This work aims to obtain a quantitative estimate of stiffness reduction in cross-ply laminates due to transverse cracks in 90-degree plies. The received Lamb wave signal in the pitch-catch transmission mode is expressed in terms of stress wave factors (SWFs) employing certain functions of the power spectral density of the received wave. The stiffness reduction in the laminate is deduced by a correlation with the stress wave factors (SWFs). The use of SWFs for damage quantification has been investigated in a previous experimental study. In the current work, cross-ply laminates of different configurations are modeled in Abaqus. The stiffness degradation due to transverse cracks is represented by a homogenized reduction of transverse Young’s modulus (E2) and in-plane shear modulus (G23) in the 90-degree plies of the laminate. When a Lamb wave propagates through a region of reduced elastic properties, reductions in the amplitude and speed of the propagating wave are expected due to the effective stiffness loss in the direction of wave propagation. One of the measured factors, SWF1, is found to capture this loss and shows a linear correlation with the laminate stiffness reduction. It is indicated that a quantitative assessment of the Lamb wave propagation in composites with damage is possible with a statistical measure of the received signal.
A classification strategy with a deep learning model to categorize stiffness reduction in cross-ply laminates from transverse cracks is presented. Deep learning models are very successful in image-based classification which can be conveniently used on structural health monitoring data. In the current study, the transverse cracks in 90-degree pliés are modeled with a finite element model in Abaqus; and are solved for fundamental Lamb wave modes (symmetric S0 and antisymmetric A0) independently. The data from the simulation models are grouped into three different classes of stiffness ranges depending on the associated crack density in the 90-degree pliés. The time-domain data for each case is then post-processed with continuous wavelet transforms, and Hilbert transforms to obtain a featured information representation with visual images. The digital image from the database is represented as a matrix encoded in red-green-blue channels (RGB matrix) and is used as an input to train a convolution neural network (CNN) model to perform a categorical classification. The results from the test and validation data obtained for identical configuration and excitation frequency show that the CNN model can classify an image into respective stiffness categories accurately. The proposed model is applied successfully on cross-ply laminates of different configurations delivering a satisfactory performance with excellent validation and test accuracy, demonstrating the potential for developing a deep learning-based tool to classify and quantify damage in composite structures.
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