PSI - Issue 5

Mikhail Tashkinov et al. / Procedia Structural Integrity 5 (2017) 577–583 Mikhail Tashkinov et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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1. Introduction

Composite materials are a common solution for creating highly demanding structures for industry and engineering applications. A topical issue is a comprehensive study of the behavior of composites structures under typical operational loads in order to optimize the functional properties that can be predetermined at the production stage. The most widely used laminate composite structures consist of layers of prepreg carbon and fiberglass. Despite the unique strength characteristics, composite materials are subject to a number of operational defects under certain loads, which can not be inspected with the naked eye. However, such defects can lead to critical damage and loss of structural load capacity. In this connection, the methods of nondestructive testing of composite structures are being actively developed. They allow to obtain information on the state of the structure during its operation. One of the common solutions is measurement of the internal state of structures using fiber-optic sensors. Studies in this field are presented in the works of de Oliveira et al. (2004), Lebid et al. (2004), Kuang et al. (2001) and others. Such sensors can be embedded between layers of the composite laminate without compromising the overall mechanical properties. Depending on the technology, fiber-optic sensors are able to detect changes in deformation fields, temperatures, etc. Fiber-optic sensors with Bragg gratings (FBG sensors), which principle is based on a registration of changes in the transmitted light wavelength under external influence, has become widespread. Recent results in this area were obtained by Dong et al. (2013), Kim et al. (2015), Tserpes et al. (2014) and others. While designing composite structures special attention is paid to modeling of mechanical behavior, which makes it possible to avoid costly and resource-consuming experiments. To create models of the required accuracy it is necessary to determine the initial mechanical constants characterizing the behavior of a particular microstructural component, laminate or the entire material at the macro-scale level. As a rule, mechanical tests are conducted for this purpose, together with analytical theories connecting characteristics of structural elements at various scales.

Nomenclature FBG fiber Bragg gratings sensors strains, obtained from FBG sensors calculated strains vector of material elastic constants applied load Jacobian of a function ̇ weight coefficients L-M Levenberg-Marquardt algorithm

Levenberg-Marquardt algorithm parameter

However, due to the peculiarities of the composite structures ’ manufacturing processes, the properties of the components implemented in the structure may differ from those obtained in experimental studies. This discrepancy can introduce a significant error in the mathematical models of composite structures, which requires correction of the initial mechanical characteristics and bringing them in correspondence with the real properties of the existing structures. This article is devoted to development of the approach in which indications of embedded FBG sensors are used for refinement of the mechanical characteristics of isotropic composite materials used in numerical models. The aim of the approach is optimization of the model constants basing on estimation of the difference between the deformation response, predicted using the model, and the data obtained via real time using monitoring tools. 2. Reverse problem statement In this article, the technique is described in relation to composite laminates, the effective properties of layers of which can be considered quasi-isotropic and brittle, subjected to elastic deformation. At the initial stage, there is a