A device-to-device (D2D) wireless network is considered, where user devices also have the ability to cache content. In such networks, users are mobile and communication links can be spontaneously activated and dropped depending on the users’ relative position. Receivers request files from transmitters, these files having a certain popularity and file-size distribution. In this work a new performance metric is introduced, namely the Service Success Probability, which captures the specificities of D2D networks for the Poisson Point Process case of node distribution and both the SNR and SINR coverage model. For all scenarios, the success probability depends not just on the content placement policy, but essentially on the transmitter association policy. Association can either be cache-aware or cache-unaware depending on information availability over cache inventories. We derive explicit expressions related to the defined performance metric using stochastic geometry analysis. We further extend the analysis from one-shot transmission to consecutive transmitter associations, where the receiver is allowed to profit from node mobility and gradually receive service by associating stepwise to nodes in its vicinity. Simulations support the analytical results and explain the influence of mobility, association, fading, file-size distribution and frequency reuse on the D2D performance, while providing intuition on how to appropriately cache content on mobile storage space. Of particular interest is the investigation on how different file-size distributions (Exponential, Uniform, or Heavy-Tailed) influence the performance. Finally, it is illustrated that D2D communications considerably benefit from multiple consecutive associations, which can guarantee service completion especially in high mobility environments.