Issue 43

L.C.H. Ricardo, Frattura ed Integrità Strutturale, 43 (2018) 57-78; DOI: 10.3221/IGF-ESIS.43.04 75 has no significant difference of crack closing stress during crack propagation. In fact it is the most conservative model from the four evaluated. During the fourth and sixth cycle the models SAE2 (crack propagation model 0.50 mm) and SAE3 (crack propagation model 0.75 mm) have no difference in the crack closing stress. The model SAE4 (crack propagation 1.0 mm/cycle) has representative difference in the crack closing stress when compared with others models in the cycles due to more residual plasticity in the crack tip. The last representative differences between crack closing stress levels in the models happen during propagation in the cycles eight to tenth. An increase of the crack propagation rate will also increase the crack closing stress. Fig. 16 shows that depending on the design criterion it is possible to apply a different crack propagation rate. For example if the criterion is to use a conservative crack closing stress it is recommended utilization of the model SAE1 (crack propagation 0.25 mm). The softest model or that one which allows the bigger crack opening and closing stresses is model SAE4 (crack propagation model 1.0 cycle/mm). C ONCLUSIONS n this work it was possible to identify the crack opening and closure using the finite element method. In the literature there are few works covering crack propagation simulation with random loads like FD&E loads histories from SAE data bank. Normally only a few load blocks are used to reduce the complexity; this should provide conservative answers when used to develop structural components. The use of different crack propagation rate in this work shows that for reproducing the effective plastic zone it is possible to use smaller or larger element sizes compared with the Irwin equation. To improve the correlation between numerical and experimental data it is necessary to increase the crack length to obtain the same qualitative results that is estimated by the Irwin equation. The next step in this work will be to perform some analyses with the same model and load history with different crack propagation rates to identify whether or not the retard effect can be observed. These data will be compared with experimental test and, if necessary, adjustment of the crack propagation model will be done to improve the crack propagation model. R EFERENCES [1] Miner, M. A., Cumulative damage in fatigue, J. of Applied Mechanics, ASME, USA, 12 (1945) A159-A164. [2] Schijve, J., Fatigue crack propagation in Light Alloy Sheet Material and Structures, NLR, Report MP195, (1960) Amsterdam. [3] Stouffer, D. C., Williams, J. F., A method for fatigue crack growth with a variable stress intensity factor, Eng. Fracture Mechanics, 11 (1979) 525-536. DOI:10.1016/0013-7944(79)90076-6. [4] Ditlevsen, O., Sobczyk, K., Random fatigue crack growth with retardation, Eng. Fracture Mech., 24 (1986) 861-878. DOI:10.1016/0013-7944(86)90271-7. [5] Wei, R. P., Shih, T. T., Delay in fatigue crack growth, Int. Journal Fracture, 10 (1974) 77-85. DOI: 10.1007/bf00955082. [6] Irwin, G. R., Journal of Applied Mechanics, 24 (1957) 361-364. [7] Irwin, G. R., Journal of Basic Engineering, Trans., 82 (1960) ASME, series D 2 417-423. DOI :10.1115/1.3662608. [8] Tada, H., Paris, P.C., Irwin G.R., The stress analysis of cracks handbook, Bethlehem, PA:, Del Research Corporation, (1985). [9] Murakami, Y., editor. Stress intensity factors handbook, Pergamon Press, New York, (1987) [10] Raju, I.S., Newman, J.C. Jr., Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite- thickness plates, Eng. Fracture Mechanics, 11 (1979) 817-829. DOI:10.1016/0013-7944(79)90139-5 [11] Newman, J.C. Jr., Raju, I., Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads. Computational methods in the mech. of fracture. In: Atluri SN, editor. Amsterdam: Elsevier, (1986) 311-334. DOI: 10.1002/zamm.19870671132 [12] 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 [13] Paris, P. C., Erdogan, F., Journal of Basic Engineering, 85 (1963) 528-534. [14] Head, A. K., The Philosophical Magazine, 44 (1953) 925-938. [15] Hairman, G. A., Provan, J. W., Fatigue crack tip plasticity revisited - The Issue of Shape Addressed, Theoretical and Appl. Frac. Mech. Journal, 26 (1997) 63-79. [16] Perez, N., Fracture mechanics, Kluwer Academic Publishers, E-4020-7861-7, New York, (2004), [17] Dugdale, D. S., Yielding of steel sheets containing slits, J. Mech. Phys. Solids, 8 (1960)100-104. I