PSI - Issue 8

A. De Luca et al. / Procedia Structural Integrity 8 (2018) 288–296 A. De Luca / Structural Integrity Procedia 00 (2017) 000 – 000

290

3

v n

velocity vector of the point on the surface where the viscous pressure is being applied unit outward normal vector to the at the point where the viscous pressure is being applied

A

displacement amplitude coupled to the actuation signal in Volt;

t

wave propagating duration;

fc V N

central frequency of the excitation signal;

maximum applied voltage;

number of cycles within the window.

NPW Nodes per wavelength DIRMSD(%)

Root Mean Square Deviation Damage Index

2. FE model

In this section the FE model technique, developed in order to simulate Lamb wave propagation in the LVI damaged plate is presented. As aforementioned, Lamb wave propagation are simulated onto a plate characterized by an initial stress-strain state and the related failures carried out by a previous impact simulation involving the same model. Such approach allows overcoming the difficulties relating to the iterative modelling of the impact damages distribution by lowering the elastic materials properties or by introducing either geometrical discontinuities or damping factors in the area in which the damage has to be modelled. However, such techniques can be characterized, rather than not acceptable approximations, by the operator mistake. Consequently, in this work a more accurate technique is presented, providing a better modelling of the interaction between Lamb waves and LVI damages in CFRP plates at different impact energy levels. In more detail, the FE results achieved by the impact simulation are updated in a following FE analysis in which the Lamb wave propagation is simulated. At the end of such operation, the CFRP plate will be characterized by the initial stress-strain state and the related failures active at the end of the impact simulation. Relatively to the impact simulation, the numerical model has been developed by means of Abaqus® 6.14 code. Reduced integration general- purpose shell elements (S4R, from the Abaqus elements’ library) have been used to model the plate (200 mm x 200 mm), which consists of 8 laminae (Fig. 1.a). Each finite element is characterized by 24 integration points through the thickness, three for each lamina. Orientation and material properties of the laminae have been associated to these points. The stacking sequence (Fig. 1.b) of the laminate is a quasi-isotropic one, [0/90/45/-45] s . Laminae are modelled by referring to the material properties shown in Table 1. 2.1. Impact FE model

Table 1. Unidirectional lamina material proprieties. Longitudinal Young Modulus, E 11

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Critical ERR-MODE II, G IIIC Longitudinal tensile strength X t Longitudinal compressive strength X c Transverse tensile strength Y t = Z t Transverse compressive strength Y c = Z c

103.05 GPa 11.55 GPa

500 J·m

Transverse Young Modulus, E 22 = E 33 In Plane Shear Modulus, G 12 = G 13

1460.7 MPa 876.42 MPa 77.145 MPa 241.43 MPa

6 GPa 6 GPa 0.312

In Plane Shear Modulus, G 23

Poisson ratio, ν 12 = ν 13

Poisson ratio, ν 23

Shear strength S 12 = S 13

0.49

90 MPa 40 MPa

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Critical ERR-MODE I, G IC Critical ERR-MODE II, G IIC

Shear strength S 23

180 J·m 500 J·m

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Ply thickness

0.312 mm

No damping factors have been defined in the material properties of the plate, in order to save computational costs. A consequence may be a slight delay between experimental and numerical signals, which is an acceptable approximation for the main goal of this work. The average characteristic length of the finite elements of the plate model is 0.5 mm. Then, the plate model counts a total of 160801 nodes and 160000 elements. The impactor, modelled by discrete-rigid-elements (R3D4, from the Abaqus elements’ lib rary), consists of a 19 mm diameter hemispherical drop mass. The impactor is