Issue 39

S. Seitl et alii, Frattura ed Integrità Strutturale, 39 (2017) 110-117; DOI: 10.3221/IGF-ESIS.39.12 112 Figure 1 : (a) 3PBT specimen geometry; (b) WST specimen geometry; (all units in mm). Herein, C and m depend on the material, the specimen geometry and the loading conditions. They are therefore different for each material and must be obtained experimentally. The Paris-Erdogan law is applicable to a wide range of materials and describes their crack propagation behaviour in a relatively correct way over a wide range of stress ratios. If the crack propagation law for a certain material is known, it is possible to calculate by integration the number of cycles required for the crack to grow from one length to another [6]. In this article, the Paris’ law parameters C and m will be used to compare the test data from both the 3PBT and WST. A NALYSIS IN ANSYS Numerical model he finite element analysis software ANSYS [1] was used to create and evaluate various numerical 3PBT and WST models. These models were built using macro’s in the ANSYS Parametric Design Language (APDL). For both geometries only one half of the test piece is modelled, since their shapes are symmetrical (Fig. 2). All calculations were executed as a simplified 2D model, using 8-node isoparametric PLANE183 elements. A comparative study was performed for the models of both geometries, in order to find a suitable mesh size which delivers results with great accuracy. For the 3PBT, four different mesh sizes were compared and it was concluded that a 1 mm mesh size is dense enough to obtain accurate results. Similarly, for the WST, a mesh size of 1.5 mm showed to be of great accuracy. In order to accurately model the stresses near the crack tip, the ANSYS command KSCON is used. This creates a dense circular around the crack tip and allows the calculation of the stress intensity factor, using the KCALC command. Since the differences in the results for the deflection and the stress fields for both 2D and a 3D models are very small [14, 21], using a 2D model is preferred. These simplified numerical models require little computing power compared to complex 3D models. For all concrete mixtures, cyclic tests under four stress ratios R were executed in the research of Korte et al. In these stress ratios, the lower load limit of was chosen to be 10% of the average ultimate load of the static tests. For the upper limit various percentages were selected: 70%, 75%, 80%, and 90% [14]. The stress ratio R is usually expressed as: min max R    (1) Using this formula, the four stress ratios are defined as: R 10-70 = 0.1429, R 10-75 = 0.1333, R 10-80 = 0.1250 and R 10-90 = 0.1111. In order to calculate the crack propagation rate and stress intensity ranges for all ratios, the numerical model was loaded under 10%, 70%, 75%, 80% and 90% of the average ultimate load of the static tests. The material input parameters for concrete were taken from [14]: Young’s modulus E VC = 38.4 GPa, E SCC1 = 38.1 GPa, E SCC2 = 35.3 GPa and Poisson ratio v c = 0.2. For the metal part in the numerical WST model, representing the roller bearing loading device, Young’s modulus E s = 210 GPa and Poisson ratio v s = 0.3 were used. T