# Numerical Study of the Toughness of Complex Metal Matrix Composite Topologies
## 5 Conclusions  
DEM simulations of fracture toughness tests were performed on CT specimens with three complex MS-TiC topologies of reinforcement (gyroid, octet-truss and FBCCZ) in order to improve performance of severely multidirectional loaded parts. The cell size of the topologies was defined according to the specimen thickness and to respect a 29% volume fraction of reinforcement. Different orientations of elementary cells were studied to see any influence on mechanical performance of the structures.  
* Since a homogeneous MS-TiC structure has poor mechanical properties, the use of a shaped MS-TiC structure increases the damage resistance by 600% according to the simulation.  
Figure 15: Broken bonds at the MS-TiC insert/MS interface. Gyroid_01 (**a**), Gyroid_02 (**b**), octet-truss (**c**), FBCCZZ_01 (**d**), FBCCZ_02 (**e**) and FBCCZ_03 (**f**).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Topology** & **Load for Crack Opening (N)** & **Free Surface (mm2)** & **Total Absorbed Energy (J)** & **Energy per Unit Area (KJ m-2)** \\ \hline \multirow{4}{*}{MS-TiC/MS} & Gyroid\_01 & 80,471 & 8011 & 84 & 66 \\  & Gyroid\_02 & 73,032 & 5773 & 60 & 48 \\  & Octet-truss & 85,269 & 7278 & 76 & 60 \\  & FBCCZ\_01 & 121,081 & 6157 & 81 & 64 \\  & FBCCZ\_02 & 132,487 & 8298 & 86 & 68 \\  & FBCCZ\_03 & 135,374 & 6897 & 95 & 75 \\ \hline MS-TiC & no structure & 48,450 & 2963 & 12 & 10 \\ MS & no structure & 138,035 & 2940 & 92 & 73 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mechanical response of each specimen configuration at the maximum load.  
* The fineness of the DEM model makes it possible to calculate a macroscopic \(K_{Ic}\) from simulations. The microscopic-macroscopic passage is validated with an error less than 10%. The microscopic constitutive relations were validated experimentally for a homogeneous MMC material.
* Concerning the topological structures, the FBCCZ structure with Y-orientation cell (FBCCZ_03) performs better, it absorbs the most energy and has the highest crack opening load. This structure absorbs more energy than the studied steel for a nearly equivalent failure stress.
* Regarding the crack path obtained by the DEM method, the crack generated during the tests tends to follow the contour of the reinforcing structures and seems to cause a decohesion at the insert/matrix interface. The trajectory deviation of the crack in gyroids is less abrupt than in micro-lattice structures because of its smoother curvature. The orientation of the struts is thus important in the crack propagation. There is an influence of the cell orientation on the fracture behavior of the structure.  
The results show a good ability of DEM to model homogeneous or complex MMC structures into a metal matrix. In future, the effect of the struts size and the cell size on the potential improvement of the mechanical properties will be studied as well as the influence of the position of the notch in relation to the topological structures on the crack initiation and propagation.  
Software, C.H.; Supervision, M.B.; Writing-original draft preparation, J.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by The ELSAT2020 project, co-financed by the European Union with the European Regional Development Fund, the French state and the Hauts de France Region.  
The authors declare no conflict of interest.