Most works on Grids have taken an approach where the system is a mixture of clusters and other resources put together with the help of some services. But this solution is a simplistic one that tries to grow from the cluster perspective. We think that the Grid model should be different and near to the p2p model, especially in the I/O field where the network and the heterogeneity of the infrastructure play an important role. In this paper we present a model to organize the DataGrid Infrastructure using concepts as data phases and a p2p approach, in order to select the adequate working policies. These concepts allow the definition of a clearer model for our DataGrid Architecture than a mixture of resources. We present a model relying on the former concepts, their implementation in an I/O middleware for Grids, called GridExpand, and the evaluation of some of the concepts presented.