R-CURVE MODELING OF RATE AND SIZE EFFECTS IN QUASIBRITTLE FRACTURE

The equivalent linear elastic fracture model based on an R-curve (a cu rve characterizing the variation of the critical energy release rate w ith the crack propagation length) is generalized to describe both the rate effect and size effect observed in concrete, rock or other quasib rittle materials. It is assumed that the crack propagation velocity de pends on the ratio of the stress intensity factor to its critical valu e based on the R-curve and that this dependence has the form of a powe r function with an exponent much larger than 1. The shape of the R-cur ve is determined as the envelope of the fracture equilibrium curves co rresponding to the maximum load values for geometrically similar speci mens of different sizes. The creep in the bulk of a concrete specimen must be taken into account, which is done by replacing the elastic con stants in the linear elastic fracture mechanics (LEFM) formulas with a linear viscoelastic operator in time (for rocks, which do not creep, this is omitted). The experimental observation that the brittleness of concrete increases as the loading rate decreases (i.e. the response s hifts in the size effect plot closer to LEFM) can be approximately des cribed by assuming that stress relaxation causes the effective process zone length in the R-curve expression to decrease with a decreasing l oading rate. Another power function is used to describe this. Good fit s of test data for which the times to peak range from 1 sec to 250000 sec are demonstrated. Furthermore, the theory also describes the recen tly conducted relaxation tests, as well as the recently observed respo nse to a sudden change of loading rate (both increase and decrease), a nd particularly the fact that a sufficient rate increase in the post-p eak range can produce a load-displacement response of positive slope l eading to a second peak.