In this study, graphene was used as a reinforcing material and added to NC-826 epoxy at three different ratios to form polymeric composite materials. In material preparation, a three-roller dispersing machine was used to disperse graphene evenly in the epoxy. The composite materials obtained were tested with laboratory instruments by subjecting them to quasi-static compression and dynamic impact at the following speeds in ascending order: 10−3s−1, 10−2s−1, 10-1s−1, 2000s−1, 3000s−1, and 4000s−1; in other words, the materials were tested at six different strain rates. After that, the fracture surfaces of the materials were analyzed by field-emission scanning electron microscopy to gain insight into the interfacial failure mechanism of the materials and evaluate the evenness of dispersion. Experimental results showed that the addition of the reinforcing material was effective in increasing the strength of the epoxy, preventing the generated cracks from expanding, allowing stress to be effectively transmitted within the matrix, and thereby enhancing the toughness of the epoxy. Therefore, the composite materials can be used as the substrate materials for pressure sensor components.