Crack initiation considering the possible stress acting on the crack surface under uniaxial tension or compression

Abstract

In the classical fracture mechanics theory, it is generally believed that the crack surface is open under tension and closed under compression. However, under uniaxial tension at a small angle with the crack surface, especially when parallel, the stress field at the crack tip calculated by traditional theory is small. Although many scholars have proved that the stress field at the crack tip needs to consider T-stress, it is just a non-singular term. This is because under small angle uniaxial tension, the crack surface may also be closed. Similarly, it may be open under uniaxial compression. Therefore, aiming at the shortcomings of the existing theories, both the far-field stress and the possible stress acting on the crack surface are considered in this paper. Based on the stress boundary conditions of the far-field and the crack surface, the stress function of the infinite plate with a single crack under complex load is deduced and the stress field at the crack tip is obtained, that is, the stress intensity factors KI, KII and T-stress. Based on the generalized maximum tangential stress (GMTS) criterion, the crack initiation angles of open or closed cracks under uniaxial tension or compression are studied respectively, the relationships between crack initiation angle θ0 and β (β: angle between the tensile/compressive direction and crack surface) are obtained. A parameter η is introduced to judge whether the crack surface is open or closed under different loading angles. Compared the above research results with the methods proposed by predecessors and experimental data, it is found that they are in good agreement. The results show that the stress intensity factors KI, KII and T-stress are related to not only the far-field stress, but also the possible stress acting on the crack surface; The stress on the crack surface changes with far-field stress; The crack surface under small angle tension regarded as closed while under compression as open is reasonable.