameter i.e., larger diameter leads to slightly larger average cell size. Fig. 2 illustrates the microstructure of the samples with initial diameter in gauge area d=2.5 mm, 4.0 mm and 6.0 mm, the diameter of the grip area was twice as much i.e., 5.0 mm, 8.0 mm, and 12 mm, respectively. These three series were printed in the same printing round. Fig.2a-2c demonstrate microstructure of the gauge part of the sample, while Fig. 2d-2f demonstrate the microstructure of the grip part of the sample. It can be seen that the tendency described by [6] is present and the larger sample diameter generally shows larger cell size, but the tendency is not that well pronounced. Although, images shown in Fig. 2 are representative of most of the area in the corresponding samples, there are also areas with varied cell size within the same sample as shown in Fig. 3 The cell structure is slightly different close to the edge of the sample as Fig. 4 indicates; there are some elongated and open cells present. But no distinct difference in microstructure is observed between bulk and the edge material. Thus, study of microstructure didn't show any unusual difference

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Achievements and Trends in Material Forming between edge and bulk material that could have explained anomalous behavior of the machined samples from series ID6 discussed in [5].

Strength Variation with Sample Cross-Section
Fig. 5 presents the average yield strength and tensile strength of the sample series as function of the sample printed diameter. The strength of the machined samples from series ID#6 is placed at d=7.0 mm which corresponds to the printed cross-section diameter before machining. The strength values from [6] are also displayed for comparison. We can see that there is about 10% difference in yield strength between unmachined samples with d=2.5 mm and d=6.0 mm, the same goes for results reported by [6], where the difference in strength of d=2.0 mm and d=5.0 mm samples is about 10%. In case when the cross section has a rough surface, a natural approach for a structural analyst would be to try do define net cross section area i.e., the area that is actually involved in carrying the load. [49] explicitly suggested that the net dimensions of the cross section deviate from measured dimensions by the values of surface roughness and thus 2 need to be subtracted to determine the net dimensions for calculations of material strength, when dealing with unmachined AM-produced tensile samples. Using this approach, the connection between measured and actual engineering stress in the samples can be expressed as: (1)

Achievements and Trends in Material Forming
Where is the engineering stress calculated using the uncorrected surface area, is the engineering stress determined using the reduced cross section area, d is initial diameter and the is the reduction due to the surface roughness. Eq. 1 can be applied to both yield strength and tensile strength. Note that [49] suggest using the average peak roughness, but here we treat simply as difference between the actual dimension and the measured one without getting into the discussion on how should be measured or whether represents actual surface roughness or is just a correction to represent the difference between measured and loaded cross-section dimensions.
Assuming the surface roughness correction to be independent of diameter, we can fit the Eq. 1 to the measured yield strength data by selecting appropriate value of . Eq. 1 fits well to our experimental results, but it is even better to fit it to result of [6] as displayed in Fig. 5 as there are more data points to utilize. The fit in Fig. 5 is set to go through the yield strength for the d=5.0 mm and the roughness correction is set to fit the rest of the data, this gives = 0.16 mm. The fit for tensile strength uses the same = 0.16 mm and is only set to go through the tensile strength point of d=5.0 mm. Thus, we observe that the value of determined to fit the variation in yield strength predicts the variation in tensile strength as well.

Discussion and Conclusions
One of the challenges that hinders a wider use of SLM products is variability of the mechanical properties of the produced parts. Hence, studying the influence of different parameters that might affect the properties of the produced alloy is vital for the further advance of applications of SLMtechnology. AM opens for shape flexibility and allows to produce samples with cross-sections of different shapes and sizes and understanding how the measured material strength is influenced by the cross-section size is important to be able to compare the result form different studies. This paper studied how the size of the printed cross section affects the properties of the SLM-produced AlSi10Mg-alloy.
The tensile tests results are consistent with the earlier findings of [6], who reported 30% decrease in strength for d=1.0 mm samples in comparison with d=5.0 mm samples. However, while [6] tend to attribute the difference in strength to differences in microstructure, our microstructure investigation do not confirm that. Some minor difference in microstructure between samples with different printed cross-section area was observed, but this variation is not enough to explain observed difference in strength. Hence, an alternative explanation was provided. It was demonstrated that the difference in strength between samples of different diameters can be explained by the surface roughness causing a difference between measured and actually loaded cross-section area. The compensation for surface roughness not only explains the difference in strength between samples of different diameters, but also makes a correct prediction about strength of the small samples based on the strength of the large ones and correctly predicts variation in tensile strength based on variation in yield strength.