Determination of fracture energy, process zone longth and brittleness number from size effect, with application to rock and conerete

TLDR: In this paper, the dependence of the fracture energy and the effective process zone length on the specimen size as well as the craek extension from the notch is analyzed on the basis of Ba<zant's approximate size effect law.

Abstract: The dependence of the fracture energy and the effective process zone length on the specimen size as well as the craek extension from the notch is analyzed on the basis of Ba<zant's approximate size effect law. The fracture energy and the effective length of the fracture process zone is defined on the basis of the extrapolation to an infinite specimen size, for which the definitions are independent of the shape of the specimen or structure. Both of these material properties are expressed in terms of the size effect law parameters and the function describing the nondimensional energy release rate. Ba<zant's size effect law for the nominal stress σN at failure is reformulated in a manner in which the parameters are the fracture energy and the effective (elastically equivalent) process zone length. A method to determine these material properties from σN-data by linear and nonlinear regressions is shown. This method permits these properties to be evaluated solely on the basis of the measured maximum loads of specimens of various sizes and possibly also of different shapes. Variation of both the fracture energy and the effective process zone length as a function of the specimen size is determined. The theoretical results agree with previous fracture tests of rock as well as concrete and describe them adequately in relation to the inevitable random scatter of the tests.