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Galaxy clusters are known to be reservoirs of Cosmic Rays (CRs), as inferredfrom theoretical calculations or detection of CR-derived observables. CRacceleration in clusters is mostly attributed to the dynamical activity thatproduces shocks. Shocks in clusters emerge out of merger or accretion, butwhich one is more effective in producing CRs? at which dynamical phase? andwhy? To this aim, we study the production or injection of CRs through shocksand its evolution in the galaxy clusters using cosmological simulations withthe {\sc enzo} code. Particle acceleration model considered here is primarilythe Diffusive Shock Acceleration (DSA) of thermal particles, but we also reporta tentative study with pre-existing CRs. Defining appropriate dynamical statesusing the concept of virialization, we studied a sample of merging andnon-merging clusters. We report that the merger shocks (with Mach number$\mathcal{M}\sim2-5$) are the most effective CR producers, while high-Machperipheral shocks (i.e. $\mathcal{M}>5$) are mainly responsible for thebrightest phase of CR injection in clusters. Clusters once merged, permanentlydeviate from CR and X-ray mass scaling of non-merging systems, enabling us touse it as a tool to determine the state of merger. Through a temporal andspatial evolution study, we found a strong correlation between cluster mergerdynamics and CR injection. We observed that the brightest phase of X-ray and CRinjection from clusters occur respectively at about 1.0 and 1.5 Gyr after everymergers, and CR injection peaks near to the cluster virial radius (i.e$r_{200}$). Delayed CR injection peaks found in this study deserve furtherinvestigation for possible impact on the evolution of CR-derived observablesfrom galaxy clusters.

Manufacturing cosmic rays in the evolving dynamical states of galaxy clusters