Laminate Free Edge Research Articles

Experimental Characterisation Framework for Laminate Free Edges by Digital Image Correlations and Validation of Numerical Predictions

This paper develops an accurate experimental framework to measure interlaminar strains on laminate free edges. Digital Image Correlation (DIC) is used with an ultra-fine speckle pattern and macro lens to resolve strain fields with a resolution of ∼ 15 µm, allowing for through-thickness deformation and strain mapping. Data analysis techniques are developed to denoise the strain field and discount the effect of random local fibre distribution.The major application of the framework is to validate numerical predictions, and it is demonstrated on angle-ply laminates over a range of ply orientations. A micropolar-based finite-element approach was compared to both a classical finite-element approach and the DIC-acquired interlaminar strain fields. Key improvements by the results include significantly overcoming the stark inconsistency of classical normal strains, and reducing the discrepancies of shear strains from 30 % to 3 ∼ 10 %. The outcomes can be extended to destructive failure analysis and the free-edge study of various other composite architectures.

A Continuum-mechanics solution of laminate free edges based on asymmetric stress and strain tensors

A meaningful attempt is made to investigate the impact of using asymmetric stress and strain formulations in the prediction of free-edge response of laminated orthotropic materials. The paper contributes to the process of making the singular free-edge stresses and strains in the literature more proximate to the bounded (realistic) solutions. Related to the singularity issue, it was previously identified that the symmetry assumption for stress and strain tensors could lead to a contradiction with the predicted free-edge stress functions. It is, therefore, reasonable to assert that the classical continuum mechanics based on tensor symmetries is unfaithful for the modelling of free edges. The present study demonstrates that for the free-edge region, stress and strain tensors naturally become asymmetric when they are enabled to be, to reach the minimum strain energy. By comparing with strain predictions generated by Digital Image Correlation technique, the new framework is shown to be able to address the notable discrepancy between the classical theoretical result and experimental result, which suggested the higher fidelity of the new framework. Moreover, by resolving the contradiction, the model is also made less sensitive to mesh refinement which sets an important basis for reaching a bounded solution in the future.

Multiscale investigation of micro-scale stresses at composite laminate free edge

The free edge effect is well understood at the laminate and lamina scale. The influence of the microstructure on micro-scale stresses and free edge cracking, however, is less known. This work aims at a better understanding of the effect of microscopic features on micro-scale stresses and the tendency of initial micro-cracking at the laminate free edge. To this end, a two-scale finite element (FE) modelling approach is developed. It consists of a meso-scale model to capture the laminate stacking sequence and the global stress field under a given loading condition, and a micro-scale model to predict the local constituent level stresses at the free edge. The two models were coupled one-way through a strain localization rule. A procedure to determine the boundary conditions for micro-scale FE models containing a free edge was proposed. The model was used to examine the 90/90 interface in [25N/−25N/90N]S IM7/8552 carbon/epoxy composite laminates. The effects of thermal and tensile loading were investigated independently to understand the influence of the interlaminar microstructure on micro-scale stresses at free edges during manufacture and under mechanical loading. The results agreed with the trend of free edge pre-cracks and progressive damage observed in experiments.

Prediction of stiffness and stresses in z-fibre reinforced composite laminates

Abstract The mechanical properties of z-pinned composite laminates were examined numerically. Finite element calculations have been performed to understand how the through-thickness reinforcement modifies the engineering elastic constants and local stress distributions. Solutions were found for four basic laminate stacking sequences, all having two percent volume fraction of z-fibres. For the stiffness analysis, a micro-mechanical finite element model was employed that was based on the actual geometric configuration of a z-pinned composite unit cell. The numerical results agreed very well with some published solutions. It showed that by adding 2% volume fraction of z-fibres, the through-thickness Young's modulus was increased by 22–35%. The reductions in the in-plane moduli were contained within 7–10%. The stress analysis showed that interlaminar stress distributions near a laminate free edge were significantly affected when z-fibres were placed within a characteristic distance of one z-fibre diameter from the free edge. Local z-fibres carried significant amount of interlaminar normal and shear stresses.

Mechanical Characterization of Angle-Ply Composite Laminates by Differential Moire Method: the Influence of Specimens' Length-to-Width Ratio

The influence exerted by the specimen proportions on the measured performance of angle-ply [+ 45°/− 45°]s composite laminates is studied. Three kinds of specimens are considered, having different length-to-width ratios, made with glass/epoxy unidirectional or fabric laminae. The static tensile characteristics are measured by means of load cells, electric strain gauges and through the Moire fringes method. The strain fields are analysed and the effects of stress concentration at the laminate-free edges are evaluated, as well as their influence on the strain distribution and the measured strength and stiffness. The results are summarized as diagrams of ultimate load and elastic modulus versus length-to-width ratio of the different specimens investigated. These diagrams allow the designer to evaluate the influence exerted by specimen proportions on the measured performance, as well as to compare characteristics which are heterogeneous, as obtained with different kinds of specimen.

Stress fields and energy release rates in cross-ply laminates

A method to model the thermoelastic response of flat laminated composites using a large radius axisymmetric hollow layered cylinder model is presented. An axisymmetric concentric cylinder model and a flat laminate model, each based on Reissner's variational principle with equilibrium stress fields, are compared. The stress components and the governing equations of the axisymmetric concentric cylinder formulation for a cylinder of infinite radius are shown analytically to be equivalent to the flat laminate formulation. Numerical results for the axisymmetric free edge stress field are shown to be nearly identical to the flat laminate free edge stress field solution. Selected results for the elastic stress fields and energy release rates in composite laminates with free edge and/or internal delaminations and transverse cracking are presented.

Effect of the free edge finishing on the tensile strength of carbon/epoxy laminates

High productivity can be achieved in the fabrication of composite laminates if molded edges are used. In this work, the fabrication process of laminates with this type of edge finishing is described. The stacking sequence effect for laminates with molded edges is experimentally studied and compared to that of laminates with machined edges. The tensile strengths of five different laminates fabricated with carbon/epoxy unidirectional tape and woven fabrics were measured. It is shown that the strength of laminates with molded edges is about 10% lower than that of laminates with machined edges but less sensitive to stacking sequence. The presence of small pockets of pure resin near the free edge of laminates with molded edges causes a reduction in the tensile strength. The stacking sequence effect may be very pronounced for laminates with woven fabric layers and machined edges.

Method for calculating the interlaminar stresses in symmetric laminates containing a circular hole

An efficient approximate solution for three-dimensional stress distributions around a circular hole in symmetric laminates under a set of far-field in-plane stresses is presented. Stress functions for each ply are assumed according to the boundary-layer equilibrium equations. In addition, all the boundary conditions for each ply and traction continuity at the ply interface are exactly satisfied. Eventually, the unknown parameters in stress functions are determined by the minimization of complementary energy of the whole laminate. Numerical examples are presented in comparison with given literature which shows that the present method is efficient. I. Introduction D UE to stiffness discontinuity between plies, it is easy to cause interlaminar stress concentrations near the freeedge region in composite laminates. Such stresses will commence delamination, matrix crackings, and failure of laminates, especially under fatigue loading. Since 1970, numerous investigations15 have used various methods to determine the interlaminar stresses at the straight free edge of composite laminates. Pipes and Pagano1 adopted the anisotropic elasticity theory in conjunction with the finite difference method to analyze a simple four-ply laminate. Wang and Crossman2 used a finite element approach to investigate this same problem. Wang and Choi3'4 derived an analytical solution based on Lekhnitskii's stress potentials and the theory of anisotropic elasticity to determine the exact order of stress singularity at the free edges of laminate. In an effort to develop an efficient method to deal with thick laminates (say 100 plies), Kassapoglou and Lagace5 used the force balance method in conjunction with the principle of minimum complementary energy to obtain an analytical solution for interlaminar stresses at straight free edges. Owing to the complicated geometry for the curved free edges as compared with the straight free edges, little work has been done for composite laminates with curved free edges. Basically, the analysis of straight free edge may be assumed as a problem with two-dimensional stress and strain variations. However, the curved free edge is a typical three-dimensional problem. This difference has rendered the analysis for the curved free edge more difficult than the straight free edge. A boundary-layer theory based on the perturbation technique for isotropic elastic plates with a circular hole developed by Reiss6 has been extended to composite laminates by Tang.7-8 This approach is based on identifying the boundary-layer problem as two equivalent problems, namely, a modified torsion problem and a modified plane strain problem. However, Tang's solution can only satisfy part of boundary conditions in an average sense, which may result in unreliable stress results near the free edges.9 In addition, Tang's solution will be very tedious for laminates with numerous plies. Zhang and Ueng10 proposed a simplified method to investigate the effect of the ratio of hole radius to laminate thickness on the interlaminar stress distributions around a hole in a (0/90 deg)s laminate under far-field tensile or shear stress; however, it is assumed that the order of stress singularity is prescribed and

Some considerations regarding the edge stress problem of laminates by finite elements

The accurate computation of stresses at the free edge of laminates continues to be a topic of great interest, as significant disagreement still exists among the various solutions proposed. The discrepancies are ascribed to the different behaviour of the numerical tools close to the bound, where it has been speculated that a stress singularity exists. In the present paper the elasticity problems of the singularity at the interface of a two-material wedge, whose exact solution is known and for which computations are compared, and at the free edge of (± 45) s laminates are discussed by means of finite elements. Such numerical tests evaluate the accuracy of conventional displacement formulated finite element methods for calculating stresses at the free edge and the influence on accuracy of the characteristics of the mesh and of its refinement. The propagation of computed characteristic stress states, involving irreducible errors from the bound of laminates and from the singular point of the wedge, have been observed. In both cases, refinement appeared unable to improve accuracy.

On the birefringent-coating method of stress analysis for fiber-reinforced laminated composites

A general relation based upon laminated-plate theory is developed which relates the state of stress throughout the thickness of the fiber-reinforced composite laminate to experimentally determined surface strains. The usefulness of the developed relation is discussed through an example given for a typical graphite-epoxy structural laminate. Birefringent coatings employed as a method to determine laminate surface strains are investigated. Isochromatic disturbances in the vicinity of a laminate free-edge, due to a Poisson's ratio mismatch between coating and laminate and interlaminar stress transfer between discrete lamina of the laminate, are investigated through exact elasticity solutions.