Structural Behaviour and Failure Analysis of CNT Reinforced Composite Plates in Hygro-Thermal Environment

Abstract

The present work deals with the formulation of inverse hyperbolic shear deformation theory (IHSDT) for modeling and analysis of carbon nanotube (CNT) reinforced plates. The theory is developed in the framework of non-polynomial shear strain function in term of shear deformation theory. The displacement field is chosen in such a way that it satisfies the zero transverse shear stress conditions at the top and bottom of the plate in thickness direction and does not require a shear correction factor. The effect of in-plane shear deformation in the displacements is defined using the shear strain shape function in terms of inverse hyperbolic function. The structural response of CNT reinforced plates is examined under the action of mechanical, thermal and moisture conditions. Firstly, the effective material properties are assumed to be temperature dependent and estimated according to the extended rule of mixture. Four types of distributions such as uniformly distributed (UD) and functionally graded (FG-V, FG-O and FG-X) are considered to reinforce the CNT in the matrix material (PmPV and PMMA). The structural responses are computed in analytical form as well as in the numerical so as to enhance the generality of the developed methodology. The closed form solutions are computed for structural response (bending, buckling and free vibration) of simply supported CNT reinforced plates using Navier approach. The validation of obtained results are demonstrated successfully by comparing with the other existing methodologies available in the literature. Further, to enhance the applicability, a C0 continuous eight noded isoparametric serendipity finite element methodology is developed using IHSDT. The developed finite element methodology is implemented to examine the static, buckling and free vibration behavior of temperature dependent CNT reinforced plates. The influence of the various parameters (volume fraction, span to thickness ratio, aspect ratio, distribution of CNT and boundary conditions) on non-dimensional central deflection, buckling load parameter and fundamental frequency are investigated in different temperature conditions. Furthermore, in order to consider the effect of hygro-thermo-mechanical conditions on the response of CNT reinforced plate, the Navier type and C0 finite element methodologies are developed. The validation of obtained results is presented by comparing the Navier type closed form solution with the numerical FE solution and it is concluded that the percentage between the closed form solution (CFS) and FE solution is ranging between 0.3-1 % for simply supported boundary conditions (SSSS). The new results are presented for dimensional central deflection of CNT reinforced plate subject to uniformly distributed linear and non-linear temperature and moisture environment. The influence of various parameters such as volume fraction, span to thickness ratio, distribution of CNT and boundary conditions on the dimensional central deflection are examined for CNT reinforced plates in the hygro-thermal environment. Finally, the emphasis has been focused to examine the effect of presence of the crack in FG-CNT reinforced plate using the extended finite element method on the static response. A C0 continuous eight noded serendipity quadrilateral element with Heaviside function and crack tip enrichment function are used to model the domain and the discontinuity in the CNT reinforced plate. The influence of various parameters such as crack length, volume fraction, span to thickness ratio and boundary condition on the non-dimensional central deflection are also assessed.