Shock compression response of additively manufactured AlSi10Mg

Additive manufacturing (AM), or 3D printing, refers to several manufacturing techniques in which a material is deposited layer by layer in an additive manner to achieve the final form.^1–7 This contrasts with traditional manufacturing and machining techniques that use subtractive methods to form the desired shape from a larger billet. AM has the potential to dramatically alter current engineering design processes through rapid prototyping, reduced material waste, and novel and complex topologies.

Though metallic AM methods have been developed to utilize sheet and wire feedstock,⁸ the majority of AM methods employ powder feedstock. In one such method, commonly termed laser powder bed fusion (LPBF) or selective laser melting (SLM),⁹ a rake is used to spread a fine layer of powder over the print area. A laser is then rastered over the powder bed, selectively melting the material. This process is repeated until the final form is achieved.

The low density, high strength, large thermal conductivity, and good corrosion resistance of Al-based alloys have made them ubiquitous in many engineering applications. One Al-based alloy commonly used in LPBF is AlSi10Mg (Al, 9–11 wt. % Si, 0.2–0.45 wt. % Mg),¹⁰ which has applications in the automotive and aerospace industries.^10–13 Its near eutectic composition of Al and Si lowers the freezing range compared to pure Al and improves weldability.⁹ The large presence of Si also improves fluidity and reduces thermal expansion, thereby producing higher print densities and reducing cracking caused by the build up of residual stresses.^11,14 Furthermore, the formation of Mg₂Si and, if excess Si is present, metastable $β′$ precipitates enable age hardening.¹⁵ However, as with most Al-alloys, oxide formation, high thermal conductivity, and high reflectivity at the laser wavelength (typically 1.06 $μ$m), require AlSi10Mg be printed with high laser powers and slow scan speeds.^9,14

Numerous studies have focused on understanding the mechanical response of LPBF AlSi10Mg to enable its adoption into engineering systems. These have included studies at quasi-static^12,16–23 and intermediate^{11,13,22,24–31} strain-rates. At quasi-static strain-rates, the LPBF AlSi10Mg exhibits a similar stiffness but higher strength and strain to failure than cast AlSi10Mg.^12,16 At intermediate strain-rates, the LPBF AlSi10Mg exhibits higher strength and hardening but lower ductility compared to the cast material.¹¹ Many studies have also shown that LPBF AlSi10Mg exhibits strong strain-rate sensitivity and anisotropy in mechanical response relative to the build direction.^{16,17,24–26,28–30}

The differences in behavior between cast and LPBF AlSi10Mg are attributed to the microstructure produced by the LPBF process.^12,29,32 The microstructure is highly sensitive to the fabrication parameters,^10,33,34 but, in general, the rapid cooling rates encountered in the AM process generate a fine microstructure of cellular eutectic Si-rich particles in an Al matrix.¹² This contrasts with the large plate-like Si-rich precipitates observed in cast AlSi10Mg.^34,35 Variations in thermal history during printing of AM AlSi10Mg lead to heterogeneities in the microstructure at the length scale of the melt pool^33,34 due to the dissolving of Si out of the saturated Al matrix.¹² 

Neutron diffraction measurements of LPBF AlSi10Mg under tensile loading have shown that Si provides significant hardening because it supports much larger lattice strains than the Al matrix.³⁶ Post-processing heat treatment of the LPBF AlSi10Mg modifies the microstructure via segregation of the Si into large precipitates, dissolving the Si-rich cellular structure generated during fabrication.^12,18,37 Heat treatment has also been shown to alter the mechanical response at both quasi-static^{12,18–21,23} and intermediate strain-rates,^28,29,31 suggesting that changes to the structure of the Si contribute to changes in the mechanical response.

Though there has been significant work at quasi-static and intermediate strain-rates, there are a few studies examining the mechanical response of LPBF AlSi10Mg at high strain-rates. Zaretsky et al.³⁵ performed a series of plate-impact experiments to a peak stress of roughly 5 GPa to measure the Hugoniot elastic limit (HEL) and spallation strength of LPBF AlSi10Mg. They found that the HEL and spallation strength of LPBF AlSi10Mg exceeded that of cast AlSi10Mg by factors of two and four, respectively. Their work did not indicate anisotropy in the material response relative to the build direction at these high strain-rates. Additionally, they observed a change in the strain-rate sensitivity of the failure and compressive strengths of the LPBF AlSi10Mg at a strain-rate of approximately $5×103$ s$−1$⁠. At that strain-rate, the failure mode was observed to transition from ductile to brittle and a stark change in the rate sensitivity of the compressive yield strength was found and attributed to a transition from thermally-activated dislocation glide to nonlinear phonon drag.

Laurençon et al.^38,39 studied the HEL and spallation strength of LPBF AlSi10Mg to peak stresses near 2.5 GPa induced by laser-driven shocks. They found that the build parameters strongly influence the observed HEL and failure response. This was attributed to variation in porosity of the material as increases in porosity lowered the HEL and spallation strength. Like Zaretsky et al.,³⁵ they observed no significant orientation dependence in the HEL or spallation response relative to the build direction. However, they did observe differences in the fracture surface as a function of material orientation and posited that these differences were related to the nature of the melt pool boundaries.

Understanding the dynamic material response of LPBF AlSi10Mg is critical for its adoption into engineering applications subjected to high strain-rates. Motivated by the need for more work in this area, we build on the previous efforts of Zaretsky et al.³⁵ and Laurençon et al.^38,39 in this paper. Specifically, we performed uniaxial plate-impact experiments to extend the stress range of measured LPBF AlSi10Mg dynamic properties and to extract the first measurement of the LPBF AlSi10Mg Hugoniot, a critical thermodynamic relationship that enables closing the Rankine–Hugoniot equations and the development of material equations of state. We present the Hugoniot, HELs, and spallation strengths as a function of material orientation up to peak impact stresses of greater than 13 GPa.

This paper begins with a discussion of the material fabrication and characterization, followed by a description of the plate-impact experiments in Sec. II. The results of these experiments are then presented in Sec. III and discussed in Sec. IV.

The LPBF AlSi10Mg investigated in this work was obtained from CalRAM Inc., a Carpenter Additive company. The material was printed on an SML 280HL machine (SML Solutions) under an inert atmosphere using virgin vacuum induction melted, N₂ gas atomized powder obtained from Carpenter Additive. The powder size ranged from 20 to 63 $μ$m, with roughly 2% of the powder volume falling above and below that range. The composition of the powder in weight percent, as given by Carpenter Additive, is provided in Table I. Carpenter Additive states that the combined total weight percentage of all other elements not directly measured in Table I is $<0.15$ wt. %, with no individual element $>0.05$ wt. %. The LPBF AlSi10Mg used in this work was printed as a large billet that was 6 in. long in the direction of gas flow (X), 4 in. long in the direction of the recoater (Y), and 5 in. long in the build direction (Z). The specific build parameters are given in Table II. The scan vector was rotated between each successive layer to increase the print density. The LPBF AlSi10Mg billet underwent a stress-relief heat treatment at 550^oF for 2 h.

The composition of the as-printed LPBF AlSi10Mg was measured for six samples taken from various locations in the billet. The average composition in weight percent for those six samples is given in Table I. The metallic elements were measured using inductively coupled plasma-mass spectroscopy (ICP-MS). The C, O, and N contents were measured using a gas fusion and combustion technique involving a LECO Corporation elemental analyzer.⁴⁰ The printing process led to slight changes in the alloy composition due to the vaporization and oxidation of Al.

Scanning electron microscopy (SEM) images were obtained normal to all three principal directions at 15 locations spaced throughout the LPBF AlSi10Mg billet. Variations in the microstructure parallel (Z) and perpendicular (X and Y) to the build direction were observed. These variations were consistent for all locations examined throughout the billet. Additionally, no significant differences in the microstructure for both perpendicular directions (X and Y) were observed. Figure 1 shows inverse pole figure (IPF) maps obtained from electron backscatter diffraction (EBSD) measurements for our LPBF AlSi10Mg parallel [Fig. 1(a)] and perpendicular [Fig. 1(b)] to the build direction. Both IPF maps shown in Fig. 1 are colored in reference to the build direction.

A clear bimodal grain structure is evident with small grains surrounding larger grains elongated in the build direction. The elongated grains show a preference for the [001] orientation. As noted in Sec. I, as-built AM AlSi10Mg exhibits a fine, cellular, eutectic structure.^33,41,42 The solidification of FCC systems grows preferentially along the $<001>$ orientation, in the direction of heat flow.⁴³ The successive melting of the subsequent layers, rotation of the scan pattern between layers, and the relatively small melt pool in AlSi10Mg produce a thermal history aligned with the build direction.^29,41 The conditions for grain elongation are more likely at the center of the melt pool,⁴¹ meaning the smaller grains formulate at the melt pool boundaries.

A higher resolution SEM image of our LPBF AlSi10Mg microstructure is shown in Fig. 2. Uniformly dispersed Si-rich particles are evident throughout the Al matrix. This uniformly distributed Si-rich phase is a result of the stress-relief heat treatment. Because the LPBF AlSi10Mg was heat treated, the cellular structure generated during the AM process erodes and Si begins to agglomerate into precipitates.^12,18,37

The density of the LPBF AlSi10Mg was measured with an Archimedes method and is given in Table III. The bulk density of the alloy (⁠$ρ0$⁠) is 2.66 g/cm³. The LPBF AlSi10Mg used in this study achieved a density of 99.4% of the theoretical maximum density (TMD). In Fig. 1, a pore is evident (white) in both IPF maps. Micro-computed tomography (micro-CT) with a 6 $μ$m voxel size was used to characterize the distribution of pores throughout the LPBF AlSi10Mg billet. The porosity was found to have a consistent size throughout the billet with an average equivalent spherical diameter of roughly 35 $μ$m. Also provided in Table III are the longitudinal (⁠$cL$⁠) and transverse (⁠$cT$⁠) sound speeds measured in the LPBF AlSi10Mg used in this study. The sound speeds are equal across the sample orientations, within the uncertainty of the measurement. Table III also shows sound speeds and densities measured in other LPBF and cast AlSi10Mg,^35,38 as well as Al-1100 (commercially pure Al), Al-6061 (nominally 97 wt. % Al, 1.0 wt. % Mg, and 0.6 wt. % Si), and Al-2024 alloys (nominally 92.7 wt. % Al, 4.4 wt. % Cu, 1.4 wt. % Mg, and 0.5 wt. % Mn).⁴⁴ Our LPBF AlSi10Mg measurements agree well with those prior studies and only minor variation in these properties is observed between the different Al-alloys. All uncertainties provided in Table III represent plus or minus one standard deviation.

Plate-impact experiments were performed at the Shock Thermodynamics Applied Research (STAR) and Dynamic Integrated Compression Experimental (DICE) facilities at Sandia National Laboratories (SNL) to measure the Hugoniot, HEL, and spallation strength of the LPBF AlSi10Mg. The LPBF AlSi10Mg samples were square prisms, with nominal square edge length of 25 mm and precision lapped to a nominal thickness of 4 mm. The sample thicknesses were measured using a NEXIV optical profilometer to quantify the micrometer-scale thickness variation. The experimental targets used at the DICE facility contained three samples, one from each of the principal directions of the LPBF AlSi10Mg relative to the build axis. The larger bore diameter on the guns at STAR enabled each target to contain four samples, one from each of the principal directions relative to the build axis along with one duplicate sample (either X, Y, or Z). Schematics of the DICE and STAR targets are shown in Fig. 3. Samples from all three principal directions were included to quantify the anisotropy in dynamic material properties. Including a duplicate sample on the STAR experiments enabled quantification of the sample-to-sample variability of the dynamic properties at each impact stress.

The targets were impacted at velocities ranging from 0.14 to 1.60 km/s. Experiments generating impact stresses below 3 GPa were performed at DICE, whereas those inducing higher stresses were performed at STAR. Each impactor consisted of a nominally 2 mm-thick Al-1100 disk backed by roughly 6 mm of polymethylmethacrylate (PMMA). Al-1100 was chosen as the impactor because its low yield strength generates a small elastic wave and its equation of state (EOS) was expected to be similar to that of our LPBF AlSi10Mg. This enabled a symmetric design for the spallation experiments. Impact velocities were measured with three electrical shorting pins for both the DICE and STAR experiments. The STAR experiments also included a collimating photonic Doppler velocimetry (PDV)^45,46 probe for a redundant measurement of the impact velocity. Impact of the LPBF AlSi10Mg by the Al-1100 drives shock waves through both materials. The resulting rarefaction fans reflected from the sample free surface and Al-1100/PMMA interface, intersected at the approximate center of the sample, and generated a rapid tensile pulse that induced spallation.

The sample free surface velocities were measured simultaneously with PDV and VISAR (velocity interferometry system for any reflector)⁴⁷ to determine the Hugoniot, HEL, and spallation strength. Measurements were taken at one free surface location in the DICE experiments and two free surface locations (spaced approximately 3.5 mm apart) in the STAR experiments. Because we fielded both PDV and VISAR, we were able to leverage these complimentary measurements for our calculations. We processed our PDV spectrograms with relatively low temporal resolution (Hann windows with 10–30 ns width and 1–5 ns advance) to provide high-precision free surface velocities. VISAR, on the other hand, provided ns-scale temporal resolution with lower velocity resolution (we used a typical velocity-per-fringe of 207 m/s). Given the superior velocity resolution of our PDV measurements and superior temporal resolution of our VISAR measurements, we primarily employed PDV data for determination of free surface velocities and VISAR data for timing of the elastic and shock wave arrivals.

Figure 4 shows a representative free surface velocity (sample Y-4) and identifies key features used for dynamic property calculations. The shock velocity (⁠$us$⁠) was calculated with the measured sample thickness (⁠$hsam$⁠), projectile impact time (⁠$ti$⁠), and shock wave arrival time at the sample free surface (⁠$ts$⁠) according to

The projectile impact time was determined from the measured longitudinal sound speed and elastic wave arrival time at the sample free surface (⁠$te$⁠) by

and the shock wave arrival time was taken as the time at which the difference between the peak free surface velocities of the elastic and shock waves reached its midpoint.^48,49 The particle velocity behind the shock wave (⁠$up$⁠) was assumed equal to half the steady-state free surface velocity after the shock (⁠$ufs,s$⁠): $up≈ufs,s/2$⁠. As noted previously by Walsh and Christian,⁵⁰ the error associated with this approximation typically does not exceed 1%.

Establishment of the relationship between the shock and particle velocities enables determination of the thermodynamic state of the material via the conservation of mass and momentum

where $ρ0$ is the initial density, $ρs$ is the post-shock density, and $σs$ is the shock-induced stress. It should be noted that the use of Eq. (4) to compute the shock-induced stress neglects material strength effects.

The HEL (⁠$σHEL$⁠) was determined from the elastic–plastic transition observed in the free surface velocity (⁠$ufs,HEL$⁠) and is given by

The corresponding elastic strain-rate for the HEL, $ε˙e$⁠, is given by

where $u˙e$ is the slope of the elastic precursor free surface velocity.

The spallation strength (⁠$σspall$⁠) was calculated according to the methodology of Kanel^51,52 and is given by

where $cB$ is the bulk sound speed (computed from the longitudinal and transverse sound speeds according to $cB=cL2−4cT2/3$⁠), $Δufs,pb$ is the velocity pull-back, and $δ$ is a velocity pull-back correction that accounts for elastic–plastic material behavior and is given by

In the correction factor, $u˙1$ is the slope of the pre-spall free surface velocity, $hspall$ is the thickness of the spalling layer, and $cF$ is the propagation speed of the spall pulse front. The thickness of the spalling layer can be determined through simulation or approximated as

where $τspall$ is the period of consecutive velocity pull-backs.⁵² The spall pulse propagation speed is given by

where $σ˙x+$ and $σ˙x−$ are the temporal stress gradients immediately ahead of and behind the spall pulse, respectively, and are given by

and

near the spall plane. Here, $u˙2$ is the slope of the post-spall free surface velocity. Kanel⁵¹ notes that, in plate-impact experiments, $σ˙x+≈0$ at the free surface and suggests a weighting scheme be employed to determine the average spall pulse propagation speed. We employed a 1D Eulerian hydrocode (CTH⁵³) to simulate our plate-impact experiments and found that, though $σ˙x+≈0$ very near the free surface, both $σ˙x+$ and $σ˙x−$ remain approximately constant through the vast majority of the spalling layer. We, therefore, follow Williams et al.⁵⁴ and assume Eqs. (11) and (12) hold throughout the propagation of the spall pulse. The tensile strain-rate during spallation is given by

The measured Hugoniot, HEL, and spallation strengths for the LPBF AlSi10Mg are provided in Table IV. Missing values in the table are due to diagnostic failures (e.g., low light return) that precluded measurements. Uncertainties on reported values were determined via propagation of material property (i.e., thickness, density, $cL$ and $cB$⁠) and experimental timing and velocity uncertainties through Eqs. (1)–(13) with Monte Carlo methods that assume a Gaussian error distribution for all parameters.⁵⁵ All reported uncertainties encompass plus or minus one standard deviation of the corresponding parameter error distribution.

The Hugoniot results are plotted in $us$–$up$ space in Fig. 5. The Hugoniot of the LPBF AlSi10Mg was measured to a peak stress of just over 13 GPa. Though some variation exists between the different sample orientations, these differences are within the uncertainty of the measurement and do not follow a consistent trend. Likewise, redundant measurements made on the same orientation are equal to within the uncertainty. The observed isotropic response motivates a single orientation-independent linear fit of the Hugoniot. Applying an inverse-variance weighting scheme yields

where the velocities have units of km/s and the uncertainty bounds conservatively describe the distribution of non-weighted fits.

The HEL, as a function of elastic strain-rate, is provided in Fig. 6. The HEL ranges from approximately 0.25 to 0.30 GPa, and the corresponding elastic strain-rates are on the order of $105$ $s−1$⁠. The HEL is also approximately isotropic, with orientation-dependent variations existing within the reported uncertainties. A clear trend in the HEL with elastic strain-rate is not evident.

The spallation strength as a function of both peak compressive stress and tensile strain-rate is shown in Fig. 7. Spallation strength varies from approximately 1.1 to 1.4 GPa and is observed to generally increase with both tensile strain-rate (which ranges from $0.7×105$ to $1.2×105s−1$⁠) and peak compressive stress (which ranges from 0.9 to 13.6 GPa). However, in our experiments, larger impact stresses are typically associated with larger strain-rates. The increase in the spallation strength observed with peak compressive stress may, therefore, be partially driven by the tensile strain-rate dependence.

Differences in spallation strength between sample orientations sometimes lie outside the measurement uncertainty; however, these differences are not consistent and do not follow a clear trend. Differences in results from some redundant measurements also exist outside the measurement uncertainty. Taken together, these findings suggest that differences in spallation strength are primarily caused by sample-to-sample variation and not by sample orientation.

This work presents the first Hugoniot measurement of LPBF AlSi10Mg. Our results can be compared to previous Hugoniot measurements of other Al-based alloys. Prior studies on Al-1100 have given a linear fit of $us=5.38+1.34up$⁠, work with Al-6061 has yielded a linear fit of $us=5.35+1.34up$ and studies of Al-2024 have provided a fit of $us=5.37+1.29up$⁠.^44,56–58 These fits match closely with the LPBF AlSi10Mg Hugoniot, we report in Eq. (14). The similarity between our fit to those of other Al-based alloys supports the treatment of the Hugoniot as a measurement of the equilibrium thermodynamic state of the material behind the shock front, primarily influenced by composition rather than microstructure. Our results indicate that, for our experimental conditions, the stress induced by shock loading is sufficiently greater than the material yield strength to enable an isotropic hydrodynamic description.^59,60 The close agreement with other Al-alloys also suggests that the approximately 0.6% porosity present in the LPBF AlSi10Mg does not generate a significant deviation from the bulk Hugoniot response.

Studies of cast AlSi10Mg³⁵ and wrought Al-AD1,^61,62 AlMg6,⁶² Al-6061,⁶³ Al-D16T,⁶⁴ and Al-1100-O⁶⁵ at strain-rates and impact stresses similar to this work reported HELs ranging from 0.2 to 0.8 GPa and spallation strengths ranging from 0.4 to 1.7 GPa. In most instances, HEL and spallation strength were observed to increase with strain-rate. Depending on the stress regime and specific alloy/treatment, spallation strength was observed to increase, not change, or even decrease with increased shock-induced stress. Our orientation-independent HELs (0.25–0.30 GPa) and spallation strengths (1.16–1.45 GPa) fall within these previously reported ranges; additionally, our finding that spallation strength increases with both stress and strain-rate is corroborated. However, it should be noted that the impact of compressive stress on the spallation strength (independent of strain-rate) is debated.³² 

In experiments with a similar (but not identical) LPBF AlSi10Mg, Zaretsky et al.³⁵ reported an HEL of approximately 0.28 GPa for a strain-rate similar to ours (⁠$105$ $s−1$⁠) and an HEL of approximately 0.56 GPa at a strain-rate higher than what we achieved here (⁠$106$ $s−1$⁠). Laurençon et al.³⁸ similarly reported an HEL of 0.50 GPa near $106$ $s−1$ in experiments with LPBF AlSi10Mg. These results, in conjunction with our own, suggest that the HEL in LPBF AlSi10Mg is sensitive to strain-rate but not to orientation.

Zaretsky et al.³⁵ reported spallation strengths in LPBF AlSi10Mg of approximately 1.25–1.5 GPa at tensile strain-rates similar to our study (⁠$105$ $s−1$⁠), and Laurençon et al.³⁸ reported spallation strengths near 1.9 GPa at tensile strain-rates much larger than ours (2–$3×106$ $s−1$⁠). Like us, Zaretsky et al. observed dependence of the spallation strength on the strain-rate but not the material orientation.

Work with Al-alloys of varying microstructures has demonstrated the capacity of grain size, orientation, and shape to alter material response to dynamic loading.^62–65 However, though the manufacturing process of our LPBF AlSi10Mg samples generated observable orientation-dependent differences in microstructure, our results do not indicate that these differences are sufficient to induce significant anisotropy in dynamic material properties.

We employed plate-impact experiments to peak stresses greater than 13 GPa to measure the Hugoniot, HEL, and spallation strength of LPBF AlSi10Mg. The LPBF AlSi10Mg alloy used in this study exhibited an anisotropic microstructure, with elongated grains in the build direction with a [001] preferred texture. The LPBF AlSi10Mg response showed no dependence on material orientation (despite observed microstructural anisotropies) and was consistent in both value and trend with previous studies on LPBF AlSi10Mg and traditionally-manufactured Al-based alloys. The Hugoniot of the LPBF AlSi10Mg was found to be well represented by a linear fit: $us=5.49+1.39up$⁠. The measured HEL ranged from 0.25 to 0.30 GPa, and the spallation strength ranged from 1.16 to 1.45 GPa. Our HEL and spallation strength results agree favorably with those reported by previous studies of LPBF AlSi10Mg. We observed limited sample-to-sample variability in the spallation strength and found spallation strength increased with both tensile strain-rate and peak compressive stress.

The authors thank the members of the DICE and STAR facilities at Sandia National Laboratories for constructing and executing these experiments: Heidi Anderson, C. Scott Alexander, Steven Dean, Bernardo Farfan, Keith Hodge, John Martinez, Lena Pacheco, Rocky Palomino, William Reinhart, Rafael Sanchez, and Joshua Usher. The authors also thank Thomas Ivanoff for acquiring the material and coordinating the microscopy and micro-CT analysis on the LPBF AlSi10Mg. The authors are grateful to Vitaly Paris of the Isreali Atomic Energy Commission (IAEC) for many helpful discussions. The authors appreciate the insights provided by Sharlotte Kramer, Colin Loeffler, Bo Song, Kyle Johnson, and John Emery. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under Contract No. DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.