PSI - Issue 42

1220 Diogo Montalvão et al. / Procedia Structural Integrity 42 (2022) 1215–1222 Montalvão, Hekim, Costa, Reis, Freitas / Structural Integrity Procedia 00 (2019) 000 – 000 In this paper, three of the asymmetric specimens described by Montalvão et al. (2019) were analysed (table 1). The reason why CT and TT specimens with biaxiality ratios ranging from Δ = ± to Δ = ± were chosen, is because these biaxiality ratios are well set apart from each other and somewhat extreme in terms of dimensions (especially for Δ = ± where substantial dimensional changes are required). However, any other specimens could have been chosen and should not condition the findings of this study. The geometry is based on a cruciform configuration, featuring corner elliptical f illets between the specimen’s arms, to reduce stress concentrations and to maximise stress at the specimen’s centre (Baptista et al., 2014, 2015). 6

Table 1. Changes in arms ’ lengths and biaxiality ratios for specimens with non-unitary biaxiality ratios analysed in this study.

Specimens type CT (shear, out-of-phase) Model (mm) (mm) CT.77 1.5 -1.95

Specimens type TT (biaxial, in-phase) Model (mm) (mm) TT.77 2 -1.55

-0.77 -0.62 -0.40

0.77 0.62 0.40

CT.62 CT.40

2.5

-4.05 -10.1

TT.62 TT.40

4

-2.5

4

10

-4

4. Results and Analysis FEA was used to determine the stresses, strains, and displacements in the 3 cartesian directions , , and . Results are shown in table 2. Hooke’s law was used to validate results (i.e., determine stresses from FEA strains and vice versa) which were found to be correct. Table 2. Stress, strain, and displacement at tips FEA results for both the CT and TT specimens with different ‘design’ biaxiality ratios. (MPa) (MPa) (MPa) (mm) (mm) CT.40 119 -221 1.1 2.67E-03 -3.61E-03 4.57E-04 1.75E-02 -4.35E-02 CT.62 218 -301 0.6 4.41E-03 -5.17E-03 3.74E-04 3.53E-02 -5.70E-02 CT.77 283 -337 1.1 5.47E-03 -5.98E-03 2.41E-04 4.80E-02 -6.23E-02 CT.100 366 -365 0.7 6.76E-03 -6.75E-03 1.21E-05 6.47E-02 -6.47E-02 TT.40 414 72 3.4 5.40E-03 -9.14E-04 -2.18E-03 9.57E-02 3.84E-02 TT.62 321 144 3.2 3.78E-03 5.20E-04 -2.09E-03 7.85E-02 4.87E-02 TT.77 267 175 3.1 2.90E-03 1.20E-03 -1.99E-03 6.82E-02 5.27E-02 TT.100 198 198 2.7 1.83E-03 1.83E-03 -1.80E-03 5.41E-02 5.41E-02 With this data, the , and biaxiality ratios can now be determined, which results are shown in table 3. Table 3. Biaxiality ratios , and for both CT and TT specimens with different ‘design’ biaxiality ratios . (= Δ ) × (= Δ ) × CT.40 -0.54 -0.74 -0.40 0.40 TT.40 0.17 -0.17 0.40 -0.03 CT.62 -0.72 -0.85 -0.62 0.62 TT.62 0.45 0.14 0.62 0.06 CT.77 -0.84 -0.92 -0.77 0.77 TT.77 0.66 0.41 0.77 0.27 CT.100 -1.00 -1.00 -1.00 1.00 TT.100 1.00 1.00 1.00 1.00