PSI - Issue 61

Izzet Erkin Ünsal et al. / Procedia Structural Integrity 61 (2024) 164–170 I.E U¨ nsal and T. Yalc¸inkaya / Structural Integrity Procedia 00 (2024) 000–000

5

168

Fig. 2. Bending example for di ff erent lenght scales l / w = 0 . 0 (left), l / w = 0 . 5 (middle), l / w = 1 . 0 (right).

3.3. Tensile Example

For the last example, rectangular plates of same sizes with the previous bending example were simulated in tensile test. All of the material properties were kept same as before. Similar to bending example, 100 × 200 quadrilateral square elements with varying local yield stresses are assigned in a tensile test. For this example, the length scale parameter was varied in accordance to the element size in the FE mesh, where ∆ h is the side length of a single element. For all length scales, three di ff erent initial yield stress distributions were simulated. Figure 3 shows the stress strain curve, averaged for all elements. For the case with l / ∆ h is zero, we see no hardening since the J 2 model behaves ideally plastic. As we increase the length scale parameter, curve shifts upwards indicating a strain hardening behavior. The e ff ects of strain hardening is minimal yet still noticeable, di ff erence between the yield stress distribution sets are even smaller. Figure 4 shows the strain patterning obtained for the yield stress distribution of set 2.

Stress vs. Strain

0.25

0.2

0.15

22

0.1

0.05

0

0

0.1

0.2

0.3

0.4

0.5

22

Fig. 3. Stress strain curves for tensile specimens.