ENERGY BALANCE SIZE EFFECT MODEL OF COMPRESSIVE STRENGTH FOR QUASI-BRITTLE MATERIALS

To address the problem of existing size effect models cannot reflect complete size effect of compressive strength and internal mechanism of quasi-brittle materials. In this paper, by analyzing energy input, storage, global-local energy dissipation during the failure process of quasi-brittle materials under uniaxial compression, mechanical model and bilinear nominal and true stress-strain curves are established to reflect global and local damage and describe the above energy evolution process respectively. On this basis, the expressions of input energy, stored elastic energy and global-local energy dissipation are determined when the nominal stress is the maximum. Finally, size effect model of compressive strength is established with energy balance principle. The energy balance size effect model of compressive strength can completely reflect the size effect of nominal compressive strength, namely with the increase of sample size, nominal compressive strength is the real strength when sample size is less than or equal to the size of local damage zone, and then gradually decreases, eventually tends to the elastic ultimate strength when the sample size approaches infinity. High to diameter ratio together with sample diameter can be taken into account in the energy balance size effect model of compressive strength. Its parameters, which can reflect the effect of real strength, elastic ultimate strength, nonlinear of nominal damage modulus, size and direction of local damage zone on nominal compressive strength size effect of quasi-brittle materials, have clear physical meaning. Experiment and numerical simulation data of various materials are utilized to validate and evaluate the energy balance size effect model of compressive strength and existing size effect models. The results indicate that the energy balance size effect model of compressive strength can well describe the nonlinear variation and internal mechanism of size effect of experiment and numerical simulation, and compared with the existing size effect models, its total average error is the smallest and less than 5%.