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Based on compressive tests, static on 810 material test system and dynamic on the first compressive loading in split Hopkinson pressure bar (SHPB) tests for Pr-Nd alloy cylinder specimens at high strain rates and temperatures, this study determined a J-C type [G. R. Johnson and W. H. Cook, in Proceedings of Seventh International Symposium on Ballistics (The Hague, The Netherlands, 1983), pp. 541-547] compressive constitutive equation of Pr-Nd alloy. It was recorded by a high speed camera that the Pr-Nd alloy cylinder specimens fractured during the first compressive loading in SHPB tests at high strain rates and temperatures. From high speed camera images, the critical strains of the dynamic shearing instability for Pr-Nd alloy in SHPB tests were determined, which were consistent with that estimated by using Batra and Wei's dynamic shearing instability criterion [R. C. Batra and Z. G. Wei, Int. J. Impact Eng. 34, 448 (2007)] and the determined compressive constitutive equation of Pr-Nd alloy. The transmitted and reflected pulses of SHPB tests for Pr-Nd alloy cylinder specimens computed with the determined compressive constitutive equation of Pr-Nd alloy and Batra and Wei's dynamic shearing instability criterion could be consistent with the experimental data. The fractured Pr-Nd alloy cylinder specimens of compressive tests were investigated by using 3D supper depth digital microscope and scanning electron microscope. [ABSTRACT FROM AUTHOR]