THE CALIBRATION OF MICRODEFECTS INDUCED EQUIVALENT DAMAGE AREA/VOLUME OF BRITTLE MATERIALS BY USING THE M-INTEGRAL

In view of the integrity, reliability and functionality of brittle materials are substantially limited by the existence of microdefects, the calibration of materials’ damage level is of great scientific value and underlying engineering applications. An unified method of evaluating the microdefects induced equivalent damage area/volume is proposed in present study by the aid of M-integral. The damage area/volume induced by underlying multiple microdefects is assumed as equivalent to the area/volume of an individual circular/spherical void while the values of M-integral are equal for the both cases. Firstly, the analytical expression of M-integral is deduced by using the Lagrangian energy density function, the corresponding physical meaning is briefly elucidated. The domain integral method is applied to numerically calculating the M-integral for both two-dimensional (2D) and three-dimensional (3D) cases. Subsequently, the damage calibration process of arbitrary dispersed microdefects is given, the corresponding equivalent damage area for 2D defects and volume for 3D defects are defined. Finally, the elastic 2D plane and 3D body under uniaxial tensile loading condition is simulated, within which a series of different defect configurations are considered, including the singular defect (void, crack and ellipse) and the dual-defects (void-void, crack-crack, void-crack). Corresponding equivalent damage area or volume are calculated, the inherent “interactive effects” and influence factors are elucidated detailedly and quantitatively. Through the proposed damage calibration method in this study, we can estimate the damage level of any microdefects within brittle solids, the calibration process is simple and convenient, which will be beneficial to the damage tolerance design and integrity assessment of engineering structures.