Issue 38

S. Tsutsumi et alii, Frattura ed Integrità Strutturale, 38 (2016) 244-250; DOI: 10.3221/IGF-ESIS.38.33 245 of structures, provided that care is taken to ensure that the model is appropriate for the analysis. The elasto-plastic model used in this paper [4-6], which reproduces cyclic elasto-plastic behaviour under high or low cyclic fatigue, has already been widely used to investigate the fatigue crack initiation life of structural components. In this study, we investigated the fatigue behaviour of a non-load carrying fillet joint under uniaxial conditions for different loading paths, while the stress path deviate from proportional one due to the geometrical complexity of the weld bead. Also, we analyzed the effects of different loading combinations on the component service life. The results were in good agreement with experimental results, although a method of predicting fatigue life under multi-axial and more generic loads has not been developed. The authors [7] suggested that it may be possible to predict fatigue life under multi-axial and variable loading conditions by using a damage parameter ( H d ), which takes into account the plastic work. We examine the relationship between H d and fatigue life by coupling the subloading surface equations with an internal damage variable. The numerical analyses were performed with two different approaches: a series of tests investigated the material response and FE analysis was applied to a steel component of a material and a non-load carrying fillet joint. The material response tests gave us information about the correlation between H d and the fatigue crack initiation life, which was used in the non-load carrying fillet joint simulations to reproduce the experimental results provided by the Japanese Society of Steel Construction (JSSC). C ONSTITUTIVE EQUATIONS AND NUMERICAL PROCEDURE Constitutive equations of the material he extended subloading surface model [4-6] describes the generation of plastic strain within the yield surface (subloading surface), which can be obtained through a similarity transformation from the conventional yield surface (referred to as the normal-yield surface in Fig. 1). Classical theories distinguish elastic and plastic regions, allowing an irreversible stretch only in the plastic region. In contrast, the subloading surface model abolishes the separation into domains, stating that a plastic response can be realized for every change in the stress state that satisfies the loading criterion. Furthermore, the use of a mobile similarity center, which is a function of the plastic strain, makes this theory particularly suitable for studying cyclic mobility problems. A detailed explanation of the model features is beyond the scope of this paper, and the reader is referred to Refs. [4-6] for a more complete discussion. The damage variable, modelled as a phenomenological loss of stiffness, was coupled with the elasto-plastic equations according to the theory proposed by authors [7]. The constitutive equations of the extended subloading surface model were modified to include the progressive relaxation of the material induced by the damage, D , which becomes function of a special variable of the cumulative plastic strain, H d , of     3 1 1 2 1 1                   d d d d D H d H (1) where d 1 , d 2 , and d 3 are material parameters that regulate the damage rate evolution, as shown in Fig. 2, and must be calibrated depending on the material. An example of a feature of the new theory is shown in Fig. 3, in which progressive material relaxation induces the opening of the loops during fully reversible cyclic loading. Fig. 3 shows the experimental stress-strain evolution, whereas Fig. 4 shows the numerical evolution calculated with the same boundary conditions and with the material parameters in Tab. 1. Material parameters Value Material parameters Value E 206,000 [MPa] R e 0 0.4  0.3 a 1; a 2; a 3 2.5; 740; 3 u 10,000 k 1; k 2; k 3 0.316; 0.5; 8 F 0 350 [MPa] d 1 ; d 2 ; d 3 0.0063; 0.0045; 1.6 Table 1: Material parameters used in this paper T