基于M积分的脆性材料微缺陷等效损伤面积/体积表征

随着脆性材料在工程中的广泛应用,对脆性材料中微缺陷进行统一的损伤水平标定,具有重要的科学研究和工程应用价值. 本研究提出一种基于M积分的材料等效损伤面积/体积标定方法, 以具有相同M积分值的圆孔面积或球孔体积来标定 复杂微缺陷构型的损伤水平,从而实现不同类型微缺陷真实损伤水平的统一表征. 首先,基于Lagrangian能量密度函数推导 了M积分定义式,并简述了M积分的物理意义,基于域积分方法实现二维/三维M积分的数值计算. 随后,提出了基 于M积分的材料缺陷等效损伤面积/体积标定方法,以圆孔面积/球孔体积来标定复杂微缺陷材料系统的损伤水平. 最后, 针对单轴拉伸载荷作用下的二维/三维脆性体含不同缺陷构型,具体计算了椭圆孔、裂纹以及双裂纹、双孔洞、裂纹和孔洞干 涉等复杂缺陷构型情况下的等效损伤面积/体积,并详细分析了缺陷之间的干涉效应及影响因素. 本研究旨在基于M积分等 效方法量化脆性材料中各类微缺陷造成的损伤程度,实现损伤等级标定,有益于工程材料及结构的损伤容限设计及完整性评估. 

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.