Second-order continuity tensor and stiffness degradation of aluminum alloy 2024T3 under large strain at room temperature

Abstract

A symmetric second-order continuity tensor is proposed to characterize anisotropic damage of anisotropic materials based on the hypothesis of equivalent elastic strain energy. On the basis of the equivalent elastic strain energy hypothesis, the relation between the effective elastic properties and the continuity tensor has been formulated. The current formulation does not require the assumption that the principal coordinate system of damage must coincide with that of the material. In a two-dimensional damage analysis, the state of damage can be represented by a Mohr’s circle of continuity. The proposed damage characterization technique has been successfully applied to an example case, where aluminum alloy 2024T3 specimens were strain-damaged by uni-axial tension. The experimental results show that the effects of strain damage can cause degradation of the material stiffness. On the other hand, the overall elastic orthotropy of the material does not increase with the degree of damage. The proposed continuity tensor has been found to be capable of describing this phenomenon. The principal values and the principal directions of the continuity tensor have been determined. The mean value of the principal values can represent the magnitude of the damage, while the principal direction of the continuity tensor may provide information about the damage mechanism.