Issue 35

O. Demir et alii, Frattura ed Integrità Strutturale, 35 (2016) 330-339; DOI: 10.3221/IGF-ESIS.35.38 334 Results of Finite Element Models In this subsection, results from mixed mode fracture analyses are presented for different loading angles. Tab. 1 summarizes results of fracture analyses from specimens with 43.5, 45, 47 mm crack lengths for 0°, 15°, 30°, 45°, 60°, 75°, 90° loading angles. 10 kN constant load is applied for all analyses. Analyses are also performed for 43.5 and 47 mm crack lengths, since fatigue pre-crack lengths measured after experiments are not always 45 mm. Using the additional analyses with different crack lengths, KI, KII and KIII SIF values corresponding to actual crack length obtained from experiments can be calculated by interpolation. In Fig. 7, variation of SIFs for 43.5, 45 and 47 mm crack lengths as a function of loading angles is given. 0° loading case i.e. mode-I loading case, is obtained by applying the load to the upper and lower left holes of the specimen using the axial loading clevis only. However load is applied to other holes of the specimen using mixed-mode clevises. Therefore, there is a high degree of change for KI SIF values between 0° and 15° loading angles. Loading Angle (°) 43.5 mm Crack Length 45 mm Crack Length 47 mm Crack Length SIFs into the crack front, (MPa·m 1/2 ) KI KII KIII (Edge Value) KI KII KIII (Edge Value) KI KII KIII (Edge Value) 0 8.78 0.00 0.00 9.13 0.00 0.00 9.59 0.00 0.00 15 4.37 0.32 0.11 4.60 0.46 0.16 5.13 0.43 0.18 30 3.91 0.65 0.22 3.91 0.82 0.24 4.59 0.94 0.33 45 3.16 0.94 0.35 3.17 1.18 0.36 3.74 1.35 0.45 60 2.23 1.15 0.40 2.20 1.48 0.50 2.63 1.72 0.57 75 1.05 1.30 0.46 1.10 1.67 0.51 1.31 1.94 0.63 90 - - - 0.00 1.73 0.55 - - - Table 1 : KI, KII and KIII stress intensity factors for different loading angles and crack front length . Figure 7 : Variation of SIFs for 43.5, 45 and 47 mm crack lengths as a function of loading angles. Stress distributions of mixed mode-I/II clevises, pins, bushes and specimen obtained from the analyses which is performed for 45 mm crack length under 10 kN load and 45° loading angle are given in Fig. 8. Furthermore, KI, KII and KIII SIFs along crack front are given in Fig. 9 (a). Stress distributions must be evaluated together with SIF values along the crack front obtained from the fracture analyses to provide small scale yielding conditions under LEFM (Linear Elastic Fracture Mechanics) rules. Although loading case is mode-I/II due to the Poisson's ratio, KIII SIF values are observed from analyses. Edges of upper and lower crack surfaces before and after applying the load are plotted in Fig. 9 (b). Owing to the applying load, upper crack surface is exposed to compressive stress and lower crack surface is exposed to tensile stress along the crack length direction. Thus, transverse expansion and contraction occur on the upper and lower crack surfaces, respectively. Consequently, this relative deformation between the upper and lower crack surfaces causes positive and negative tearing mode SIF on the two sides of the specimen. For this reason in Tab. 1, KIII SIF values represent the edge values of crack front, since KIII SIF values are zero at the center of the crack front.