Time Domain Spectral Finite Element Simulation of Ultrasonic Wave Propagation in Composite with Defects

Abstract

Ultrasonic guided wave-based detection of structural defects or damages is one of the promising methods for structural health monitoring (SHM). A significant proportion of structural elements in an aircraft structure and other civil and marine structures are thin structures and those components can be monitored using ultrasonic guided wave. Piezoelectric transducers have been extensively applied to ultrasonic wave based non-destructive inspection (NDI). SHM is considered an extension of NDI adding a new dimension to the way future structures will be designed. In recent years, research on the behavior of guided wave in structures, especially targeted for aerospace application, received enormous significance. Guided wave interaction with structural features and defects/damages creates complicated wave field patterns. Experimental observation is limited to the availability of sophisticated instrumentation and tomography techniques to visualize the wave pattern even on the surface of a structure and simulation is the only way various details regarding internal patterns of the waves in a complex geometry can be analyzed. Analytical approach to deal with the wave propagation in a structure is limited to simple geometries and simple forms of damage. Guided wave in a simple geometry like beam/plate is modeled using analytical as well as semi-analytical methods. But when it comes to complicated problems like structures with actual damage/fracture or geometrical complexity which includes curvature and components with joints etc., one requires efficient computational schemes to simulate the behavior. Contents x There are various numerical tools developed in last few decades, such as finite difference, finite element, boundary element methods etc. In high frequency guided wave propagation problems, higher-order modes participate. Moreover, to detect a small damage, a high-frequency wave is needed. To deal with such kind of problems incorporating standard polynomial incorporation based finite element schemes need very fine mesh, which makes the computations of such problem enormously expensive, sometimes prohibitive. Time domain spectral element (TSFE) method is an efficient numerical method that can capture higher order field and therefore can deal with wave propagation problems efficiently and with better accuracy. TSFE uses higher order highly convergent interpolation functions based on the Chebyshev or Lobatto nodal distributions. TSFE based on the Lobatto nodal distribution and Legendre-Lobatto quadrature rule makes the mass matrix diagonal, which reduces the computer memory requirement to a great extent. As the number of nodes increases, accuracy increases exponentially and hence the term spectral finite element. The present thesis incorporates this idea and formulates a TSFE scheme to simulate guided wave propagation in laminated composite materials with damages such as material uncertainty/degradation, micro-cracks, and delaminations. Various benchmark problems are solved to validate the simulated results and establish superior convergence properties. Because of anisotropy of composite laminate and direction dependent properties of its constituent, composite laminate has various damage modes including matrix crack, fiber break, delamination etc. Among those damage modes, in this thesis, a special focus is given on delamination detection problem as it grows in the interfacial plane under repeated loading and reduces load-carrying capability to a great extent. Those damage modes are internal hence invisible. In wave propagation based detection methods, delamination can be identified and localized from the wave scattering from it. But it is of great interest to quantify the damage in terms of various parameters such as delamination length as well as the thickness and position of the laminate. Delamination scatters an incident wave and the strength of the reflection depends on the frequency/wavelength, length and thickness position of the delamination for a given structure. Simulation results show that the near-field effect of the damaged region provides crucial information about the scattering and reflected wave characteristics. Delamination in a laminate divides the damaged region into sub-laminates which are thinner compared to the base laminate. Each sub-laminate behaves like a separate waveguide. The vibration of the sub-laminates during the propagation of the wave through the damaged region Contents xi is of great interest. The energy of scattered waves and dissipation/conversion of energy due to the damage depends on the resonance characteristics of the sub-laminates. Therefore, the resonance phenomenon is correlated to the damage quantification problem with the help of simulation. Detection of damage near the structural boundary is one of the most challenging tasks as the scattering from the damage is overlapped by the strong reflection from the boundary. Effect of incident wave frequency/wavelength on the delamination near a structural boundary is studied. Damaged region behaves like the material degradation and in some frequency range the energy is trapped inside the damaged region and slow dissipation/conversion of the trapped energy into other forms of vibration creates a significant difference in the reflected wave and the simulated results help to identify the presence of damage. Impact-induced damage in composite has a great influence on the integrity and life of a composite structure. In most cases, initially, it develops material degradation in terms of matrix cracks at micro-scale. Although in composite structural design, micro-scale matrix cracks are not considered, however, as these micro-cracks coalesce, it gives initiate delamination. Under a severe dynamic impact loading, such small size delamination can grow and can lead to catastrophic failure of the structure. Ultrasonic wave propagation in composite with matrix crack is one of the major subjects of study which can predict the delamination onset in the composite. In the present thesis, wave scattering due to matrix cracks is studied and behavior of wave reflection from matrix cracking zone is investigated for various damage severity, which is expressed in terms of matrix crack density. Moreover, the matrix cracks along with delamination initiated from the zone, which is a kind of mixed-mode damage zone, appears more commonly in a composite structure than an ideal single-mode damage like a sharp crack or delamination. A mixed-mode damage complicates the modeling problem to be dealt with considering complex nature of near-field scattering of the incident wave. In the present thesis, this aspect is studied in details and damage severity effects are correlated to the scattered wave packet properties. Guided wave has a special characteristic that it is guided by the material media geometrically even when the structure is curved. This advantage can be exploited in developing damage detection scheme, for example, by bringing the scattered wave field located behind the curvature in a structural component without direct access to the surface where inspection cannot be carried out using local methods. Another important aspect of Contents xii guided wave is that propagation through a curved region not only produces reflection, it also generates mode converted waves which appear in both the reflected and transmitted waves. In the present thesis, wave transmissibility and signal loss at various frequencies and the effect of the radius of curvature is studied in detail. The simulation results provide a new insight regarding the wave mode and frequency for inspection for a given curved structure. Delamination near the curved region and T-joint is modeled and simulation shows correlation where the wave scattering due to delamination is possible to discriminate from that due to curved junctions. In composite, material uncertainty is inherent because of limited control over the fabrication processes, which in turn affects the proportion of the constituent materials or the fiber orientation. Significant material property variation can take place due to the variability in fiber volume fraction or the distortion in the stacking angle. The location of a damage and various other parameters are directly influenced by the material property variations. Therefore, the deterministic study is not sufficient to deal with these problems. In the present thesis, a Monte-Carlo method based simulation of wave scattering is carried out. The study primarily focuses on the problem of quantification of uncertainty in various damage detection parameters such as wave scattering coefficient and variation in the time of flight of the scattered packet, wave velocity etc. Detailed analysis is carried out regarding how the simulation based inspection method can be developed that gives better insight on the probabilistic distribution of the detection parameters of interests.