Issue 35

L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 35 (2016) 456-471; DOI: 10.3221/IGF-ESIS.35.52 467 In Fig. 10, it is possible to see the finite element model used for crack propagation elaborated by Wu & Ellyin [113]. The model was prepared using layers of elements, considering the size of the smaller elements in the reverse plastic zone computed by Irwin equation and then increasing the size of the hexahedron elements until arriving the region where the results will not affect the stress level in the crack propagation area. Spring elements were used for node release, cycle after cycle, as in Newman [45]. Wu and Ellyin [113] had used a truss element together with pairs of contact elements and the element death option for crack propagation simulation. This technique used in plane stress and plane strain models is usual in commercial finite element codes. The element death option was incorporated to remove truss elements. With their approach, a node can be released any time during a load cycle irrespective of the magnitude of the deformation caused by the release of the node. Consequently, fewer problems with convergence were encountered and also several nodes could be released simultaneously if desired. C ONCLUSIONS he paper provides a review of some crack retardation models under variable amplitude loadings. It was discussed, also, the small scale yield model using finite element method. The Miner’s rule crack initiation approach can be conservative in some applications, in special if the structures should develop cracks under variable amplitude loading. It is presented the standards loadings histories normally used in automotive and aeronautics structures. Several crack advance schemes are presented and it is possible to observe that there is no agreement in the science community about the best strategy to edit experimental signals to be applied in numerical models aiming to obtain good correlation between numerical and experimental data. The crack propagation simulation under constant amplitude loading in plane stress has good agreement with experimental data. Plane strain need complex models with large number of nodes and it is necessary to define and work with contact between the crack surfaces and, therefore, perform nonlinear analysis to identify when the crack open or close. Regarding variable amplitude loading until the moment the authors do not identify a consistent methodology and procedure for crack propagation simulation. The problem should be related with the random fatigue phenomenon and to determine when the crack opens or closes, either using experimental or numerical data, is a challenge to be achieved. The computers are improving their processing and storage capacity with possibility to increase the size of models and decreasing the element size becoming more realistic the crack propagation simulation. In the near future it will be necessary to perform more and more tests to validate the numerical models hoping that the correlation between numerical and experimental results becomes better and better. R EFERENCES [1] Miner, M. A., Cumulative damage in fatigue, Journal 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, Amsterdam (1960). [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(6) (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, 79 (1953) 361. [7] Irwin, G. R., Journal of Basic Engineering, Trans., ASME, series D, 82(2) (1960) 417. D OI : 10.1115/1.3662608 [8] Tada, H., Paris, P.C, Irwin, G.R., The stress analysis of cracks handbook, Bethlehem, PA, Del Research Corporation, USA,(1985). [9] Murakami, Y., editor. Stress intensity factors handbook. New York: Pergamon Press, USA (1987). [10] Raju I.S., Newman JC 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. T