numero25

V. Veselý et alii, Frattura ed Integrità Strutturale, 25 (2013) 69-78; DOI: 10.3221/IGF-ESIS.25.11 74 d c W a e e W /4 W /2 W /4 W /2 W /2 W h i 1 2 P 1 2 P 1 2 P P f alt. breadth B W a e e f alt. breadth B h W /4 W /8 3 W /8 W /2 W /2 W v P sp n v v v 1 2 P v P sp P P sp 1 2 P v d c W n ef W ef 1 2 P 1 2 P P v v v P W /4 (a) (b) Figure 3 : Sketch of the modeled WST specimen with considered variants of boundary conditions. The numerical study was conducted in the ANSYS FEM software [35]. All simulations were modeled in 2D under plane strain condition. The FE mesh was generated from 8-nodes isoparametric elements. Linear elastic isotropic material of the cementitious composite specimen and the steel loading platens was defined by Young’s moduli E = 40 and 210 GPa and Poisson’s ratios  = 0.2 and 0.3, respectively. Fig. 4a and b shows a static scheme and FE model for a variant of the WST with platens II and one central support (a half of the specimen with symmetry conditions). A detail of the near-crack-tip FE mesh is depicted in Fig. 4c and d. Fig. 4d shows utilization of the quarter-point singular elements at the very crack tip (used for calculation of K and T , or B 1 and B 2 , via the first two mentioned methods), in Fig. 4c the (near-crack-tip) ring of nodes is indicated from which coordinates and computed displacements are used as inputs into the ODM for determination shape functions g n . R ESULTS AND DISCUSSION , APPLICATION OF THE MULTI - PARAMETER FRACTURE MECHANICS his section presents some of the results obtained within the conducted study. In agreement with the definition of the normalized dimensionless expressions of the coefficients of the Williams series’ terms mentioned above, the influence of boundary conditions on the stress and displacement fields’ description is indicated in graphs in Figs. 5 and 6. Fig. 5 shows the parameters B 1 and B 2 as functions of the relative crack length  . Differences in the boundary conditions are apparently distinguishable for the latter one, particularly they are evident for short cracks (up to approx. a < 0.4, which corresponds to the influence of the loading platens, see differences between the "platens I" and "platens II" cases) as well as long cracks (i.e. from approx. a > 0.4, influence of the number and mutual distance of supports). It is also clearly seen, and that is true for almost the whole studied range of  , that the neglecting of the compressive force P v produces larger error if a single support is used. Effect of boundary conditions on the first term of the series is rather low, as can be expected, since the singular term domain is the very vicinity of the crack tip only. The graphs in Fig. 6 show shape functions corresponding to two selected higher-order terms coefficients, g 4 and g 7 , and only the effect of supports can be investigated. Both curves are from simulations with loading platens II, therefore no differences between the curves are obvious up to a fracture process stage when the crack tip approaches the back-face of the WST specimen (see the magnified sections of the graphs in Fig. 6b and d). Differences are apparent only for the relative crack lengths around 0.9 and larger provided that compressive component of the loading force P v is considered. If T