We propose a simple way to create tunable plasmonic cavities in the infrared (IR) range using graphene films suspended upon a silicon carbide (SiC) grating and present a numerical investigation, using the finite element method, on the absorption properties and field distributions of such resonant structures. We find at certain frequencies within the SiC reststrahlen band that the structured SiC substrate acts as a perfect reflector, providing a cavity effect by establishing graphene plasmon standing waves. We also provide clear evidence of strong coupling phenomena between the localized surface phonon polariton resonances in the SiC grating with the graphene surface plasmon cavity modes, which is revealed by a Rabi splitting in the absorption spectrum. This paves the way to build simple plasmonic structures, using well-known materials and experimental techniques, that can be used to excite graphene plasmons efficiently, even at normal incidence, as well as explore cavity quantum electrodynamics and potential applications in IR spectroscopy.