PSI - Issue 28

946 4

R. Moreira et al. / Structural Integrity Procedia 00 (2019) 000–000

R. Moreira et al. / Procedia Structural Integrity 28 (2020) 943–949

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(6) Where ( � , � , � , …, � ) are coefficients for the axial component and ( � , � , � , …, � ) are the coefficients for the shear component of the bi-dimensional third degree polynomial. �� is the strain level and is the strain amplitude ratio. The subscripts and denote the axial and the shear components, respectively. The subscript � � �� � � � denotes the six specific points of the hysteresis loop described in figure 1. 3. Experiments The AZ31B-F magnesium alloy specimens used on the experiments were machined along the extrusion direction. These experiments were performed at room temperature under strain-controlled regimes and ended when the specimens were totally separated. The specimen geometry and dimensions are presented in figure 2. All the tests were performed considering the ASTM E2207 standard instructions and using a servo-hydraulic machine. A biaxial extensometer was used for the axial and the torsional strain measurements. j j sl j j sl j j sl j sl j j sl j sl a b c d e f g h i j                         , , shear n sl P

Fig. 2. Specimen geometry and dimensions (mm), Anes et al. (2019).

To evaluate the implemented model in UMAT, experimental tests were performed with the loading paths of the figure 3. The following tests were performed: pure axial loading; pure shear loading; proportional loading with strain amplitude ratio for the condition of 30º, 45º and 60º; non-proportional loading with strain amplitude ratio for the condition of 45º and a phase shift of 90º.

(a) (f) Fig. 3. Loading paths in strain control (a): pure axial loading; (b): pure shear loading; (c), (d) and (e): proportional loading with strain amplitude ratio for the condition of 30 ° , 45 ° and 60 ° , respectively; (f) non-proportional loading with strain amplitude ratio for the condition of 45 ° and a phase shift of 90 ° . 4. Results and Discussion In addition to analytical HYPS model (implemented in Abaqus UMAT subroutine) a second model was considered for correlation, namely, the Armstrong-Frederick model, a nonlinear kinematic hardening model presented in Abaqus/Standard 6.14 library. (b) (c) (d) (e)