PSI - Issue 44

Alessia Monaco et al. / Procedia Structural Integrity 44 (2023) 806–813 A. Monaco et al. / Structural Integrity Procedia 00 (2022) 000 – 000

808

3

0 d    

r A

=

C

(1)

In Eq. (1),  0 is the vacuum dielectric constant  0 = 8.8542·10 r is the Kapton dielectric constant  r = 3.4 while A and d are respectively the area of the electrodes and the gap between them. The area of the capacitor is A = 346.36 mm 2 and the opening corresponds to the thickness of the Kapton. The architecture of the system is modelled through the FE method taking advantage of its symmetry in order to generate an axisymmetric model with the finite element software Abaqus (Abaqus/CAE 2020). The finite elements used for all material layers are linear quadrilateral elements of type CAX4R, with an average mesh size of 25×75  m for Kapton and copper and 100×75  m for the FR4. The constitutive behaviour assumed for the modelling of the copper layers is linearly elastic and isotropic, with elastic modulus E copper = 128 GPa and Poisson’s coefficient  copper = 0.36. Also the Kapton is modelled by adopting a linear elastic behaviour, with E Kapton = 2.5 GPa and  Kapton = 0.34. Conversely, the constitutive model assumed for the FR4 layers is a transversally isotropic linear elastic behaviour with in-plane elastic modulus E FR4,p = 20 GPa and transversal elastic modulus E FR4,t = 2 GPa. The primary Poisson’s ratio is 0.2. – 3 pF/mm and 

(a)

(b)

(c)

(d)

1

2

4

6

6

3

5

2

1

1. Copper: D=40mm; s= 35  m 2. FR4: D=40mm; s=0.8 mm

3. Kapton: D=40mm; s=25  m

4. Gap (top): 0.5 mm

5. Gap (down): 1 mm

6. Tin weld: 0.2 mm

Fig. 1. CSS architecture: (a) global view; (b) electrical scheme; (c) detail of the mesh; (d) dimensions.

3. Numerical vs experimental correlation analysis 3.1. Description of the experimental tests

The numerical modelling of the CSS behaviour is validated against the results of a cyclic uniaxial compression test conducted on a pilot cylindrical mortar specimen endowed with both CSSs inside and LVDTs on the external surface. The test has been conducted at the Laboratory of Materials and Structures of University of Palermo. The diameter of the tested sample is 160 mm and the height 340 mm. Three LVDTs are placed at 120° according to the scheme reported in Fig. 2; similarly, three CSSs are placed inside the specimen, in correspondence to the three external LVDTs, in the mid-section plane of the cylinder. A universal testing machine is used for applying a cyclic loading history able to induce in the specimen a uniform uniaxial compression. The loading history is reported in Fig. 3: the load is applied in displacement control until displacement values that correspond to the loading force in the intervals reported in the figure. In detail, in the first loading phase, three loading/unloading cycles between 0-18 kN are applied; in the second phase, the loading/unloading cycles are in the range 0-35 kN, while in the third phase, the loading/unloading interval is 0-55 kN. The maximum loading force is set in order to achieve about the 40% of the mortar compressive strength, which is equal to 6.3 MPa. The elastic modulus of the mortar is 6 GPa. Both compressive strength and elastic modulus