PSI - Issue 42

F. Cesarano et al. / Procedia Structural Integrity 42 (2022) 1282–1290 F. Cesarano, M. Maurizi, C. Gao, F. Berto, F. Penta, C. Bertolin / Structural Integrity Procedia 00 (2019) 000 – 000

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shell, which conforms to the assumptions of the technical theory of the beam, it was possible to compare the theoretical and geometric curvature generated by the application of a thermal load using the geometric equation (1) and the theoretical equation (equation 2) (dependent on component thickness (h), Young's modulus ratio ( ∗ ) and strain difference (Δε) equal to Δα ΔT where Δα is the thermal expansions difference of the materials). The curvature results in the function of ΔT are shown in Fig. 2. = 12∆ ℎ( ∗ + 14 + 1 ∗ ⁄ ) It was noted that as the dimensions along the Y-direction increased (thus moving away from the dimensional assumptions of the technical theory of the beam), there was an increase in the flexural curvature (Fig. 3, pink line). After these initial comparisons, it became clear as the geometric relationship was valid in calculating the curvature of the specimens subjected to the experiments as it was derived graphically without taking into account the simplified assumptions of the technical theory of the beam (dimensions and isotropy). Furthermore, the validity was even more confirmed by the results as the theoretical ones were comparable with the values obtained by the finite element analysis. (2)

Fig. 2: Analytic (top) and FEM (bottom) curvature comparison

Fig. 3: FEM curvatures comparison

Thus the first test experiments were carried out to understand the reference specimen and the correct testing approach. After many attempts (which considered dimensional variations and different arrangements in the oven), it was determined that the reference specimen has dimensions 50x10x0.4 [ mm ], i.e. with two 0.2 millimetre layers each, a fibre arrangement at 0° and 90° (to obtain pure bending), and a filling density of 100% (Fig. 4a). Concerning the arrangement in the oven, it took place using a heat-insulating line passing through small central holes in the specimen so that without constraints, all possible deformations are permitted due to the SME's release of residual stresses (Fig. 4b). Running the experiments with the reference specimen and the right set up conditions in the oven, a pure bending deformation was obtained as the expected programme deformation described in van Manen et al. 2017 [2]. Then, several tests were conducted to understand the correct testing methodology. The first method of experimentation (Fig. 5a) consists of placing the specimen inside the oven starting from room temperature (RT) and subjecting it to a complete cycle of homogeneous thermal elevation up to the target temperature (60°C, 70°C, and 80°C) with a dwell time of a few seconds. On the other hand, the second experimental method (Fig. 5b) consists of placing the specimen in the oven only when it has already reached the desired target temperature and then holding it at that temperature for several minutes.