Diagnostic Method for Delamination Monitoring of CFRP Plate using Kriging Interpolation Method

The present paper proposes a new diagnostic tool for the structural health monitoring that employs a Kriging Interpolation. Structural health monitoring is a noticeable technology for aged civil structures. Most of the structural health monitoring systems adopts parametric method based on modeling or non-parametric method such as artificial neural networks or response surfaces. The conventional methods require FEM modeling of structure or a regression model. This modeling needs judgment of human, and it requires much costs. The present method does not require the process of modeling, in order to identify the damage level using the discriminant analysis. This suggest us, this technique is applicable to the health monitoring system, which identifies the damage of the structure, easily. In the present paper, we developed the damage diagnostic methods using Kriging method for identifying delamination from data. Kriging method is a interpolation technique which shown in geostatistic. We applied this method to identifications of delamination crack of CFRP structure. Delamination cracks are invisible and cause decrease of compression strength of laminated composites. Therefore, health-monitoring system is required for CFRP laminates. The present study adopts an electric potential method for health monitoring of graphite/epoxy laminated composites. The electric potential method does not cause strength reduction and can be applied existing structures by low cost. As a result, it was shown that this method is effective for identification of damages. Introduction CFRP has high specific tensile strength and stiffness, and are good for the major structures of airplanes and space instruments. The intensity between the layers of CFRP is weak and delamination cracks between layers can be produced by a comparatively slight impact. Such delamination cracks are invisible and cause a decrease of the compression strength of laminated composites. Therefore, a method for diagnosing delamination cracks in laminated composites is required. The present study adopts an electrical potential method for the diagnosis of delaminations in CFRP laminates. Since carbon fiber in a composite material has conductivity, by using an electric potential method, the damage present in a large area of a structure can be diagnosed by conducting electricity through composite structure. The electric potential method does not cause strength reduction and can be applied to existing structures at a low cost. The present study focuses on the electrical potential method of detecting damage in CFRP in the form of delamination cracks. Recently, many studies have described an electric resistance change method to identify internal damage in CFRP laminates [1,2]. The electric resistance change method does not require expensive instruments. Since the method adopts reinforced carbon fiber itself as sensors for damage detection, this method does not cause a reduction in static strength or fatigue strength, and it is applicable to existing structures. The effectiveness of the electric potential method has been demonstrated in our previous reports [3,4]. In these studies, a delamination crack in a composite beam was identified based on the change in electric potential between electrodes attached to the surface of the composite beam. Key Engineering Materials Vols. 353-358 (2007) pp 1422-1426 online at http://www.scientific.net © (2007) Trans Tech Publications, Switzerland Online available since 2007/Sep/10 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.33-14/04/08,13:10:01) The relation between the delamination crack and the change in electric potential is identified by solving an inverse problem. The inverse problem in damage identification is an optimization problems involving estimation error minimization, and is usually solved through the use of such common optimization tools as neural network and genetic algorithm. But in general, trial and error processes are required to derive optimum solutions when using these methods, and these processes demand much calculation and human cost. We thus propose a method that identifies damage based on statistical analyses for the purpose of constructing a simple method for damage identification. In this method, we use the kriging interpolation as solver for inverse problem. Using the kriging interpolation, damage identification that requires only simple calculation can be performed. In this study, this new method is applied to identify delamination cracks in CFRP beams using the electric potential method. The effectiveness of this method is investigated analytically. Identification of delamination in a CFRP beam using electric potential method Analytical model. As mentioned previously, this method for damage diagnosis is applied to the identification of delaminations in a CFRP Beam, and the accuracy of the method is experimentally investigated. FEM analyses are employed for investigations in present study. A detailed description of FEM analysis is provided in our previous studies [3]. The configuration of the specimen used in the present study is shown in Figure 1. The specimen is a CFRP Beam with a thickness of 2mm and a stacking sequence of [02/902]s. In order to measure the change in electric potential caused by a delamination crack, seven electrodes are mounted on the one surface of specimen. The lengths of the electrodes are 10mm. FEM analyses were performed using the commercially available FEM tool named ANSYS. In the present study, four-node-rectangular elements are adopted for analysis; each element is approximately 0.125 mm by 0.125 mm. The specimen model was divided into 28,160 2D elements using the auto-mesh generation system of the ANSYS. A delamination crack is modeled by the release of a nodal point of the element. The electric conductance ratio is obtained from an experimental result regarding a CFRP laminate whose volume fraction is 62% as shown in Table 1. Procedure for identifying delamination crack. The procedure for identifying a delamination crack using ordinal kriging is as follows: (1) to (3) show the procedure for creating the model variogram(as follow) and (4) to (7) show the procedure for the identification of individual. (1) The change in electric potential is measured in the various sizes and locations of delamination cracks. These data are referred to as data for learning. (2) The variogram cloud and the empirical variogram are created based on the data for learning. (3) Decision of the variogram model, and optimization of the model. (4) New data is measured for estimation. This data is referred to as individual. (5) Calculation of the weight matrix. (6) Estimation of the individual using the ordinal kriging(as follow). In this study, cross inspections of 474 data are conducted. One data is selected as individual, and the ordinal kriging matrixs are created from other 473 data. This procedure is performed 474 times. In order to simplify the calculations, procedure (2) and (3) are conducted by using all the data. Kriging Interpolation. Kriging interpolation is one of statistical interpolation method used in geostatistic[5]. The kriging interpolation is used for estimation of parameters which fluctuate depending on space coordinates. The method is mainly used for quality presumption of a mine and a water resources or weather forecast. By the kriging interpolation, the value of arbitrary coordinates is Table.1 Electric conductivity of the specimen σ0° 5535[Ω] σ90°/σ0° 3.71×10 -2 σtickness/σ0° 3.77×10 -3 Fig. 1 Specimen configuration ε 2