Issue 35

G. Kullmer et alii, Frattura ed Integrità Strutturale, 35 (2016) 368-378; DOI: 10.3221/IGF-ESIS.35.42 369 symmetrical opening of the crack surfaces. Mode II is valid for shear loading causing in-plane sliding of the crack surfaces. Mode III represents shear loading generating anti-plane sliding of the crack surfaces. F F F F F F Mode I Mode II Mode III x y z x y z x y z Figure 1 : Basic crack opening modes, Richard and Sander [1]. Since the present study only deals with plane problems, mode III is irrelevant. Whereas a crack propagates self-similar under mode I-loading it deflects under mode II-loading about the angle φ 0 ≈ 70° as represented in Fig. 2. Under plane mixed-mode-loading with continuously changing ratios of mode I and mode II curved cracks form in the x-y-plane according to Fig. 1. Figure 2 : Crack propagation under different crack opening modes, Richard and Sander [1] S IMULATION MODEL FOR THE INVESTIGATION OF THE FATIGUE CRACK GROWTH IN THE NEIGHBOURHOOD OF CHANGES IN STIFFNESS imulation models based on the CT-specimen, see Fig. 3, are used to investigate the basic influence of line-shaped regions with differing stiffness and different orientation on the path of fatigue cracks. The default thickness of the specimen is 5mm and the default value of Young´s modulus is 210.000MPa. The material behaviour is idealised as linear elastic, isotropic and homogeneous. Poisson´s ratio is zeroed to avoid stresses in thickness direction of the specimen and thickness influences and therefore to ensure a state of plane stress in spite of using a three-dimensional model. A three-dimensional model is required for the present investigation since the crack growth is simulated with the program system ADAPCRACK3D developed by the Institute of Applied Mechanics of the University of Paderborn (Fulland [2]). As shown in Fig. 3 a rectangular partition inserted into the CAD-model of the CT-specimen represents the line-shaped region with differing stiffness. The simulation models differ since Young´s modulus, the thickness, the distance to the starter notch and the orientation of the line-shaped change in stiffness vary. To evaluate the influence of the stiffness mismatch, on the one hand, with default thickness Young´s modulus of the line-shaped region is varied and on the other hand, with standard Young´s modulus the thickness of the line-shaped region is modified. To analyse the influence of the orientation of the change in stiffness in relation to the nominal global mode I-loading of the initial crack, the orientation of the change in stiffness is varied by stepwise rotation of the line-shaped region about the centre A. Thus, for a fixed distance d = 9.7mm the orientation angle α varies between 90° and 30°. To investigate the influence of the distance d between the starter notch and the change in stiffness with default thickness and constant orientation angle α = 45° the distance d varies in steps of 2.5mm from 9.7mm to 19.7mm. For this investigation, Young´s modulus of the line-shaped region is once double and once half the value of default Young´s modulus. S