## 3 Results and Discussion
### Simulated Ratcheting Results  
The ratcheting response of AM Al 4043 samples under different stress levels was simulated through the finite element method and different element types, shapes, and nodes. The Chaboche kinematic hardening rule as a material model in Ansys software was employed to evaluate the ratcheting response of Al 4043 samples with three different element types. Figure 9 illustrates the simulated ratcheting strain curves for aluminum samples tested at 75 \(\pm\) 55 MPa, 70 \(\pm\) 55 MPa, 65 \(\pm\) 65 MPa and 75 \(\pm\) 60 MPa. In each loading condition, the simulated ratcheting curves through using quadratic brick elements resulted in larger magnitudes, while the ratcheting level declined, respectively, for the quadratic  
Figure 8: The simulation of backstress increments over the first fifty loading cycles for different element types and at different stress levels of (**a**) 75 \(\pm\) 55 MPa, (**b**) 70 \(\pm\) 55 MPa, (**c**) 65 \(\pm\) 65 MPa, and (**d**) 75 \(\pm\) 60 MPa. tetrahedron and the linear brick elements. The simulated curves based on different element types revealed that the ratcheting amount was increased by increasing the stress levels. The ratcheting magnitude was increased by as high as 12% in Figure 9b as compared with the simulated ratcheting curve in Figure 9a as the stress amplitude was increased from 70 MPa to 75 MPa. The simulated ratcheting curves closely agreed with the experimental values. The deviation of simulated ratcheting curves from those of measured values stayed between 2% and 12%. Figure 10 represents the simulated stress-strain hysteresis loops for AM Al 4043 samples at various stress levels of 75 \(\pm\) 55 MPa, 70 \(\pm\) 55 MPa, 65 \(\pm\) 65 MPa and 75 \(\pm\) 60 MPa. Hysteresis loops for the 1 st and 250 th cycles are, respectively, simulated through FE analysis and the use of three different element types. Figure 10a,c,e,g present the first-order simulated stress-strain hysteresis loops for the first stress cycle applied with different stress levels. These figures present simulated hysteresis loops constructed based on different element types and those obtained experimentally. In the first cycle, the simulated loops based on the quadratic tetrahedron, linear brick, and quadratic brick elements resulted in a small difference as compared with the measured loops. As the number of cycles increased, samples with the linear brick elements tested at 75 \(\pm\) 55 MPa (see Figure 10b) and 70 \(\pm\) 55 MPa (see Figure 10d) closely agreed with the measured loops. At these stress levels, samples meshed with the quadratic tetrahedron as well as quadratic brick elements resulted in simulated loops with larger deviations, respectively. At stress levels of 65 \(\pm\) 65 MPa (see Figure 10f) and 75 \(\pm\) 60 MPa (see Figure 10h), the simulated loops by the second-order brick elements demonstrated a better agreement with the experimental values. Figure 9: Simulated and measured ratcheting curves for AM Al 4043. The simulation was conducted for three different element types and at different stress levels of (**a**) 75 \(\pm\) 55 MPa, (**b**) 70 \(\pm\) 55 MPa, (**c**) 65 \(\pm\) 65 MPa, and (**d**) 75 \(\pm\) 60 MPa. mental loops at the 250 th cycle. The evolution in hysteresis loops during 250 stress cycles revealed that the loops obtained from the quadratic brick element progressed more than the simulated loops with the quadratic tetrahedron and linear brick elements. In Figure 10, the stress-strain hysteresis loops for the first cycle were found to be almost identical in shape and width as compared with the corresponding measured loops. The decrease in the width of hysteresis loops over the number of cycles manifested the cyclic hardening response in AM Al 4043, leading to a drop in the ratcheting rate of aluminum samples.