Spatial Wavelet Approach to Local Matrix Crack Detection in Composite Beams with Ply Level Material Uncertainty
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Spatial Wavelet Approach to Local Matrix Crack Detection in Composite Beams with Ply Level Material Uncertainty G. Sarangapani · Ranjan Ganguli · C. R. L. Murthy
Received: 8 August 2012 / Accepted: 1 October 2012 / Published online: 20 October 2012 © Springer Science+Business Media Dordrecht 2012
Abstract Wavelet coefficients based on spatial wavelets are used as damage indicators to identify the damage location as well as the size of the damage in a laminated composite beam with localized matrix cracks. A finite element model of the composite beam is used in conjunction with a matrix crack based damage model to simulate the damaged composite beam structure. The modes of vibration of the beam are analyzed using the wavelet transform in order to identify the location and the extent of the damage by sensing the local perturbations at the damage locations. The location of the damage is identified by a sudden change in spatial distribution of wavelet coefficients. Monte Carlo Simulations (MCS) are used to investigate the effect of ply level uncertainty in composite material properties such as ply longitudinal stiffness, transverse stiffness, shear modulus and Poisson’s ratio on damage detection parameter, wavelet coefficient. In this study, numerical simulations are done for single and multiple damage cases. It is observed that spatial wavelets can be used as a reliable damage detection tool for composite beams with localized matrix cracks which can result from low velocity impact damage. Keywords Spatial wavelet · Matrix crack · Gabor wavelet · Damage detection · Composite beam · Monte Carlo Simulation
G. Sarangapani · R. Ganguli (B) · C. R. L. Murthy Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India e-mail: [email protected] G. Sarangapani e-mail: [email protected] C. R. L. Murthy e-mail: [email protected]
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Appl Compos Mater (2013) 20:719–746
1 Introduction In composite structures, the failure analysis is much more complicated than traditional metallic structures due to various damage mechanisms such as delamination, fiber-matrix debonding, fiber breakage, fiber pull-out and matrix cracking [1–4]. Matrix cracking is the result of formation of random micro cracks and their coalescence under load. The onset of matrix cracking is controlled by ply thickness and the constraining effect of adjacent plies [5]. Applied stress and the constraints provided by neighboring plies cause increase in matrix crack density proportionally. The stiffness of the matrix which is much lower than the fiber stiffness causes substantial amount of strain magnification in the matrix during transverse loading of plies. Among the aforementioned failure modes in composite structures, the first mode of failure observed is matrix cracking parallel to the fibers in the off-axis plies. The failure strains of off-axis plies are smaller than the plies which are aligned in the loading direction. In each ply, the process of matrix cracking may continue until the cracks in eac
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