Issue 38

M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 38 (2016) 128-134; DOI: 10.3221/IGF-ESIS.38.17 134 Fig. 4 shows the ratio between the EP and the pseudo Mises strain    Mises Mises and stress    Mises Mises for a particular case of a tension-torsion multiaxial loading assuming a proportionality stress ratio between equivalent shear and normal nominal stresses   3 R .The LE stress concentration factors for this sharply notched shaft are K tσ = 6.70 for normal stresses and K tτ = 3.75 for pure shear stresses. The two solid lines for both strains and stresses show the numerically obtained EP results obtained from the FE simulations, which are overestimated by both Neuber’s (  U  1 , the rule adopted in Dowling’s multiaxial model) and Glinka’s rules (  U  2 ). The third dashed lines also for both strains and stresses are the better estimates obtained from the proposed UNR, calibrated for  U  1.979. These results show that the proposed rule is able to improve significantly the traditional estimates from Neuber’s and Glinka’s models, in particular for notched components with high transversal constraints around the notch tip, the case of the studied sharply notched shaft. Finally, as expected, all predictions tend to the         1 Mises Mises Mises Mises under low stresses. C ONCLUSIONS n this work, a Unified Notch Rule (UNR) was proposed to predict elastoplastic stresses and strains at a notch roots from linear elastic calculations, for uniaxial and in-phase proportional multiaxial histories. The UNR can interpolate between Neuber’s and Glinka’s rules using its  U parameter calibration to account for the magnitude of the transversal constraint around the notch tip, or even to extrapolate them to better reproduce increased constraint effects around sharp notch tips. Moreover, the proposed UNR allows biaxiality ratios  3  3 /  1  0 , an improvement over Dowling’s model, which always assume  3 = 0 . Even though the derivation of the UNR model assumed an integration for a monotonic load, the resulting equations could be applied to cyclic loadings, as long as they are also in-phase and proportional, and the appropriate biaxiality ratios can be assumed constant. R EFERENCES [1] Castro, J.T.P., Meggiolaro, M.A., Fatigue Design Techniques: Vol. II - Low-Cycle and Multiaxial Fatigue. CreateSpace Publishing Company, Scotts Valley, CA, USA, (2016). [2] Köettgen, V.B., Barkey, M.E., Socie, D.F., Fatigue Fract Eng Mat Struct, 18 (1995) 981-1006. [3] Socie, D.F., Marquis, G.B., Multiaxial Fatigue, SAE, (2000). [4] Hoffmann, M., Seeger, T., A generalized method for estimating multiaxial elastic plastic notch stresses and strains, Part I: Theory, J Eng Mat Tech, 107 (1985) 250-254. [5] Hoffmann, M., Seeger, T., A Generalized Method for Estimating Multiaxial Elastic-Plastic Notch Stresses and Strains. Part 2: Application and General Discussion, J Eng Mat Tech, 107 (1985) 255-260. [6] Dowling, N.E., Brose, W.R., Wilson, W.K., In: Fatigue Under Complex Loading: Analysis and Experiments, AE-6, SAE, (1977). [7] Neuber, H., Theory of stress concentration for shear-strained prismatic bodies with arbitrary nonlinear stress- strain law, J Appl Mech, 28 (1961) 544-551. [8] Molski, K., Glinka, G., A method of elastic-plastic stress and strain calculation at a notch root, Mat Sci Eng, 50 (1981) 93-100. [9] Ye, D., Hertel, O., Vormwald, M., A unified expression of elastic-plastic notch stress-strain calculation in bodies subjected to multiaxial cyclic loading, Int J Solids Struct, 45 (2009) 6177-6189. [10] Kujawski, D., On energy interpretations of the Neuber's rule, Theor Appl Fract Mech, 73 (2014) 91-96. [11] Ince, A., Glinka, G., A numerical method for elasto-plastic notch-root stress–strain analysis, J Strain Analysis Eng Design, 48 (2013) 229-224. [12] Newman, J.C. Jr, Crews, J.H., Bigelow, C.A., Dawicke, D.S. ASTM STP 1244 (1995) 21-42. [13] Chu, C.C., The analysis of multiaxial cyclic problems with an anisotropic hardening model, Int J Solids Struct, 23 (1987) 567-579. [14] Jiang, Y.R., Sehitoglu, H., Materials Engineering – Mechanical Behavior Report #413, University of Illinois, Urbana, Illinois, (1992). I