Evaluation of energy release rate related to crack kink and simulation of surface crack shape change of round bar

Abstract

Fracture damage usually occurs from pre-existing defects or small cracks in service. These cracks influence the stress distribution in the component and can result in significant reduction in its strength and service life. As an important impact on the safety of engineering components, the crack problem is an interesting research area. In this paper, two topics are studied about the crack problem. One is the evaluation of the energy release rate related to crack kink under mixed-mode loading. The other one is the prediction of shape change of surface crack subjected to tension based on the three-parameter model. Most of the researches on crack kink are focused on the crack under two kinds of loading situation, the mixed-mode I-II-III loading situation is rarely mentioned, and the validity of conclusions reached cannot be evaluated yet. The energy release rate related to crack kink under mixed-mode loading for aluminum alloy material has been investigated using both numerical methods and theoretical derivation. A relatively simple and precise numerical method was established to evaluate the energy release rate associated with stress intensity factors under mixed mode loading, based on the concept that the energy release rate is equal to the change rate of the energy difference before and after crack kink. Based on the numerical method, a series of spatial inclined ellipses in Mode I-II and ellipsoids in Mode I-II-III with different propagation angles computed from the non-dimensional value (K⁄√EG) were fitted by MATLAB, and the expression of energy release rate with crack propagation angle was obtained. A theoretical expression of energy release rate at any propagation 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. It is confirmed that the deduced theoretical expression could provide results as accurate as of the present numerical method. The results of the proposed method are consistent with experimental data. The error, which is lower than 5%, can be accepted considering that the specimens are not manufactured using an ideal elastic material. Consequently, the proposed method can achieve an accurate evaluation of the energy release rate with concise calculation. Meanwhile, the initiating and propagation analysis of surface crack is critical for structural integrity prediction of cylindrical metallic components with a circular cross-section, since these components have been applied widely in engineering. Most attempts to predict fatigue growth of a surface crack in an un-notched or very mild notched bar have focused on the ‘almond’ crack employing a certain shape with a fixed center, which reduced the fatigue calculations to one-or two-dimensional problems. Few efforts have been made utilizing a three-parameter model. The fatigue propagation of a surface crack in a round bar subjected to tension loads has been investigated. The crack growth circles method is developed for the surface cracks of a round bar, and the circles are tangent to both current and new crack fronts. A three-parameter model with fewer shape restraints whose center is allowed to move along the vertical axis is built, and the shape change of a fatigue crack is predicted more precisely. The nominal aspect ratio of an ellipse, which is the ratio of the maximum crack depth to the chord length, is considered, instead of the actual aspect ratio of an ellipse semi-axis. A relatively large crack growth increment can be used by adopting the equivalent stress intensity factor ∆Ke based on the stress intensity factors along the current and new crack fronts. The crack propagation process is described accurately based on the ratio of vertical growth toward the horizontal surface. It can be seen that the crack propagation paths differ with different initial flaws, but will converge asymptotically. The present results demonstrate good convergence speed and accurate prediction of crack shape patterns. Comparisons have been done to verify the proposed solutions, it is illustrated that the proposed solutions agree well with experimental data and is better than other numerical solutions.