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The irreversibility line and second magnetization peak of heavily overdoped Cu-rich Bi2Sr2CaCu2O8+x (Bi2212) single crystals are studied by accurate magnetization measurements with a field H\parallel c . Compared with optimally-doped and Pb-doped Bi2212 single crystals, the present system exhibits an enhanced pinning behaviour and higher dimensional crossover field. The temperature dependences of the critical current densities at the first and the second peaks exhibit different behaviour before and after the dimensional crossover. Above the crossover field, the irreversibility line obeys an exponential temperature dependence. Our results suggest that the second peak is caused by the switch of the flux pinning from three-dimensional flux line pinning to two-dimensional (2D) collective pinning, and the irreversibility line is the depinning line of the 2D vortex lattice.