Analysis of Multi-Site Damage With Damage Mechanics

The phenomenon of Multi-site damage (MSD) has been observed in aging aircraft structures. The MSD refers in general to the presence of randomly distributed micro-cracks induced by cyclic loading in the form of fatigue damage. Although the conventional theory of fracture mechanics has been often employed to study the behaviors of multi-side damage, the theory should only be used to characterize a well-defined macro-crack rather than a cloud of micro-cracks. Consequently, satisfactory solution to the MSD problem is yet to emerge. The phenomenon of MSD may well be best suited for characterization by the emerging technology of damage mechanics which takes into account the presence of micro-cracks. In the study of MSD in aging aircraft structures, two separate tasks must be properly addressed, although they are not mutually exclusive. The first one is to quantify the extent of MSD in an existing structure and the second one is to estimate the residual life of the structure suffering from the MSD. Naturally, the first task must be accomplished before the second one is to be undertaken. This paper aims to address the first task by presenting an anisotropic model of multi-site damage to quantify the extent of multi-site damage in engineering structures. This is achieved by extending the application of an anisotropic model of damage mechanics recently proposed by Chow and Wang (1987a, b, c; 1988a, b; Wang and Chow, 1989). The effect of plastic damage on multi-site damage is taken into account by establishing the required evolution equations of plastic damage. The elastic and plastic constitutive equations of stress and strain are modified with the effects of damage. The parameters required for the proposed damage model are evaluated from the experimental data of uniaxial fatigue with smooth specimens. A finite element program taking into account the effects of the multi-site damage in a structure and plastic damage is developed. The multi-site damage near a notch root is quantified and depicted by contour curves, from which the characteristics of multi-site damage are discussed. The calculated results reveal an important phenomenon that around the notch root there is a marked stress re-distribution during the damage evolution, a phenomenon that cannot be properly quantified using the conventional fracture mechanics approach.