Mixed mode fracture of geometrically similar FRUHPC notched beams with the localizing gradient damage model

Abstract

A localizing gradient damage model is proposed in this paper to capture the mechanisms underlying the fracture of fiber reinforced ultra-high performance concrete (FRUHPC): (i) an initially expanding damage process zone due to the formation of numerous fine cracks, each widening up slowly due to the fiber bridging effect; (ii) a gradual formation of a localized macroscopic crack, when at least one of the fine cracks has opened up sufficiently to trigger a fiber pull-out process. Restricting to tensile-shear dominated failures in monotonic loadings, the simplest form of damage model is adopted, where an isotropic damage variable is driven by a strain-like variable. The performance of the proposed localizing gradient damage model is first demonstrated by comparing the damage evolution process against the corresponding intensity of acoustic emission (AE) events obtained experimentally, for a notched FRUHPC beam in three-point bending. It was shown that the model is able to reproduce the slightly widening fracture process zone (FPZ) during strain hardening, as well as the eventual localized damage process zone during strain softening. Specifically, during strain hardening, the proposed localizing gradient damage model predicts an energy dissipation bandwidth that compares well with the AE energy maps, together with a consistent propagation of crack front. With a correct description of the underlying damage mechanisms, the predictive capability of the proposed model is next demonstrated through the mixed mode fracture of a series of geometrically similar FRUHPC notched beams. Since the specimens are of the same casting batch as those in the three-point bending test, the numerical material parameters calibrated earlier are adopted directly for the mixed mode fracture tests. Without any further undue calibrations, the localizing gradient damage model is shown to predict well the structure responses and size effect of the series of geometrically similar FRUHPC notched beams in mixed mode fracture.