We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle fragmentation. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure is kept constant and the packing is subjected to biaxial com- pression. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the fragmentation process is highly inhomogenious both in the fragment sizes and their locations inside the packing. In particu- lar, a number of large particles never break whereas a large number of particles break up into small fragments. As a result, the packing keeps the memory of its initial particle size distribution whereas a power-law distribution is observed for particles of intermediate size resulting from consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive evolution towards a pseudo-steady state is observed instead. We also show that the shear strength of the packing is well expressed in terms of contact anisotropics and force anisotropics. The force anisotropy increases while the contact orientation anisotropy decreases for increasing internal cohesion of the particles. These two effects compensate each other such that the shear strength is nearly independent of internal cohesion.