PSI - Issue 39

Jesús Toribio et al. / Procedia Structural Integrity 39 (2022) 484–487 Author name / Procedia Structural Integrity 00 (2021) 000–000

486

3

where the dimensionless SIF K * at points A and B was calculated by means of the linear three dimensional (3D) finite element method (FEM) and the J -integral using the MSC Marc software. Results of dimensionless SIF were fitted to third grade polynomial equations as a function of ligament diameter d / D and ligament eccentricity ε / D . 3. Numerical results In bars starting from a certain value of eccentricity (higher for more elevated d / D ) partial contact appears between the crack faces. In these bars from a certain value of the misalignment (of lower value with the increase in diameter d / D ), as a consequence of the bending effect, the crack remains closed in the area near the point of lower depth B ( full contact ) at which the SIF value is equal to zero. The curves ε / D vs . d / D corresponding to partial and full contact beginning are shown in Fig. 2, together with the maximum eccentricity considered in the calculations.

0.20

calculated maximum eccentricity

0.15

full contact beginning

0.10

ε /D

partial contact beginning

0.05

0.00

0.3 0.4 0.5 0.6 0.7 0.8

d/D

Fig. 2. ε / D vs . d / D curves for partial and full contact beginning.

Fig. 3 represents the crack propagation paths, showing the crack fronts for a few given ligament diameters ( d / D from 0.75 to 0.3 in increments of 0.05) during growth for initial geometries of the circular ligament ( d / D ) 0 = 0.75 and ( ε / D ) 0 = {0.0001, 0.001, 0.01}. The Paris exponents (property that characterizes the material) for the calculation were m = 2, 3 and 4. Green crack fronts indicate that there is no contact between the crack faces, the orange ones that partial contact appears and the red ones that full contact exists. The crack growth due to fatigue causes the eccentricity of the ligament to increase with the decrease in the diameter of the ligament during propagation, so that this asymmetric crack growth accelerates with decrease in the ligament until appearance of partial contact, instant from which there is practically no propagation at point B of the crack front. This phenomenon is more pronounced as the initial relative ligament eccentricity ( ε / D ) 0 rises or the Paris exponent m increases. Thus, for the crack path corresponding to ( ε / D ) 0 = 0.0001 and m = 2 only a partial contact appears for the last crack front presenting the least asymmetry of all analyzed cases, while for the crack path corresponding to ( ε / D ) 0 = 0.01 and m = 4 full contact (in addition to partial contact) occurs with the last crack being very asymmetric (high ligament eccentricity in relation to the bar axis).