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

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Finite element analysis of notched specimen was carried out with a displacement of Δ y = 0,6 mm applied to the nodes located on the upper line of the geometry of the 1/4 th specimen, which corresponds to a displacement of Δ y = 1,2 mm for the entire specimen. Material properties of homogeneous and FGM specimen were defined the same as for the rectangular unnotched specimens. The resulting plastic strain fields of homogeneous specimen with an introduced notch, as well as two cases of FGM specimens are shown in Figure 9. Plastic strain data was interpolated and mapped to 40 equally spaced points in x direction with y -coordinate of 0 mm which resulted in a diagram shown in the Figure 9. The homogeneous specimen exhibits the highest values of plastic strain, followed by the specimen which is modeled as surfaced hardened prior to creation of notch (FGM 1). The specimen modeled as surface hardened after the notch creation (FGM 1) exhibits the lowest values of plastic strain which is to be expected since the notch has the highest hardness of the three cases.

Homogeneous

FGM 1

FGM 2

0,25

0,00

Plastic strain, mm/mm

2,5

10,0

Distance from surface x , for y = 0, mm

Fig. 9. Plastic strain fields in homogeneous, and specimens modeled with functionally graded material properties. Diagram of plastic strain as a function of a distance from surface defined for y = 0 mm.

Figure 10 displays the force – displacement graph obtained from the analysis for the force obtained in the y direction. The data was recorded for the nodes located at the top line of the specimen, specifically at y = 70 mm. It is evident that the FGM specimen demonstrated higher resistance to force compared to the homogeneous material, which is consistent with the behavior of surface-hardened materials.

Homogeneous

FGM 1

FGM 2

120 160

0 40 80

Force, kN

0,00

0,60

1,20

Displacement, mm

Fig. 10. Force-displacement graph for the notched specimens.

4. Discussion and conclusions This study demonstrated a modeling approach to simulate the mechanical behavior of functionally graded material specimens. FGM specimens were represented using the pseudo-temperature method. Temperature was assigned to nodes which resulted in a continuous variation of the temperature field as it is interpolated to the Gauss integration points. Subsequently, temperature was assigned to different multilinear isotropic curves using a developed simplification algorithm that optimizes number and position of data points to improve curve approximation . This resulted in a continuous distribution of material properties through one dimension of specimen simulating surface hardened component. The results of this study showed that the stress and plastic strain distribution is affected by the distribution of hardness in the FGM with specimens that are not surface hardened showing highest values of plastic strain as opposed to surface hardened specimens. Results of mechanical behavior of specimens from the developed numerical model demonstrated that the distribution of hardness in functionally graded materials (FGM) significantly influenced the stress and plastic strain distribution. Specimens modeled as homogeneous, without surface hardening, exhibited higher levels of plastic strain compared to their surface-hardened counterparts, which is in accordance with