Issue 41

T. Morishita et alii, Frattura ed Integrità Strutturale, 41 (2017) 45-53; DOI: 10.3221/IGF-ESIS.41.07 46 I NTRODUCTION tructural components and materials such as aircrafts and nuclear equipment undergo complex non-proportional multiaxial loadings where directions of stress and strain are changed into various directions under multiaxial stress and strain states. It is difficult for engineers to analyze histories of stress and strain. Therefore, development of suitable models for the design of actual components where variation of principal directions of stress and strain vs. time is considered 3-dimensionally is required [1-8]. To evaluate fatigue lives under multiaxial loading condition, multiaxial fatigue models which relate fatigue lives to uniaxial fatigue properties have been established. Equivalent strains and stresses based on von Mises and Tresca are considered as the most common theory. However, they lead to significant overestimation of fatigue lives under non-proportional loadings, thus a few other classical models such as critical plane approaches that correlate stress or strain with multiaxial fatigue lives have been proposed in recent years. However, some disadvantages on these approaches have been reported. Therefore, in order to avoid these disadvantages, Itoh et al. proposed a strain parameter related to material property and loading path, which are available in both of short-life and long-life fatigue regimes. The parameter takes response to material deformation and is expressed by simple calculation based on strain model [9-15]. Based on the IS-method proposed by Itoh et al., analyses for pipes subjected to cyclic multiaxial/non-proportional loading are performed. Under non-proportional loading, it is expected that the reduction of material fatigue life occurs. There are a lot of structural components that are subjected to non-proportional multiaxial loading, but the verification of shortened fatigue life has not been carried out mostly. Therefore, in order to have a guarantee for safety and soundness of structural components, an appropriate understanding and damage evaluation under non-proportional multiaxial loading are strongly urged [4-8]. In this study, on the basis of the method of Itoh-Sakane criterion (IS-method) which evaluates the state of stress and strain in a non-proportional multiaxial cyclic loading, the program is developed for the visualization and analysis of stress/strain state and the evaluation of failure life under non-proportional loading with constant or random amplitude was performed. M ULTIAXIAL F ATIGUE L IFE E VALUATION M ODELS number of multiaxial fatigue models have been proposed based on stress and strain models. Stress-based models are more widely used and are suitable for the large class of components that are operated near or below the fatigue threshold. Many of the stress-based models can be used successfully in the finite life regime if the plastic strains are small. In a word, stress based multiaxial damage criteria are suitable for infinite or high-cycle finite life evaluation. Development of strain-based models started in 1970s, which are more useful for low-cycle fatigue analysis. They may be written in strain alone or some product of stress and strain. When principal directions of strain correspond to axes of coordinates employed, the most common equivalent strain models are [3-8]: Maximum normal strain theory  1 :   B 3 A 3 B 2 A 2 B 1 A 1 1 , , Max     (1) Maximum shear strain theory  1 :            2 , 2 , 2 Max 2 B 3 A 3 B 2 A 2 B 1 A 1 1 (2) Where  1 i ,  2 i ,  3 i ( i =A, B) and  1 i ,  2 i ,  3 i are principal strains and principal shear strains at arbitrary times A and B in a cycle and ‘Max’ takes maximum value in brackets. Mises’ equivalent strain theory  eq :           2 1 3 2 3 2 2 2 1 2 2 eq 3 2 3 1         (3) S A