Structural size effect in the mode I and mixed mode I/II fracture of strain-hardening cementitious composites (SHCC)

The size effect in the fracture of solids represents a highly critical issue with a prolonged history of research. The size effect of traditional quasi-brittle materials can already be well described through the size effect model. However, there is still a lack of research on the size effect of strain-hardening cementitious composites (SHCC), a special type of fibre-reinforced concrete with macro-scale strain-hardening behaviour after first cracking. Being distinct from traditional quasi-brittle materials with softening nature, SHCC is thus expected to behave differently in terms of size effect. In this research, the structural size effect problem of SHCC is comprehensively studied by experimental investigation and theoretical analysis. Geometrically similar notched three-point bending specimens were tested in mode I and mixed mode I/II fracture condition. The whole-process of failure and matrix cracking zone around the main crack was captured with high resolution by digital image correlation technology. Experimental results showed that apparent fracture energy, nominal strength, structural ductility and fracture resistance curve are all structural size-dependent. The apparent fracture energy was shown to arise with specimen size within the tested range. This is related to large-scale pseudo yielding, i.e., enlargement of matrix cracking zone (like the yielding zone in metals) with increasing structural size. It thus provides an indirect method for the estimation of cohesive fracture energy of single crack with constitutive nature. Due to the scaled matrix cracking zone, an intermediate asymptote exists in the size effect curve of nominal strength, in addition to the plastic and LEFM asymptotes in the Bazant original size effect law. This resembles the recent finding of intermediate asymptote in plastic-hardening metal. The size-dependence of R-curve was also examined. Though size-dependent, the equivalent LEFM-based R-curves are shown to have three common stages reflecting different cracking processes. Based on experimental results, the size effect of fracture energy and nominal strength are finally modelled theoretically in the Bazant's framework of equivalence between energy release and fracture resistance.