Issue 41

J. Klon et alii, Frattura ed Integrità Strutturale, 41 (2017) 183-190; DOI: 10.3221/IGF-ESIS.41.25 188 dissipated in small specimens is much more less than it should correspond to the current area of the specimen’s ligament. For example, the specimen D 040 with the initial notch   = 0.075 has the amount of the dissipated energy smaller by 75 % than the value obtained by theoretical calculations. With the increasing size of the specimen the deviation is reducing as much, that for the biggest specimen (D 500) the ratio of the dissipated energy is almost 2.9 times bigger than in the case of the smaller one (D 215). Comparison of the values of the dissipated energy obtained by FEM analysis and theoretical calculation for specimen D 500 with the initial notch of the length   = 0.075 shows the deviation under 20 %. This phenomenon is repeated for all initial notch length variants. The deviations varied from 80 % (small specimens of size D 040) to 30 % (the biggest specimens of size D 500). The opposite trend was observed for the specimens with the low order of value of the specific fracture energy G f = 70 N/m. For the smallest specimens, the deviation from the theoretical calculation was lower than for the biggest specimens. While the dissipated energy determined from FEM analysis for the small specimen D 040 reaches the maximum deviation of 13 %, the biggest specimen D 500 exceeds 120 %, see Fig. 12. Described behavior is certainly related to the way of failure which differs for the selected values of the specific fracture energy. It is clear from Fig. 8, that not only the area under the loading curve but also the maximum reached loading force changes. The peak force is approximately two times bigger comparing two subsequent values of the specific fracture energy G f . Similarly, the specimen response is also changing with the level of the specific fracture energy used: the response of the specimen with the middle level of the specific fracture energy corresponds to the quasi-brittle fracture. Fracture progress in the specimen with the lower level of the specific fracture energy corresponds to brittle fracture, where the FPZ does not develop. Significant ductile behavior is typical for the highest level of the specific fracture energy used. This tendency can be seen in Fig. 5 to 7 where the finite element mesh is shown and the way of fracture failure for each level of the specific fracture energy. It is obvious that the wider band of elements is damaged by cracks for the higher level of the specific fracture energy than in the case of the lower one (FPZ is not developed). This behavior is probably caused by the use of the crack band model, that is implemented in ATENA 2D software tool. It is clear from the displayed results that it is necessary to pay attention to the use of the proper level of the specific fracture energy when ATENA tool shall be used for modelling of structures and following evaluation of results. It was found out that the selected value of the specific fracture energy reflects not only the total amount of the dissipated energy during fracture, but also maximum loading force achievement and the way of structural response. Figure 10 : Value of the fracture energy G F(num) dissipated during the crack propagation for all variants of numerical models – obtained from the area under the l - d curve ( R – a diagram respective) simulated in ATENA.