Collaborative research efforts to study the fragmentation processes of heavy nuclei in matter using heavy ion beams of the Bevatron/Bevalac are described. The goal of the program is to obtain the single particle inclusive spectra of secondary nuclei produced at 0 deg by the fragmentation of heavy ion beam projectiles. The process being examined is B+T yields F + anything, where B is the beam nucleus, T is the target nucleus, and F is the detected fragment. The fragments F are isotopically identified by experimental procedures involving magnetic analysis, energy loss and time-of-flight measurements. Effects were also made to: (a) study processes of heavy nuclei in matter, (b) measure the total and partial production cross section for all isotopes, (c) test the applicability of high energy multiparticle interaction theory to nuclear fragmentation, (d) apply the cross section data and fragmentation probabilities to cosmic ray transport theory, and (e) search for systematic behavior of fragment production as a means to improve existing semi-empirical theories of cross-sections.