A strength criterion for size effect on quasi-brittle fracture with and without notch

Abstract

This study shows it is sufficient to use only the tensile strength ft to describe the size effect on quasi-brittle fracture behaviors of brittle heterogeneous solids such as rock and concrete. Another essential material property, the average grain size G for rock or the maximum aggregate size dmax for concrete, should be determined separately before fracture analysis. Quasi-brittle fracture behaviors of heterogeneous specimens or structures, small or large and notched or un-notched, can all be described by the "one-parameter ft criterion" evolved from the boundary effect model (BEM). Using the mean and standard deviation from normal distribution analysis of test data, the simplified BEM can predict the mean quasi-brittle fracture curve and statistical scatters with 95% reliability, covering the entire fracture range from the strength ft criterion to the fracture toughness KIC criterion (LEFM), and the quasi-brittle fracture region in-between. KIC is fully determined by ft and G, making the oneparameter ft approach possible. This one-parameter approach thus requires only "one measurement" from a group of specimens of any size with any notch length. The 95% reliability band established statistically can be conveniently used in design applications.

Multigene Genetic Programming Based Prediction of Concrete Fracture Parameters of Unnotched Specimens

“…They concluded that the size effect coefficient could be directly calculated from the modulus of rupture [22]. The fracture energy of concrete was size dependent and for non-linear models, two fracture parameters were needed to define the concrete fracture behaviour [23]. The water-cement ratio (w/c) had a significant bearing on the interfacial transition zone between concrete paste and aggregate, thereby affecting the strength of concrete [24].…”

Multiple Regression Approach to Fracture Energy Determination of Normal Strength Concrete Using Experimental Evidence

“…Ince and Cetin (2019) [18] have reported that the fracture parameters of concrete are influenced by compressive strength, maximum aggregate size, water-cement ratio, and aggregate type in testing. Chen Yi et al (2019) [19] have established the sufficiency of the tensile strength of quasi-brittle materials to describe the size effect on test results. Mobasher (2022) [20] has proposed an energy equivalence between the externally imparted energy on the test specimens and the energy dissipated in crack propagation.…”