Issue 33

T. Itoh et alii, Frattura ed Integrità Strutturale, 33 (2015) 289-301; DOI: 10.3221/IGF-ESIS.33.33 290 Low cycle fatigue (LCF) lives are reduced under strain controlled non-proportional loading accompanied by additional cyclic hardening compared with proportional loading [3-8] and an appropriate design method of evaluating the non- proportional fatigue life is needed for a reliable design and maintenance of structural components. Classical models particularly applicable in multiaxial fatigue life evaluation under proportional loadings lead to overestimate the lives under non-proportional loadings. For life evaluation under non-proportional loading, commonly proposed models are critical plane approaches that consider specific plane applied the critical damage, such as a Simith-Watoson-Topper [9] and a Fatemi-Socie [10] models. The authors also proposed a strain parameter (Itoh-Sakane model) estimating the non- proportional LCF lives for several materials under various strain histories [6, 7, 11-15]. This parameter is the strain based model with introducing two parameters, non-proportional factor and material constant. The former one reflects the intensity of non-proportional loading reducing life and the latter one is related to the material dependence for degree of life reduction due to non-proportional loading. The Simith-Watoson-Topper, the Fatemi-Socie and the Itoh-Sakane models have been demonstrated to be applicable to life evaluation under non-proportional loading using hollow cylinder specimens in a laboratory level. That is, these models can be applicable to the life evaluation under limited non-proportional loadings such as the loadings in the plane stress state. However, many components and structures such as turbine blade, pressure vessel and pipe which receive combined thermal and mechanical loadings undergo non-proportional loading in which principal directions of stress and strain are changed into various directions under wider multiaxial stress and strain states [8, 13, 16-18]. Therefore, a development of suitable models for the design of actual components where variation in principal directions of stress and strain vs time is changed 3-dimensionally is required. This study presents a method of evaluating the principal stress and strain ranges and the mean stress and strain, and also presents a method of calculating the non-proportional factor which expresses the severity of non-proportional loading in 3-dimantional (3D) stress and strain space (6 stress/strain components). Based on the method proposed, non- proportional strain and stress ranges are derived and applicability of the range to the life evaluation of type 304 stainless steel under 15 proportional and non-proportional strain paths are also discussed. This study also shows a method of visually presenting the stress/strain, the non-proportionality of loading and the damage evaluation. S TRESS AND STRAIN UNDER NON - PROPORTIONAL LOADING Definition of stress and strain ig. 1 illustrates three principal vectors, S i ( t ), applied to a small cube in material at time t in xyz -coordinates (spatial coordinates), where “ S ” is the symbol denoting either stress “  ” or strain “  ”. Thus, S i ( t ) are the principal stress vectors for the case of stress and are the principal strain vectors for the case of strain. The subscript, i, takes 1, 2 or 3 in descending order of principal stress or strain. The maximum principal vector, S I ( t ), is defined as S i ( t ) whose absolute value takes maximum one, i.e. , S I ( t )= S 1 ( t ) when S 1 ( t ) takes maximum magnitude among S i ( t ). The maximum principal value, S I ( t ), is defined as the maximum absolute value of S i ( t ) as, I I 1 2 3 ( ) ( ) Max ( ) , ( ) , ( ) t       S S S S S t t t t (1) Figure 1 : Principal stress and strain in xyz coordinates. F