Issue 41

J. Klon et alii, Frattura ed Integrità Strutturale, 41 (2017) 183-190; DOI: 10.3221/IGF-ESIS.41.25 184 process. Currently, many numerical tools can predict fracture behaviour – but just in the case that the proper material parameter inputs are available, like the specific fracture energy. This paper focuses on the investigation of the impact of the specific fracture energy G f used in the numerical calculation on the work of fracture W f , which can be obtained by means of evaluation of the loading diagram. The idea of this research is based on the general problem of numerical testing when the current material properties obtained from the experimental testing shall be used. Determination of properties like fracture energy relates to the evaluation of experimental l - d (load-deflection) curves. Then the area under the curve is considered. But, if this value of fracture energy shall be used in numerical calculation, there is a restriction – it is not possible to use it due to the fact that it varies by order of the magnitude in dependence on many various factors, such as specimen size, boundary conditions and others. Value of the fracture energy G F is obtained from the area under the loading curve as work of fracture W f divided by the area of the cracked ligament A f (without the initial crack area), so G F = W f /( a − a 0 )/ B . Fracture failure of quasi-brittle materials occurs in FPZ by micro cracking (but micro cracks are closed after final failure of the test specimen), so there is a hypothetical problem of accurate evaluation of cracked ligament area A f . It is believed that this is the main reason why the value of G F (identified from various experimental testing) strongly differs. Therefore, an iteration procedure how to optimize the inputs needs to be performed to include the real l – d diagram in numerical calculations. This study shows the impact of the specific fracture energy inputted into numerical software (considering the fracture failure) on the value of the fracture energy obtained from the area under the load–deflection curve (obtained from the numerical calculation). ATENA [12,13] nonlinear software is used for this purpose, so the results are valid mainly for it. For the verification of the impact of the specific fracture energy, the series of experimental test specimens subjected to three-point bending was chosen with the geometry displayed in Fig. 1. Four different sizes of test specimens were created by Ch. Hoover ([14], see the next section) for the purpose of validation of the size effect [1], [7]. In the paper, two approaches are compared. First uses the area under the load–deflection curve to obtain G F(num) . This l – d curve is obtained from the numerical model (created in ATENA sw.) with the inputted value of the specific fracture energy G f (three various levels). The latter approach is the theoretical one – the value of the fracture energy is obtained from the basic formula G F(theor) = G f ( a − a 0 ) B . Figure 1 : Schema of the three-point bending test configuration. Green color indicates dimensions of the test specimen (see Tab. 1) and CMOD – crack mouth open displacement; blue color represents area of the ligament, where the crack propagation is indicated.