Abstract
The evaluation of energy release rate with angle is still a challenging task in metal crack propagation analysis, especially for the mixed Mode I-II-III loading situation. In this paper, the energy release rate associated with stress intensity factors at an arbitrary angle under mixed mode loadings has been investigated using both a numerical method and theoretical derivation. A relatively simple and precise numerical method was established through a series of spatial-inclined ellipses in Mode I-II and ellipsoids in Mode I-II-III, with different propagation angles computed from simulation. Meanwhile, a theoretical expression of the energy release rate with angle for a crack tip under a I-II-III mixed mode crack was deduced based on the propagation mechanism of the crack tip under the influence of a stress field. It is confirmed that the theoretical expression deduced could provide results as accurately as the present numerical method. The present results were confirmed to be effective and accurate by comparison with experimental data and other literature.
Highlights
The understanding of mixed-mode fracture is an important subject in fracture mechanics, as material flaws or pre-cracks may inevitably occur in the manufacturing process
It is confirmed that the theoretical expression deduced could provide results as accurately as the present numerical method
From the output data of the simulation, the energy release rate and stress intensity factors can be obtained corresponding to the required condition
Summary
The understanding of mixed-mode fracture is an important subject in fracture mechanics, as material flaws or pre-cracks may inevitably occur in the manufacturing process. To describe crack propagation under mixed-mode loading, the classical formula of energy release rate G was expanded in this hypothesis that crack extends collinearly with the initial crack: G=. The validity of Irwin’s formula for the energy release rate for any kink angle, material anisotropy and loading condition was proved by Abbas Azhdari and Sia Nemat-Nasser [17]. The objective of this paper was to evaluate the energy release rate associated with stress intensity factors at any angle under mixed mode loading. A theoretical expression of energy release rate with angle for a crack tip under I-II-III mixed mode crack was deduced based on the propagation mechanism of the crack tip under the influence of a stress field. The validity of the present methods will be shown by comparing them with experimental data and other literature
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