PSI - Issue 72

H.G.E. da Silva et al. / Procedia Structural Integrity 72 (2025) 26–33

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Table 5. Summary of 3PB results for configurations 1 and 2.

Configuration

P m [N]

τ [MPa]

 f [MPa]

s 1 [N/mm]

 at P m [mm]

P1 P2

847.3 1.059 937.6 1.165 892.5 1.112 917.9 1.173 955.5 1.221 936.7 1.197 63.9 0.075

113.8 125.2 119.5 98.9 102.9 100.9 8.1

161.1 166.0 163.5 161.9 168.6 165.3 3.4

6.622 7.289 6.956 0.472 6.721 7.039 6.880 0.225

1

Average value

Standard deviation

P1 P2

2

Average value Standard deviation

26.6

0.034

2.9

4.7

3.2. Adhesive and skin stresses Fig. 3 (a) presents shear (  xy ) stresses in the adhesive layer on the upper and lower skin of configuration 1. The ordinate axis shows the  xy stress in the xy plane normalized to the average  xy stress (  avg ). The abscissa axis shows the position of the values normalized to the length of the specimen.  xy stresses are identical between the two skins, with nearly constant values between the punch and both supporting cylinders, while  xy =0 in the punch vicinity. In configuration 1, the highest  xy stresses in the adhesive occurred at a horizontal distance of 20.5 mm from the punch for the lower skin (i.e., near the punch) and at 94.5 mm for the upper skin (near the supporting cylinders). Fig. 3 (b) shows  xy stresses in the adhesive for configuration 2. The maximum adhesive  xy stresses were recorded at a horizontal distance of 56.5 mm from the punch for the lower skin and at 48.5 mm for the upper skin, i.e., at very close longitudinal locations in the adhesive. In general, it was noted that the maximum  xy stresses in the adhesive were found close to the punch area, but with similar values over an extent of approximately 75 mm, on each side of the punch. Comparing the two skin layups, configuration 1 presents slightly higher peak  xy stresses than configuration 2 (0.4%). However, by comparing both plots, it can be concluded that the skin layup has a negligible effect on adhesive stresses, and that its modification should not induce significant differences in the overall behavior nor change the failure mode.

1.4

1.4

1.2

1.2

1

1

0.8

0.8

τ xy / τ avg

τ xy / τ avg

0.6

0.6

0.4

0.4

0.2

0.2

0

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x/L

x/L

Upper Skin

Lower Skin

Upper Skin

Lower Skin

a)

b)

Fig. 3.  xy stress distribution for configuration 1 (a) and 2 (b) during 3PB test.

Fig. 4 (a) presents peel (  y ) stresses in the upper and lower adhesive layer of the sandwich during 3PB test for configuration 1. The ordinate axis shows  y stresses normalized by the average  xy stress. The maximum adhesive  y stresses were found in the punch area (upper skin due to the punch contact), while  y stresses are mostly nil along the adhesive layer, apart from the supporting cylinders. Fig. 4 (b) presents  y stresses in the upper and lower adhesive layer for configuration 2. Similarly to configuration 1, adhesive  y stresses are highest in the punch area (upper skin). Comparing the layup, configuration 1 presents  y stresses slightly higher values than configuration 2 (7.9%). Higher relative peak  y stresses exist at the specimen edges, compared to configuration 1, but without exceeding  avg . Overall, it is not expected that peel failures take place in the adhesive layer.