Failure process of a bundle of plastic fibers

We present an extension of fiber bundle models considering that failed fibers still carry a fraction $0 \leq \alpha \leq 1$ of their failure load. The value of $\alpha$ interpolates between the perfectly brittle failure $(\alpha = 0)$ and perfectly plastic behavior $(\alpha=1)$ of fibers. We show that the finite load bearing capacity of broken fibers has a substantial effect on the failure process of the bundle. In the case of global load sharing it is found that for $\alpha \to 1$ the macroscopic response of the bundle becomes perfectly plastic with a yield stress equal to the average fiber strength. On the microlevel, the size distribution of avalanches has a crossover from a power law of exponent $\approx 2.5$ to a faster exponential decay. For localized load sharing, computer simulations revealed a sharp transition at a well defined value $\alpha_c$ from a phase where macroscopic failure occurs due to localization as a consequence of local stress enhancements, to another one where the disordered fiber strength dominates the damage process. Analysing the microstructure of damage, the transition proved to be analogous to percolation. At the critical point $\alpha_c$, the spanning cluster of damage is found to be compact with a fractal boundary. The distribution of bursts of fiber breakings shows a power law behaviour with a universal exponent $\approx 1.5$ equal to the mean field exponent of fiber bundles of critical strength distributions. The model can be relevant to understand the shear failure of glued interfaces where failed regions can still transmit load by remaining in contact.