Damage characterization of CFRP laminates using acoustic emission and digital image correlation: Clustering, damage identification and classification

Damage mechanisms in composite laminates are quite complex, and it is necessary to perceive their effects on the degradation of laminate mechanical properties. This work employs acoustic emission (AE) and digital image correlation (DIC) techniques to describe the evolution of intra/inter-laminar damage modes in the CFRP laminates under in-plane/out-of-plane loading conditions. In this study, laminates of stacking sequences , , , and under tensile load are investigated to distinguish the intra-laminar damages like matrix cracking, fiber–matrix debond, and fiber breakage. Double cantilever beam, end notch flexure, and mixed-mode bending specimens are used to characterize delamination failure in the laminate. An unsupervised -means clustering technique is used to classify the AE data based on peak frequency and amplitude. The surface displacement and strain data are evaluated using the DIC technique to understand the damage evolution in the laminates. Post failure analysis is carried out using a digital microscope, and fractography studies are used to identify and assign the damages to different AE clusters. This investigation yields a taxonomy of damage modes, their sequence of occurrence, and failure strains that can be used for structural health monitoring and progressive damage modeling of composite laminates

Analysis and design for the moderately deep postbuckling behavior of composite plates

It is widely acknowledged that tracking the postbuckling response of structures made from thin plates can be problematical. Such difficulty is associated with highly nonlinear effects, including mode jumping, imperfection sensitivity, and their combined interactions. Two widely used techniques that are currently used involve path following and asymptotic expansion. The former is often implemented in commercial finite element codes but can prove unreliable at representing branch switching. The latter is a relatively quick technique due to its recursive linear nature but is only reliable in the vicinity of bifurcations. Due to the overall complex nonlinearity, analytical closed-form solutions do not exist for path following and exist rarely for quadratic asymptotic expansions where simple forms have been adopted. This paper presents an analytical-based approach that enables the efficient optimal design of “moderately deep” nonlinear postbuckling behavior of laminated composite plates under uniaxial or biaxial loading. It provides a closed-form solution that more reliably reflects a deeper postbuckling response than the state of the art. Subsequently, highly efficient postbuckling optimization is attributed to the newly derived closed-form solution and a recent two-level optimization framework

Buckling analysis of variable angle tow composite plates using differential quadrature

Variable Angle Tow (VAT) placement allows the designer to tailor the composite structure to enhance the structural response under prescribed loading conditions. VAT technology allows curvilinear placement of tows within the plane of a structure and gives freedom for altering pointwise in-plane, coupling and flexural stiffnesses of a plate. This stiffness tailoring improves the buckling performance of VAT plates by allowing re-distribution of loads from the critical regions of the plate. In the present work, the Differential Quadrature Method (DQM) is investigated for performing buckling analysis of VAT panels. The governing differential equations are derived for the in-plane and buckling analysis of symmetric VAT plate structure based on classical laminated plate theory. DQM was applied to solve the buckling problem of simply supported VAT plates subjected to uniform edge compression. To show the accuracy and robustness of DQM, the results obtained using DQM are compared with finite element analysis. In this work, Non-Uniform Rational B-Splines (NURBS) curves are used to model the fibre path and the fibre orientation can be designed by modifying the control points within the domain of the plate. The NURBS representation allows general fibre angle variation of tow resulting in wider design space of VAT panels. Also, the number of design variables for VAT panels are reduced by using NURBS curves and the fibre manufacturing constraints can be handled easily. Genetic Algorithm (GA) has been coupled with DQM to determine the optimal tow path for improving the buckling performance

Postbuckling optimisation of variable angle tow composite plates

The potential for enhanced postbuckling performance of flat plates using variable angle tow (VAT), in comparison with conventional laminated composites, has been shown previously. This paper presents an optimization strategy for the design of postbuckling behaviour of VAT composite laminates under axial compression. The postbuckling performance of composite laminated plates for a given compression loading is assessed by studying both the maximum transverse displacement and the end-shortening strain. For the postbuckling analysis of VAT composite plates, an efficient tool based on the variational principle and the Rayleigh-Ritz method is developed. In the optimization study, a mathematical definition based on Lagrangian polynomials, which requires few design parameters, is used to define a general fibre angle distribution of the VAT plate. A generic algorithm is subsequently used to determine the optimal VAT configuration for maximum postbuckling performance. The optimization of square VAT laminates under compression loading for different in-plane boundary conditions is studied and compared with straight fibre designs

Framework for the Buckling Optimization of Variable-Angle Tow Composite Plates

Variable-angle tow describes fibers in a composite lamina that have been steered curvilinearly. In doing so, substantially enlarged freedom for stiffness tailoring of composite laminates is enabled. Variable-angle tow composite structures have been shown to have improved buckling and postbuckling load-carrying capability when compared to straight fiber composites. However, their structural analysis and optimal design is more computationally expensive due to the exponential increase in number of variables associated with spatially varying planar fiber orientations in addition to stacking sequence considerations. In this work, an efficient two-level optimization framework using lamination parameters as design variables has been enhanced and generalized to the design of variable-angle tow plates. New explicit stiffness matrices are found in terms of component material invariants and lamination parameters. The convex hull property of B-splines is exploited to ensure pointwise feasibility of lamination parameters. In addition, a set of new explicit closed-form expressions defines the feasible region of two in-plane and two out-of-plane lamination parameters, which are used for the design of orthotropic laminates. Finally, numerical examples of plates under compression loading with different boundary conditions and aspect ratios are investigated. Reliable optimal solutions demonstrate the robustness and computational efficiency of the proposed optimization methodology

A comparison of variational, differential quadrature, and approximate closed-form solution methods for buckling of highly flexurally anisotropic laminates

The buckling response of symmetric laminates that possess strong exural-twist coupling are studied using different methodologies. Such plates are dfficult to analyse due to localised gradients in the mode shape. Initially, the energy method (Rayleigh-Ritz) using Legendre polynomials is employed and the difficulty of achieving reliable solutions for some extreme cases is discussed. To overcome the convergence problems, the concept of Lagrangian multiplier is introduced into the Rayleigh-Ritz formulation. The Lagrangian multiplier approach is able to provide the upper and lower bounds of critical buckling load results. In addition, mixed variational principles are used to gain a better understanding of the mechanics behind the strong exural-twist anisotropy effect on buckling solutions. Specifically, the Hellinger-Reissner variational principle is used to study the effect of exural-twist coupling on buckling and also to explore the potential for developing closed form solutions for these problems. Finally, solutions using the differential quadrature method are obtained. Numerical results of buckling coefficients for highly anisotropic plates with different boundary conditions are studied using the proposed approaches and compared with finite element results. The advantages of both Lagrangian multiplier theory and variational principle in evaluating buckling loads are discussed. In addition, a new simple closed form solution is shown for the case of a exurally anisotropic plate with three sides simply supported and one long edge free

Postbuckling analysis of variable angle tow (VAT) composite plates

Variable angle tow (VAT) placement techniques provide the designer with the ability to tailor the point-wise stiffness properties of composite laminates according to structural design requirements. Whilst VAT laminates exhibiting substantial gains in buckling performance have been shown previously, beneficial ways of using VAT techniques to improve structural performance of composite laminates in the postbuckling regime remain unclear. In the present study, a semi-analytical formulation based on a variational approach is developed and the Rayleigh-Ritz method is subsequently applied to solve the postbuckling problem of VAT plates. The generality of the proposed formulation allows effective modelling of the pure or mixed stress boundary conditions and also provides a computationally effcient means to determine the postbuckling strength of VAT plates. The proposed methodology is applied to the postbuckling problem of simply supported VAT plates under uni-form edge displacement compression. To show the accuracy and robustness of the proposed approach, results are validated using finite element analysis. The postbuckling characteristics of VAT plates subject to different in-plane boundary conditions are analysed by studying their nonlinear load-end shortening and transverse deflection responses. Furthermore, a parametric study on the postbuckling response of VAT plates with linear variation of fibre angle is performed and the stiffness values of VAT plates in both pre- and postbuckling ranges are compared with the results of straight-fibre laminates

Optimal postbuckling design of variable angle tow composite plates

Perturbation-based approximation methods are widely used in preliminary design studies of thin-walled structures. In this paper, postbuckling analysis of a variable-angle-tow composite plate is performed using the perturbation-based asymptotic numerical method, which transforms the nonlinear problem into a set of well-posed recursive linear problems. These linear problems are solved using a novel generalized differential-integral quadrature method, and the postbuckling solutions are sought over a finite load step size around the critical buckling point using asymptotic expansions. The accuracy of the asymptotic numerical method in evaluating the initial postbuckling of variable-angle-tow plates under compression is investigated. Subsequently, a novel postbuckling optimization approach based on asymptotic numerical method results is proposed for the design of variable-angle tow laminates. The postbuckling features obtained from asymptotic numerical method are used in an efficient two level optimization framework for the design of variable-angle-tow plates. At the first level, a globally convergent method of moving asymptotes is adopted to determine the optimal lamination parameter distributions that maximize the postbuckling performance of the variable-angle-tow plate. At the second level, a genetic algorithm is used to convert the optimal lamination parameter distributions into realistic variable-angle-tow layups. The optimization studies are performed for square variable-angle-tow plates for axial/biaxial compression under different in-plane boundary conditions

Instabilities in a compressible hyperelastic cylindrical channel due to internal pressure and external constraints

Pressurised cylindrical channels made of soft materials are ubiquitous in biological systems, soft robotics, and metamaterial designs. In this paper, we study large deformation of a long, thick-walled, and compressible hyperelastic cylindrical channel under internal pressure. The applied pressure can lead to elastic bifurcations along the axial or circumferential direction. Incremental theory is used to derive the partial differential equations that govern the bifurcation behaviour of the cylindrical channel. Two cases of boundary conditions on the outer surface of the cylinder, namely, free and constrained are studied to understand their influence on the buckling behaviour. The derived equations are solved numerically using the compound matrix method to evaluate the critical pressure. The effects of the thickness of the cylinder and the compressibility of the material on the critical pressure are investigated for both the boundary conditions. The results reveal that for an isotropic material, the bifurcation occurs along the axial direction of the cylinder at lower critical pressure compared to the circumferential direction for all cases considered. Finally, we demonstrate the tailorability of bifurcation behaviour of the cylinder by adding reinforcements along the length of cylinder. The anisotropic hyperelastic material behaviour for triggering the bifurcation in the circumferential direction is studied by varying the material parameters.Comment: 27 pages, 14 figure

Fracture studies on synthetic fiber reinforced cellular concrete using acoustic emission technique

Cellular lightweight concrete (CLC) is increasingly used for low strength non-structural and structural applications. The effects of synthetic fiber reinforcement on the fracture behavior of CLC is investigated. In particular, acoustic emission (AE) technique is employed to study the influence of macro (structural), micro polyolefin synthetic fibers and their combinations on the fracture behavior of CLC beams. Notched fiber reinforced CLC beams were tested to study the crack initiation and propagation characteristics using AE sensors. Different AE parameters are correlated with the crack growth and damage accumulation. An attempt has been made to correlate the crack mouth opening displacement (CMOD) with the number of AE hits. The variation of cumulative acoustic energy release of the cracks is studied with respect to applied load and CMOD. Three dimensional source location of cracks is carried out based on the AE events picked by the sensors bonded to the CLC specimens. The analysis of AE results indicates that the crack source location identification from AE is consistent with the actual crack development. Analysis of AE signals reveal that the CLC matrix cracking produces signals with less number of hits that lie in the notched plane in bending. Moreover, the signals from the post peak regime correspond to more number of hits which tend to be scattered around the plane of notch due to the fiber pull out