Issue 37

A. Eberlein et alii, Frattura ed Integrità Strutturale, 37 (2016) 1-7; DOI: 10.3221/IGF-ESIS.37.01 4 To get a better knowledge of such facet formation under mixed-mode I + III-loading for its consideration in existing hypotheses for crack growth prediction under 3D-mixed-mode-loadings a facet quantification was performed, which is presented and discussed in the next section. C HARACTERIZATION OF C RACK FRONT SEGMENTATION he first step to understand the crack growth behaviour under mode I-mode III-loading conditions is to quantify the crack front segmentation respectively the facet formation. Therefor some characteristic dimensions and angles were defined. Definition of characteristic Dimensions First of all, the geometry of each facet will be simplified to a circular shape. Then due to the non-planar shear stress τ z facets initiate twisted under a facet angle ψ F as Fig. 5 a) shows. Reflecting the work of Lin et al. [7] this facet quantification distinguishes between two facet types – ascending facets f as indicated in Fig. 5 b) by red lines – and falling facets f fa indicated in Fig. 5 b) by dashed lines, which finally connects the ascending facets f as . Ascending facets f as initiate induced by a local opening mode-loading [8] whereas falling facets f fa form in a bridging region B making a connection to each f as facet. Figure 5 : Definition of characteristic dimensions for facet quantification: a) Schematic facet formation at the crack front due to τ z; b) Facet’s geometry and characteristic dimensions in the y-z-plane The f fa facets are unfavourable oriented to a local opening mode-loading. Consequently, another local mechanisms, like local friction or plasticity [7], are probably responsible for their formation. So higher energies respectively loads for the creation of f fa facets are required. As a conclusion such facet formation proceeds at a later crack growth stage as the initiation of f as facets [3, 7]. Other characteristic dimensions for facet quantification are the projected facet length d , the facet distance c and the width e of the bridging region B (see Fig. 5 b)). Approach for Quantification of Facet’s Geometry For facet quantification the fractured surfaces were analysed microscopically. Hereby the crack’s profile was measured close to the initial notch that is after a short crack extension Δ a . Fig. 6 illustrates a typical crack’s profile of a mode III fractured surface. The measurement plane of crack’s profile, indicated by the arrow, lies in a distance of about Δ a ≈ 285 µm from the wire eroded notch. In the front view (indicated by the red arrow) the crack’s profile looks as in Fig. 6 b) shown. Thereby the f as facets, which were considered for the quantification, are marked in the graph. Furthermore, it is visible that in the middle of the specimen the biggest facets creates. The analysis of all f as facets reveals an average projected facet length of d = 1.23 mm and an average distance of c = 1.63 mm. The biggest facet angles ψ F exhibit the f as facets f as,3 , f as,4 and f as,5 (see Fig. 6 b)). The angles ψ F lie within an expected range between 42.3° and 49.3°. Starting from the middle of the specimen to the specimen borders a decreasing facet angle was noted. The reason for this is the decreasing shear stress τ z and an increasing mode II-part by moving from the middle of the specimen to the border. Due to no pure mode III-loading condition facets near the specimen border initiate under smaller twist angles. The measurement of the bridging regions B exposed an average width e of 342 µm. Such a systematic analysis approach for facet quantification was performed for all fractured surfaces within this experimental research. In the next section the results of facet quantification are shown and discussed. T