In ordinary solids, material disorder is known to increase the size of the process zone in which stress concentrates at the crack tip, causing a transition from localized to diffuse failure. Here, we report experiments on disordered 2D lattices, derived from frictional particle packings, in which the mean coordination number $\langle z \rangle$ of the underlying network provides a similar control. Our experiments show that tuning the connectivity of the network provides access to a range of behaviors from brittle to ductile failure. We elucidate the cooperative origins of this transition using a frictional pebble game algorithm on the original, intact lattices. We find that the transition corresponds to the isostatic value $\langle z \rangle = 3$ in the large-friction limit, with brittle failure occurring for structures vertically spanned by a rigid cluster, and ductile failure for floppy networks containing nonspanning rigid clusters. Furthermore, we find that individual failure events typically occur within the floppy regions separated by the rigid clusters.
Berthier, E., Kollmer, J. E., Henkes, S. E., Liu, K., Schwarz, J., & Daniels, K. E. (2018). Rigidity percolation control of the brittle-ductile transition in disordered networks. Phys. Rev. Materials. https://doi.org/10.1103/PhysRevMaterials.3.075602