Numerical Analysis of Some Experimental Results Relative to Size Effects on the Fracture Parameters

In order to study the compatibility of some theoretical models referring to the size effects on the fracture parameters relative to the experimental data, some experimental results [1], [2], referring to the tensile strength σN, critical strain wu, and to the fracture energy GF of some concrete and rock specimens, respectively, were studied by means of the procedures of the numerical analysis [3]. It was pointed out that for some concrete specimen (e.g. for some dry and wet samples [1]), the obtained experimental results were not homogeneous, some individual values of wu having the character of rough errors. Taking into account the particular interest shown by the fractal descriptions of the size effects on the fracture parameters, the experimental results of the classical work [4] were analyzed also. We have found that the experimental results of Fig.1 [4] correspond better to a multi-fractal [a spectral (size) distribution of limited fractals] than to a unique (ideal) fractal. The compatibility of some basic theoretical models [5], [6] of the size effects on the fracture parameters relative to the existing experimental data was studied by means of a new processing procedure [7]. The obtained results seem to indicate that the fractal character of fracture surfaces and the (classical) elasticity theory implications on the size-effects represent cooperative processes, the most accurate descriptions implying (generally) contributions of both these factors, with properly chosen specific weights. Some new similitude expressions of the fracture parameters in terms of the specimen size are also proposed.