13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- The algorithm is applied to simulate the fatigue crack growth including path and propagation rate in a thin-walled, hollow cylindrical specimen (see Figure 1) with a notch. The corresponding experimental data were obtained by Brüning [9]. In the experiment two common used materials were tested, the aluminium alloy AlMg4.5Mn and steel S460N. The combined non-proportional cyclic tension and torsion loading with phase angles of 45° and 90° were applied to the specimens with an R ratio of -1. The results of 4 specimens marked as A7, A8, S7 and S13 could be used here for comparison purpose because the loading was relatively low to meet small scale yielding requirements. 65 47 297 90 2 52.3 36 37 Figure 1. Specimen and notch geometry (dimensions in millimetres) The algorithm consists of three main modules: (a) determination of the crack initiation position; (b) calculation of the maximum equivalent stress intensity factor Keq in one loading cycle, which is taken as the crack driving force parameter; (c) crack growth process. Module (b) and (c) are repeated until the crack growth path can be presented clearly. Brief expression of each module is introduced in the following sections, more details can be found in reference [8]. 2.1. Location of crack initiation The crack initiation will occur in the notch root at the position where the locally uniaxial notch stress is maximum in one loading cycle. A 3-dimensional finite element model was created using ABAQUS software for stress analysis. Refined mesh was applied in the crack growth region as shown in Fig 2 (a). Along the notch root, there are four potential crack initiation sites numbered 1, 2, 3 and 4 clockwise, shown in Fig 2 (b). The analysis indicated that the maximum tangential stress in one loading cycle along the notch root on the inside edges is almost 2 times larger than the tangential stress on the outside edge, therefore a corner crack is considered to be a reasonable shape to initial crack simulation. As can be expected, the initial corner crack will propagate through the thickness of the notch and extend to the outside surface of the specimen in the crack growth process. An incipient corner crack was inserted into the inside edge of the notch root where tangential stress is maximum by program Fracture Analysis Code 3D (FRANC3D). This program package is designed to simulate crack growth in engineering structures or components with arbitrary crack
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