We study the Ising axis conversion in a mixed Tb0.5Dy0.5Cu2 single crystal. Interest is focused on how changes in the exchange interactions due to rare earth substitutions influence the existence of magnetic phases and the critical field values for the Ising axis conversion. From magnetisation measurements we determined the (H - T ) phase diagram for magnetic fields parallel to the easy a-axis and the temperature dependence of the critical field for the Ising axis conversion. Both properties for the mixed crystal follow a simple composition scaling behavior. But in contrast to previous studies on the pure compounds TbCu2 and DyCu2 the changes of magnetic and structural properties at the conversion cannot be recovered completely by thermal treatment. Only a small part (10 % of the sample volume) goes back to the virgin state after warming the sample to 500 K. This behavior is of great interest for further neutron or X-ray diffraction studies of the Ising axis conversion allowing to study the converted phase under routinely used experimental conditions.