#
Cold Forming of Al-TiB_{2} Composites Fabricated by SPS: A Computational Experimental Study

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}composites fabricated by Spark Plasma Sintering (SPS) were investigated. The effective flow stress at room temperature for different TiB

_{2}particle volume fractions between 0% and 15% was determined using compression experiments on cylindrical specimens in conjunction with an iterative computational methodology. A different set of experiments on tapered specimens was used to validate the effective flow curves by comparing experimental force–displacement curves and deformation patterns to the ones obtained from the computations. Using a continuum damage mechanics approach, the experiments were also used to construct effective failure curves for each material composition. It was demonstrated that the fracture modes observed in the different experiments could be reproduced in the computations. The results show that increasing the TiB

_{2}particle volume fraction to 10% results in an increase in material effective yield stress and a decrease in hardening. For a particle volume fraction of 15%, the effective yield stress decreases with no significant influence on the hardening slope. The ductility (workability) of the composite decreases with increasing particle volume fraction.

## 1. Introduction

_{2}O

_{3}and B

_{4}C. TiB

_{2}is also a promising candidate for aluminum reinforcement [10]. The volume fraction of the ceramic particles is expected to have a significant influence on the mechanical properties. For example, in [11] the stress–strain relation in tension of A380 + 5% TiB

_{2}was shown to have a clear strengthening effect (in both yield and ultimate tensile stress) by the TiB

_{2}particles, compared to the A380 alloy alone. In [12] it was shown that the increase of TiB

_{2}content from 5% to 10% in sintered Al-TiB

_{2}preforms decreased its strain to failure. The study in [13] compared A359 with 0%, 10%, 20% and 30% particle volume fractions of SiC. In quasi-static compression conditions, the A359 with 10% SiC material exhibited a significantly lower hardening compared to the reference matrix material. A higher SiC content does not affect the hardening significantly. Additionally, an increase in the yield strength is observed for higher SiC content. However, the relation between the particle volume fraction and the mechanical properties is not always direct. In an AMC system of AA7075 with SiC particles, it was shown that a small addition of SiC particles (1%) improved the material’s strength, whereas the addition of 5% caused the strength properties to deteriorate compared tothe original matrix material [14].

_{2}composite produced using SPS.

## 2. Materials and Methods

_{2}volume fraction on the effective mechanical response and failure modes of an Al-TiB

_{2}composite. The effective flow stress is determined using compression tests on cylindrical specimens in conjunction with finite element analysis. Failure modes are investigated using a continuum damage approach for which the effective failure initiation curves are constructed based on the experimental methodology outlined in [16]. An outline of the research methodology is presented in Figure 2.

#### 2.1. Material and Specimen Preparation

_{2}(Grade F, H.C. Stark GmbH, Giessen, Germany) powders were used to obtain 0, 5, 10 and 15 vol.% of Al-TiB

_{2}powder mixes. The particle size distribution of the original powders was analyzed using the QICPIC dynamic image analysis system (Sympatec@GmbH, Clausthal-Zellerfeld, Germany). Details about the measurement procedure is described in [18] and results are given in Table 1.

^{3}) using a POWTEQ M10 tumbler (at 25 rpm) in a 1 L container (100 mm diameter). For the 10 and 15 vol.% TiB2, 10 alumina balls (a diameter of 21 mm each, ~205 gr total weight) were added to improve powder mix homogeneity. X-ray diffraction (XRD) (Rigaku RINT 2100 Tokyo, Japan with Cu Kα radiation with λ = 1.54 Å), with operating parameters of 40 kV and 30 mA in the 2θ range from 20° to 80°, with a step size of 0.02° and a scan step time of 1 s, was used to determine the mixing powder homogeneity (samples were taken from the upper, middle and bottom portions of the powders mix) and phase content. The XRD patterns (see Figure 5) of the powders were analyzed to confirm Al-TiB

_{2}composition using a whole pattern fitting approach (MDI Jade 2019 version 7.7 software, Livermore, CA, USA). Samples from the sintered billets were mechanically ground and polished down to 1 μm for microstructural characterization. Scanning electron microscope (SEM, JEOL JSM-7400F, Tokyo, Japan) combined with energy-dispersive X-ray spectroscopy (EDS, Thermo Fisher Scientific, Waltham, MA, USA) detector was used for morphology characterization and to determine sample’s local composition and homogeneity. Back-scattered electron (BSE) imaging and the open-source software Paint Net (v4.2.1, dotPDN LLC, San Francisco, Ca, USA) were used to determine the distribution of the principal phases.

_{2}particles, the microstructure is characterized by large particles of Al with numerous small TiB

_{2}particles arranged around the Al particle boundaries.

_{2}powders, within a range of 2θ = 33–47° are shown in Figure 5, indicating an increase in the TiB

_{2}peak intensities with the increase of TiB

_{2}volume fraction.

#### 2.2. Experimental Setup

_{2}particle volume fractions and used to determine the effective flow stress for the different compositions. The flow stress was obtained by an iterative experimental/computational procedure similar to the one described by the authors in [21,22].

#### 2.3. The Computational Models

_{2}(Von-Mises) yielding criterion with isotropic strain hardening in the plastic range.

#### Continuum Damage Model

## 3. Results

#### 3.1. Effective Flow Stress Curves as a Function of Particle Volume Fraction

_{2}volume fraction is shown in Figure 11. A comparison of computed and observed deformation, triaxiality and equivalent plastic strain for the same specimen is shown in Figure 12, at two different stages of the experiment.

#### 3.2. Determination of Damage Initiation Curves and Influence of Damage Evolution Curves

_{2}particle volume fraction is presented in Figure 16.

## 4. Discussion

_{2}particle volume fraction has on two aspects: the effective flow stress of the Al-TiB

_{2}composite; and failure initiation and evolution at room temperature. In the case of the Al-TiB

_{2}composites produced by SPS, the TiB

_{2}particles are not chemically bonded to the Al particles. This fact greatly influences both the effective flow stress and failure initiation as explained below.

#### 4.1. Effective Flow Stress of Al-TiB_{2}

_{2}composite can be described by two parameters: (a) the effective yield stress, (b) the effective hardening slope. The results demonstrate (see Table 4) that addition of 5% and 10% volume fraction of TiB

_{2}particles increases the effective yield stress of the material. Following this, at some point, further increase in particle volume fraction does not result in an increased yield stress but a slight decrease as shown when the volume fraction increased to 15%. With respect to the strain hardening slope, the addition of the ceramic particles decreases the strain hardening parameter n. The addition of up to 10% TiB

_{2}particles decreases the hardening slope significantly; however, further increase of particle volume fraction does not have a significant influence on the hardening slope.

_{2}particles. It is assumed that the initial increase in yield stress can be attributed to the fact that the ceramic particle obstructs initial dislocation movement between adjacent Al particles. When the volume fraction of TiB

_{2}particles is further increased, plastic deformation is no longer limited to dislocation movement in the Al grains but is enabled by relative sliding of Al particles because of the TiB

_{2}relative movement across the interface. This mechanism may be the reason for the decrease in yield stress, which is observed at large TiB

_{2}particle volume fractions. This mechanism also explains the apparent decrease in effective strain hardening coefficient. With increasing TiB

_{2}volume fraction, more of the Al particle surface area is surrounded by TiB

_{2}particles. This results in more instances of relative sliding between Al particles during deformation which leads to a decrease in observed effective strain hardening.

#### 4.2. Failure and Fracture of Al-TiB_{2}

_{2}. The experiments show that failure mainly occurs by mode I (opening mode) and mode III (out of plane shear), as reported in past studies for Al-2024 and steel specimens [16]. The results demonstrate that increasing the volume fraction of the TiB

_{2}particles decreases the effective ductility of the material. The decreased ductility influences the workability of the material at room temperature conditions (the ability to undergo cold forming). This is clearly evident from the effective failure curve in the principal strain space (Figure 14), as the area under the 2D failure curve can be directly linked to the material workability and it decreases monotonically for increasing particle volume fraction.

_{2}composites produced by SPS, the TiB

_{2}particles are not chemically bonded to the Al particles. This implies that each TiB

_{2}particle (or aggregate of particles) is essentially a void in the aluminum matrix. Increasing the particle volume fraction theoretically increases the number of voids within the matrix, thereby decreasing the material’s ductility. Increasing the number of particles also means that the Al particles are more loosely joined to one another.

_{2}particle volume fraction (as evident from the function $D\left(\overline{u}\right)$). The reduction in fracture energy can be linked to the decrease in Al-Al particle interfaces.

_{2}particle size or shape will influence the effective flow stress and effective failure curves obtained in this study. It is assumed that variations in particle size and shape will have some influence on the effective flow stress but that the main effect will be on the effective failure curves and effective fracture energy density. Such phenomena can be explored using a micro-macro computational approach, which will be considered in future work.

## 5. Conclusions

_{2}composites fabricated using SPS were investigated. The effective flow stress for different TiB

_{2}particle volume fractions was determined using an iterative computational and experimental methodology. A different set of experiments (changing specimen geometry) was used to validate the effective flow curves by comparing experimental force displacement curves and deformation patterns to the ones obtained from the computations.

_{2}particle volume fraction up to 10% results in an increase in material effective yield stress and a decrease in hardening. For a particle volume fraction of 15%, the effective yield stress decreases with no significant influence on the hardening slope. The ductility (workability) of the composite decreases for increasing particle volume fraction. This result is evident from the decreasing value of strain to failure for the entire range of triaxiality values

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A2.**Convergence in global solution parameters: strain energy (

**a**), force–displacement curve (

**b**).

**Figure A3.**Convergence in local solution parameters extracted at the point on the specimen surface where initial failure was obtained: stress triaxiality (

**a**), equivalent plastic strain (

**b**), circumferential strain (

**c**), axial strain (

**d**).

**Figure A4.**Convergence in damage initiation and damage evolution: damage initiation parameter prior to local failure initiation (

**a**), damage evolution parameter D after initial failure (

**b**), damage evolution parameter following cracking of the specimen surface (

**c**).

## References

- Hunt, W.H.; Herlling, D.R. Aluminum metal matrix composites. Adv. Mater. Process.
**2004**, 162, 39–42. [Google Scholar] - Karamis, B.; Nair, F. Effects of reinforcement particle size in MMCs on extrusion die wear. Wear
**2008**, 265, 1741–1750. [Google Scholar] [CrossRef] - Popescu, I.N.; Zamfir, S.; Anghelina, F.V.; Rusanescu, C.O. Processing by P/M route and characterization of new ecological Aluminum Matrix Composites (AMC). Int. J. Mech.
**2010**, 3, 43–52. [Google Scholar] - Hayun, S.; Meir, S.; Kalabukhov, S.; Frage, N.; Zaretsky, E. Phase Constitution and Dynamic Properties of Spark Plasma-Sintered Alumina-Titanium Composites. J. Am. Ceram. Soc.
**2016**, 99, 573–580. [Google Scholar] [CrossRef] - Zhou, J.; Duszczyk, J. Preparation of Al-20Si-4.5Cu alloy and its composite from elemental powders. J. Mater. Sci.
**1999**, 34, 5067–5073. [Google Scholar] [CrossRef] - Luan, B.F.; Hansen, S.; Godfrey, A.; Wu, G.H.; Liu, Q. High strength Al–Al2O3p composites: Optimization of extrusion parameters. Mater. Des.
**2011**, 32, 3810–3817. [Google Scholar] [CrossRef] - Soltani, N.; Jafari Nodooshan, H.R.; Bahrami, A.; Pech-Canul, M.I.; Liu, W.; Wu, G. Effect of hot extrusion on wear properties of Al–15 wt.% Mg
_{2}Si in situ metal matrix composites. Mater. Des.**2014**, 53, 774–781. [Google Scholar] [CrossRef] - Zhou, J.; Druzdzel, A.T.; Duszczyk, J. The effect of extrusion parameters on the fretting wear resistance of Al-based composites produced via powder metallurgy. J. Mater. Sci.
**1999**, 34, 5089–5097. [Google Scholar] [CrossRef] - Hosford, W.F.; Caddell, R.M. Metal Forming Mechanics and Metallurgy; Cambridge University Press: New York, NY, USA,, 2011. [Google Scholar]
- Kumar, N.; Gautam, G.; Kumar Gautam, R.; Mohan, A.; Mohan, S. Synthesis and characterization of TiB
_{2}reinforced aluminum matrix composites: A review. J. Inst. Eng. India Ser. D**2016**, 97, 233–253. [Google Scholar] [CrossRef] - Liu, X.; Liu, Y.; Huang, D.; Han, Q.; Wang, X. Tailoring in-situ TiB
_{2}particulates in aluminum matrix composites. Mater. Sci. Eng. A**2017**, 705, 55–61. [Google Scholar] [CrossRef] - Ahasan, M.; Davidson, M.J.; Selvakumar, N. Experimental investigations on the densification and deformation behavior of Al-TiB
_{2}composite preforms. Trans. Indian Inst. Met.**2016**, 69, 1059–1068. [Google Scholar] [CrossRef] - Li, Y.; Ramesh, K.T.; Chin, E.S.C. The compressive viscoplastic response of an A359/SiC metal matrix composite and of the A359 aluminum alloy matrix. Int. J. Solids Struct.
**2000**, 37, 7547–7562. [Google Scholar] [CrossRef] - Kumar, P.; Kumar, V.; RaghavendraJoshi, B.P.; Manjunatha, T.H.; Kumar, R.S. Evaluation of Al 7075 Reinforced with SiC for its mechanical properties and surface roughness by drilling. Mater. Today
**2018**, 5, 25121–25129. [Google Scholar] - Silva, C.M.A.; Alves, L.M.; Nielsen, C.V.; Atkins, A.G.; Martins, P.A.F. Failure by fracture in bulk metal forming. J. Mater. Process. Technol.
**2015**, 215, 287–298. [Google Scholar] [CrossRef] - Martins, P.A.F.; Bay, N.; Tekkaya, A.E.; Atkins, A.G. Characterization of Failure loci in metal forming. Int. J. Mech. Sci.
**2014**, 83, 112–123. [Google Scholar] [CrossRef] - Bao, Y.; Wieszbicki, T. On fracture locus in the equivalent strain and stress triaxiality space. Int. J. Mech. Sci.
**2014**, 46, 81–98. [Google Scholar] [CrossRef] - Rosenthal, I.; Tiferet, E.; Ganor, M.; Stern, A. Selective Laser Melting additive manufacturing: AlSi10 Mg powder characterization. Ann. Duna. Univ. Galati Fascicle XII Weld. Equip. Technol.
**2014**, 25, 35–40. [Google Scholar] - Ben-Haroush, M.; Dikovsky, G.; Kalabukhov, S.; Aizenshtein, M.; Hayun, S. Spark Plasma Sintering of MgO-Strengthened Aluminum. J. Mater. Eng. Perform.
**2016**, 25, 648–655. [Google Scholar] [CrossRef] - Meir, S.; Kalabukhov, S.; Frage, N.; Hayun, S. Mechanical properties of Al
_{2}O_{3}\Ti composites fabricated by spark plasma sintering. Ceram. Int.**2015**, 41, 4637–4643. [Google Scholar] [CrossRef] - Mittleman, B.; Priel, E.; Navi, N. A finite element study of thermo-mechanical fields and their relation to friction conditions in Al1050 ring compression tests. J. Manuf. Process.
**2018**, 2, 83. [Google Scholar] [CrossRef] [Green Version] - Priel, E.; Mittelman, B.; Trabelsi, N.; Cohen, Y.; Koptiar, Y.; Padan, R. A computational study of equal channel angular pressing of molybdenum validated by experiments. J. Mater. Process. Technol.
**2019**, 264, 469–485. [Google Scholar] [CrossRef] - ABAQUS 6.14, Dassault systèmes, Providence, RI, USA. 2018.
- Cockcroft, M.G.; Latham, D.J. Ductility and the workability of metals. Int. J. Met.
**1968**, 96, 33–39. [Google Scholar] - Hillerborg, E.; Modeer, M.; Petersson, P.E. Analysis of crack formation growth by means of fracture mechanics and finite elements. Cement Concr. Res.
**1976**, 6, 773–781. [Google Scholar] [CrossRef]

**Figure 1.**An example of a fracture initiation curve in the 2D principal strain space (

**a**) and the effective strain–stress triaxiality space (

**b**).

**Figure 2.**Schematic representation of the research methodology used in this study: Determination of flow stress for each particle volume fraction (

**A**), validation of flow stress curves (

**B**), construction of failure initiation curves (

**C**), validation of failure initiation curves (

**D**).

**Figure 3.**Specimen fabrication using the SPS method. (

**a**) The powder mixture used for the specimens. (

**b**) A schematic description of the SPS method. (

**c**) An example of a specimen obtained from the SPS. (

**d**) The SPS process pressure and temperature.

**Figure 4.**SEM images of Al powder (

**a**) and TiB

_{2}powder (

**b**), and BSE images of 5, 10 and 15 vol.% of Al-TiB

_{2}composites fabricated by SPS (Green color denotes TiB

_{2}particles) (

**c**).

**Figure 7.**Experimental setup: high-resolution camera (

**a**), lighting source (

**b**), MATLAB code for image processing (

**c**), test specimen (

**d**), markings for tracking specimen deformation (

**e**).

**Figure 9.**Methods for modeling damage evolution: (

**a**) stress–equivalent plastic displacement relation; (

**b**) damage parameter as a function of equivalent plastic displacement.

**Figure 10.**Comparison between computed (black line) and experimental (red dots) force displacement curve. (

**a**) Al-0% TiB

_{2}; (

**b**) Al-5% TiB

_{2}; (

**c**) Al-10% TiB

_{2}; (

**d**) Al-15% TiB

_{2}.

**Figure 11.**Comparison between computed (black line) and experimental (red dots) force displacement curves for a tapered specimen containing 5% TiB

_{2}particle volume fraction.

**Figure 12.**Computed vs. experimental deformation for the tapered and cylindrical specimen containing 5% TiB

_{2}volume fraction prior to specimen failure (

**a**); a cut across the specimen showing distribution of equivalent plastic strain (PEEQ) and triaxiality (TRIAX) (

**b**).

**Figure 13.**Fracture modes for the different specimen types: Mode III for the cylindrical specimens (

**a**); and Mode I for the Tapered specimens (

**b**).

**Figure 15.**Principal strain path for different loading cases for specimens containing 5% volume fraction of TiB

_{2}particles.

**Figure 17.**Computed failure mode obtained for different damage evolution curves: fast propagation of damage (

**a**) and slow propagation of damage (

**b**); color indicates the damage parameter D.

**Figure 18.**Computed and observed crack formation at different heights along the cylindrical specimen axis, Colors indicate value of the damage initiation parameter ${\omega}_{d}$ (see Equation (1)).

**Figure 19.**Some discoloring contours observed in the metallurgical examination which can be correlated with the computed damage initiation parameter.

Cumulative Volume Distribution | TiB_{2} (µm) | Al (µm) |
---|---|---|

10 (%) | 6 | 7 |

50 (%) | 7 | 32 |

90 (%) | 13 | 70 |

Nominal TiB_{2} vol.% | Mixing Period (h) | Additional Alumina Balls | Vol.% of TiB_{2} from XRD |
---|---|---|---|

0 | - | - | - |

5 | 48 | - | 5.3 ± 0.2 |

10 | 72 | Yes | 9.9 ± 0.7 |

15 | 96 | Yes | 14.0 ± 0.4 |

**Table 3.**Dimensions of the experimental specimens used in the study (notations as in Figure 6).

Specimen Type | Notation | H_{0} (mm) | D_{0} (mm) | D_{1} (mm) | t (mm) |
---|---|---|---|---|---|

Cylindrical | C | 10 | 12.7 | - | - |

Tapered | T | 17 | 25 | 17 | 5 |

Particle Volume Fraction (%) | K (MPa) | n (-) | ${\mathit{\sigma}}_{\mathit{y}}\text{}\left(\mathbf{MPa}\right)$ |
---|---|---|---|

0 | 140 | 0.2 | 42 |

5 | 150 | 0.175 | 50 |

10 | 145 | 0.15 | 57 |

15 | 131 | 0.148 | 51 |

Model Parameters | Mode I Fracture | Mode III Fracture | ||||
---|---|---|---|---|---|---|

${\mathit{D}}_{1}$ | ${\mathit{D}}_{2}$ | ${\mathit{D}}_{3}$ | ${\mathit{D}}_{1}$ | ${\mathit{D}}_{2}$ | ${\mathit{D}}_{3}$ | |

Al-5%TiB_{2} | 0.140 | 0.075 | −10.0 | 0.05 | 1.3 | −11.5 |

Al-10%TiB_{2} | 0.123 | 0.055 | −10.0 | 0.01 | 2.5 | −11.5 |

Al-15%TiB_{2} | 0.049 | 0.0013 | −16.3 | 0.006 | 0.05 | −7.2 |

Damage Parameter D | 0 | 0.25 | 0.5 | 0.75 | 0.85 | 0.9 | 0.95 | 1 | |
---|---|---|---|---|---|---|---|---|---|

u_{p} (mm) | Al-5%TiB_{2} | 0 | 0.002 | 0.004 | 0.008 | 0.012 | 0.016 | 0.024 | 0.032 |

Al-10%TiB_{2} | 0 | 0.001 | 0.002 | 0.004 | 0.006 | 0.008 | 0.012 | 0.016 | |

Al-15%TiB_{2} | 0 | 0.0001 | 0.0002 | 0.0004 | 0.0006 | 0.0008 | 0.0012 | 0.0016 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Priel, E.; Navi, N.U.; Mittelman, B.; Trabelsi, N.; Levi, M.; Kalabukhov, S.; Hayun, S.
Cold Forming of Al-TiB_{2} Composites Fabricated by SPS: A Computational Experimental Study. *Materials* **2020**, *13*, 3456.
https://doi.org/10.3390/ma13163456

**AMA Style**

Priel E, Navi NU, Mittelman B, Trabelsi N, Levi M, Kalabukhov S, Hayun S.
Cold Forming of Al-TiB_{2} Composites Fabricated by SPS: A Computational Experimental Study. *Materials*. 2020; 13(16):3456.
https://doi.org/10.3390/ma13163456

**Chicago/Turabian Style**

Priel, Elad, Nissim U. Navi, Brigit Mittelman, Nir Trabelsi, Moshe Levi, Sergey Kalabukhov, and Shmuel Hayun.
2020. "Cold Forming of Al-TiB_{2} Composites Fabricated by SPS: A Computational Experimental Study" *Materials* 13, no. 16: 3456.
https://doi.org/10.3390/ma13163456