Damage detection using GUWs is really promising but the complexities involved during ultrasonic measurements cannot be faced without resort to theoretical aspects and modeling. In this context the introduction of simulations can aid the research and development because they are suited to:
• remove uncertainties related to measurements which prevent to clarify method-ology criticalities (consider the case of phantom damage or dispersion effect on ToF analysis);
• introduce parametric investigations which cannot be experimentally conducted (i.e. effects of location, dimension and severity of damage);
• set new strategies based on the system characteristics revealed by simulations;
• reduce costs and time of experimental campaigns;
• quantify the performances of the system under variable conditions.
However to fulfill the whole range of aiding purpose while dealing with simulated environments for GUWs-based SHM implementation and verification, it is desirable to have:
• a reasonable propagation simulation of the selected Lamb wave mode;
• a damage interaction simulation in line with experiments while oriented to similar flaw identification (i.e. reasonable results in terms of DI);
• a rigorous replication of the operating environment in which the structure is monitored.
Such requirements define the multi-side validation required to release an effective and efficient modeling environment suited for reproducing the experiment peculiarities and to improve the methodologies.
With regards to the global SHM approach using direct propagating waves, the first requirement can be verified through a wave field analysis in order to intercept the cor-rect behavior of A0 mode propagating in the structure, such as the characterization proposed in Sec. 4.1 based on considering dispersive and pattern behaviour as com-parative items and verification criteria. The second condition implies that the damage
. ∼ Multi-side validation for global damage detection
has to be appropriately simulated looking at: (i) the conformation of damage induced by impact on the structure and (ii) the sensitivity to damage dimension in terms of extracted features.
Regardless the former aspects, investigated in detail in the following sections, the third requirement is crucial for the reproducibility of the damage detection system within simulated environments. Although the proposed global SHM approach leads to a reliable identification, measurements carried out both on the undamaged and dam-aged structures show that the same structural configuration interrogated at different times returns non zero values of damage indicators. The noise in the signal response does not allow to clearly distinguish between noisy and significant response. As a con-sequence, it happens that some paths that are indeed affected by the damage do not show a response suggesting the presence of such damage. Moreover, in such cases the change in signal response can be relevant even if no changes occur. In the first case, the decision-making strategy leads to a non-correct censure of the signal response.
Instead, a false alarm occurs in the second case. From a practical point of view, the operating environment in which the structure is monitored may be very variable and it appears to be very difficult to keep repeatability at small values. Slightly different measurement conditions could lead to significant changes in the signal response with a misinterpretation of results. From the experimental standpoint, these events can be analyzed using a statistical approach, namely the decision making framework to select the paths indeed affected by the damage. Instead, when a simulated environment is considered, no such variations can be appreciated due to repeatability and repro-ducibility of the simulations. Indeed, the SHM algorithm should be able to gather correct information in each type of monitoring condition, and a correct model assisted analysis should take in consideration this aspect.
To account for the uncertainties of environmental conditions, two different strate-gies can be followed:
• introduce appropriate variability in the source model achieving a multiple dataset by multiple simulations;
• introduce appropriate variability in the output of a single simulated interroga-tion;
For saving time considerably, the second approach is pursued and the generic recorded signal s(t) is modeled as filtered Gaussian white noise adding white Gaussian noise η(t)to the simulated time history:
y(t) = s(t) + η(t) (4.4)
. ∼ Multi-side validation for global damage detection
Figure 4.13: Numerical time histories of A0mode without (a) and with (b) added noise.
The pseudo experimental data generation is focused on the energy of the captured sig-nal. The random noise η(t) is added looking for the same sensitivity index. According to the decision-making procedure, once the system noise is characterized in term of mean and variance of the normal distribution fitted on that index, random numbers are generated to obtain the same variability with the same number of samples and the simulated experimental noise is added with numerical signals. An example of the effect of noise introduction is showed in Figure 4.13. In this way, different simulated measurementsare obtained for each couple of PZTs and for each structural condition, as in the experimental case. Then the making decision procedure can be employed as well as after a measurement stage.
About the other validation items, generally, in addition to their inherent simplicity and low computational cost, ESL models often provide a sufficiently accurate descrip-tion of global response for thin and moderately thick laminates. Among these theories, the FSDT provides the best compromise between solution accuracy, economy and sim-plicity, as demonstrated in Sec. 4.1. However, the ESL models have limitations that prevent them from being used to solve the whole spectrum of composite laminate problems:
• the accuracy of the global response predicted by the ESL models deteriorates as the laminate becomes thicker;
• the ESL models are often incapable of accurately describing the state of stress and strain at the ply level near geometric and material discontinuities or near regions of intense loading (which are the areas where accurate evaluations are mostly needed).
In the next sections the other numerical aspects are explained in detail looking at verify the aforementioned conditions to avoid any lack of agreement with measurements.
. ∼ Multi-side validation for global damage detection
Stacking sequence Dimensions [5H/B45/U/B/U/B45/U/B]s 600 × 600 × 1.6[mm3]
Table 4.4:Lamination sequence of the 6mm-thick bay of the tapered wing panel presented in Sec. 3.1.2.
Properties Biaxial Uniaxial 5Harness
ρ [kg/m3] 1790 1790 1770
E1[MPa] 81000 152000 158420
E2= E3 [MPa] 8800 8800 8800
G12= G13= G23 [MPa] 4100 4100 3600
ν12= ν13= ν23 0.31 0.31 0.31
Table 4.5:Elastic properties of graphite-epoxy laminae adopted for the 6mm-thick bay of the tapered wing panel presented in Sec. 3.1.2.
4.2.1 Wavefield simulation
The 6mm-thick bay of the tapered wing panel presented in Sec. 3.1.2 is discretized resorting to a 600mm × 600mm × 6mm layered composite plate on which 12 PZT transducers are mounted and arranged in a circular network. The plate is laminated using unidirectional laminae with fibers along 0° (UD) and biaxial laminae with orien-tation 0°/90° (B) and ±45° (B45) which are stacked between 5Harness (5H) external plies according to Table 4.4. The plies are discretized as single layers modeling the material properties reported in Table 4.5 and material orientation according to the stacking sequence. The behavior of laminates respect to the wave propagation shows many complexities. From a practical point of view, propagating waves result in signals acquired through an array of sensors distributed over a structure. They are indeed affected by the material characteristics, including the level of anisotropy, the layered stacking through the thickness and geometric discontinuities (such as thickness vari-ation), frequency of excitation and boundaries, generating scattering, diffraction and reflection of the waves. A congruent request is that the numerical modeling assump-tions allow to respect the discussed dependencies. According to the characterization carried out in Sec. 4.1, the dispersive behavior is indeed a key validation tool if the direct waves are considered for damage detection.
The ESL approach is here again adopted for transient finite element analysis of wave propagation. The ABAQUS/Explicit® code is used to integrate the dynamic problem to evaluate the group velocity of the first antisymmetric Lamb wave mode in order to compare the observed response with the calculated one. In detail, the
. ∼ Multi-side validation for global damage detection
Figure 4.14:Overall scheme adopted in the simulation environment for the arrival time correlation (a) and group velocity comparison along several directions at 60kHz (b). Maximum percentage error, 5%.
FSDT is used to idealize the structure with an equivalent layer. To this purpose, the S4R element available in the ABAQUS/Explicit®is adopted again correcting the transverse shear inconsistency of FSDT introducing an SCF equal to 56, according to the evidence shown in [170, 171, 172] when a large number of plies are considered.
About the plate idealization, the mesh density is chosen to be sufficiently small to resolve the characteristic wavelength and correctly capture the desired 60kHz wavefield (i.e.: the interrogation frequency) response resulting in a 1mm×1mm mesh. All sensors are discretized as single nodes because they have very small size when compared to the distance between sensors, and their local effect on the global wavefield behavior can be neglected. The central PZT actuator is constrained with an out of plane displacement using a windwed 4.5 cycles sine burst in time domain. The out of plane displacements in the 12 PZT receivers located on the circular pattern (φ = 300mm) is registered to evaluate the arrival time in several directions, as depicted in Figure 4.14 (a). The STFT method is adopted to calculate the arrival time and thus group velocity, whose comparison with measurement outcomes in Figure 4.14 (b) highlights the reasonable result obtained. Indeed, the maximum percentage error of 5% is obtained.
Again the FSDT-based ESL approach, with which the laminate is idealized as a single layer with the same stiffness properties of the pristine structure, provides a good balance between computational efficiency and accuracy for the global structural behavior in wave propagation problems if the transverse shear effects are correctly ad-dressed. Then, the final crucial aspect deals with the damage idealization, as explained in the next section.
. ∼ Multi-side validation for global damage detection
4.2.2 Damage modeling
It is worth noting that the modeling stage for monitoring purpose needs the prediction of the wave-damage interaction, whose characteristics depend upon the idealization approach as well. Obviously, the unknown nature of the hidden flaw requires a com-prehensive analysis of the specific type of damage in the reality. In the case of impact induced damage, it is very difficult to imagine the material degradation when a barely visible damage (BVID) appears. From a theoretical standpoint, it can be seen as a complex discontinuity through the thickness. By definition, a discontinuity in a waveg-uide is an abrupt change of the gwaveg-uide’s characteristics along its propagation direction.
Composite panels can be characterized by the presence of inner discontinuities related to the local change of cross-section along the panel length. As aforementioned, at these discontinuities are called “delaminations” to indicate the separation between plies in a composite laminated panel. However the induced damage is not simply a unique sepa-ration between adjacent layers. In order to understand what really happens within the multilayered plate due to the impact load, a comprehensive non destructive evalua-tion (NDE) is performed through Olympus®Omniscan MX1 on the panel upper side.
The C-scan image in Figure 4.15 shows the overall extension of the hidden flaws in the x-y plane but does not gather information on the flaw severity trough the thickness.
Instead, the B-scan and S-scan images reveal the complex discontinuity. Although the indentation is barely visible, the whole thickness appears to be affected by de-laminations and intralaminar cracks, in a completely non continuous stacking through the thickness. A similar result is obtained performing the NDE on the plate lower side, confirming the “tapered-conical” defect. Due to such NDI results, the damage is simulated via local stiffness degradation in the finite element formulation. Indeed, the stiffness matrix of a structural system depends upon the material properties, ge-ometry and boundary condition. Even if from a theoretical point of view a single delamination do not leads to a high global stiffness reduction, the through thickness complex discontinuity shown in Figure 4.15 as a combination of intralaminar and in-terlaminar damages justifies the stiffness reduction approach, already proposed in the literature for several purposes [173] and here simulated adopting degraded elements within ABAQUS®environment. In specific, the structure is divided in a set of finite areas discretized into a set of finite elements categorized into undamaged or damaged states with different degradation levels through the thickness. The damage parameters available are the in plane extension and depth of the damage, the degradation level of the finite elements, and the shape and conformity of the damage. For validation purpose, a quadrilateral region with degraded stiffness is discretized to idealize the damage, keeping a structured mesh as well. Then, the experimental methodology is replicated with few efforts in the simulated environment and the DIs are evaluated
. ∼ Multi-side validation for global damage detection
Figure 4.15:Non destructive evaluation of the impact induced damage. C-scan (a), B-scan (b) and S-scan (c) of the impacted region. Scan length, 200mm.
d[mm] t[mm] DI [%]
10 2.25 5
15 3.0 13
20 3.75 22
20 4.5 25
25 3.75 25
25 4.5 42
Table 4.6:Damage indicators obtained in the simulated environment for different damage dimensions.
along damaged and undamaged lines of sight under several conditions. Considering the in-plane dimensions of the hidden flaw set to d × dmm2 and a given depth of t[mm] along the thickness, few results obtained along a damaged path are reported in Table 4.6. The severity of the damage is well appreciated and both the in-plane dimension and depth of the damage appear to be parameters which can be evaluated from propagation analysis. The results obtained are again reasonable, correctly show-ing an effective change when such damage is simulated along the corresponded line of sight and no change when the damage is far from the line of sight (i.e. before the introduction of a noisy level).
. ∼ Monitoring and model assisted perspectives
Figure 4.16:Tomographic analysis of the investigated panel in the simulated environment. Map of damage (a) and contour of isolevel curves (b).