PSI - Issue 13

Gustavo Henrique Bolognesi Donato et al. / Procedia Structural Integrity 13 (2018) 1879–1887 Gustavo H. B. Donato and Felipe C. Moreira / Structural Integrity Procedia 00 (2018) 000–000

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3.2. Modified Boundary Layer Model (MBL) In order to obtain reference stress fields under high stress triaxiality conditions, Modified Boundary Layer (MBL) models were developed. All details can be found in Nevalainen and Dodds (1995) and it can be considered more convenient than the HRR field since: i) the HRR field presents some inconsistencies for the case of crack-tip radius reaching zero; ii) it is based on small geometry chance and cannot take into account crack tip blunting after relevant plasticity takes place (ANDERSON, 2005). The developed MBL models were loaded by remote fields to simulate a structure of large dimensions in accordance to the linear solution of Williams (1957); as a result, the models provides the stress fields in the crack region considering high stress triaxiality and including local plasticity. Such fields are considered as the reference for the determination of M values as presented in section 3.4. 3.3. Analysis matrix Tale 2 presents the analysis matrix developed for C(T), SE(B) and clamp-loaded H/W = 10 SE(T) specimens. It is clear the comprehensiveness of the analyses in terms of crack relative depths, material properties, thicknesses and loading modes (geometries). Table 2. Developed analysis matrix. ⁄ n Thicknesses ( mm ) Geometry Quantity of models 0.1; 0.2; 0.3; 0.4; 0.5; 0.6; 0.7 5; 10; 20 252 models 3.4. Determination of the deformation limit - M Based on the described elastic-plastic FE analyses, it becomes feasible to determine M values for the different laboratory geometries under investigation. In simple terms, the stress fields of a geometry being tested (for example one SE(B) specimen) are compared to the MBL reference stress fields while loading and plasticity increase. All numerical procedures were implemented in a MaLab code. As presented by Fig. 3, dashed lines represent the MBL model, while solid lines represent the studied geometry. M value is determined, using Eq. 1, for the J -value that represents a 15% deviation in stresses if compared to the reference high triaxiality fields. In this work, a normalized radius of 2 was employed, as presented by the same figure and detailed by Anderson (2005) and Cravero (2007). J values whose stress fields deviate more than ~ 15% are usually considered by the literature as beyond the validity limits of the EPFM. pl-ε; 12.5; 25,.4; 50.8 C(T), SE(B), SE(T) – H/W = 10

Fig. 3. Example of the strategy for determining M value for n = 10 and normalized radius r = 2.