PSI - Issue 54

Ela Marković et al. / Procedia Structural Integrity 54 (2024) 156 – 163 Ela Markovi ć et al. / Structural Integrity Procedia 00 (2023) 000–000

160

5

subjected to a displacement Δ y equal to 0,3 mm. The FEA solution of homogeneous strip with notches considering only elastic range converged already with mesh that had around 6 elements around the circumference of a quarter of a notch, as seen in Figure 4, which is taken as the minimum number of elements that have to be used to mesh the notch area in later analysis. The data labels in percentages on the diagram in Figure 4 indicate the difference between the stress value obtained with the current mesh parameters and those at the previous point. The optimal number of required elements per circumference of the curvature of the notch are consistent with a study conducted by Chmelko et al. (2022).

2650 2700 2750 2800 2850

0.017%

0.027%

0.042%

3.904%

0.021%

0.033%

0.160%

notch

2 4 6 8 10121416

Maximal stress in

Number of elements around the circumference of the notch

Fig. 4. Mesh around the notch area with number of elements around the circumference of a quarter of the notch ranging from 2 to 16, and diagram of the convergence of maximal stress at the notch with respect to number of elements around the circumference of the notch.

2.4. Modeling functionally graded material To simulate component with functionally graded material, a pseudo temperature method proposed by Rousseau and Tippur (2000) was employed. This method requires the ability to define material properties at distinct temperature values and to vary temperature throughout the body, as stated in Hassan Ahmed and Kurgan (2022), both features available in Ansys. Temperature variation throughout the body was conducted by assigning temperature values to nodes which later ensures a continuous variation in material properties as a function of specimens’ spatial coordinates. Limitation of the method is that the temperature itself does not have any physical significance, and thermal strains must be suppressed, Martínez-Pañeda (2019). The multilinear isotropic model in Ansys software supports up to 20 temperatures for which data can be provided, Ansys Inc. (2010). For that purpose, the hardness distribution function (Eq. 2) was discretized into 20 optimally spread points using the Visvalingham-Wyatt simplification algorithm (details in Visvalingam and Whyatt (1993)) for the distance from the surface of the specimen to its center, as shown in Figure 5.

250 350 450 550 650

Hardness, HV

0

5

10

15

20

Distance from surface x , mm

Fig. 5. Relationship between hardness and the distance from surface discretized into 40 points.

Yield strength and strength coefficient were calculated for each of the 20 hardness distribution points using Eqs. 3 and 4, respectively. These values were then employed to establish multilinear isotropic curves for varying hardness values, using a modified Ramer-Douglas-Peucker algorithm outlined in the previous section. Each curve corresponded to a distinct temperature, representing different distances from the surface to the specimen's core. Figure 6 shows 20 multilinear piecewise curves mapped to 20 different values of temperature and consequently hardness, which defined the functionally graded specimen. Between the provided material curves, linear interpolation is employed to determine specific material property value.