Interlaminar Stress Analysis Research Articles

A refined model for functionally graded graphene nanoplatelets reinforced composite beams under thermal loads

Graphene is highly regarded as a promising material for various engineering purposes due to its remarkable physical characteristics. However, existing higher-order shear deformation theories may struggle to accurately capture the interlaminar mechanical response of functionally graded graphene nanoplatelets (FG-GNP) reinforced composite beams subjected to thermal loads. This arises from the pronounced discrepancies in material properties and thermal expansion coefficients among the various layers, making the interlaminar mechanical behavior of composite structures exceedingly complex under thermal loading. As a result, a meticulous analysis of interlaminar stresses becomes necessary for the structural assessment of GNP-reinforced composite beams under temperature variations. To overcome this limitation, we propose an advanced model incorporating transverse normal thermal deformation, tailored specifically for FG-GNP reinforced composite beams subjected to thermal loads. The developed model primarily boasts two advantages. Firstly, although transverse normal deformation is introduced into the displacement field, no additional displacement variables are increased, thereby maintaining model simplicity and efficiency. Secondly, the model achieves a high-precision interlaminar shear stress field taking into account the interlaminar continuity conditions and temperature effects. Furthermore, the elimination of second-order derivatives of in-plane displacement parameters from the transverse shear stress components leads to a simplification in the finite element implementation. Based on the proposed model, a simple three-node beam element is constructed. The 3D elasticity solutions and the results from alternative modeling frameworks are used to assess the performance of the developed model. Additionally, a comprehensive investigation is conducted to explore the effects of various parameters on the deformations and stresses of GNP-reinforced composite beams.

PREDICTION OF INTERLAMINAR STRESSES ACTING IN THE ANGLE PLY E-GLASS EPOXY COMPOSITES USING ANALYTICAL AND NUMERICAL METHODS

Prediction of interlaminar stress is the leading research area in the field of composite structures nowadays. Many research works related to the interlaminar stresses induced in the composite structures, such as the formulation of analytical solutions to predict the interlaminar stresses, finding out the additional provision to be made in the experimental set-up for the measurement of interlaminar stress, and the development of various theories for the accurate determination of inter-laminar stresses and free edge stresses are going on. Among the research works carried out so far, cross-ply composites have been concentrated more because of their more application areas. The present work considers an angle ply E-Glass epoxy composite structure for the interlaminar stress analysis. Interlaminar stresses induced in the considered angle ply composite for the given loading condition have been predicted using analytical and numerical analyses, and the results have been compared.

Electro-mechanical coupling model and interlaminar stress analysis of laminated plates containing GSR actuator

Due to its remarkable physical features, graphene nanosheets (GPN) are one of the most appealing reinforcing materials for composites. For polyvinylidene fluoride (PVDF), GPN reinforced composites can dramatically increase its piezoelectric and mechanical characteristics. If the interlaminar shear deformation of laminated plates containing uniform graphene sheets reinforced (GSR) smart piezoelectric layer, which material properties vary widely from layer to layer and subjected to electromechanical loading cannot be accurately predicted, the interlaminar stresses may be very high, eventually leading to interlaminar failure. In light of this, an effective mechanoelectrical coupling model for the accurate prediction of interlaminar stress for composite plates contains GSR actuators is developed in present study. Meanwhile, the finite element formulation (FEF) can be substantially simplified due to the expression of transverse shear stress components becoming more succinct. Therefore, by using the suggested electro-mechanical coupling theory, a three-node FEF is easily constructed. The refinement of transverse shear stress prediction in the context of electromechanical coupling can be accomplished through the application of the Reissner mixed variation theory (RMVT). The performance of the recommended plate model will be evaluated using the results derived from three-dimensional (3D) elastic theory and the selected model. By employing the RMVT method, we improve predictions of transverse shear stresses while considering the electromechanical coupling effect. The results from our model are compared with alternative models and 3D elasticity theory, demonstrating its superiority in satisfying the continuity requirements of transverse shear stresses and exhibiting excellent agreement with exact solutions. This validates the accuracy and applicability of our proposed model. Further to that, the prediction of mechanical characteristics for laminated plates with GSR actuators were systematically studied from the thoroughly perspectives of electromechanical load, piezoelectric layer thickness, graphene volume fraction, and some other parameters.

Electro-mechanical analysis of functionally graded graphene reinforced composite laminated plate with macro fiber composite actuator

Graphene is considered to be a desirable reinforcement material for composite materials due to its exceptional mechanical properties. However, there is a lack of research on the interlaminar stress analysis of graphene reinforced composite plates bonded with a macro fiber composite (MFC) actuator subjected to electro- mechanical loads. Inaccurate descriptions of interlaminar shear deformations can significantly affect the mechanical performance of the MFC piezoelectric graphene reinforced composite plate due to the electro-mechanical coupling feature and abrupt change in material properties at the interfaces of neighboring layers. To address this issue, this study proposes an attractive plate model for the analysis of MFC piezoelectric laminated plate. The three-dimensional (3D) elasticity equations and the Reissner mixed variational theorem (RMVT) are employed to improve the precision of interlaminar shear stresses. The 3D elasticity solutions and results obtained from other models are used to evaluate the proposed model. Furthermore, this study thoroughly investigates the effect of several significant parameters on the deformations and stresses of the MFC piezoelectric plates with reinforcements.

A new electro-mechanical finite formulation for functionally graded graphene reinforced composite laminated thick plates with piezoelectric actuator

Graphene is regarded as one of the most attractive reinforcements for composite materials attributing to the extraordinary physical characteristics. However, existing models in the literatures might meet severe challenges for the interlaminar stress prediction of functionally graded graphene reinforced composite (FG-GRC) laminated thick plate integrated with piezoelectric fiber reinforced composite (PFRC) actuator under electro-mechanical loadings. If transverse shear deformations cannot be described accurately, the mechanical performance of FG-GRC laminated plate with PFRC actuator will be significantly impacted by the electro-mechanical coupling effect and the sudden change of material characteristics at the interfaces. Thereby, a new electro-mechanical coupled plate model with only seven independent displacement variables is to be proposed in this paper. Employing the Reissner mixed variational theorem (RMVT), the precision of the transverse shear stresses considering the electro-mechanical coupling effect can be improved. Moreover, the second-order derivatives of in-plane displacement parameters have been removed from the transverse shear stress components, which can greatly simplify the finite element formulation. Thus, based on the proposed electro-mechanical coupled plate model, a simple C0-type finite element formulation is developed for interlaminar shear stress analysis of FG-GRC laminated thick plate with a PFRC actuator. The 3D elasticity solutions and the results obtained from other models are used to assess the performance of the proposed finite element formulation. Additionally, comprehensive parametric studies are achieved for the influences of graphene volume fraction, distribution pattern, electro-mechanical loading, boundary conditions, lamination scheme and geometrical parameters of the plate on the deformations and stresses of the FG-GRC laminated plate with a PFRC actuator.

Continuous interlaminar shear stress analysis of laminated FG-CNTRC beams based on an extended high-order layerwise model

This article presents continuous interlaminar shear stress analysis of laminated beams with functionally graded single-walled carbon nanotube reinforced composite (FG-CNTRC) layers based on an extended high-order layerwise model in the framework of the Carrera Unified Formulation (CUF). By considering the CNTs uniformly or functionally graded (FG) distributed through the thickness of each layer, the extended rule of mixture is adopted to estimate the effective material properties of the FG-CNTRC layers. The extended layerwise theory for laminated FG-CNTRC beams is formulated based on layerwise description of transverse shear stress field. With the introduction of stress variables at interfaces, a priori continuity of the transverse shear stress field is fulfilled. In the formulation of the extended model, the independent variations of material properties along the thickness of each FG layer are fully taken account. Then, finite element solution for static analysis is developed based on the proposed model. Comparisons with the results of other theoretical and high-fidelity finite element models well demonstrate the accuracy of the present model in predicting transverse shear stress analysis of laminated FG beams with different features. Besides, parameters studies are presented including the effects of CNTs distributions and CNTs orientation angles on bending behaviors of laminated FG-CNTRC beams.

Interlaminar stress analysis of functionally graded graphene reinforced composite laminated plates based on a refined plate theory

Nowadays, graphene is considered as one of the most ideal reinforcements for composite materials due to the outstanding mechanical properties. From the literature survey, it is found that the researches on interlaminar stress analysis of functionally graded graphene reinforced composite (FG-GRC) laminated structures are scarce in literature. If transverse shear deformations are unable to be described accurately, the reasonable design of FG-GRC laminated structures will meet severe challenges due to the differentiation of material properties at the adjacent layers. Thereby, such issue is less studied by using the efficient models, so an advanced mixed-form plate theory is to be proposed for transverse shear stress analysis of FG-GRC laminated plates. The proposed theory can meet beforehand compatible conditions of transverse shear stresses at the interfaces of adjacent laminates and only contains seven independent displacement variables. By applying the three- dimensional (3D) equilibrium equations and the Reissner mixed variational theorem (RMVT), the accurate transverse shear stresses are obtained. The 3D elasticity solutions and the results computed by using the chosen models are selected to appraise the capability of the proposed model. Numerical results show that the proposed plate model can yield accurately transverse shear stresses without any post-processing procedure. In addition, the effects of graphene volume fraction, graphene distribution pattern, lamination sequence, span-to-thickness ratio and aspect ratio on the displacements and stresses of the FG-GRC laminated plates are thoroughly investigated.

Interlaminar Stress Analysis of Orthotropic Laminated Doubly-Curved Shells on Rectangular Planform under Concentrated Force

AbstractThis paper aims to investigate the interlaminar stresses of laminated composite doubly-curved shells on a rectangular planform subjected to concentrated force using various equivalent singl...

A simple analytical method for determining interlaminar shear stresses in symmetric laminates

An analytical procedure for the analysis of interlaminar shear stresses in symmetric laminates is presented. The approach is based on the fact that the coupling effects of each part of the laminate are compensated by the adjacent parts. In a first step, a half of the laminate is considered for determining forces and moments per unit length that prevent the global deformation of the whole laminate. These forces and moments are obtained by solving a homogeneous second order differential equation. Then, the interlaminar shear stresses are computed by applying the stress equilibrium equations and by imposing the continuity of the stresses in the layer interfaces. The analytical results are checked by means of Finite Element Method in the case of quasi-isotropic laminates.

Multiscale analysis of interlaminar stresses near a free-edge in a [±45/0/90]s laminate

A multiscale model for a [±45/0/90]s tape laminate under uniaxial extension was used to investigate the effect of modeling the heterogeneous microstructure near a free-edge. A random fiber arrangement was used for the 0° and 90° plies and homogenized properties for the 45° and −45° plies. The predicted interlaminar normal stress was compared to the prediction using a classical homogeneous model. When fibers and matrix were modeled discretely, the local stress state was shown to be sensitive to the proximity of fibers, which caused a complex stress distribution along the 0–90 ply interface. Next, the effect of reducing the size of region modeled at the microscale was investigated, since this would significantly reduce the computational effort. Reducing the region modeled at the microscale in the direction normal to the 0–90 ply interface to a size that was 25% and 10% of the ply thickness only changed the peak stresses by 3% and 8%, respectively. Reducing the microscale region in the direction normal to the free-edge to be one and two ply thicknesses in size did not have a significant effect on the predicted interlaminar normal stress at points within 75% of a ply thickness of the free-edge.

Analysis of damage and interlaminar stresses in laminate plates with interacting holes

In a laminate plate with an open hole, the damage initiation and progression and the interlaminar stresses that appear close to hole edge are modified when a second hole is made close to the first. The purpose of this study is to analyse the interaction between two holes when the plate is subjected to compressive loads. The Serial/Parallel Mixing Theory is used as the constitutive law of the composite, and a Continuum Damage Model is applied to predict failure initiation and propagation due to fibre microbuckling and matrix cracking. The model is validated using data from the literature. The developed model is able to predict the differences in the initiation and propagation of damage due to fibre microbuckling and matrix cracking in the area around the two holes. The variation of the distance between holes significantly modifies the damage due to both mechanisms. Also, the interlaminar stresses along the laminate thickness are changed. The results of this study can be applied to predict the critical distance between holes to avoid damage initiation by matrix cracking and microbuckling.

Numerical analysis of interlaminar stresses in open-hole laminates under compression

In this paper, the interlaminar stresses in open-hole laminates subjected to compressive loads are analysed using a numerical model. This model implements the Serial/Parallel Mixing Theory (S/PMT) and a Continuum Damage Mechanics (CDM) approach. The S/PMT estimates the global stiffness in the laminate from fibre and matrix properties. The CDM approach models the damage initiation due to fibre microbuckling. The global response estimated by the model was verified with experimental data from the literature. The model predicts that the damage initiates in the laminate middle-plane where the thickest block of plies oriented in the load direction is located, and progressively propagates to the nearest block of layers with the same orientation. Two laminate stacking sequences were analysed. The interlaminar stresses around the hole presented symmetry with respect to the load direction and the perpendicular axis, being located the maximum and minimum values in different angular positions for each stress component and laminate.

Two-dimensional analysis of interlaminar stresses in thin anisotropic composites subjected to inertial loads by regularized boundary integral equation

Evaluation of interlaminar stresses in composites plays a crucial role to ensure structural integrity. It is quite often to have composites consisting of very thin anisotropic multilayers. Traditional domain modeling of ultra-thin multilayers usually requires a tremendous amount of refined elements that might cause computation overloading. This article proposes an efficient computational methodology for evaluation of two-dimensional interlaminar stresses in thin anisotropic composites subjected to inertial loads. This analysis is by the regularized boundary integral equation (BIE) that employs only very coarse meshes. In the present work, the directly transformed boundary integral equation is regularized using the scheme of integration by parts and analytical integration. By the proposed approach, modeling of very thin layered composites can be performed simply by very coarse mesh. The obvious advantage of the present method over conventional methods is the much less modeling efforts that are required for analyzing very thin multi-layered composites. For verifications, a few benchmark examples are presented in the end.

A variational model for free-edge interlaminar stress analysis in general symmetric and thin-ply composite laminates

A variational model is developed to exactly determine both stress and displacement fields at free edges of general symmetric composite laminate strips under thermomechanical loads. By partitioning the total stresses in a composite with free edges into unperturbed (without free edge) and perturbation stresses and using the minimum complementary energy principle, the optimal stress and displacement fields are derived that exactly satisfy equilibrium, compatibility, boundary and continuity conditions. The paper extends the theory of stress-based variational stress transfer so that the effects of both applied traction and displacement loads can be considered. It has been also shown how the displacement field can be determined for a stress-based variational approach. The results are compared to refined finite element results. The superiority of the developed method over finite element method, both in terms of accuracy and computational efficiency, is discussed. The method is also applicable to thin-ply laminates and is computationally efficient.

Interlaminar stress analysis of multilayered composites based on the Hu-Washizu variational theorem

Up to date, accurate prediction of interlaminar stresses is still a challenging issue for two-node beam elements. The postprocessing approaches by integrating the three-dimensional equilibrium equation have to be used to obtain improved transverse shear stresses, whereas the equilibrium approach requires the first-order derivatives of in-plane stresses. In-plane stresses within two-node beam element are constant, so the first-derivatives of in-plane stresses are close to zero. Thus, two-node beam elements encounter difficulties for accurate prediction of transverse shear stresses by the constitutive equation or the equilibrium equation, so a robust two-node beam element is expected. A two-node beam element in terms of the global higher-order zig-zag model is firstly developed by employing the three-field Hu-Washizu mixed variational principle. By studying the effects of different boundary conditions, stacking sequence and loading on interlaminar stresses of multilayered composite beams, it is shown that the proposed two-node beam element yields more accurate results with lesser computational cost compared to various higher-order models. It is more important that accurate transverse shear stress has active impact on displacements and in-plane stresses of multilayered composite beams.

Theoretical and finite element investigation of inter-laminar stresses for laminated composite beam

The advantage of material properties and flexibility of choosing material have made composite materials a primary preference for structural and aircraft applications. Unlike isotropic materials, the parametric study and optimization analysis of composite structures is complicated due to high number of parameters involved in designing like material properties, fiber orientation and stacking sequence, besides geometric dimensions. The objective of this study focuses on the development of an analytical method for inter-laminar stress analysis of laminated composite I-beam by extending the applicability of lamination theory usually used at laminate level to composite structure level. Analytical expressions for calculating the properties of laminated beam section such as centroid, axial and bending stiffness have been derived. These properties of section are then used to calculate the stresses of each ply of I-beam at any given level. Further, a finite element model has been created using ANSYS 15.0. The stress results obtained analytically have been found to be in excellent agreement with the results obtained from the finite element analysis.

Interlaminar stress analysis in general thick composite cylinder subjected to nonuniform distributed radial pressure

ABSTRACTInterlaminar stresses in thick a composite cylinder with general layer stacking subjected to uniform and nonuniform distributed radial pressure are studied. The layerwise theory of Reddy is employed for formulation of the problem. An analytical method is presented for solving the governing equations. To increase accuracy, interlaminar stresses are obtained by integrating the equilibrium equation of elasticity. After a convergence study, the accuracy of the layerwise laminate theory is investigated using the predictions of finite element method. Predictions of Hooke's law and integration method for interlaminar stresses are compared. Uniform and nonuniform internal and external loads are considered and a parametric study is done for various cylinders.

Interlaminar stress analysis of magneto-electro-elastic composite layered laminates using a stress function based iterative approach

In this paper, we propose a stress function based iterative approach for predicting the interlaminar stresses in magneto-electro-elastic (MEE) composite layered laminates induced by both mechanical and piezomagnetic excitations. The proposed iterative methodology adopts the Lekhnitskii stress functions as stress fields which satisfy the pointwise equilibrium condition under plane strain state and the stress trial functions are separated into the in-plane stress function and out-of-plane stress function. The iteration initiates from an assumption of the out-of-plane stress function as a combination of harmonic functions. By taking the principle of complementary virtual work, the governing equations are derived and the in-plane stress function can be obtained by solving a general eigenproblem. The obtained in-plane stress function is further used as the known function and the out-of-plane stress function is solved in the next iteration. Through the iterations, the interlaminar stress distributions are calculated from the iterative process and the accuracy is improved. The results are validated by the 3-D FEM results under the mechanical load and the convergence study is also conducted. The proposed approach is accurate and efficient in predicting the interlaminar stresses of MEE composite layered laminates.

Dynamic Stability and Interlaminar Stress Analysis of Cylindrical Shells Subjected to Elevated Thermal Field

Three-dimensional thermo-mechanical stress analyses of cylindrical shell structures made with laminated Fibre Reinforced Polymer (FRP) composites have been carried out. Brick 8-node 185 layered solid elements have been used in the present finite element simulation. Due to curved geometry and interaction of different coupling modes at the ply-interfaces, stress concentration effects have been realized throughout the domain of the laminated shell structure. Appropriate finite element mesh size obtained through convergence study has been adopted to capture these stress concentration effects. Thermal field induced out-of-plane interlaminar stresses (σrr, τθr, τzr) responsible for delamination damage initiations have been analyzed in details. Effect of different stacking sequences on thermo-mechanical dynamic stability of shell structures has also been studied. It has been observed that, structural dynamics of composite shell structures get significantly affected under elevated thermal field.

Damage mechanisms in cementitious coatings on steel members under axial loading

Cementitious coatings have been widely used as fire protection for steel structures, but they are vulnerable to structural deformations or vibrations, which may lead to reduction in their effectiveness and cause severe economic loss in the event of a fire. For buildings in practice, the problem can be critical because the coatings are assumed to be in good condition as they are usually hidden underneath architectural finishes, making it difficult and expensive to carry out routine inspection. To determine the actual fire resistance of a building after a moderate or severe loading event or a relatively long period of service, it is imperative to understand the performance of the coatings and to develop effective damage estimation methodologies. Loading conditions in a real buildings can be complex, however as there is inadequate previous work in this field, it is considered more important at this stage to determine the fundamental damage mechanisms in cementitious coatings on steel members subjected to axial loading, as investigated in this paper through experimental and numerical studies. At first, tests are carried out to obtain mechanical properties of the coating and the bond properties between the coating and the steel substrate. Then, a series of monotonic loading tests are conducted on axially loaded steel members to observe damage propagation in coating specimens. Subsequently, a cohesive zone finite element (CZFE) scheme is presented for modelling the damage with both interfacial and internal damage considered. The effectiveness of the proposed CZFE scheme is validated by comparison with different numerical approaches, interlaminar stress analysis and monotonic loading tests. From monotonic loading tests and CZFE numerical analyses, damage mechanisms in cementitious coatings on axially loaded steel members are clearly revealed. Under tensile loading, the damage begins with interfacial cracks at both ends, followed by transverse cracks within the coating resulting in its ultimate fracturing into segments. Under compressive loading, the damage also initiates at the ends with interfacial cracks and propagates towards the centre until the coating completely peels off. The findings from this research build a solid foundation for estimating the damage of cementitious coatings for trusses and large space structures, as most of the structural components in these structures are axially loaded. This work also provides an effective approach for further research on understanding damage mechanisms in cementitious coatings in steel frame structures under more realistic loading conditions.