Issue 37

C. Riess et alii, Frattura ed Integrità Strutturale, 37 (2016) 52-59; DOI: 10.3221/IGF-ESIS37.08 58 An essential point of the optimization is the identification of critical locations. The aim of the identification is to find the node, which has the highest probability of crack initiation, in a simple manner. Size effects may have a large influence for notched components, but under non-proportional stresses they are not yet well defined. Thus, in this work notch support because of size effects is omitted. An explicit consideration of size effects could help to increase the accuracy of the identification. Therefore, the influence of size effects under transient stress gradients and transient highly stressed volumes or surfaces needs to be investigated. To ensure, that the crack initiation site in the physical test coincides with the critical node crit x , a solution with a strong damage localization is favorable. The iterations of the optimization are scanned manually for solutions with higher localization of the damage parameter (see Fig. 4), but sufficiently high non-proportionality. A satisfactory parameter set (tradeoff) is identified ( 0 9032 .   and 1 2274 .   ) with NPF of 0.572 at the critical node. C ONCLUSION new inertia based non-proportionality factor for the evaluation of pseudo-elastic stress paths is introduced. Calculations of the NPF are performed according to a modified version of the MOI method from Meggiolaro. The use of the tresca-diagram     x y xy 2 {( )| } makes the NPF invariant with respect to the coordinate system. Furthermore a numerical optimization, which searches for a test set-up with high non-proportionality at the potential crack initiation site, is developed and implemented. A selective weakening of the chosen component is necessary in order to get a high NPF at the critical location. A possible weak point of the optimization is that size effects are not considered. Therefore, further investigations should focus on the influence of size effects under non-proportional stresses. In order to get a robust test set-up, a tradeoff is derived. Experimental investigations with constant and variable amplitudes are going to be performed on the basis of this tradeoff. R EFERENCES [1] Tanaka, E., A nonproportionality parameter and a cyclic viscoplastic constitutive model taking into account amplitude dependences and memory effects of isotropic hardening, Eur. J. Mech. A/Solids, 13 (1994) 155-173. [2] Kanazawa, K., Miller, K.J. and Brown, M.W., Cyclic deformation of 1% Cr-Mo-V steel under out-of-phase loads, Fatigue Fract. Eng. Mater. Struct., 2 (1979) 217–228. DOI: 10.1111/j.1460-2695.1979.tb01357.x [3] Bishop, J.E., Characterizing the non-proportional and out-of-phase extent of tensor paths, Fatigue Fract. Eng. Mater. Struct., 23 (2000) 1019-1032. DOI: 10.1046/j.1460-2695.2000.00355.x [4] Gaier, C., Lukacs, A. and Hofwimmer, A., Investigations on a statistical measure of the non-proportionality of stresses, Int. J. Fatigue, 26 (2004) 331-337. DOI: 10.1016/j.ijfatigue.2003.08.023 [5] Bolchoun, A., Wiebesiek, J., Kaufmann, H., Sonsino, C.M., Application of stress-based multiaxial fatigue criteria for laserbeam-welded thin aluminium joints under proportional and non-proportional variable amplitude loadings, Theor. Appl. Fract. Mech., 73 (2014) 9-16. DOI: 10.1016/j.tafmec.2014.05.009 [6] Meggiolaro, M.A., Castro, J.T.P., Prediction of non-proportionality factors of multiaxial histories using the Moment Of Inertia method, Int. J. Fatigue, 61 (2014) 151-159. DOI: 10.1016/j.ijfatigue.2013.11.016 [7] Chu, C.C., Conle, F.A. and Hübner, A., An integrated uniaxial and multiaxial fatigue life prediction method, VDI Berichte, 1283 (1996) 337-348. [8] Dreßler, K., Carmine, R., Krüger, W., The multiaxial rainflow method, in: Rie, K.T. (Ed.), Low cycle fatigue and elasto-plastic behaviour of materials, Elsevier Science Publ., London, (1992) 325-331. [9] 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. DOI: 10.1016/j.ijfatigue.2011.10.014 A