Micro-failure Theory For Brittle Materials And Shakedown Analysis 0f Structures With Damage

The macro-and micro-failure theory of materials is a very important research subject of solid mechanics and material science. In the thesis, both phenomenological and micromechanical damage models for brittle and ductile materials are reviewed. Attention is focused on the micro-damage and fracture of brittle materials as well as the shakedown of elastic-plastic structures with damage.A rather complete micromechanical damage model for quasi-brittle materials is established, which is called the damage mode of domain of microcrack growth (DMG) and can be used to analyze the micro-damage and constitutive response in all stages from the initial undamaged state to the ultimate macro-failure of brittle materials subjected to triaxial tension or triaxial compression. The domain of microcrack growth is defined and used to describe the damage state of microcrack-weakened brittle materials. Based on this concept, the problems of micro-damage evolution and macro-constitutive response can be solved easily. The constitutive relation of brittle materials is classified into four stages: namely linear elasticity, pre-peak nonlinear hardening, rapid stress drop and strain softening. The microscopic damage mechanisms in all these stages are investigated. The rapid stress drop reflects the transition from continuous distributed damage to damage localization. The damage and failure modes of brittle materials under tension and compression are different. The self-similar growth of open microcracks under tension, the frictional sliding, mode-n self-similar growth and kinking of closed microcracks under compression and their influences on the mechanical properties of materials are studied in detail. Moreover, an experimental method based on the equivalence of compliance is proposed to determine the anisotropic damage state in brittle materials.The damage and fracture behaviors at the tip of a mode- I macroscopiccrack in brittle materials are studied. For a class of brittle materials with a stage of damage saturation, the stress shielding effect by microcracking at the tip of a mode- I crack is analyzed by using the effective elastic media method based on the micromechanical damage model of DMG. The stress and strain fields near the crack tip are obtained. A new method of modified J-integral is presented to calculate the shielding ratio by microcracking and its numerical result is compared with that obtained by the previous method of J-integral conservation. It is pointed out that due to the stress drop and strain softening of brittle material damage localization will occur ahead of a macroscopic crack under external loads. The method of calculating the length of damage localization band is given.The shakedown theory of structures with damage is developed also in this thesis. The close relationship between damage of materials and shakedown of structures is revealed. The ductile damage factor is adopted as the control parameter of the failure criterion of elastic-plastic structures subjected to variable loads. A mathematical programming method is presented to calculate the lower bound of safety load domain and the upper bound of damage factor in either elastic-perfectly plastic or strain hardening structures at shakedown.Feng Xiqiao (Solid Mechanics) Directed by Professor Yu Shouwen...