Issue 38

M. Springer et alii, Frattura ed Integrità Strutturale, 38 (2016) 155-161; DOI: 10.3221/IGF-ESIS.38.21 160 The corresponding spatial material failure is depicted in the right images. The damage zone is evolving from the location of crack emergence towards the neutral axis and is decreasing from the midplane to the outside of the beam. The decreasing reaction force versus the number of load cycles is displayed in Fig. 3. The experimental results [22] are compared to the numerical simulation. After one thousand load cycles material failure modeling starts and a degrading structural behavior is obtained. Compared to the experimental observation the degradation in the simulation is progressing more quickly than the degradation of the test specimen. C ONCLUSION fatigue damage modeling approach capable of predicting fatigue crack nucleation and propagation in one combined numerical simulation has been presented. A multiaxial critical plane concept combined with damage accumulation is utilized as Fatigue Damage Indicator to identify locations of crack emergence. Local material degradation is modeled in the pristine structure and the cyclic loading is continued until the next occurrence of material failure is detected. Applying this procedure in a repetitive way, an evolving spatial zone of material failure is simulated, representing fatigue crack propagation. This way, a changing structural response of the initial perfect structure with respect to the number of applied load cycles is obtained. The combination of fatigue crack nucleation and crack propagation has been successfully exemplified in a numerical FEM analysis of a cyclic loaded cantilever beam. A CKNOWLEDGEMENT he authors would like to thank Balamurugan Karunamurthy from Kompetenzzentrum Automobil- und Industrieelektronik GmbH for providing valuable input for this work. This work was jointly funded by the Austrian Research Promotion Agency (FFG, Project No. 846579) and the Carinthian Economic Promotion Fund (KWF, contract KWF-1521 | 26876 | 38867). R EFERENCES [1] Basquin, O. H., The exponential law of endurance tests, Proc. ASTM., 10(2) (1910). [2] Coffin, LF Jr., A study of the effects of cyclic thermal stresses in ductile metals, ASME, 76 (1954). [3] Manson, S. S., Behaviour of materials under cyclic stress, NACA, TN 2933 (1953). [4] Suresh, S., Fatigue of materials, Cambridge university press (1998). [5] Paris, P. C., Gomez M. P., William, E. A., A rational analytic theory of fatigue, Trend. Engng., 13 (1961) 9-14. [6] Paris, P. C., Erdogan, F., A critical analysis of crack propagation laws, J. Basic Engng, 85 (1963) 528-533. [7] Newman, J. C., The merging of fatigue and fracture mechanics concepts: a historical perspective, Progress in Aerospace Sciences, 34 (1998) 347-390. DOI: 10.1016/S0376-0421(98)00006-2 [8] Barenblatt, G. I., Botvina, L. R., Incomplete self-similarity of fatigue in the linear range of crack growth, Fatigue Fract. Eng. Mater. Struct., 3 (1980) 193-202. DOI: 10.1111/j.1460-2695.1980.tb01359.x [9] Pugno, N., Ciavarella, M., Cornetti, P., Carpinteri, A., A generalized Paris’ law for fatigue crack growth, J. Mech. Phys. Solids, 54 (2006) 1333-1349. DOI: 10.1016/j.jmps.2006.01.007 [10] Pugno, N, Cornetti P., Carpinteri A., New unified laws in fatigue: from the Wöhler’s to the Paris’ regime, Eng, Fract. Mech., 74 (2007) 595-601. DOI: 10.1016/j.engfracmech.2006.07.009 [11] Ciavarella, M., Dibello, S., Demelio G., Conductance of rough random profiles, Int. J. Solids Struct., 45 (2008) 879- 893. DOI: 10.1016/j.ijsolstr.2007.09.009 [12] Carpinteri, A., Paggi M., A unified interpretation of the power laws in fatigue and the analytical correlations between cyclic properties of engineering materials, Int. J. Fatigue, 31 (2009) 1524-1531. DOI: 10.1016/j.ijfatigue.2009.04.014. [13] Darveaux, R., Effect of simulation methodology on solder joint crack growth correlation and fatigue life prediction, J. Electronic Packaging, 124 (2002) 147-154. DOI: 10.1115/1.1413764. [14] Lau, J. H., Pan S. H., Chang, C., A new thermal-fatigue life prediction model for wafer level chip scale package (WLCSP) solder joints, J. Electronic Packaging, 124 (2002) 212-220. DOI: 10.1115/1.1462625. A T