Delamination Modeling and Detection in Composite Structures
Keshava Kumar, S
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Composite laminated structures are prone to delamination. Rotorcraft flexbeams, apart from many other aerospace primary load carrying members are made up of composite laminated structures. A delaminated primary load carrying member can lead to catastrophic failure of the system of which it is a part. Delamination modeling and detection in composite laminated structures are challenging areas of ongoing research worldwide. Existing literature falls short of addressing effects of widthwise partial delamination on the modal characteristics of beams. To address this issue, a new partial delamination model for composite beams is proposed and implemented using the finite element method. Homogenized cross-sectional stiffness of the delaminated beam is obtained by the proposed analytical technique, including extension-bending, extension-twist and torsion-bending coupling terms, and hence can be used with an existing finite element method. A two-noded C1-type Timoshenko beam element with four degrees of freedom per node for dynamic analysis of beams is implemented. The results for different delamination scenarios and beams subjected to different boundary conditions are validated with available experimental results in the literature and/or with a 3-D finite element simulation using COMSOL. Results of the first torsional mode frequency for the partially delaminated beam are validated with the COMSOL results. The key point of the current work is that even partial delamination in long structures can be analyzed using a 1-D beam model, rather than using computationally more demanding 3-D or 2-D models. Rotor craft flexbeams are prone to delaminations, which in most realistic situations are partial along both the length and the width. However, the effect of partial delamination on the modal characteristics of the beam is not studied by researchers to the best of the author’s knowledge. Addressing this issue, a rotorcraft flexbeam is analysed here in the presence of delamination. A set of nonlinear governing equations for the rotating flexbeam are developed in hybrid basis. The ﬂexbeam model developed has axial stretch, transverse displacement and flexural rotation in flapwise direction and twist as its degrees of freedom. The nonlinear governing differential equations are linearised and solved for eigenvalues and eigenvectors using a finite element method. The effects of angular speed and delamination size and location on the ﬂexbeam modes are analysed. The results obtained using the proposed model are validated with the COMSOL 3-D finite element simulations. Next, the issue of delamination detection in beams is addressed. Mode shape curvature and Katz fractal dimension are used to detect the presence of partial delaminations in a beam. The effects of boundary conditions and location of delamination on the fractal dimension curve are studied. Usage of higher mode shape data for detection of delamination in beams is evaluated. Limitations of the Katz fractal dimension curve for delamination detection are enumerated. It is shown that fractal dimension measure and mode shape curvature can be used to detect the presence of partial delamination in beams. It is found that the torsional mode shape is best suited for partial delamination detection in beams. Apart from beams, Shell-and plate-like structures are also extensively used in aerospace structures. The modeling of multilayered plates is introduced herein with the intention to model delaminations in 2D. Carrera Unified Formulation(CUF)plate model, developed using variational formulations, is used to derive the stiffness matrices and to apply, the Principle of Virtual Displacement(PVD) and the Reissner Mixed Variational Theorem (RMVT). It is known that FEM implementation for plates leads to the phenomenon of numerical locking: the so-called membrane and shear locking effects. A well-known remedy for addressing locking is the use of the Mixed Interpolated Tensorial Components(MITC) technique. A strategy similar to MITC approach in the RMVT formulation is used to construct an advanced locking-free finite element to treat the multilayered plates. Composite laminated plates are prone to delamination. Implementation of delamination in the CUF frame work using nine-noded quadrilateral MITC9 elements is discussed. MITC9 elements are devoid of shear locking and membrane locking. Delaminated structures, as well as the corresponding healthy structures, are analysed for free vibration modes. The results from the present work are compared with those from available experimental or/and theoretical research articles or/and the 3-D finite element simulations. The effects of different kinds and different percentages of interfacial area of delaminations on the first three natural frequencies of the structure are discussed. The presence of the open-mode or breathing mode delamination mode shape for large delaminations within the first three natural frequencies is discussed. Also, the switching of the places between the second bending mode and the first torsional mode frequencies is discussed. Results obtained from different ordered theories are compared in the presence of delamination. Advantage of layer wise theory as compared to equivalent single layer theories for very large delaminations is stated. The effects of different kinds of delamination and its effect on the second bending and first torsional mode shapes are discussed.
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