Issue34

A. Campagnolo et alii, Frattura ed Integrità Strutturale, 34 (2015) 190-199; DOI: 10.3221/IGF-ESIS.34.20 192 different control volumes, subjected to wide combinations of static loading [14 - 16] and the fatigue strength of notched components [17, 18]. As described in [13, 19] an intrinsic advantage of the SED approach is that it permits automatically to take into account higher order terms and three-dimensional effects. The parameter is easy to calculate in comparison with other well-defined and suitable 3D parameters [20, 21] and can be directly obtained by using coarse meshes [13, 19]. Another advantage of the SED is that it is possible to easily understand whether the through-the-thickness effects are important or not in the fracture assessment for a specific material characterized by a control volume depending on the material properties. Some brittle materials are characterized by very small values of the control radius and are very sensitive to stress gradients also in a small volume of material [13]. On the other hand more ductile materials have the capability of stress averaging in a larger volume and for this reason are less sensitive to the variations of the stress field through the thickness of the component. The SED, once the control volume is properly modeled through the thickness of the disc or plate, is able to quantify the 3D effects in comparison with the sensitivity of the specific material so providing precious information for the fracture assessment. F INITE ELEMENT MODELLING Tresses and stress intensity factors have been examined in detail for 100 mm diameter discs [2] and 100 mm square plates [3] of various thicknesses under anti-plane (nominal mode III) loading. The thickness is t for both components while in the discs case the radius, r , is 50 mm. A through thickness crack has its tip at the centre of the component, so its length, a , is 50 mm. Calculations have been carried out using ANSYS 11 for t/a = 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75 and 3. Poisson’s ratio is taken as 0.3 and Young’s modulus as 200 GPa. In the discs case, displacements corresponding to K III = 1 MPa  m 0.5 (31.62 N·mm 0.5 ) have been applied to the cylindrical surface, while in the plates case a displacement of 10 -3 mm has been applied to the edge of the plate. Stress intensity factors have been calculated from stresses on the crack surface near the crack tip using standard equations [7,11]. The strain energy density has been calculated from a control volume at the crack tip. One quarter of the cracked component has been modelled. An overall view of the finite element meshes is shown in Fig. 1a for the discs case and in Fig. 1b for the plates one. Figure 1 : Overall view of finite element meshes. (a) disc and (b) plate. R ESULTS rack surface stresses, τ yz and τ xy have been extracted from the finite element results at distances, s , from the disc and plate surfaces of 0 mm, 0.25 mm and 1 mm. Results for t/a = 1 and s = 0 mm and 1 mm, plotted on logarithmic scales, are shown in Figs. 2-3 with reference only to discs case for the sake of brevity. Results for other values of t/a and with reference to plates case are generally similar, but with some differences in detail. When the plot is a straight line its slope is - λ . Values of λ taken from straight line plots, related to both discs and plates, are shown in Tabs.1 and 2. Where no value is shown the plot could not be regarded as a straight line. S C