# Effect of Low-Temperature Annealing on Creep Properties of AlSi10Mg Alloy Produced by Additive Manufacturing: Experiments and Modeling

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## Abstract

**:**

## 1. Introduction

#### 1.1. AlSi10Mg Alloy Produced by Additive Manufacturing: Main Structural Features

^{6}°C/s) and the sequence of passes, each of which acts as a thermal treatment on the lower and already solidified layers, produce an extremely fine structure with interesting mechanical properties [4,5,6]. The complex structure typical of AlSi10Mg AM products can be schematically described as follows:

- i.
- at a macroscopic level (100 μm–1 mm), the most noteworthy features are: (a) the high surface roughness resulting from the presence of melt pools; (b) the possible presence of porosities [7];
- ii.
- iii.
- at a microscopic level (10 nm–1 μm), the long cells are subdivided into equiaxed subcells, again with diameters of a few hundreds of nm, separated by a network of Si-rich eutectic regions. The eutectic regions are richer in Si [10] and contain densely spaced Si particles, the size and distribution of which can vary as a function of process parameters [7,8] or part size [9].

#### 1.2. AlSi10Mg Alloy Produced by Additive Manufacturing: Effect of Stress Relieving/Low Temperature Annealing

_{H}and σ

_{S}are the stresses acting on the hard and soft zones, respectively, and f

_{H}is the volume fraction of the hard regions [15,16,17].

_{a}is the yield stress of an alloy containing 0.5% Mg (60 MPa), which includes the solute hardening contribution of this alloying element, and σ

_{Or}

^{i}is the Orowan stress in the i-region (soft or hard). The Orowan stress, in turn, can be estimated by its simplest formulation [18], namely

_{H}= 0.25. Both cells and eutectic regions contain fine Si particles of initial size d

_{0}. The initial surface-to-surface interparticle distance is assumed to be equivalent to d

_{0}in the hard zones and to 200 nm in cell interiors.

_{calc}) and interparticle distance after annealing are presented in Appendix A. The calculated variations in yield stress Equations (2) and (3) obtained for MM with different d

_{0}values are presented in Figure 1. An analysis of the figure suggests that, in general terms, the combination of MM with the equations describing the Ostwald ripening phenomena of Si particles gives a reasonable description of the yield stress reduction after annealing. Nevertheless, at a closer look, some specific features emerge, namely:

- i.
- in some cases (see, for example data from [13]), the yield stress monotonically decreases with increasing annealing temperature. The phenomenon is quite correctly described by the model curves;
- ii.
- in other cases (see data from [5] and evidence presented in [10]), precipitation of Si is not completed during the AM process. Thus, in the early stages of low-temperature annealing, an additional precipitation of fine Si particles results in an increase in yield stress. This secondary precipitation is not accounted for by the equations presented in Appendix A, since the model assumes that ripening starts immediately upon annealing. This fact is easily confirmed when comparing the estimated value of the Si crystallites (d
_{est}) [5] and the calculated value of Si particle size (Figure 1). The secondary precipitation results in a finer particle size than the one predicted by the ripening equations.

#### 1.3. AlSi10Mg Alloy Produced by Additive Manufacturing: Creep Response

_{0}was assumed to be equivalent to the Orowan stress and the particle size at the time corresponding to the minimum in creep rate was calculated using the equations in Appendix A, by assuming d

_{0}= 50 nm. The stress corresponding to the given strain rate was then expressed by Equation (1). The resulting model curves are presented in Figure 2.

## 2. Materials and Methods

## 3. Results

_{m}) as a function of the minimum creep rate. The data align on a single line of slope −1. The fact that the experimental data conform to the simple equation

## 4. Discussion

#### 4.1. Analysis of the Effect of Low-Temperature Annealing on Creep Response

^{ad}and σ

^{ht}are the stresses applied to obtain a given value of the minimum strain rate in as-deposited and heat-treated alloys, respectively (Figure 6). Figure 6 only includes data for 150 and 175 °C, since at the higher temperature the experimental results for heat-treated and as-deposited alloys substantially overlap.

^{−6}s

^{−1}. By contrast, at 175 °C, Δσ monotonically decreased from 47 to 7 MPa with decreasing minimum creep rate. The softening obviously originates from the microstructural evolution during high-temperature exposure. Postprocessing annealing results in ripening/coarsening of the Si particles, which are the major sources of strengthening at high temperatures. At low testing temperatures, where ripening is a sluggish phenomenon, the advantage in creep strength is maintained until the time of exposure becomes so long that particles start to coarsen even in the as-deposited material. At 175 °C ripening is more rapid and the initial advantage of the as-deposited state, i.e., the presence of smaller particles in the microstructure, is rapidly lost and the two materials progressively become more and more similar. Although reasonable, this qualitative explanation needs to be supported by a more quantitative analysis of the relationship between creep response (the minimum creep rate) and the microstructural features (Si particle size and interparticle distance), which will be dealt with in the following section.

#### 4.2. Modeling the Effect of Low-Temperature Annealing on Creep Response

_{0}= 50 nm, as in [14], after 2 h at 225 °C a particle size close to 59 nm can be obtained. Equation (A6) and Equation (9) can then be combined and used to estimate the size of the particles at t

_{m}for a given value of the minimum strain rate. Since the surface-to-surface interparticle spacing can be expressed as

_{m}constant, which was, in fact, the only experimental value obtained from Figure 4, were calculated for the as-deposited alloy, the accuracy of the description is remarkable. The model significantly overestimates the material strength only in the very high strain rate region.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

_{0}is the initial particle size, d the particle size at time t, γ the interfacial energy, C

_{∞}the equilibrium concentration of the species that form the particles and V

_{m}the molar volume of the particle.

_{Ls}= D

_{0Ls}exp(−Q

_{Ls}/RT) is the lattice diffusion coefficient of the element forming the particle, D

_{ps}= D

_{0ps}exp(−Q

_{ps}/RT) the corresponding pipe diffusion coefficient and ρ

_{m}the mobile dislocation density. A

_{p}

_{2}is the effective sectional area for diffusion which takes into account the scavenging effect of solute atoms by moving dislocations. The mobile dislocation density can be obtained with the Orowan equation

_{m}is the dislocation velocity. Combined with Equation (A1), Equation (A2) gives

_{p}

_{2}is indeed supposed to be proportional to the dislocation velocity v

_{m}, then

_{0ps}/D

_{0Ls}is a constant. Equation (A5) is formally analogous to a similar equation proposed by Cohen [25]. The Ostwald ripening equation thus becomes

_{g}was neglected. The activation energies in Equation (A6) were considered to be Q

_{Ls}= 124 kJ mol

^{−1}and Q

_{ps}= 0.6 Q

_{Ls}; the calculation in [14] gave D

_{0Ls}K

_{g}= 2 × 10

^{17}nm

^{3}h

^{−1}and B = 10 s

^{−1}.

**Figure A2.**Comparison between the calculated particle size (the black circles in the insert, which qualitatively show the microstructure of the model material) and the real structure after annealing for 30 h. The diameter of the black circles in the inserts corresponds to the calculated particle size at the given magnification. (

**a**) 175 °C, calculated size of Si particles = 53 nm; (

**b**) 200 °C, calculated size of the particles = 63 nm.

## Appendix B

_{ρ}= αmGbρ

^{1/2}is the dislocation hardening term. The stress σ

_{0}represents the strengthening contribution due to the interaction between fine particles and dislocations. This formulation of the Taylor equation does not take into account the stress required to move the dislocation in the absence of other dislocations nor the viscous drag stress due to solute atoms, since both these quantities, in a dilute solid solution reinforced by a fine dispersion of particles, are usually negligible when compared to the strengthening term due to particle–dislocation interaction.

_{l}is the dislocation line tension (τ

_{l}= 0.5Gb

^{2}), M

_{cg}is the dislocation mobility and L* is the dislocation mean free path. At high temperatures, the equation can be simplified to

_{max}is the maximum strength of the alloy, tentatively quantified at room temperature as 1.5 times the ultimate tensile strength (R

_{UTS}) of the alloy. The U

_{ss}term describing the energy necessary for solute atoms to jump in and out of the clouds formed around dislocations has the form [27]

## References

- Aboulkhair, N.T.; Simonelli, M.; Parry, L.; Ashcroft, I.; Tuck, C.; Hague, R. 3D printing of Aluminium alloys: Additive Manufacturing of Aluminium alloys using selective laser melting. Prog. Mater. Sci.
**2019**, 106, 100578. [Google Scholar] [CrossRef] - Herzog, D.; Seyda, V.; Wycisk, E.; Emmelmann, C. Additive manufacturing of metals. Acta Mater.
**2016**, 117, 371–392. [Google Scholar] [CrossRef] - Hebert, R.J. Viewpoint: Metallurgical aspects of powder bed metal additive manufacturing. J. Mater. Sci.
**2016**, 51, 1165–1175. [Google Scholar] [CrossRef] - DebRoy, T.; Wei, H.L.; Zuback, J.S.; Mukherjee, T.; Elmer, J.W.; Milewski, J.O.; Beese, A.M.; Wilson-Heid, A.; De, A.; Zhang, W. Additive manufacturing of metallic components—Process, structure and properties. Prog. Mater. Sci.
**2018**, 92, 112–224. [Google Scholar] [CrossRef] - Rosenthal, I.; Shneck, R.; Stern, A. Heat treatment effect on the mechanical properties and fracture mechanism in AlSi10Mg fabricated by additive manufacturing selective laser melting process. Mater. Sci. Eng. A
**2018**, 729, 310–322. [Google Scholar] [CrossRef] - Read, N.; Wang, W.; Essa, K.; Attallah, M.M. Selective laser melting of AlSi10Mg alloy: Process optimisation and mechanical properties development. Mater. Des.
**2015**, 65, 417–424. [Google Scholar] [CrossRef][Green Version] - Trevisan, F.; Calignano, F.; Lorusso, M.; Pakkanen, J.; Aversa, A.; Ambrosio, E.P.; Lombardi, M.; Fino, P.; Manfredi, D. On the selective laser melting (SLM) of the AlSi10Mg alloy: Process, microstructure, and mechanical properties. Materials
**2017**, 10, 76. [Google Scholar] [CrossRef][Green Version] - Wu, J.; Wang, X.Q.; Wang, W.; Attallah, M.M.; Loretto, M.H. Microstructure and strength of selectively laser melted AlSi10Mg. Acta Mater.
**2016**, 117, 311–320. [Google Scholar] [CrossRef][Green Version] - Takata, N.; Kodaira, H.; Suzuki, A.; Kobashi, M. Size dependence of microstructure of AlSi10Mg alloy fabricated by selective laser melting. Mater. Charact.
**2018**, 143, 18–26. [Google Scholar] [CrossRef] - Fousová, M.; Dvorský, D.; Michalcová, A.; Vojtěch, D. Changes in the microstructure and mechanical properties of additively manufactured AlSi10Mg alloy after exposure to elevated temperatures. Mater. Charact.
**2018**, 137, 119–126. [Google Scholar] [CrossRef] - Li, W.; Li, S.; Liu, J.; Zhang, A.; Zhou, Y.; Wei, Q.; Yan, C.; Shi, Y. Effect of heat treatment on AlSi10Mg alloy fabricated by selective laser melting: Microstructure evolution, mechanical properties and fracture mechanism. Mater. Sci. Eng. A
**2016**, 663, 116–125. [Google Scholar] [CrossRef] - Uzan, N.E.; Shneck, R.; Yeheskel, O.; Frage, N. Fatigue of AlSi10Mg specimens fabricated by additive manufacturing selective laser melting (AM-SLM). Mater. Sci. Eng. A
**2017**, 704, 229–237. [Google Scholar] [CrossRef] - Cerri, E.; Ghio, E. AlSi10Mg alloy produced by Selective Laser Melting: Relationships between Vickers microhardness, Rockwell hardness and mechanical properties. Metall. Ital.
**2020**, 7–8, 5–17. [Google Scholar] - Paoletti, C.; Santecchia, E.; Cabibbo, M.; Cerri, E.; Spigarelli, S. Modelling the creep behavior of an AlSi10Mg alloy produced by additive manufacturing. Mater. Sci. Eng. A
**2021**, 140138. [Google Scholar] [CrossRef] - Nix, W.D.; Ilschner, B. Mechanisms Controlling Creep of Single Phase Metals and Alloys; Haasen, P., Gerold, V., Kostorz, G., Eds.; Pergamon: Aachen, Germany, 1979; Volume 3, pp. 1503–1530. ISBN 978-1-4832-8412-5. [Google Scholar]
- Meier, M.; Blum, W. Modelling high temperature creep of academic and industrial materials using the composite model. Mater. Sci. Eng. A
**1993**, 164, 290–294. [Google Scholar] [CrossRef] - Spigarelli, S. Constitutive equations in creep of Mg-Al alloys. Mater. Sci. Eng. A
**2008**, 492, 153–160. [Google Scholar] [CrossRef] - Orowan, E. Dislocations in Metals; Cohen, M., Ed.; The Institute of Metals Division, the American Institute of Mining and Metallurgical Engineers: New York, NY, USA, 1954. [Google Scholar]
- Spigarelli, S.; Sandström, R. Basic creep modelling of Aluminium. Mater. Sci. Eng. A
**2018**, 711, 343–349. [Google Scholar] [CrossRef] - Paoletti, C.; Regev, M.; Spigarelli, S. Modelling of creep in alloys strengthened by rod-shaped particles: Al-Cu-Mg age-hardenable alloys. Metals
**2018**, 8, 930. [Google Scholar] [CrossRef][Green Version] - Spigarelli, S.; Evangelista, E.; Cucchieri, S. Analysis of the creep response of an Al-17Si-4Cu-0.55Mg alloy. Mater. Sci. Eng. A
**2004**, 387–389, 702–705. [Google Scholar] [CrossRef] - Uzan, N.E.; Shneck, R.; Yeheskel, O.; Frage, N. High-temperature mechanical properties of AlSi10Mg specimens fabricated by additive manufacturing using selective laser melting technologies (AM-SLM). Addit. Manuf.
**2018**, 24, 257–263. [Google Scholar] [CrossRef] - Toschi, S. Optimization of a354 Al-Si-Cu-Mg alloy heat treatment: Effect on microstructure, hardness, and tensile properties of peak aged and overaged alloy. Metals
**2018**, 8, 961. [Google Scholar] [CrossRef][Green Version] - Salleh, M.S.; Omar, M.Z.; Syarif, J.; Alhawari, K.S.; Mohammed, M.N. Microstructure and mechanical properties of thixoformed A319 aluminium alloy. Mater. Des.
**2014**, 64, 142. [Google Scholar] [CrossRef] - Buffington, F.S.; Cohen, M. Self-Diffusion in Alpha Iron Under Uniaxial Compressive Stress. JOM
**1952**, 4, 859–860. [Google Scholar] [CrossRef] - Sandström, R. Basic model for primary and secondary creep in copper. Acta Mater.
**2012**, 60, 314–322. [Google Scholar] [CrossRef] - Sandström, R. Influence of phosphorus on the tensile stress strain curves in copper. J. Nucl. Mater.
**2016**, 470, 290–296. [Google Scholar] [CrossRef] - Sandström, R. The role of cell structure during creep of cold worked copper. Mater. Sci. Eng. A
**2016**, 674, 318–327. [Google Scholar] [CrossRef]

**Figure 1.**Effect of a 2-h postprocessing heat treatment on yield strength (on the left, the values for the as-deposited alloys) [5,10,11,12,13]. The figure also plots the roughly estimated value of the yield stress calculated by taking into account the effects of the Ostwald ripening of Si particles of different initial size (see Appendix A for details on the calculation of the Si particle size d

_{calc}, and Table 1 for the meanings of symbols). In addition, data on the observed crystallite size, d

_{est}, are reported [5].

**Figure 2.**Experimental values of the minimum creep rate in as-deposited additive manufacturing (AM) AlSi10Mg and material model (MM) curves (see Appendixes A and B for the constitutive equations used in combination with the composite model, Equation (1), with d

_{0}= 50 nm) [14].

**Figure 3.**Experimental creep curves: (

**a**) example of strain vs. time curve; (

**b**) strain rate vs. strain curves at different experimental conditions.

**Figure 4.**Minimum creep rate dependence on applied stress for the annealed and as-deposited [14] alloy.

**Figure 7.**Model curves calculated for the material heat treated at 225 °C for 2 h. The only experimental datum used to calculate the curves is the relationship shown in Figure 4.

**Figure 8.**(

**a**) Model curves calculated for the as-deposited and the heat-treated (225 °C for 2 h) alloy; (

**b**) minimum creep rate obtained at 225 °C for the as-deposited alloy [14] and for the alloy annealed for 2 h at 225 °C (this study) and at 300 °C [22]; (

**b**) also includes the model curves calculated by combining the MM and the equations reported in Appendixes A and B.

Symbol | Meaning |
---|---|

σ | True applied stress (MPa) |

${\dot{\mathbf{\epsilon}}}_{\mathit{m}}$ | Minimum creep rate (s^{−1}) |

σ_{0} | Particle strengthening term (Orowan stress) (MPa) |

α | Constant: 0.3 |

m | Taylor factor: 3.06 |

R | Gas constant: 8.314 (J mol^{−1}K^{−1}) |

G | Shear modulus: 30,220–16 T (MPa) |

b | Burgers vector: 2.47 × 10^{−10} (m) |

ρ | Dislocation density (m^{−2}) |

σ_{ρ} | Dislocation hardening term: =αmGbρ^{1/2} (MPa) |

τ_{l} | Dislocation line tension: =0.5Gb^{2} (N) |

R_{max} | Maximum strength at the testing temperature [MPa) |

k | Boltzmann constant = 1.38 × 10^{−23} (J K^{−1}) |

D_{0L} | Pre-exponential factor in the Arrhenius equation describing the temperature dependence of the vacancy diffusion coefficient: 8.3 × 10^{−6} (m^{2}s^{−1}) [19] |

Q_{L} | Activation energy in the Arrhenius equation describing the temperature dependence of the vacancy diffusion coefficient: 122 (kJ mol^{−1}) [19] |

U_{ss} | Energy necessary for Si (and Mg) atoms still in solid solution to jump in and out of the atmospheres that spontaneously form around dislocations; previous calculations gave values close to 10–15 kJ mol^{−1} for Mg [20]. For the sake of simplicity, here U_{ss} is assumed to be 10 (kJ mol^{−1}) |

R_{UTS}^{a} | Room temperature tensile strength of an alloy with the same impurity level, similar content of elements in solid solution and coarse intergranular intermetallics, in the absence of fine Si particles, here roughly estimated to be 115 (MPa) |

L | Surface-to-surface interparticle spacing (m) |

G_{T}, G_{RT} | Shear modulus at the testing temperature and at 25 °C, respectively (MPa) |

M_{cg} | Temperature dependent dislocation mobility |

d_{0} | Initial dimension of Si particles |

d_{est} | Experimental estimate of the size of Si particles at time t |

d_{calc} | Calculated value of the size of Si particles at time t |

σ_{yi} | Yield stress |

σ_{a} | Yield stress of an alloy containing 0.5% Mg but no Si particles |

σ_{Or}^{i} | Orowan stress in the i-region (i = H,S) |

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**MDPI and ACS Style**

Paoletti, C.; Cerri, E.; Ghio, E.; Santecchia, E.; Cabibbo, M.; Spigarelli, S. Effect of Low-Temperature Annealing on Creep Properties of AlSi10Mg Alloy Produced by Additive Manufacturing: Experiments and Modeling. *Metals* **2021**, *11*, 179.
https://doi.org/10.3390/met11020179

**AMA Style**

Paoletti C, Cerri E, Ghio E, Santecchia E, Cabibbo M, Spigarelli S. Effect of Low-Temperature Annealing on Creep Properties of AlSi10Mg Alloy Produced by Additive Manufacturing: Experiments and Modeling. *Metals*. 2021; 11(2):179.
https://doi.org/10.3390/met11020179

**Chicago/Turabian Style**

Paoletti, Chiara, Emanuela Cerri, Emanuele Ghio, Eleonora Santecchia, Marcello Cabibbo, and Stefano Spigarelli. 2021. "Effect of Low-Temperature Annealing on Creep Properties of AlSi10Mg Alloy Produced by Additive Manufacturing: Experiments and Modeling" *Metals* 11, no. 2: 179.
https://doi.org/10.3390/met11020179