  The mechanical properties of heterophase interfaces are critically important
for the behaviour of graphene-reinforced composites. In this work, the
structure, adhesion, cleavage and sliding of heterophase interfaces, formed
between a ZrB$_2$ matrix and graphene nanosheets, are systematically
investigated by density functional theory, and compared to available
experimental data. We demonstrate that the surface chemistry of the ZrB$_2$
matrix material largely shapes the interface structures (of either Zr-C-Zr or
B-C-B type) and the nature of the interfacial interaction. The Zr-C-Zr
interfaces present strong chemical bonding and their response to mechanical
stress is significantly influenced by graphene corrugation. In contrast B-C-B
interfaces, interacting through the relatively weak $\pi$-$\pi$ stacking, show
attributes similar to 2D materials heterostructures. Our theoretical results
provide insights into the interface bonding mechanisms in graphene/ceramic
composites, and emphasize the prospect for their design via interface
engineering enabled by surface contacts.
