Free-edge Delamination Research Articles

Validation of two-dimensional calculations of free edge delamination in laminated composites

In this paper the use of two-dimensional calculations, which are often applied for the analysis of free edge delamination in a T-bone specimen, is validated by comparing the results with complete three-dimensional calculations. The specimen that is discussed shows mode-I delamination in the midplane of the specimen which is modelled in the analysis by means of an orthotropic damage model for interface elements. Although symmetry does not exist because of the material lay-up, use is made of assumed symmetry conditions, which are validated by analyses without symmetry conditions. It is shown that a two-dimensional analysis suffices for the determination of the ultimate load bearing capacity of the strip, but that a three-dimensional analysis is necessary to obtain a reliable view of the evolution of the delamination zone.

A Geometrically Nonlinear Model for Laminated Composite Strips With Extension-Twist Coupling in the Presence of Delamination

A geometrically nonlinear analysis for the extension-twist coupling in pretwisted laminated composite strips in the presence of delamination is developed. Closed-form solutions for strips with internal and edge delaminations are obtained. A parametric study is performed to investigate the influence of delamination length, material system, and stacking sequence on the extension-twist coupling in a class of hygrothermally stable laminates. The model predictions are in good agreement with test data. The results indicate that internal delamination has a negligible influence on the extension-twist coupling behavior while free-edge delamination could result in a significant drop in coupling.

A simple method to calculate mode components of strain energy release rate of free-edge delaminations in composite laminates

A simple method, which calculates the mode components of the strain energy release rate of free-edge delaminations in the laminates, is proposed. The interlaminar stresses are evaluated as an interface moment and interface shear forces that are obtained from the equilibrium equations at the interface between the adjacent layers. Deformation of an edge-delaminated laminate is calculated by using a generalized quasi-three dimensional classical lamination theory developed by the author. The analysis provides closed-form expressions for the three components of the strain energy release rale. The analyses are performed on [+30/−30/90]s laminates subjected to uniaxial extension, with free-edge delaminations located symmetrically and asymmetrically with respect to the laminate midplane. Comparison of the results with a finite element solution using the virtual crack closure technique shows good agreement. The simple nature of this method makes it suitable for primary design analysis for the delaminations of composite laminates.

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.

A Method to Predict the Effect of Thermal Residual Stresses on the Free-Edge Delamination Behavior of Fibre Reinforced Composite Laminates

A method is presented which accounts for the effect of process-induced thermal residual stresses on the free-edge delamination behavior of fibre reinforced laminates. A strain energy release rate fracture mechanics formulation is derived based upon the Irwin crack closure integral. The finite element method is then used to calculate Mode I and Mode II crack opening displacements and stiffnesses for free-edge delamination cracks originating at a specified ply interface from which strain energy release rates due to thermal and mechanical loading are then obtained. The effect of processing temperature on strain energy development is included in the calculation of thermal energy release rates by using experimentally measured material property data. To verify the model, (+352/-352/02/902)s graphite-reinforced PEEK tensile test specimens were manufactured and tested to failure. Measured delamination strains agree well with predictions when the effect of thermal residual stresses is included. Neglecting residual stresses over-estimates the tensile delamination strength by approximately 32%.

Stress intensity factors as the fracture parameters for delamination crack growth in composite laminates

A “mutual integral” approach is used to calculate the mixed-mode stress intensity factors for a free-edge delamination crack in a laminate under tensile loading conditions. This “mutual integral” approach, for generalized plane strain conditions, is based on the application of the path-independent J integral to a linear combination of three solutions: one, the problem of the laminate to be solved using the quasi 3-D finite element method, the second, an “auxiliary” solution with a known asymptotic singular solution, and the third, the particular solution due to the out-of-plane loading. A comparison with the exact solutions is made to determine the accuracy and efficiency of this numerical method. With this “mutual integral” approach, it was found that the calculated mixed-mode stress intensity factors of the free-edge delamination crack remain relatively constant as the crack propagates into the laminate. It was also found that the fracture criterion based on the mixed-mode stress intensity factors is more consistent with the experimental observations than the criterion based on the total energy release rate, and hence demonstrates the importance of the ability to calculate each individual component of the stress intensity factors. Furthermore, it was found that the fracture toughness measurements from double cantilever beam specimens can be used directly to predict the onset of delamination crack growth between two dissimilar laminae. Using these fracture toughness measurements from the double cantilever beam specimens, some examples are given to show that the fracture criterion based on the mixed-mode stress intensity factors can accurately predict the failure load for various laminates under tensile loading conditions.

Edge delamination in curved (04/±456)s glass-fibre/epoxy beams loaded in bending

An approach to predicting delamination due to the free-edge effect in a curved beam specimen loaded in bending is presented. Stress-based criteria do not give satisfactory results because of the stress singularity at the free edge. The conventional fracture-mechanics approach for free-edge delamination cannot be used because the strain-energy release rate does not reach an asymptotic value. An improved approach is developed on the basis of an assumed initial defect. The strain-energy release rate is calculated by using finite elements and this is then used to predict the failure load. Good correlation with the experimental results is obtained.

Simplified method for predicting onset of open-mode free edge delamination

Simplified method for predicting onset of open-mode free edge delamination

A Simplified Method for Determining Modal Strain Energy Release Rate of Free-Edge Delaminations in Laminated Composite

A simplified method for determining the mode components of the strain energy release rate of free-edge delaminations in laminated composite is proposed. The interlaminar stresses are evaluated as an interface moment and interface shear forces that are obtained from the equilibrium equations at the interface between the adjacent layers. Deformation of an edge-delaminated laminate is calculated by using a generalized quasi-three dimensional classical laminated plate theory developed by the authors. The analysis provides closed-form expression for the three components of the strain energy release rate. Comparison of results with a finite element solution using the virtual crack closure technique shows good agreement. In the present study, laminated composite with stacking sequences of [30/-30/90] were examined. The simple nature of the method makes it suitable for primary design analysis for the delaminations of laminated composite.e.

Stress intensity factors as the fracture parameters for delamination crack growth in composite laminates

A ‘mutual integral’ approach is used to calculate the mixed-mode stress intensity factors for a free-edge delamination crack in a laminate under tensile loading conditions. This ‘mutual integral’ approach, for generalized plane-strain conditions, is based on the application of the path-independent J integral to a linear combination of three solutions: one, the problem of the laminate to be solved by using the quasi 3D finite element method; the second, an ‘auxiliary’ solution with a known asymptotic singular solution; and the third, the particular solution due to the out-of-plane loading. A comparison with the exact solutions is made to determine the accuracy and efficiency of this numerical method. With this ‘mutual integral’ approach, it was found that the calculated mixed-mode stress intensity factors of the free-edge delamination crack remain relatively constant as the crack propagates into the laminate. It was also found that the fracture criterion based on the mixed-mode stress intensity factors is more consistent with the experimental observations than the criterion based on the total energy release rate, and hence demonstrates the importance of the ability to calculate each individual component of the stress intensity factors. Furthermore, it was found that the fracture toughness measurements from double cantilever beam specimens can be used directly to predict the onset of delamination crack growth between two dissimilar laminae. By using these fracture toughness measurements from the double cantilever beam specimens, some examples are given to show that the fracture criterion based on the mixed-mode stress intensity factors can accurately predict the failure load for various laminates under tensile loading conditions.

Effects of a free edge delamination on buckling of rectangular composite plates with two fixed loading and one simply-supported side edges

An experimental and analytical investigation is conducted on the compressive buckling behavior of an orthotropic plate with a free edge delamination. The plate is a simplified model of stiffener plates. In the present paper two loading edges are fixed and a side edge is simply-supported. The delamination locates at the free edge over the whole length. A Rayleigh-Ritz approximation method is adopted in the analysis. A constrained point is used to allow contacts between the two delaminated surfaces. At this point, relative displacement and two relative slopes are constrained through imaginary springs. The buckling load of the geometrically admissible buckling mode is obtained by an ordinary eigenvalue analysis. The analytical results are compared with the experiment and the results agree well. The effects of the width and the location of the delamination on the buckling behavior are studied analytically for the plates with various aspect ratios. Low local delamination buckling can occur at very low load whe...

Boundary layers in wedges of laminated composite strips under generalized plane deformation—Part II: Complete numerical solutions

A procedure for finding complete numerical solutions for the elastic boundary layer field in wedges of a laminated composite strip under the generic loadings of generalized plane deformation is discussed together with numerical examples for free edge problems and delamination crack problems. The procedure yields the solution in terms of loading parameters and is applicable to an arbitrary wedge angle and ply orientation and any type of loadings within the range of generalized plane deformation. For the free edge problem, the so called free edge stress intensity and the mode vector are defined and the free edge stress intensity is found to be a single parameter governing the fracture or failure behaviour near the free edge for a given pair of adjacent materials (plies). The effect of relative ply thickness upon the stress intensity and the energy release rate is also discussed for various types of loadings.

Development of a multiobjective optimization procedure for reducing edge delamination stresses in composite plates

This paper addresses the development of an optimization procedure for the reduction of interlaminar stresses in composite plates. The goal is to reduce the interlaminar stress trends near the free edges of composite plates subjected to single and combined loadings. A simplified analytical approximation is used for predicting the free edge delamination stresses. Ply orientations are used as design variables and constraints are imposed on the in-plane material-axis ply stresses, the buckling load and the interlaminar normal stress interior to the free edge of the plate. The problem is formulated with multiple design objectives and the Kreisselmeier-Steinhauser multiobjective optimization technique is used to solve the nonlinear problem. The procedure yields significant reductions in the interlaminar stresses. Results are presented and compared with a reference or baseline design for four Gr/Ep composite plates with symmetric ply arrangements.

Compressive buckling of rectangular composite plates with a free-edge delamination

An experimental and analytical investigation is conducted on the compressive buckling behavior of orthotropic plates with a delamination. The plates, which have three simply supported edges and one free edge, are a simplified model of stiffener plates of a stiffened panel. A uniform width delamination is located at their free edges over the whole length. In the analysis, the Rayleigh-Ritz approximation method is adopted. A constrained point is introduced to allow the contact between the two delaminated surfaces. Imaginary springs about relative displacement and two relative slopes are introduced at the constrained point. With the constraint, buckling loads of physically admissible buckling modes can be obtained by ordinary buckling analysis. The global buckling load reduction is found to be significant and almost proportional to the delamination width. Local delamination buckling is found to occur when the delamination is located near the surface and its size is relatively large compared with that of the plate. The local buckling mode is different from the global one, and more wave number in loading direction and constrained points are necessary to obtain physically admissible solutions. The analytical results agree well with the experimental ones.

Mode II Free-Edge Delamination in Linainated Composites under Uniaxial Compression

The influence of interlaminar shear stress on mode II free-edge delamination at the free-edge in composite laminate is studied experimentally and analytically. Delamination tests are conducted under uniaxial compressive load to eliminate transverse cracking. Test laminates are designed to have compressive interlaminar normal stress and various ratios of interlaminar shear stresses at the interfaces of interest. The laminates treated in this paper are [θ4/-θ4/904] s, [(±θ2)2/904] s, and [(±θ)4/904] s, where θ is 30 and 45 degrees. The experimental results are discussed with the analyzed results obtained by the finite element method. The fracture surface of delamination is further examined for the determination of the predominant mode of delamination using a scanning electron microscope. It is found that some laminates can be delaminated only by the effect of mode II interlaminar shear stress even though it is zero at the free-edge.

Suppression of interlaminar damage in carbon/epoxy laminates by use of interleaf layers

Carbon fiber reinforced plastics (CFRP) have been widely used as a structural material. In general, fiber orientation angle of each lamina in these laminates is variously chosen in order to taylor a material which meets the particular requirement for the material properties in arbitrary direction of laminate. Quasi-isotropic lamination, in which the laminate consisted of laminae with fiber orientation of 0[degree], +45[degree], [minus]45[degree] and 90[degree] to loading axis, is most commonly employed in the actual application. However, quasi-isotropic carbon/epoxy laminates are known to develop the interlaminar stress concentrations near the free edge region. These laminates have a strong tendency to delaminate near the edges when subjected to axial in-plane loading. Such a free edge delamination under loading in the plane of the laminate is a unique problem to laminated composites. This paper summarizes the author's investigation which was performed to reduce the free edge interlaminar stresses in the laminate by incorporating interleaf films between plies and thus to improve the mechanical properties of these materials. In their previous work, the authors have shown that these laminates exhibit a high vibration damping capability. Loss factor values for these CFRP/interleaf laminates which were measured in cantilever beam tests, are 5 to 50more » times as large as that for conventional CFRP. In this paper, discussion will be provided on the mechanical properties of the interleaved quasi-isotropic carbon/epoxy laminate, [0/[+-]45/90][sub s], with a special emphasis on the optimum design of interply locations to incorporate the interleaf films for the particular requirement such as static strength, elastic modulus, fatigue resistance and so on.« less

Three-Dimensional Finite Element Analysis of Free Edge Stresses and Delamination of Composite Laminates

A 24-node, 64-degree-of-freedom, solid hexahedronal finite element is used to analyze the interlaminar free edge stresses and delamination of composite laminated plates. The difficulty due to the requirement of large storage space which is frequently encountered in the modeling of contoured delamination problems is resolved by using the preconditioned conjugate gradient method. One of the advantages of this method is that there is no need to store the fill-in elements in the stiffness matrix decomposition process, which leads to a significant reduction in storage space required, thereby making the numerical analysis of the complicated contoured delamination problem feasible as well as effective. To evaluate the accurateness of the present formulation, numerical algorithm and computer program, free edge stress analyses are performed for a [0/901 cross-ply and a [+ 45], angle-ply laminated plate. Both plates are subjected to an axial tensile strain loading. The present three-dimensional results are found to be in good agreement with those obtained using an alternative quasi-three-dimensional methods. To further demonstrate the applicability of the present development, the strain energy release rate of a [+25/90], graphite-epoxy rectangular laminated plate subjected to tensile strain is studied. Two initial delaminations are assumed to be located in the midspan of the two opposite free edges and also at the middle of the thickness. The delamination contour is assumed to be a straight line segment joined by two circular arcs. The strain energy release rates along the delamination front are calculated using the modified crack closure method. As a step beyond the solution using quasi-3D assumption, the present results show the non-uniform distribution of mode I strain energy release rate G1 along the boundary of the delamination front which fluctuates to a maximum value when approaching both ends at the free edge of the laminate.

Analysis of a symmetric laminate with mid-plane free edge delamination under torsion: theory and application to the edge crack torsion (ECT) specimen for mode III toughness characterization

A shear deformation theory is developed to analyze a symmetric laminate with mid-plane edge delamination under torsion loading. The theory is based on an assumed displacement field which includes shear deformation. The governing equations and boundary conditions are obtained from the principle of virtual work. Closed-form solutions for the compliance and strain energy release rate are obtained. The theory is used to analyze a mid-plane Edge Crack Torsion (ECT) specimen used for characterizing the mode III delamination behavior of composites. The prediction of the present theory for a [90, (±45)n, (±45)n, 90]s class of laminates is compared with existing test data, and good agreement is observed. In addition, the Classical Lamination Theory (CLT) is found to be less accurate for the analysis of the edge crack torsion specimen. The layup effect on the behavior of some ECT specimens is analyzed using the present theory.

Influence of free-edge delaminations on the extension-twist coupling of elastically tailored composite laminates

A closed form solution is developed in order to analyze the influence of free-edge delaminations on elastically tailored composite laminates. The analysis is based upon a shear deformation theory and a sublaminate approach. The solution is applied to predict the influence of free-edge delamination on the behavior of a class of laminates exhibiting extension-twist coupling. Comparison of analytical predictions with test data from laminates with mid-plane and off mid-plane free edge delaminations is performed. The results indicate that free-edge delamination can have a significant influence on extension-twist coupling.

Free edge delamination in carbon-epoxy laminates: a novel numerical/experimental approach

A geometrically and physically nonlinear finite element approach is presented for the analysis of mode-I and mixed-mode free edge delamination in composite laminates which properly accounts for the effects of initial thermal and hygroscopic stresses. A constitutive model based on nonlinear fracture mechanics is used to describe delamination. An orthotropic softening plasticity model is used to determine the initiation and propagation of delamination. Although the orthotropic yield surface is based on stresses, it is proved, that, in combination with a softening type of post-failure response controlled by the fracture toughness, the approach results in a unique and physically realistic solution upon mesh refinement. The results from the nonlinear finite element computations, including predictive analysis, are compared with mode-I and mixed-mode free edge delamination experiments. This comparison shows that the numerical results are within 10% of the experimental data.