Issue 38

H. Wu et alii, Frattura ed Integrità Strutturale, 38 (2016) 99-105; DOI: 10.3221/IGF-ESIS.38.13 105 [3] Castro, F.C., Araújo, J.A., Mamiya, E.N., Pinheiro, P.A., Combined resolved shear stresses as an alternative to enclosing geometrical objects as a measure of shear stress amplitude in critical plane approaches, Int. J. Fatigue, 66 (2014) 161-167. [4] Dang Van, K., Griveau, B., Message, O., On a new multiaxial fatigue limit criterion: Theory and application, in: M. W. Brown, K. J. Miller (Eds.), Biaxial and Multiaxial Fatigue EGF3, Mechanical Engineering Publications, London, (1989) 479-496. [5] Li, B., Santos, J.L.T., Freitas, M., A unified numerical approach for multiaxial fatigue limit evaluation, Mech. Struct. Mach., 28 (2000) 85-103. [6] Zouain, N., Mamiya, E.N., Comes, F., Using enclosing ellipsoids in multiaxial fatigue strength criteria, European J. Mech.- A/Solids, 25 (2006) 51-71. [7] Araújo, J.A., Dantas, A.P., Castro, F.C., Mamiya, E.N., Ferreira, J.L.A., On the characterization of the critical plane with a simple and fast alternative measure of the shear stress amplitude in multiaxial fatigue, Int. J. Fatigue, 33 (2011) 1092-1100. [8] 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. [9] 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. [10] Meggiolaro, M.A., Castro, J.T.P., The moment of inertia method to calculate equivalent ranges in non-proportional tension–torsion histories, J. Mat. Res. Tech., 4 (2015) 229-234. [11] Meggiolaro, M.A., Castro, J.T.P., Wu, H., On the use of tensor paths to estimate the non-proportionality factor of multiaxial stress or strain histories under free-surface conditions, Acta. Mech. in press (2016). [12] MATLAB, The MathWorks Inc., Natick, MA, (2016). [13] Castro, J.T.P., Meggiolaro, M.A., Fatigue Design Techniques (in 3 volumes), CreateSpace, Scotts Valley, CA, USA (2016). A PPENDIX atlab implementation of the MOI method for a shear-shear stress history. For shear-shear strain histories, it is enough to replace all shear stress with shear strain data. %INPUTS: tauA = [0 100 100 0 0]; %single event, e.g. rectangular path in MPa tauB = [0 0 50 50 0]; perimeter = 0; tauAm = 0; tauBm = 0; Iorigin = 0; %initialize variable for i = 1:(size(tauA,2)-1) %for all elements of load path dtauA = (tauA(i+1)-tauA(i)); %increment of shear A dtauB = (tauB(i+1)-tauB(i)); %increment of shear B dtau = sqrt(dtauA^2+dtauB^2); %length of the shear increment perimeter = perimeter + dtau; %perimeter of the entire shear path tauAc = (tauA(i+1)+tauA(i))/2; %centroid of the shear A segment tauBc = (tauB(i+1)+tauB(i))/2; %centroid of the shear B segment tauAm = tauAm + dtau*tauAc; %mean of the shear A path tauBm = tauBm + dtau*tauBc; %mean of the shear B path Iorigin = Iorigin + dtau*(dtau^2/12 + tauAc^2 + tauBc^2); %PMOI end Iorigin = Iorigin/perimeter; %polar MOI requires division by perimeter tauAm = tauAm/perimeter; %mean component of the shear A path tauBm = tauBm/perimeter; %mean component of the shear B path I = Iorigin - (tauAm^2 + tauBm^2); %PMOI with respect to path mean %OUTPUTS: mean_component = [tauAm tauBm] %output mean component of 2D shear path equivalent_range = sqrt(12*I) %output equivalent range M