Issue 41

F. Berto, Frattura ed Integrità Strutturale, 41 (2017) 475-483; DOI: 10.3221/IGF-ESIS.41.59 477 by anti-plane loading of a straight through-the-thickness crack in linear elastic plates by means of accurate three- dimensional finite element (FE) models. An extended version of the present work has recently been published in the literature [3]. The material is assumed to be a homogeneous isotropic continuum, and its behaviour is assumed to be linearly elastic. Due to the uncertainties in the definition of the stress intensity factors on the free surfaces, as stated above, the strain energy averaged in a control volume (SED) has been employed in the present contribution to quantify the stress intensity through the thickness of the plate. For a review of the SED the reader can refer to [13]. This parameter has been successfully used by Lazzarin and co-authors to assess the fracture strength of a large bulk of materials, characterized by 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 plate. The SED, once the control volume is properly modeled through the thickness of the 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 n the present calculations, stresses, stress intensity factors and displacements are examined in detail for 100 mm square plates of various thicknesses under anti-plane (nominal mode III) loading. One half of the plate geometry used is shown in Fig. 2. The thickness is t . A through thickness crack has its tip at the centre of the plate, so its length, a , is 50 mm. Calculations are 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. A displacement of 10 -3 mm is applied to the edge of the plate. Stress intensity factors are calculated from stresses on the crack surface near the crack tip using standard equations [7,11]. The strain energy density is calculated from a control volume at the crack tip. One quarter of the plate is modelled. An overall view of the finite element mesh is shown in Fig. 3. Details of the mesh at the outer surface and crack tip are shown in the figure. Figure 1 : Notation for crack tip stress field. I