Issue 33

T. Itoh et alii, Frattura ed Integrità Strutturale, 33 (2015) 289-301; DOI: 10.3221/IGF-ESIS.33.33 289 Focussed on multiaxial fatigue Evaluation and visualization of multiaxial stress and strain states under non-proportional loading T. Itoh, M. Sakane Ritsumeikan University, Japan itohtaka@fc.ritsumei.ac.jp, sakanem@se.ritsumei.ac.jp T. Morishita College of Science & Engineering, Ritsumeikan University, Japan gr0202xp@ed.ritsumei.ac.jp A BSTRACT . This paper presents a simple method of determining stresses and strains and a severity of loading history under non-proportional loadings with defining the rotation angles of the maximum principal stress and strain in a three dimensional stress and strain space. Based on the method, non-proportional stress and strain ranges are derived and applicability of the range to the life evaluation for low carbon steel under non-proportional random strain paths are discussed. The strain range taking account of intensity of loading path reducing life can be suitable parameter for multiaxial fatigue life evaluation under multiaxial non-proportional loading. This paper also shows a method of visually presenting the principal stress and strain that assists designers to understand the loading mode whether proportional or non-proportional under 3 dimensional (6 stress/strain components) multiaxial loading. K EYWORDS . Fatigue; Low cycle fatigue; Multiaxial loading; Non-proportional loading; Stress and strain evaluation; Random loading; Visualization of multiaxial loading. I NTRODUCTION ost design codes use equivalent values to express the intensity of multiaxial stress or strain, like von Mises or Tresca equivalent stress and strain, and fatigue lives are usually estimated using equivalent values under multiaxial stress and strain states. The equivalent value means a scalar parameter that expresses intensity of a physical phenomenon in multiaxial stress states and should be reduced to be a uniaxial value in uniaxial stress state. Most widely used equivalent parameters are the von Mises and the Tresca equivalent stresses and strains. The von Mises equivalent stress physically expresses the intensity of shear strain energy and the Tresca equivalent stress that of the maximum shear stress. For example, ASME Section III, Division 1 NH [1] uses the von Mises equivalent strain and ASME Section VIII, Division 3 [2] the maximum shear stress. However, the von Mises equivalent stress and strain have no negative values so that they have a difficulty of expressing stress and strain ranges. The Tresca equivalent stress and strain have negative values but they also have a difficulty to put a sign to the shear stress and strain under multiaxial loading. Especially, in non-proportional loading where the principal stress and strain change their directions, giving a sign to them becomes more difficult. A simple and clear method of calculating stress and strain ranges is needed for describing multiaxial fatigue. M