13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Three-dimensional Fatigue Crack Growth Path Simulation under Non- proportional Mixed-mode Loading Ying Yang1,*, Michael Vormwald1 1 Material Mechanics group, Technische Universität Darmstadt, Petersenstaße 12, 64287 Darmstadt (Germany) * Corresponding author: yang@wm.tu-darmstadt.de Abstract An algorithm based on linear elastic fracture mechanics (LEFM) for three-dimensional fatigue crack growth simulation under non-proportional mixed-mode loading is proposed in the present paper. Combined non-proportional cyclic tension and torsion loading with different phase angle and loading ratio MT/F are considered. The maximum tangential stress (MTS) criterion is performed as the main theory to predict crack propagation direction. Under some specific loading cases, especially for high stress intensity factors, the crack growth direction needed to be modified in order to be in accordance with the experimental results. By analyzing the simulated crack growth paths, three distinct features are observed that are tension mode dominated crack paths, shear mode dominated crack paths and transitional crack paths. When crack growth changes from tension to shear mode, the latter is described by the maximum shear stress (MSS) criterion. A preliminary proposal is made to predict the transitional mode. Keywords Linear elastic fracture mechanics, Non-proportional loading, Mixed mode, Transitional fracture 1. Introduction Considering that a great amount of structures or components are subjected to mixed mode loading during the service time, research on material fracture under this kind of loading type has attracted more attention in recent years. Crack propagation direction is one of the major problems in this field. Since the maximum tangential stress criterion was first proposed by Erdogan and Sih [1], the minimum strain energy density criterion (S-Criterion), the maximum energy release rate criterion and maximum tangential strain criterion [2–4] and so on were suggested subsequently. All the mentioned criteria present similar crack propagation direction for proportional mixed mode loading, showing small deviation with the experiment results. The crack growth directions display a tension mode feature following the direction which minimizes the KII values. However, large distinction between experimental crack propagation direction and the predicted crack kink angle were also observed for some materials. In these cases, the crack growth occurred in the plane that KII values were maximum. As a result the maximum shear stress (MSS) criterion was proposed. Crack growth in shear mode was summarized in a literature review by H. W. Liu [5]. The criteria represented by MTS and MSS are deduced according to the stress field solution in the vicinity of crack tip on the basis of linear elastic fracture mechanics. Strictly speaking, these criteria are appropriate only in monotonic loading condition. Nevertheless, Highsmith et al. [6] pointed out that the criteria can be performed straightforward to fatigue crack growth under proportional mixed mode loading. Fatigue crack growth under non-proportional mixed mode loading is a more complex situation and there are insufficient experiments and hypotheses for application. Vormwald et al. [7] reviewed some research consequences in recent years. Six relevant factors which influence the crack growth behavior under non-proportional loading were denoted and an algorithm based on LEFM for three-dimensional fatigue crack growth simulation under non-proportional mixed-mode loading is proposed [8]. The emphasis in the present paper is focusing on the crack growth path behavior. A description of the algorithm is presented. 2. Application of the algorithm
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