Issue 33

A. Bolchoun et alii, Frattura ed Integrità Strutturale, 33 (2015) 238-252; DOI: 10.3221/IGF-ESIS.33.30 251 C ONCLUSION number of measures for the non-proportionality of the loadings were presented and used for evaluation of fatigue life of aluminum and magnesium welded joints. In general if a non-proportionality measure yields values between 0 and 1 it can be applied with any stress-based fatigue life hypothesis. The Eq. (25) can be used to modify a suitable stress value and hence take the non-proportionality into account. So it is a plausible requirement for a non-proportional measure to yield values between 0 and 1. There are also measures such as the factor  used in MWCM (Eq. (23)), which is required to interpolate between axial and torsion Wöhler-lines and cannot be easily interchanged with any other non-proportionality measure discussed in this paper. Also the non-proportionality measures are subdivided into integral and critical-plane-based ones. The latter group contains two measures discussed in this paper: the measure according to Kanazawa (Eq. (21), (22)) and the measure  used in MWCM according to Susmel (Eq. (23)). The value of this measures can rapidly change due to a small change in the loading, since such a change can lead to a change in the position of the critical plane. As a result two very similar loads can get very different non-proportionality evaluation. This problem can be avoided if an integral measure of non- proportionality is used. In order to use non-proportionality measures safely for arbitrary loadings, experimental results under loadings with different degrees of non-proportionality are required. In particular this can mean different phase-shifts between axial and torsion loadings and different amplitude ratios. All non-proportional measures presented in this paper are “global” i.e. they deliver information on the non- proportionality of a loading path as a whole. The question arises, whether these measures still work in an adequate manner, if a loading path consists of a number of pieces with different degrees of non-proportionality. Is it possible to provide some “local” measure of non-proportionality? As can be observed for the magnesium welded joints taking into account non-proportionality does improve the evaluation, however it can be further improved for variable amplitude loadings if the slopes of the Gassner-lines are taken into account correctly by the hypotheses. R EFERENCES [1] Sonsino, C.M., Influence of material’s ductility and local deformation mode on multiaxial fatigue response, Int. J. Fatigue, 33(8) (2011) 930-947. [2] Sonsino, C. M., Küppers, M., Eibl, M., Zhang, G., Fatigue strength of laser welded thin steel structures under multiaxial loading, Int. J. Fatigue, 28 (5-6) (2006) 657-62. [3] Störzel, K., Wiebesiek, J., Bruder, T., Hanselka, H., Betriebsfeste Bemessung von mehrachsig belasteten Laserstrahlschweißverbindungen aus Stahlfeinblechen des Karroseriebaus. Fraunhofer-Institut für Betriebsfestigkeit und Systemzuverlässigkeit LBF, LBF-Bericht Nr. FB-235, Darmstadt (2008). [4] Küppers, M., Betriebsfestigkeit von Aluminiumschweißverbindungen unter mehrachsigen Spannungszuständen mit konstanten und veränderlichen Hauptspannungsrichtungen. Dissertation: Fachbereich Maschinenbau, Fachgebiet SzM, TU Darmstadt (2006), LBF-Bericht Nr. FB-233 [5] Wiebesiek, J., Festigkeitshypothesen zum Schwingfestigkeitsverhalten von dünnwandigen Laserstrahlschweißverbindungen aus Aluminium unter mehrachsigen Beanspruchungen mit konstanten und veränderlichen Hauptspannungsrichtungen, Dissertation, Shaker Verlag, Aachen (2012). [6] Exel, N., Schwingfestigkeit laserstrahlgeschweißter Magnesiumlegierungen unter mehrachsigen proportionalen und nichtproportionalen Beanspruchungen, Dissertation., Shaker Verlag, Aachen (2013). [7] Sonsino, C. M., Multiaxial fatigue of welded joints under in-phase and out-of-phase local strains and stresses, Int. J. Fatigue, 17(1) (1995) 55-70. [8] Susmel, L., Multiaxial notch fatigue, Woodhead, Cambridge (2009). [9] Bishop, J. E.. Characterizing the non-proportional and out-of-phase extent of tensor paths, Fatigue Fract. Engng. Mater. Struct. 23 (2000) 1019-1032. [10] Gaier, C., Lukacs, A., Hofwimmer, K., Investigations on a statistical measure of non-proportionality of stresses, Int. J. Fatigue, 26 (2004) 331-337. A