PSI - Issue 79

H.G.E. da Silva et al. / Procedia Structural Integrity 79 (2026) 97–104

102

Table 5. 4PB tests results for configurations 1 and 2.

Configuration

P m [N] 1307.4 922.8 1115.1 ±272.0 1340.6 1310.3 1325.45

τ [MPa] 1.602 1.134 1.368 1.756 1.704 1.730 ±0.331 ±0.0371

 f [MPa]

s 1 [N/mm]

 at P m [mm]

P1 P2

74.87 52.99 63.93 63.63 57.56 60.60 ±4.29 ±15.47

482.30 435.97 459.135 ±32.8 457.33 444.73 451.03

3.872 2.518 3.195 ±1.0 3.935 3.893 3.914 ±0.0

1

Average value Standard deviation

P1 P2

2

Average value Standard deviation

±21.4

±8.9

3.2. Failure modes

Upon analysis of the experimental failures in the different sandwich structures, it was assumed that the numerical failure is achieved corresponds to core failure. Thus, to assess the numerical failure point and P m , the increment in which peak  stresses of the core equal the average core shear strength in Table 4 was checked. Fig. 7 and Fig. 8 correspond to the Tsai-Wu criterion for the skins and the  stress for the core at the P m increment.

a)

b)

Fig. 7. Tsai-Wu criterion on the skins for configuration 1 (a) and configuration 2 (b)

a)

b)

Fig. 8. Shear stresses in the core of configuration 1 (a) and configuration 2 (b)

The Tsai-Wu criterion (Fig. 7) shows that, in the 4PB test, none of the laminate layers fail, but some zones are close to unity (failure) in configuration 1. In configuration 2, it was observed that the laminate layers do not exceed the criterion ’ s limit value and, thus, failure does not occur. In configuration 1 (Fig. 8 a), the core numerically reaches  =1.256 MPa, which is the closest increment to the shear strength value of 1.3 MPa (Table 4). In configuration 2 (Fig. 8 b), the failure value is reached (  =1.260 MPa), leading to the failure estimation for this sandwich configuration. 3.3. Strength evaluation The numerical P -  curves for each configuration in each test are compared with the respective experiments in Fig. 9. The point at which the specimen numerically fails was estimated when  stresses in the core equalled the shear strength defined in Table 4. The P m values are shown in the numerical P -  curves. For configuration 1 (Fig. 9 a), the numerical failure point corresponds to  =2.8 mm and P =1113.79 N. For configuration 2 (Fig. 9 b), the failure point was at  =2.7 mm, with P =1088.30 N. Table 6 compiles the numerical and experimental values of τ and σ and the relative error between the numerical and experimental values, for the 4PB test of each configuration.