Abstract
Damage and failure of quasi-brittle materials are caused by the evolution and coalescence of micro-cracks. To solve the problem of elliptical micro-crack growth at the elastic deformation stage, a method of complex potential functions is proposed and the effect of the initial orientation on micro-crack growth and deflection is discussed. The critical stress condition for the initial damage is derived according to the criterion of micro-crack growth. Based on energy conservation during wing-crack propagation, a damage constitutive model is developed with the strain criterion created in the condition of micro-crack coalescence. The stress-strain curves of quasi-brittle materials in uniaxial compression obtained based on this model are examined with the experimental results.
Highlights
Damage and failure of quasi-brittle materials are caused by the evolution and coalescence of micro-cracks
The elastic modulus of a material gradually decreases with increase in the number and size of micro-cracks in it during its evolution
Krajcinovic, Sumarac and Fanella [3–6], Ju and Lee [7–9] developed their micromechanical damage models for brittle materials subjected to simple axisymmetric loading by introducing the mechanism of micro-crack propagation
Summary
Let 0 , and the displacement at the tip of the long axis of the elliptical micro-crack is obtained: uax. The lengths of the long and short half shafts of the elliptical micro-crack, respectively, become a a0 uax 2 ua2y ,. (4)–(10), the relative growth rates of the long half shaft, short half shaft, and the deflection angle of the elliptical micro-crack can be obtained, respectively, as shown in Figures 2 and 3.
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