Brittle-to-quasibrittle transition in bundles of nonlinear elastic fibers.

Abstract

Properties of the fiber bundle model have been studied using equal load-sharing dynamics where each fiber obeys a nonlinear stress (s)-strain (x) characteristic function s=G(x) till its breaking threshold. In particular, four different functional forms have been studied: G(x)=e^{αx},1+x^{α},x^{α}, and xe^{αx} where α is a continuously tunable parameter of the model in all cases. Analytical studies, supported by extensive numerical calculations of this model, exhibit a brittle to quasibrittle phase transition at a critical value of α_{c} only in the first two cases. This transition is characterized by the weak power law modulated logarithmic (brittle) and logarithmic (quasibrittle) dependence of the relaxation time on the two sides of the critical point. Moreover, the critical load σ_{c}(α) for the global failure of the bundle depends explicitly on α in all cases. In addition, four more cases have also been studied, where either the nonlinear functional form or the probability distribution of breaking thresholds has been suitably modified. In all these cases similar brittle to quasibrittle transitions have been observed.