The ATLAS collaboration will upgrade its semiconductor pixel tracking detector with a new Insertable B-layer (IBL) between the existing pixel detector and the vacuum pipe of the Large Hadron Collider. The extreme operating conditions at this location have necessitated the development of new radiation hard pixel sensor technologies and a new front-end readout chip, called the FE-I4. Planar pixel sensors and 3D pixel sensors have been investigated to equip this new pixel layer, and prototype modules using the FE-I4A have been fabricated and characterized using 120 GeV pions at the CERN SPS and 4 GeV positrons at DESY, before and after module irradiation. Beam test results are presented, including charge collection efficiency, tracking effici...