Issue 41

M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 41 (2017) 98-105; DOI: 10.3221/IGF-ESIS.41.14 105 Tab. 1 also shows Miner’s rule predictions for the square/cross and square/circle/diamond paths, calculated from the observed lives of the four specimens subjected to the cross, diamond, circle and square paths. For the square/cross path, Miner’s prediction for the number of blocks B is such that 1/B = 1/772  1/1535, giving B = 514 blocks, an error of approximately 50%. Besides the usual scatter in fatigue (due to undetected microscopic defects) and of Miner’s rule predictions, this error might also be attributed to the difficulty to detect a small crack on the surface, which was used as the initiation criterion to measure the number of blocks. Moreover, the critical plane of the square, cross and square/cross path specimens, where the microcrack initiates, could be significantly different, requiring the application of the critical plane approach to account for this and only then apply Miner’s rule. For the square/circle/diamond path, Miner’s prediction is such that 1/B = 1/772  1/837  1/976, giving B = 285 blocks, an unusually small prediction error of only 1%. This result is reassuring towards the continued use of Miner’s rule, at least for such NP loading paths with similar stress levels and amplitudes. But since Miner’s rule is not a physical law, it can still result in significant prediction errors for some particularly ordered histories, or in variable amplitude histories with large variations in stress or strain amplitude. C ONCLUSIONS oad order effects can be very important in crack initiation, and must be considered to properly account for residual stress effects and micro/macro plastic memory in general, especially under low-cycle conditions. Nevertheless, Miner’s rule can be applied for both high and low-cycle fatigue, as long as any significant plasticity effect is considered, in the original order it was applied. It was found that Miner’s rule provides reasonable predictions for selected non-proportional tension-torsion histories, at least when the variable amplitude loading cycles have equivalent amplitudes that do not differ too much from each other. Finally, be aware that, in general, non-linear damage accumulation rules are not robust; therefore, Miner’s linear damage rule still is the best choice in multiaxial fatigue calculations, giving accurate predictions when combined e.g. with the critical-plane approach. R EFERENCES [1] Palmgren, A., Die lebensdauer von kugellagern (Life time of bearings). Verfahrenstechinik, 68 (1924) 339-341. [2] Miner, M.A., Cumulative damage in fatigue, J. App. Mech., 12 (1945) A159-A164. [3] Fatemi, A., Yang, L., Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials. Int. J. Fatigue, 20 (1998) 9-34. [4] Lemaitre, J., A Course on Damage Mechanics, Springer, (1996). [5] Lemaitre, J., Chaboche, J. L., Mécanique des Matériaux Solides, 2ème ed. Dunod, (2004). [6] Juvinall, R.C., Stress, Strain and Strength, McGraw-Hill, (1967). [7] Castro, J.T.P., Meggiolaro, M.A., Fatigue Design Techniques - v. 2: Low-Cycle and Multiaxial Fatigue. Createspace (2016). [8] Schijve, J., Fatigue of Structures and Materials, Kluwer, (2001). [9] Elber, W., Fatigue crack closure under cyclic tension, Eng Fract Mech, 2 (1970) 37-45. [10] Elber, W., The significance of fatigue crack closure. ASTM STP 486 (1971) 230-242. [11] DuQuesnay, D.L., Topper, T.H., Yu, M.T., Pompetzki, M.A., The effective stress range as a mean stress parameter, Int. J. Fatigue, 14 (1992) 45-50. [12] DuQuesnay, D.L., Pompetzki, M.A., Topper, T.H., Fatigue life predictions for variable amplitude strain histories. SAE paper 930400, (1993). [13] Meggiolaro, M.A., Castro, J.T.P., Wu, H., Zhong, Z., Generalization of the Moment of Inertia method to predict equivalent amplitudes of non-proportional multiaxial stress or strain histories. 14th Pan-American Congress of Applied Mechanics, Chile (2014). [14] Meggiolaro, M.A., Castro, J.T.P., An improved multiaxial rainflow algorithm for non-proportional stress or strain histories - part I: enclosing surface methods, Int. J. Fatigue, 42 (2012) 217-226. L