Issue34

B. Schramm et alii, Frattura ed Integrità Strutturale, 34 (2015) 280-289; DOI: 10.3221/IGF-ESIS.34.30 287 N UMERICAL INVESTIGATIONS OF FRACTURE MECHANICAL GRADED MATERIALS or lifetime prediction of components and the determination of the entire crack propagation analytical methods and programs can only be used in a restricted way due to the increasing complexity (geometry of the component, material gradation, stress situation). Hence, numerical crack propagation programs, which are usually based on the finite-element-method (FEM), are required. In the following, simulations with the two-dimensional program FRANC/FAM*, which is modified by the TSSR-concept to be able to consider the influence of the fracture mechanical gradation, and the three-dimensional program ADAPCRAKC3D are used. More information and further examples considering the crack simulation in fracture mechanical graded structures can be found in [4, 8, 9]. 2D-Simulations with FRANC/FAM* For the two-dimensional simulations with FRANC/FAM* a CT-specimen is used which is subjected to a cyclic load and a stress ratio of R = 0.1. The application of force as well as the bearings are shown in Fig. 9a. The occurring crack propagation in the case of a homogeneous and isotropic CT-specimen is presented in Fig. 9b. The stress situation Mode I caused by the global load results in a crack propagation within the initial area of the crack. a) b) Figure 9: a) Geometry of CT-specimen and boundary conditions, b) simulated crack propagation in a homogeneous and isotropic structure for Mode I loading. In another simulation (Fig. 10) a fracture mechanical graded CT-specimen with the gradation angle of  M = 60° is considered. The initial crack is within the martensitic microstructure, whereas the crack tip sees both fracture mechanical different material regions. As shown in Fig. 10a, the application of the TSSR-concept determines the gradation angle  M = 60° as the occurring kinking angle  TSSR for the first simulation step. Hence, the crack kinks in the first step and grows along the transition. In further simulation steps the local gradation angle M  = 0° is determined as the subsequent crack propagation direction, so that the crack propagates exclusively along the material transition. a) b) Figure 10: a) Gradation angle  M = 60° and prediction of TSSR-concept for Mode I loading for the first simulation step, b) simulation of the entire crack propagation along the material transition. F