Mid-plane Delamination Research Articles

Dynamic Analysis of FGM Plates with Variable Delamination Parameters by the Chebyshev–Ritz Method

Delamination is one of the failure modes of functionally graded materials (FGM), resulting in the critical change of vibration characteristics. The Chebyshev polynomials are commonly used as admissible functions to improve the computational efficiency of numerical algorithms and avoid the occurrence of ill-conditioned problems. This paper extends the Chebyshev–Ritz method to the free vibration analysis of delaminated FGM plates, in which the material variation through the plate thickness follows the exponential-law distribution. A plane crack that is considered to be perpendicular to the thickness direction penetrates through the width direction. Based on the region approach, the analysis of FGM plates with a mid-plane delamination is divided into four sub-regions. The kinetic energy and potential energy of each sub-region are derived by the thin plate theory and von Kármán nonlinear strain–displacement relation. The modal functions of the displacement fields of FGM plates can be constructed in accordance with the displacement continuity conditions of the delamination interface and the boundary conditions of such plates. The effects of asymmetric material distribution, delamination length ratio, Young’s modulus ratio, and boundary support on the vibration behavior of FGM plates are investigated. This semi-analytical study provides a reasonable theoretical basis for the behavior prediction and delamination identification of composite structures.

Scattering of the Fundamental Anti-symmetric Lamb Wave by a Mid-plane Edge Delamination in a Fiber-composite Laminate

This paper investigates the scattering of the fundamental anti-symmetric Lamb wave mode by a delamination along the edge of a quasi-isotropic fiber-composite laminate. Delaminations pose a serious threat to the structural integrity of composite laminates as they often show no visible signs of damage on the surface. Due to the anisotropic nature of composites, analytical solutions are often complicated to derive for such problems. This investigation uses 3D Finite Element (FE) analysis and experimental tools to characterize the scatter by a mid-plane delamination in composites. A 5.5 cycle Hann windowed wave train was used as the input signal for both FE and experiments. A 2D Fast Fourier Transform was used to identify the mode and amplitude of the scattered field along various scattered directions. The experimental wave field image was captured using a 3D Laser Vibrometer. The results indicate that the scatter pattern is much more complex than previously obtained results for an isotropic plate. Even for the simple case of mid-plane delamination, the fiber steering effects in the outermost plies have a significant effect on the scattering pattern, relative to the isotropic case where the dominant part of the scattered field is an edge-guided wave. Computational and experimental results are presented for the scattering pattern and scattering amplitude as a function of damage size relative to wavelength. The implications of these results for the optimal placement of actuators and sensors for Structural Health Monitoring (SHM) purposes, and for devising effective approaches for the inverse problem of damage detection and sizing, are briefly discussed.

Determination of the critical load and energy release rate in mode II delamination using a meshfree method

AbstractSimulation of fracture by using numerical methods is important to treat geometries that change in time. In this study, both numerical and experimental investigations are presented for the delamination under mode II loading, detailing the derivation of the formulations in numerical simulations of fracture. The simulation of the delamination under mode II loading based on the cohesive segments model was investigated by using a meshfree method. Then, an experimental investigation was used to verify the meshfree method’s results. For tests under mode II loading, three-point end-notched flexure specimens, which are made of carbon/epoxy laminate (AS4/3501-6) which consists of 10 plies in [0]10 and [0/90/0/90/0]s lay-up with delamination inserted in the middle of the laminate, were used for the interlaminar fracture toughness tests. The problem was solved for [0]10, [0/45/-45/90/0]s, [0/90/0/90/0]s, [0/90/0/90/30]s, [0/90/0/90/45]s and [0/90/0/90/60]s laminates with mid-plane delaminations, and the results were verified for different composite materials. The critical fracture force, which can be experimentally measured, was used to calculate the mode II delamination fracture toughness of the carbon/epoxy laminate. In addition, values of the integral for 209 (11×19) and 253 (11×23) background meshes with equivalent interval sizes were compared. For a relatively fine background mesh, the critical load was converged. Results obtained from the meshfree element-free Galerkin method showed very good agreement with experimental data for single-mode delamination under mode II loading. The results presented will help in the implementation of mesh design techniques that protect numerical accuracy while minimizing computational expense.

Finite element bending behaviour of discretely delaminated composite conoidal shell roofs under concentrated load

Laminated composites are increasingly getting used in civil engineering structural components including shell structural units due to their light weight, high specific strength and stiffness properties. One of the major causes of failure in these laminated composites is delamination resulting from the interlaminar debonding between the laminae forming the laminate. A review of literature that exists on composite shells reveals that the research reports on delaminated shells are very few in numbers. Among the shell forms used popularly in the industry, the conoidal ones are aesthetically pleasing and also easy to fabricate being singly ruled surfaces. To use these conoids widely with confidence, behaviour of these forms with possible delamination damage has to be studied in depth. Hence, in this paper, a study on bending behaviour of delaminated composite conoidal shells is done. An eight noded isoparametric element with five degrees of freedom per node is used together with Sanders’ strain displacement relationships. To satisfy the compatibility of displacements and rotations along the crack edges a multipoint constraint algorithm is incorporated. Benchmark problems are solved to validate the present approach and a wide variety of composite conoidal shell problems with midplane delaminations are solved by varying the stacking sequence, extents of delamination and boundary conditions under central point load. The results are critically discussed to arrive at conclusions of engineering significance highlighting particularly the differences in behaviour between undamaged and damaged shells. Keywords: Laminated composite, conoidal shells, delamination, finite element method, roofs, concentrated load.

Free vibration analysis of delaminated beams using mixed finite element model

Free vibration analysis of laminated beams with delamination has been presented in this paper. A 2-D plane stress mixed finite element model developed by the authors [G.S. Ramtekkar, Y.M. Desai, A.H. Shah, Natural vibrations of laminated composite beams by using mixed finite element modeling, Journal of Sound and Vibration 257(4) (2002) 635–641.] has been employed. Two models, namely the unconstrained-interface model and the contact-interface model have been proposed for the computation of frequencies and the mode shapes of delaminated beams. Laminated beams with mid-plane delamination as well as off-mid-plane delamination have been considered and the results have been compared with various theoretical and experimental results available in the literature. It has been concluded that the contact-interface model presents a realistic behaviour of the dynamics of delaminated beams whereas the unconstrained-interface model under-predicts the frequencies, particularly at the higher modes

Identification of the local stiffness reduction of a damaged composite plate using the virtual fields method

The present study aims at taking advantage of the availability of full-field measurements and adapted inverse identification procedures in order to not only locate the damage but also to identify the local stiffness reduction of a damaged composite plate. To do so, full-field heterogeneous curvature fields are obtained through a deflectometry technique. The virtual fields method (VFM) is used as an inverse procedure to process curvatures for the identification of the local loss of stiffness. The VFM is based on a relevant use of the equilibrium equations through the principle of virtual work. It has been adapted to the case of a plate with stiffnesses varying with the space variables. Two parameterization methods for the stiffness reduction were developed: discrete (piecewise) and continuous (polynomial). In this study, the procedure is described, validated on simulated measurements and several experimental results are given. The method not only picks up the location of the damage but also provides a fairly good estimate of the stiffness reduction in the damaged area when through-the-thickness displacement distribution in the damaged region is linear. However, the current methodology shows unsatisfactory identification if the distribution is not linear, which is the case for a single mid-plane delamination.

Determination of fracture energy and tensile cohesive strength in Mode I delamination of angle-ply laminated composites

Abstract The energy release rate in delamination of angle-ply laminated double cantilever composite beam specimens was calculated using the compliance equation, and interlaminar cohesive strengths were obtained. Instead of the traditional approach of a beam on an elastic foundation, a second-order shear-thickness deformation beam theory (SSTDBT) was considered. The equilibrium equations were obtained using the principle of minimum total potential energy and the system of ordinary differential equations were solved analytically. The problem was solved for [0°]6 , [±30°]5, and [±45°]5 laminates with mid-plane delaminations and the results were verified using experimental evidence available in the literature.

Mode II fracture behaviour monitoring for composite laminates using embedded fibre Bragg grating sensors

This paper presents the utility of embedded fibre Bragg grating (FBG) sensors for monitoring mode II fracture behaviour of glass fibre-reinforced epoxy (GF/EP) composite beams bearing a mid-plane delamination. Stress concentration at the delamination tip of the beam, induced during an end notched flexure (ENF) test, was monitored by means of the reflection spectrum obtained from the FBG sensor whose centre was located at the tip of delamination. The Bragg wavelength shift, bandwidth and intensity in such a reflection spectrum associated with a load–displacement graph were then used to characterize the fracture behaviour of the delaminated beam.

A non-classical, energy release rate based approach for predicting delamination growth in graphite reinforced laminated polymeric composites

A non-classical, energy release rate based approach is applied to predict delamination growth in four different graphite reinforced laminated polymeric matrix composites, and the results are compared to those obtained using classical, linear elastic fracture mechanics. Both methods predict delamination advance by comparing the energy release rate in a structure to its critical value, or toughness, where the toughness is obtained from a series of tests on unidirectional laminates with midplane delaminations. However, the non-classical method uses a “crack tip element/non-singular field” approach to decompose the energy release rate, which results in non-classical mode I and mode II components. Matrix materials considered include an epoxy, a blended thermoplastic toughened epoxy, a thermoplastic particulate interlayer toughened epoxy, and a thermoplastic. For all materials, the non-classical approach is shown to provide relatively accurate predictions, whereas relatively poor results are obtained when using the classical approach. In view of the range of materials studied, it is concluded that the non-classical approach will likely apply to other current and future generation graphite reinforced polymeric matrix composites, and that this approach will continue to give more accurate results than one that is classically based.

Self-healing structural composite materials

A self-healing fiber-reinforced structural polymer matrix composite material is demonstrated. In the composite, a microencapsulated healing agent and a solid chemical catalyst are dispersed within the polymer matrix phase. Healing is triggered by crack propagation through the microcapsules, which then release the healing agent into the crack plane. Subsequent exposure of the healing agent to the chemical catalyst initiates polymerization and bonding of the crack faces. Self-healing (autonomic healing) is demonstrated on width-tapered double cantilever beam fracture specimens in which a mid-plane delamination is introduced and then allowed to heal. Autonomic healing at room temperature yields as much as 45% recovery of virgin interlaminar fracture toughness, while healing at 80 °C increases the recovery to over 80%. The in situ kinetics of healing in structural composites is investigated in comparison to that of neat epoxy resin.

Postbuckling behaviour of a blade-stiffened composite panel loaded in uniaxial compression

Abstract The postbuckling behaviour of a panel with blade-stiffeners incorporating tapered flanges was experimentally investigated. A new failure mechanism was identified for this particular type of stiffener. Failure was initiated by mid-plane delamination at the free edge of the postbuckled stiffener web at a node-line. This was consistent with an interlaminar shear stress failure and was calculated from strain gauge measurements using an approximate analysis based on lamination theory and incorporating edge effects. The critical shear stress was found to agree well with the shear strength obtained from a three-point bending test of the web laminate.

Mode II fracture toughness evaluation using four point bend, end notched flexure test

A four point bend, end notched flexure test is described for determining the mode II fracture toughness of laminated composites. The test consists of a unidirectional laminate with a midplane delamination loaded in four point bending. The test configuration is analysed by beam theory and by finite element analysis. When the delamination front is in between the inner load ing rollers the energy release rate, expressed in terms of the applied load, is independent of delamination length. In addition, delamination growth is shown to be stable for a displacement controlled test. The advantages of this test over conventional mode II tests are the reduction of frictional effects and the ability to perform an experimental compliance calibration as the delamination advances. Further, an R-curve characterisation may be conducted. This results in a reduced time to conduct tests to generate mode II data compared with the tests currently used by industry.

Global/Local Approach using Partial Hybrid Finite Element Analysis of Stress Fields in Laminated Composites with Mid-Plane Delamination under Bending

A global/local approach using partial hybrid elements is presented to study the interlaminar stress distribution around delamination crack tips in composite laminates subjected to out-of-plane loading. The cracked composite laminate is modeled with three types of elements. 20-node three-dimensional sublaminate partial hybrid elements are used in the local region where the stress gradients are expected to be sharp, 8-node degenerated partial hybrid plate elements are used in the global region and 15-node transition elements are employed to connect the local and global regions. The results show that the global/local approach yields accurate solutions with much less active degrees of freedom, less consumption of computer space and CPU time as compared with the conventional displacement element. Experiments are performed for cross-ply laminates with midplane delamination crack subjected to three-point bending. The predicted critical loads by finite element analysis based on both a strength-based criterion and a fracture mechanics approach are in good agreement with the experimental data.

Beam analysis of angle-ply laminate mixed-mode bending specimens

An analysis of angle-ply laminated beam fracture specimens loaded in a mixed-mode bending (MMB) apparatus is presented. The analysis is based on superposition of compliance and strain-energy release rate expressions previously derived from laminated beam theory for DCB and ENF angle-ply laminate specimens. Elastic interactions between the two arms of the specimen, asymmetry in lay-up, and interlaminar shear deformation are incorporated in the analysis. It was found that the ratio between G I and G II is only slightly sensitive to ply angle in the angle-ply laminates, where G I and G II denote the mode I and mode II components of the strain energy release rate, G. The ratio G I/ G II, likewise, is only weakly dependent on crack length. An experimental study on glass/polyester quasi-unidirectional and angle-ply laminates was conducted. Specifically, [0] 6, [±30] 5 and [±45] 5 laminates with mid-plane delaminations were tested at various mode ratios ( G I/ G II). Predicted compliance values were in good agreement with experimental data. The fracture toughness, G c, increased with decreased ratio G I/ G II. G c increased with increased ply angle θ in the angle-ply laminates except for pure mode I conditions. Nonuniform and skewed crack fronts were observed for the angle-ply laminates as a result of elastic coupling in the laminate beams of the cracked region.

Beam analysis of angle-ply laminate DCB specimens

Analysis and experiments on quasi-unidirectional and angle-ply laminate DCB fracture specimens are presented. The analysis treats the DCB specimen as two Bernoulli–Euler-type laminate beams joined at the mid-plane by a Winkler-type elastic foundation to accomodate transverse elasticity of the uncracked region of the specimen. An experimental study was conducted on glass/polyester quasi-unidirectional and angle-ply laminate DCB specimens. Specifically, [0] 6, [±30] 5 and [±45] 5 laminates with mid-plane delaminations were considered. Compliance values predicted by the elastic-foundation model were in good agreement with experimental data. The initiation fracture toughness was largest for the unidirectional composite and decreased with increased angle in the angle-ply laminates. The fracture toughness, G c, increased with increased crack length and became steady-state after some crack propagation for the angle-ply laminates. The R-curve behavior is attributed to the work associated with debonding of transversely oriented fiber bundles and fracture of fibers that bridged the crack surfaces. The angle-ply laminates displayed more yarn debonding and bridging, and steep resistance curves. For all laminates it was observed that the crack propagated in a nonuniform manner across the width of the specimen as explained by elastic coupling effects of the laminate beams.

Beam analysis of angle-ply laminate end-notched flexure specimens

Analysis and experiments on quasi-unidirectional and angle-ply laminate end-notched flexure specimens are presented. The analysis is based on laminated beam theory incorporating first-order shear deformation theory. Compliance and strain-energy release rate determined for relatively thin unidirectional and angle-ply laminate ENF specimens were in good agreement with a previous classical plate theory formulation. For thicker laminates, however, effects of shear deformation on the compliance of the ENF specimen become significant. An experimental study on glass/polyester quasi-unidirectional and angle-ply laminate ENF specimens was conducted. Specifically, [0] 6, [±30] 5 and [±45] 5 laminates with mid-plane delaminations were considered. Experimental compliance data agreed well with analytical predictions. The fracture toughness increased with increased angle θ at the ±θ interface. This is attributed to the fracture work associated with the debonding of transversely oriented fiber bundles in the quasi-unidirectional plies. The angle-ply laminates displayed more yarn debonding than the quasi-unidirectional laminate. For all laminates it was observed that the crack propagated in a non-uniform manner which is correlated with elastic coupling effects with cracked regions of the laminate beams.

Search Strategies for Identifying a Composite Plate Delamination Using Built-In Transducers

Search strategies are compared that can potentially identify single, rectangular, midplane delaminations in composite plates using the signals from surface-mounted piezoceramics. The strategies are demonstrated by repeatedly assuming a single delamination and then running a delaminated plate model, also described, that predicts transducer frequency responses. An objective function compares the responses to those for a hypothetical plate with unknown damage. When the objective function is minimized, the responses agree, and the assumed delamination is the best-estimate. The chosen objective function is well-behaved but has several local minima; therefore, rardom search strategies are used to find the global minimum. The most efficient strategy starts with assumed delaminations selected from a uniform random distribution at discrete points in the parameter space (i.e., a combinatorial search). Some of these points will be close to local minima. The strategy continues by using a random walk with shrinking step size across the parameter space. This latter search is made more robust by using probabilistic hill climbing acceptance tests, also known as simulated annealing. The overall technique systematically investigates several possible local minima and identifies a best-estimate delamination to a preset accuracy.

Effect of Remote Ply Orientation on the Perceived Mode I and Mode II Toughness of θ/θ and θ/−θ interfaces

Results are presented from an investigation of the effect of remote ply orientation on the perceived mode I and mode II toughness of a laminated graphite/epoxy. Experimental and numerical studies were conducted on four commonly used stacking sequences. Each sequence contained a midplane delamination and was subjected to bending loads that produced either predominantly mode I or predominately mode II conditions. Of the four sequences, two contained delaminations at 30/30 interfaces, and two contained delamination at 30/-30 interfaces. For each interface type, one stacking sequence exhibited a relatively small transverse curvature under the applied loadings but a relatively large twisting curvature, whereas the other sequence exhibited a small twisting curvature but a large transverse curvature. For the two types of loadings (mode I and mode II), each of the four sequences was analyzed by three dimensional finite element analyses and tested in precracked and non-precracked configurations. Using appropriate nondimensional parameters, the results of this study are combined with the results of companion numerical investigations to make recommendations regarding the choice of stacking sequences for the determination of the toughness of arbitrary interfaces.

Strain-energy release rate of delaminated composite plates using continuous analysis

A continuous analysis procedure is introduced for determining the strain-energy release rate for composite plates containing arbitrarily located delamination regions of arbitrary shapes. The plates are considered to be simply supported along their four edges, and double Fourier series solutions are used. A simpler case for a symmetrically loaded double identical plate system having mid-plane delamination resulting in mode I deformation is studied first, and the general case involving the determination of all three modes of the strain-energy release rate for a system of two orthotropic plates bonded by a layer of adhesive is considered subsequently. Some numerical results are presented for illustrative purposes.

On modelling of laminates containing free-edge delaminations

The stress field ahead of the delamination tip and the strain-energy release rate in symmetric composite laminates with mid-plane delamination subjected to mechanical and thermal strains have been studied with the aid of a modified form of the Whitney-Sun theory. The procedure considers the laminate cross-section in three zones based on the geometry. Governing equations have been derived from the principle of virtual displacements, and solutions have been obtained by enforcing the boundary and continuity conditions. Interlaminar normal stresses ahead of the delamination tip and the strain-energy release rates are presented for various sizes of the delamination and are compared with some of those available in the literature.