© 2021 Elsevier LtdThis study investigates the crack initiation and its progression in two-dimensional functionally graded (FG) plates under dynamic and quasi-static loading conditions by using an ordinary state-based PeriDynamic (OSB PD) theory. Functionally gradient materials (FGMs) are a new class of advanced materials that provide a smooth transition among the layers of materials to meet the desired requirements in engineering structures. The effective material properties in the FG plate were functionally tailored in two directions by employing a rule of mixture. The present OSB PD theory is very suitable for the failure analysis of materials without the use of surface and volume correction factors. The robustness of the present approach on monitoring the mixed-mode fractures is established with the experimental results under various loading conditions. The PD predictions successfully captured the critical load levels and damage evolutions. Subsequently, numerical analyses were carried out to assess the influence of the one- and two-dimensional material variations, boundary, and loading conditions on the fracture behavior of the FG plates. The compositional gradient exponent played a major role on the reaction force levels and crack trajectories. It was observed that two-dimensional material variations paved the way for increasing the plate strength and fracture resistance.