Sublaminate Approach Research Articles

Exploring guided wave propagation in composite cylindrical shells with an embedded delamination through refined spectral element method

The elastic wave propagation in a thin-walled composite structure carries information concerning its material properties and structural discontinuities. Towards the damage identification, a refined spectral element method (SEM) is presented to explore the guided wave propagation in composite cylindrical shells with embedded delamination. The governing equations and the natural boundary conditions are derived using the first-order shear deformation theory along with the Hamilton's principle. The spectral shell element is established via the exact strong-form solutions, and the dynamic stiffness matrix is formulated through the force-displacement relations. Transforming the wave differential equations into the frequency domain, the numerical Laplace transform is applied to solve the inverse problems. Following a sub-laminate approach, the delamination is modeled by means of four spectral elements and the interface continuity conditions. In addition, the stiffness reduction method is introduced to approximate the delamination. A comparison with published results in terms of the natural frequencies is made to verify the accuracy of the SEM. The dispersion characteristics of the cylindrical shell are examined including the wave number, phase and group velocities. The interaction of guided waves with the delamination is revealed. The influences of the length, depth, and position of the delamination on the wave responses are demonstrated.

An improved model of refined zigzag theory with equivalent spring for mode II dominant strain energy release rate of a cracked sandwich beam

In this paper, an improved model, the refined zigzag theory with equivalent tangential spring (RZTES) in conjunction with the sub-laminate approach, for cracked sandwich beam (CSB) is developed. The kinematics of the refined zigzag theory (RZT) assumes that the axial displacements of a sandwich beam follow piecewise linear distribution across the thickness. This theory can accurately model the zigzag displacement in a sandwich beam without delamination. However, the kinematics of the RZT does not meet the deformations near the crack tip, which contain more complicated displacement distributions. It results in underestimations of both the compliance and mode II dominant strain energy release rate (SERR). The RZTES is developed to correct the inaccuracies due to this underestimation. In RZTES, an equivalent spring is inserted to decrease the local stiffness near the crack tip so that the compliance of the CSB is increased. Based on the procedure developed in this study, the equivalent spring constant can be determined according to the Young’s modulus and shear modulus of the core. Then a gap determined from the equivalent spring constant can be determined and be used to re-formulate the continuity conditions at the crack tip of a CSB. In order to validate RZTES, the CSB is calculated by commercial finite element method (FEM) software ANSYS with two-dimensional elements. The compliances are also validated by experiments. The results show that the RZTES can increase both the compliance and strain energy release rate. The case studies with various ranges of geometric parameters and material properties of the CSB are solved by RZT, RZTES and ANSYS. For the case with soft core or thick beam thickness, the calculation results by RZT need more corrections. By comparing RZT, both the compliances and SERRs calculated by RZTES are more accurate.

Nonlinear Modal Responses of Damaged Shell Structures: Numerical Prediction and Experimental Validation

The nonlinear finite element (FE) modeling approach has been adopted to model and predict the modal responses of the combined damaged (crack and delamination) layered shell structures. The damaged panel structure has been constructed mathematically using a circular meshing approach of the FE technique to include the crack. Similarly, the sublaminate approach has being used to introduce delamination of the layered structure on a mutual center. The structural distorted geometry and the deformations were modeled through the full geometrical nonlinear strain-displacement (Green–Lagrange) relations in association with higher-order polynomial functions. The modal responses of the damaged structure were obtained through an iterative method in association with the nonlinear FE technique. The predicted response accuracies were established with two-step verifications: that is, the numerical solution stability (elemental sensitivity) and the degree of deviation with published data. The maximum deviation between the developed numerical model and the reference result (first-order shear deformation theory) was 8.3%. The model’s competence and responses were compared with experimental data, with and without damages. Finally, new examples have been solved for different structural geometry-dependent parameters (shell configurations, delamination shapes, crack positions/lengths, end boundaries, etcetera) affecting final modal values. A detailed in-depth understanding of the damage and curvature (unequal/equal curvature) effects on modal responses will be discussed.

Wave propagation in thin pretwisted composite strips with an embedded delamination

In this work, a thin pretwisted and delaminated composite strip is modeled using the variational asymptotic method (VAM). The original 3D problem is reduced to a 2D cross-sectional analysis and a 1D problem along the length of the strip. Damage, in the form of an embedded delamination, is accounted in the strip by following a sublaminate approach. The 1D governing elastodynamic equations of the strip model is solved using the spectral finite element (SFE) method, wherein the structure is modeled as a wave guide. In SFE method, the governing elastodynamic equations are solved in transformed frequency domain to obtain the dynamic stiffness matrix. The guided wave response of the delaminated composite structure for different loads and boundary conditions are subsequently computed. Modal and wave response from SFE using the reduced 1D model are validated by comparing results with those reported in the literature and in some cases with the results obtained from a 3D model using a direct finite element (FE) package. Modal and wave propagation analysis is performed for various dimensions of delamination and composite layup. The analysis provides insight into the dynamic characteristic of partially delaminated strip. The usage of SFE is expected to yield a faster result and lesser computation time than the conventional direct FE method for analyzing and monitoring the delaminated strip exposed to high frequency excitations. Additionally, the capability of the model to investigate the inverse problem of damage detection is demonstrated.

Strain-rate-dependent progressive damage modelling of UHMWPE composite laminate subjected to impact loading

A comprehensive strain-rate-dependent (SRD) finite element modeling procedure, based on continuum damage mechanics has been developed to predict the behavior of ultra-high molecular weight polyethylene (UHMWPE) fiber composite laminates under impact loading. A user-defined material subroutine implemented into ABAQUS/Explicit is used to define SRD constitutive damage model of UHMWPE composite. The effect of strain rate on the material properties is adapted to the experimental data by introducing a new hyperbolic function and the strain-rate effect factor (SEF) for use in the modeling. The range of [Formula: see text] to [Formula: see text] is considered for strain rate, which includes both high velocity and low velocity impact regimes. A homogenized sub-laminate approach is employed to more accurately capture the out-of-plane failure mechanisms. Cohesive Zone Model (CZM) with the constitutive model based on bilinear traction-separation is implemented to simulate the inter-laminar delamination between the sub-laminates. High velocity ballistic impact as well as low velocity drop-weight impact are simulated, and the results are validated with experimental observations from the literature. Results show that the presented SRD model, offers more accurate prediction of the projectile residual velocity compared to the SRD model using logarithmic function or without considering the strain rate effect. Moreover, detailed views of failure modes such as tension/shear fiber and matrix shear in layers, and the delamination patterns are obtained and investigated.

Nonlinear steady-state responses of weakly bonded composite shell structure under hygro-thermo-mechanical loading

The nonlinear micromechanical finite element (FE) model is derived to compute the steady-state time-dependent deflections of the weakly connected layered composite panel. The distorted structural geometry is modelled mathematically via the nonlinear strain kinematics in the framework of two different displacement theories (constant and linear functions of the through-thickness stretching term). The thermo-elastic constitutive relation is invoked to count the modified composite properties due to the change in environment. Besides, a sub-laminate approach with end continuity conditions is adopted to model the loosely bonded layers. The equation of motion of shallow panel under the mechanical excitation and the environmental effect is expressed through Hamilton’s principle due to the environmental changes. The deflection parameters due to the steady-state loadings are predicted using the combinations of three different techniques, i.e., the FE, the direct iterative method and Newmark’s constant acceleration. The nonlinear model responses are compared with published data considering all of the strain terms to capture the actual structural distortion. The applicability of the micromechanical FE model is deliberated by taking the combined influences of geometry, property, end constraints and the debonding parameters (size, location and position). A few conclusions are dawn on the micromechanical model after the numerical experimentations.

Ballistic performance of UHMWPE laminated plates and UHMWPE encapsulated aluminum structures: Numerical simulation

The ballistic performance of ultra-high molecular weight polyethylene (UHMWPE) laminated plates and UHMWPE encapsulated aluminum structures were numerically characterized. Full three-dimensional continuum model for each type of target was built, and the UHMWPE was simulated using a sub-laminate approach with a composite material model. Simulation results were compared with existing experimental measurements, with good agreement achieved both on final deformation morphology and ballistic data. Underlying penetration mechanisms of laminated plate were then explored, and the effect of interface strength was quantified. The ballistic improvement of UHMWPE encapsulated aluminum structures was mainly attributed to the stretching of lateral swathing laminates. However, the benefit of encapsulation decreased as the initial impact velocity or lateral dimensions of encapsulated structure were increased. These findings are helpful for designing lightweight UHMWPE composite structures with superior ballistic resistance.

Nonlinear thermal free vibration frequency analysis of delaminated shell panel using FEM

The current research reported the thermal free vibration characteristics of the debonded composite shell structure considering the large geometrical deformation. The delaminated composite panel structural model is derived using two different higher-order polynomial kinematics. The nonlinear structural geometry has been modeled via Green-Lagrange relations in conjunction with temperature loading. The separation between the adjacent layers of the composite has been incurred through a sub-laminate approach and the corresponding displacement continuity imposed at the boundaries (laminated and delaminated). Moreover, the isoparametric Lagrangian type of element (eighty-one and ninety degrees of freedom) is adopted for the discretization of the physical shell structure. The nonlinear governing equation of motion of heated shell (healthy and debonded) structure derived using Hamilton principle and the nonlinear frequency responses computed using the direct iterative technique for the computational purpose. The solution (numerical) stability and the accuracy have been established as a priori by solving a series of examples available in the literature. The conclusions regarding the model applicability for debonded (size, location and position) structural analysis represented with or without temperature effect.

Nonlinear transient analysis of delaminated curved composite structure under blast/pulse load

The nonlinear time-dependent displacement values of the curved (single/doubly) composite debonded shell structure are examined under different kinds of pulse loading in this research. The structural curved panel model is derived mathematically using the higher-order displacement theories containing the thickness stretching effect, whereas the sub-laminate approach is adopted for the inclusion of delamination between the subsequent layers. The structural geometry distortion under variable loading has been included in the current theoretical analysis through Green–Lagrange type of strain kinematics. Further, the governing differential equation order has been reduced with the help of 2D finite element formulation via the nine-noded isoparametric Lagrangian elements with variable degrees of freedom (eighty-one and ninety) for two different higher-order kinematics, respectively. The final equation of motion is solved computationally to evaluate the transient responses through an original computer code including the direct iterative technique and Newmark’s average acceleration method. The convergence criteria of the current numerical solution are established as a priori and the subsequent validity is demonstrated via comparing the current responses with available published data. Further, the comprehensive behavior of the debonded structure under the influence of the variable loads (time and area dependent) is evaluated by solving different numerical illustrations for variable geometrical configuration and described in detail.

Finite element modelling of Dyneema® composites: From quasi-static rates to ballistic impact

A finite element methodology to predict the behaviour of Dyneema® HB26 fibre composites at quasi-static rates of deformation, under low velocity drop weight impact, and high velocity ballistic impact has been developed. A homogenised sub-laminate approach separated by cohesive tied contacts was employed. The modelling approach uses readily available material models within LS-DYNA, and is validated against experimental observations in literature. Plane-strain beam models provide accurate mechanisms of deformation, largely controlled through Mode II cohesive interface properties and kink band formation. Low velocity drop weight impact models of HB26 give force-deflection within 10% of new experimental observations, with in-plane shear strain contour plots from models directly compared with experimental Digital Image Correlation (DIC). Ballistic impact models utilising rate effects and damage showed similar modes of deformation and failure to that observed in literature, and provide a good approximation for ballistic limit under 600 m/s impact speed.

Nonlinear finite element solutions of thermoelastic deflection and stress responses of internally damaged curved panel structure

• A novel numerical model is developed to study the deflection and stress values of the pre-damaged composite structure. • The internal damage has been modeled via sub-laminate approach including two kinematic theories. • The nonlinear FEM solutions are obtained under the combined thermomechanical loading. • The numerical solutions (deflection and stress) are evaluated for different panel geometries via the derived models. Thermoelastic deflection and corresponding stresses of the pre-damaged layered panel structure are investigated numerically in this article including the large deformation kinematics under the linearly varying temperature field. The composite structural deformation kinematics is derived using two different polynomial type of kinematic theories including the through-thickness stretching effect. The inter-laminar separation between the adjacent layers is incurred via the sub-laminate approach and Green–Lagrange strain to count the total structural deformation. Also, the intermittent displacement continuity conditions are imposed in the current mathematical model to establish the displacement continuity between the separated layers. The variational principle is adopted for the evaluation of the nonlinear structural equilibrium equations and solved via total Lagrangian approach . The convergence and the corresponding validity of the currently derived nonlinear finite element solutions are checked by solving different sets of numerical examples. Additionally, the comprehensive inferences are drawn from various numerical examples for the well-defined important input parameter including the size, position, and location of delamination .

Numerical nonlinear frequency analysis of pre-damaged curved layered composite structure using higher-order finite element method

The influence of the internal debonding on the structural stiffness and the nonlinear modal characteristics of the layered structure are examined extensively in the current research article. For the investigation purpose, the shell frequency responses are obtained numerically for both the linear and the nonlinear cases via a generic type of mathematical formulation using the Equivalent Single Layer (ESL) theory in the framework of two kinematic models. The current formulation not only includes the influence of the transverse shear deformations but also satisfies the parabolic variation of transverse shear stress through the thickness. Additionally, the geometrical nonlinear distortion modeled via Green–Lagrange strain–displacement relations. Further, the internal debonding between the adjacent layers are modeled using sub-laminate approach and the displacement continuity between segments (laminate and delaminate) have been established through the intermittent continuity conditions. The nonlinear system governing equation of the vibrated structure is obtained via Hamilton’s principle and converted to set of nonlinear algebraic equations through the isoparametric finite element (FE) steps. The desired responses are solved numerically with the help of robust (direct iterative method) technique and compared with available results to demonstrate the solution accuracy. Subsequently, an adequate number of examples are solved for the delaminated structure using the current higher-order nonlinear models and the influential parameters discussed in detail.

Numerical Analysis of Transient Responses of Delaminated Layered Structure Using Different Mid-plane Theories and Experimental Validation

The present article mainly focuses on the fundamental frequency and the time-dependent deflection responses of the layered composite plate structure considering the effect of debonding between the adjacent layers introduced via sub-laminate approach. The responses are mainly obtained numerically using a newly developed finite element model of the delaminated composite plate using two types of higher-order mid-plane shear deformable kinematics. The debonded plate model is discretized using a nine-noded quadrilateral isoparametric Lagrangian element to obtain the elemental equation and assembled subsequently for the evaluation of the final form of equation of motion. The structural responses (natural frequency and time-dependent deflection) are obtained computationally using a specialized computer code via MATLAB with the help of currently proposed model. Further, the convergence and subsequent comparison study have been performed using the similar examples from the earlier published literature. In addition, the present results are also compared with those of the experimental responses of the fabricated glass-/epoxy-laminated composite plate including the different size of delamination. The elastic material properties and the frequency responses of the fabricated laminate are evaluated using tensile test and vibration measuring experimental set-up. Finally, the dynamic responses of debonded plate have been measured for different sets of structural parameters to show the influence of each parameter as well as the size of debonding on the final responses.

Effect of matrix cracks and delamination on extension-twist coupling of thin pretwisted composite strips

An asymptotically exact cross-sectional model coupled with geometrically nonlinear one-dimensional (1D) theory is developed for a thin composite strip in the presence of defects. Two types of defects are considered: intralaminar cracks and interlaminar cracks. Model development is based on the dimensional reduction of laminated shell theory to nonlinear 1D theory using the variational asymptotic method. The cross-sectional nonlinearity accounts for matrix cracks, quantified in terms of crack density and delamination, quantified in terms of the delamination width. For modeling intralaminar cracks continuum damage mechanics based framework is used along with computational micromechanics to account for intralaminar cracks in laminate plies in different orientations. Delamination modeling follows a methodology adapted from the sublaminate approach. The model developed is used to investigate the effect of defects on the trapeze effect – nonlinear axial-twist coupling in strip with Winckler kind of layup. It was found that cracks in transverse plies enhance the trapeze effect; on the contrary, symmetric edge mid-surface delamination leads to decrease in the coupling effect. This contrarian behavior of the two types of defects on the trapeze effect is explained on the effect these defects have on the various cross-sectional coupling stiffness terms influencing the coupling behavior. Model predictions are presented for strip stiffness degradation due to matrix cracks and delamination.

Simulation Study of Stress and Deformation Behaviour of Debonded Laminated Structure

The bending strength and deformation characteristics of the debonded laminated plate under the uniformly distributed loading (UDL) have been investigated in this research article. For the simulation study, an internally damaged laminated plate structure model has been developed in ANSYS based on the first-order shear deformable kinematic theory via ANSYS parametric design language (APDL) code. The internal debonding within the laminated structure is incorporated using two sub-laminate approach. Further, the convergence (different mesh densities), as well as the validity (comparing the responses with published results) of the present simulation model, have been performed by solving the deflection responses under the influence of transversely loaded layered structure. Also, to show the coherence of the simulation analysis the results are compared with the experimental bending results of the homemade Glass/Epoxy composite with artificial delamination. For the experimental analysis, Glass/Epoxy laminated composite seeded with delamination at the central mid-plane of the laminate is fabricated using an open mould hand lay-up composites fabrication technique. For the computational purpose, the necessary material properties of fabricated composite plate evaluated experimentally via uniaxial tensile test (Universal Testing Machine INSTRON-1195). Further, the bending (three-point bend test) test is conducted with the help of Universal Testing Machine INSTRON-5967. Finally, the effect different geometrical and material parameters (thickness ratio, modular ratio, constraint conditions) and magnitude of the loading on the static deflection and stress behaviour of the delaminated composite plate are investigated thoroughly by solving different kinds of numerical illustrations and discussed in detail.

Nonlinear analysis of a thin pre-twisted and delaminated anisotropic strip

The present work is aimed at the development of an efficient mathematical model to assess the degradation in the stiffness properties of an anisotropic strip due to delamination. In particular, the motive is to capture those nonlinear effects in a strip that arise due to the geometry of the structure, in the presence of delamination. The variational asymptotic method (VAM) is used as a mathematical tool to simplify the original 3D problem to a 1D problem. Further simplification is achieved by modeling the delaminated structure by a sublaminate approach. By VAM, a 2D nonlinear sectional analysis is carried out to determine compact expression for the stiffness terms. The stiffness terms, both linear and nonlinear, are derived as functions of delamination length and location in closed form. In general, the results from the analysis include fully coupled nonlinear 1D stiffness coefficients, 3D strain field, 3D stress field, and in-plane and warping fields. In this work, the utility of the model is demonstrated for a static case, and its capability to capture the trapeze effect in the presence of delamination is investigated and compared with results available in the literature.

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.

Effects of matrix cracking and hygrothermal stresses on the strain energy release rate for edge delamination in composite laminates

A simple theoretical model based upon the equivalent constraint model 1,2 and a sublaminate approach 3 is used to determine the strain energy release rate, G ed, in [± ϑ m 90 n ] s carbon/epoxy laminates loaded in tension. The analysis provides closed-form expressions for the reduced stiffness due to edge delamination and matrix cracking and the total strain energy release rate. The parameters controlling the behaviour are identified. The effect of laminate stacking sequence, matrix crack density and hygrothermal stresses on G ed is examined. Results show that the available energy for edge delamination is increased notably due to transverse ply cracking. Also, residual thermal stresses increase substantially the strain energy release rate and this effect is magnified by the presence of matrix cracking. Finally, predictions for the edge delamination onset strain are in acceptable agreement with experimental measurements.

A simple sublaminate approach to the design of thick composite laminates for suppression of free-edge delamination

A simple stacking method is presented for the suppression of the free-edge delamination in balanced symmetrical laminates subjected to a uniaxial load. The stacking method is determined by analyzing various laminates with different fiber orientations and stacking sequences. The method is that one half of a thin laminate is disposed to be symmetrical with respect to the value of the effective Poisson's ratio, and thick laminates are constructed by the repetition of sublaminates in which the value of the effective Poisson's ratio is symmetrical. Delamination tests have been performed on (35/-35/90) and (90/45/-45) laminate families consisting of 24 plies with different stacking sequences in order to examine the stacking method. The (35/-35/90) laminate family were tested under static tension and the (90/45/-45) family under static compression to eliminate the effect of transverse cracking on free-edge delamination. The experimental results are discussed together with the results of the analysis.

Interlaminar stress predictions for laminated composites under bending, torsion and their combined effect

A simple analytical formulation is used to predict the interlaminar stresses in a symmetric laminate under extension, bending, torsion and their combined effect. The method is based on a shear deformation theory and a sublaminate approach. The solution is obtained in closed form and the controlling parameters are isolated. Extensive comparisons with a finite element solution are made to verify the model for the case of laminates subjected to torison loading. An assessment of the induced curvature predicted from classical lamination theory and the present approach is provided. The influence of the induced curvature on the interlaminar stress prediction is investigated for torsion loading. The interlaminar stresses in laminates subjected to combined bending and torsion are obtained by superposition.