Issue 38

M. Lutovinov et alii, Frattura ed Integrità Strutturale, 38 (2016) 237-243; DOI: 10.3221/IGF-ESIS.38.32 237 Focussed on Multiaxial Fatigue and Fracture A comparison of methods for calculating notch tip strains and stresses under multiaxial loading M. Lutovinov, J. Černý, J. Papuga FME CTU in Prague, Technická 4, 166 07 Prague 6, Czech Republic maxim.lutovinov@fs.cvut.cz jiri.cerny2@fs.cvut.cz jan.papuga@fs.cvut.cz, http://orcid.org/0000-0001-9569-4997 A BSTRACT . Selected methods for calculating notch tip strains and stresses in elastic–plastic isotropic bodies subjected to multiaxial monotonic loading were compared. The methods use sets of equations where hypothetical notch tip elastic strains and stresses obtained from FEM calculations serve as an input. The comparison was performed within two separate groups of methods: the first group consists of the methods intended for cases of multiaxial proportional loading and the second group deals with multiaxial non-proportional loading. Originally, the precision of the methods was validated by comparison with results obtained from elastic–plastic FEM analyses. Since computer performance at the time was lower than nowadays, verification of the proposed methods on FEM models with a finer mesh was needed. Such verification was carried out and is presented in this paper. The effect of various formulations of material stress–strain curve was also evaluated. K EYWORDS . Notch stresses; Multiaxial loading; FEM; Neuber’s rule; ESED rule. Citation: Lutovinov, M., Černý, J., Papuga, J., A comparison of methods for calculating notch tip strains and stresses under multiaxial loading, Frattura ed Integrità Strutturale, 38 (2016) 237-243. Received: 28.04.2016 Accepted: 05.06.2016 Published: 01.10.2016 Copyright: © 2016 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION here are several ways to obtain notch tip stresses and strains: numerical simulation, experiment, and estimation methods. Since the first two approaches are time consuming, it is desirable to use estimation methods that provide results based on elastic FE simulation only. Such methods have been developed since the last century and can work with different types of loading, including cyclic loading [1], [2]. The essence of those methods is in using results from elastic FE analyses and converting these results into elastic–plastic estimates using suitable sets of equations. In this paper, two sets of methods were selected for comparisons. The first set consisted of the methods intended for multiaxial proportional monotonic loading. The selected methods were Moftakhar’s method [3], Reinhardt’s method [4], and Hoffmann–Seeger’s method [5]. The second set consisted of the methods intended for multiaxial non-proportional monotonic loading. The selected methods were Singh’s method [6] and Buczynski’s method [7]. T