Issue 41

J. Klon et alii, Frattura ed Integrità Strutturale, 41 (2017) 183-190; DOI: 10.3221/IGF-ESIS.41.25 186 Figure 2 : Work of fracture indication at the current stage of fracture process in the loading diagram (peak-deflection curve). Figure 3 : Work of fracture indication at the current stage of fracture process in the R -curve. Experiment made by Hoover et al. In the experimental campaign reported in [14], four beam sizes of widths W = 500, 215, 93 and 40 mm (marked as A to D, see) with three relative notch lengths  0 = 0.075, 0.15, and 0.3 were subjected to three-point bending tests. Ratio of the smallest and the largest tested specimen is remarkable, namely 1:12.5. Several samples were tested for each W and  0 , for details see [14]. Nominal dimensions of the test specimen are shown in Tab. 1. N UMERICAL MODELS umerical models (see Fig. 4 to 7) were created with respect to the geometry given in Fig. 1 and Tab. 1 and the plane stress conditions were met. Connection of steel loading platens with concrete in the part around the groove is solved by using contact elements due to more realistic behavior of platens during the load process by increment of deformation (as a function of load step). Monitoring points were used to observe values of horizontal and vertical displacements and applied forces (reactions). Material model (in ATENA sw. referred to as 3D Non Linear cementitious 2) was used for the simulation of the quasi- brittle specimen with following parameters: Young’s modulus E = 34 GPa, Poisson’s ratio   = 0.172, tensile strength f t = 5.40 MPa, compressive strength f c = 49.00 MPa, three levels of specific fracture energy G f = 7; 70; 700 N/m, Hordijk’s exponential softening. The finite element mesh was generated with regard to the area of the expected extent of FPZ (Fig. 4) with finite element size of 1 mm. Steel loading platens were modelled by 2D elastic isotropic material model with E = 210 GPa and  = 0.3. Figure 4 : Numerical model of the test specimen D 500 with the initial relative crack length   = 0.15; detail of the FE mesh in ATENA 2D software. Figure 5 : Numerical model of the test specimen D 500 with the initial relative crack length   = 0.15; fracture failure at stage  = 0.7 considering the specific fracture energy G f = 7 N/m. It is obvious that the response of the test specimen on the loading progress strongly differs in the way of used level of the specific fracture energy G f (see Fig. 8). For the highest value of G f = 700 N/m the peak value of the loading force is two times higher than in the case of G f = 70 N/m (this can be also applied for comparison of the lowest and the middle value of G f ). Each value of used G f has also significant impact on the way of fracture failure (Fig. 9). Brittle fracture corresponds N