Interlaminar Normal Stress Research Articles

Mechanical simulation and debonding risk analysis of OLED panels with optically clear adhesives

This paper presents a mechanical simulation model and analysis method for OLED panels. The functional layers within the panel are bonded using optically clear adhesives (OCAs), which are pressure-sensitive adhesives (PSAs), resulting in a soft interface bonding problem. It was discovered that the normal tensile debonding strength of OCAs was significantly lower than the shear debonding strength. To address this issue, a three-layer structure simulation model of “hard + soft + hard” is established, which allows for analyzing the screen folding problem of any radius. Additionally, a suitable element mesh generation strategy for multi-layer structure screens is proposed. A debonding risk index based on pressure is introduced by comparing the interlaminar normal and maximum principal stress. The influence of thickness, bending radius, and Young’s modulus on longitudinal stress and debonding risk index is examined. It is observed that the influence of thickness and Young’s modulus on debonding risk is non-monotonic, indicating the presence of an optimal solution. The high debonding risk area is located at the beginning of the folding mechanism and screen bonding. The proposed debonding risk index is not only applicable to OCAs but also to all PSA with similar structures.

An interlaminar fatigue damage model based on property degradation of carbon fiber-reinforced polymer composites

Interface delamination is a significant damage mechanism in fiber-reinforced polymer (FRP) laminated composites caused by interlaminar normal and shear stresses. This is due to the low interlaminar properties including interface stiffness and strength that continuously degrade to cause fatigue crack nucleation and growth. In this respect, an interlaminar fatigue damage model is proposed to accurately address the reliability aspect of the FRP composite materials and structures. The model considers a damage process that consists of two stages: (1) fatigue damage evolution due to interlaminar properties degradation to the onset of crack nucleation. A cyclic cohesive zone model with a bilinear softening behavior is introduced along with the fatigue life model to capture the mean stress effect of the interface. This is followed by (2) the crack nucleation process leading to the physical separation/debonding of the interface material point, as governed by the cycle-dependent fracture energy dissipation. The mechanical prediction of the interlaminar fatigue damage process is illustrated through finite element simulation of a mixed-mode flexural test of a carbon fiber-reinforced polymer (CFRP) composite beam subjected to fatigue loading. The results indicate that the interlaminar normal and shear crack opening displacement increases exponentially with the larger number of load cycles. In addition, the high-stress gradient is limited to the interface crack front zone with the normal and shear stress peaks at 69.2 and 16.5 % of the respective interlaminar strength. Moreover, controlled interlaminar crack growth is initially foreseen at 7.0 × 10-6 mm/cycle, followed by an abrupt crack “jump” at 287,000 load cycles.

Numerical analysis on the thermal mismatch stress of quasi-isotropic strand with square cross section during cool-down

The quasi-isotropic strands (Q-IS) with high current-carrying capacity can effectively improve the anisotropy of the critical current in the magnetic field. However, when a quasi-isotropic strand is cooled from room temperature (300 K) to the liquid helium temperature (4.2 K), it may cause the irreversible degradation of the critical current, the plastic deformation, and even mechanical damage. In order to achieve the safe and stable operation of quasi-isotropic strands, it is important to analyze the thermal mismatch stress during cool-down. In this study, two mechanical models (i.e. a bulk model and a contact model) were developed by considering different material elastoplastic characteristics to study the mechanical behaviors of quasi-isotropic strands with square cross section in the cooling process. Compared with the bulk model, the contact model can simulate the contact and separation between adjacent REBCO conductors in quasi-isotropic strands. Therefore, the contact model should be chosen to estimate the thermal mismatch stress of quasi-isotropic strands during cool-down. In addition, plastic deformation was clearly observed in the Cu and Ag layers with peak equivalent plastic strains of 0.016% and 0.171%, respectively. When the stainless steel sheath is replaced by the copper sheath to encase a quasi-isotropic strand, the interlaminar normal tensile stress between the superconducting layer and Hastelloy substrate was decreased from 101 MPa to 16.2 MPa. Therefore, a quasi-isotropic strand encased in a copper sheath could reduce the risk of delamination during cool-down.

A Fatigue Model to Predict Interlaminar Damage of FRP Composite Laminates Subjected to Mode I Load.

In fiber-reinforced polymer (FRP) composite laminate structures operating under fluctuating stresses, interface delamination is seen as one of the significant damage mechanisms. The constant degradation of their relatively low interlaminar strength and stiffness are the primary reasons for delamination. This study develops an interlaminar fatigue damage model to quantify the mechanics of the damage process and address the reliability of composite structures. The model considers the failure process in two stages: (1) damage due to degradation of interlaminar elastic properties, and (2) damage due to dissipation of fracture energy through the damage evolution process. The model is examined for a case study of mode I fatigue loading of a carbon-fiber-reinforced polymer (CFRP) composite laminate. The results show that the interlaminar normal stress is confined to the crack front region, with tensile stress peaks at 70% of the interlaminar strength. Furthermore, a stable interface crack growth is predicted initially, followed by a sudden crack "jump" at 14,000 cycles. The simulation results are compared with the experimental data, with very good agreement, showing a successful validation of the fatigue model.

Study of Allowable Interlaminar Normal Stress Based on the Time-Temperature Equivalence Principle in Automated Fiber Placement Process.

Automatic fiber placement (AFP) is a type of labor-saving automatic technology for forming composite materials that are widely used in aviation and other fields. In this process, concave surface delamination is a common defect, as existing research on the conditions for this defect to occur is insufficient. To predict the occurrence of this defect, the concept of allowable interlaminar normal stress is proposed to define its occurrence conditions, and based on this concept, probe tests are carried out using the principle of time–temperature equivalence. Through the laying speed/allowable normal stress curve measured in the probe experiment, the physical meaning of allowable normal stress is discussed. At the same time, the measured curve is quantitatively analyzed, combined with viscoelastic theory and the molecular diffusion reptation model, and the dominating effect in the formation of a metal/prepreg layer and prepreg/prepreg layer is determined. Finally, the experimental data are used to guide the parameter selection in an automatic placement engineering case and prove its correctness.

Failure analysis of tapered composite propeller blade

This research provides a thorough investigation on aspects of the structural integrity of composite blades for a range of operating conditions using fluid-structure interaction analysis based on Computational Fluid dynamics (CFD) and Finite Element Method (FEM). Both shell elements and layered solid elements were used in the finite element model. The strength was assessed against Tsai-Wu, Hashin, and Hoffman criteria. The blade is subjected to combined loads of bend and twist that varying in magnitude, direction, and acting point therefore, the critical failure mode is shown to be highly affected by operating conditions which necessitates evaluating the strength for the whole operating range. The safe operating range was analyzed according to a guidance note recently released by Bureau Veritas (BV) which defines safety limits for individual and combined stresses across each ply. Interlaminar normal stress failure is shown to be the most critical mode of failure, hence a solid model is recommended over the shell model. The blade strength meets the requirement of BV rules when assessed by Hoffman criteria however, other failure criteria show insufficient strength at the design condition.

Interlaminar stress analysis of composite shell structures using a geometrically nonlinear layer-wise shell finite element

This work aims to calculate interlaminar stress distribution through the thickness of multilayered composite shell structures by employing a novel nonlinear layer-wise shell finite element formulation. Adapting the Mindlin– Reissner theory in each layer, the shear-deformable layer-wise shell element presents the interlaminar shear stress distributions by increasing the number of layers. The interlaminar normal stress distribution is then determined using the finite difference solution of the general form of equilibrium equation in the non-orthogonal curvilinear grid along the Gaussian points. Two boundary conditions at the bottom and the top surfaces are satisfied by adopting the linear Lagrange interpolation function. The developed formulation is assessed through some illustrative problems solved using a proprietary finite element computer program. The results compare very well with those available in the literature and those obtained by simulations with the commercial finite element software Ansys.

Three-dimensional modelling of interlaminar normal stresses in curved laminate components

This paper presents the interlaminar normal stress distribution across the width of L-shaped composite components in bending, with special emphasis on the free edge effects and the induced loading due to boundary conditions. As L-shaped composite components are becoming more commonplace in engineering applications, it is of vital importance to understand their failure mechanisms and stress fields. An extensive literature review reveals that interlaminar delamination is the critical failure mode for curved composite components. Despite this, most literature only provides a two-dimensional analysis of the interlaminar stresses and the free edge effects and asymmetry due to induced torsion are not considered. This paper uses three-dimensional finite element modelling to address the following with respect to L-shaped laminate components in bending: (i) radial stress due to the presence of curvature, (ii) effect of lay-up on the free edge effect, (iii) determining how induced torsion affects the interlaminar normal stress distribution. The necessity of using a three-dimensional model to analyse the interlaminar normal stress across the width of a curved composite component is discussed. It was concluded that using a two-dimensional model could underpredict the interlaminar normal stresses by up to 37% for the lay-ups analysed in this research.

Predicting the relative magnitude of interlaminar stresses due to edge effects in thin angle-ply laminates using macroscopic finite element modeling

Carbon-epoxy and other composite materials are widely used in the design of aircraft and other structural components, but can be susceptible to delamination at free edges due to the presence of out-of-plane stresses. Finite element (FE) modeling can be used to predict the magnitude and location of these edge stresses, but the often used macroscopic approach to representing laminates can result in predictions that vary considerably due to the numerical singularities that are created. In this study, two macroscopic FE approaches are tested for thin angle-ply laminates in tension, and recommendations are made for the most effective method for evaluating the edge-effect phenomenon early in the design process. It has been determined that perfect interface models cannot be used for predicting maximum interlaminar stresses at free edges. Perfect interface models can effectively predict the relative magnitude of the interlaminar shear stress, τxz but resin interface models must be used for the interlaminar normal stress, σz.

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.

Effect of heterogeneity at the fiber–matrix scale on predicted free-edge stresses for a [0°/90°]s laminated composite subjected to uniaxial tension

The effect of the free-edge on the interlaminar stresses that develop in a thin-ply [0°/90°]s laminated composite under uniaxial tension was explored using finite element models that directly modeled the random heterogeneous microstructure and a model that treated the plies as homogeneous, orthotropic materials. The deformed cross-sections were compared for the two cases, showing that the homogeneous model generally captured the displacement field well but the heterogenous model exhibited local perturbations due to the microstructure. The interlaminar normal stress distributions along the ply interfaces were very different for two models. The heterogeneous model exhibited a complex pattern of stresses that were sensitive to nearby fibers. A comparison of the interlaminar shear stress distributions for the two models showed better agreement, though the heterogeneous model greatly differed from the homogeneous model when fibers or matrix pockets were close to the ply interface. After separating the effect of the fibers and the free-edge effect, the stresses that develop due to the free-edge effect matched well between the two models, except very close to the free-edge. It was shown that the Poisson’s ratios of the fibers and matrix significantly affect the stress distributions along the ply interface, and a matrix Poisson’s ratio could be selected that reduces the effect of the microstructure on the interlaminar normal stress. The study highlighted that a full 3D analysis can provide new insights for classical problems, and more optimal design of composites will require consideration of microstructural effects.

Evaluation of Progressive Failure of Composite T-Joint Using Mixed Mode Cohesive Zone Model

T shaped stiffeners are the most commonly used structures in aerospace components. De-lamination/de-bond initiation followed by its growth is one of the most common reasons for failure in a fiber reinforced composite structure. It is caused by the interlaminar normal and shear stresses between different structural constituents. In a typical structural T-joint, the failure mechanism and location may differ based on the structural design parameters like fillet radius, thickness, layup sequence, filler stiffness, etc. In this study, finite element analysis has been performed using cohesive zone model (CZM) on a composite T-joint to simulate the pull out test conditions. A simplified plane strain model coupled with CZM is proposed, which can evaluate the failure initiation and progression accurately with lesser computational efforts. The final failure occurs at a displacement of 8.04 mm and the computed failure load is 2240 N. The results obtained by the proposed numerical model are validated by experimental results and it is observed that predicted regions of failure, failure displacements and failure load calculated are correlating reasonably well with the experiment.

Evaluation of Interlaminar Stresses in Composite Laminates with a Bolt-Filled Hole Using a Linear Elastic Traction-Separation Description

Determination of the local interlaminar stress distribution in a laminate with a bolt-filled hole is helpful for optimal bolted joint design, due to the three-dimensional (3D) nature of the stress field near the bolt hole. A new interlaminar stress distribution phenomenon induced by the bolt-head and clamp-up load, which occurs in a filled-hole composite laminate, is investigated. In order to efficiently evaluate interlaminar stresses under the complex boundary condition, a calculation strategy that using zero-thickness cohesive interface element is presented and validated. The interface element is based on a linear elastic traction-separation description. It is found that the interlaminar stress concentrations occur at the hole edge, as well as the interior of the laminate near the periphery of the bolt head. In addition, the interlaminar stresses near the periphery of the bolt head increased with an increase in the clamp-up load, and the interlaminar normal and shear stresses are not at the same circular position. Therefore, the clamp-up load cannot improve the interlaminar stress distribution in the laminate near the periphery of the bolt head, although it can reduce the magnitude of the interlaminar shear stress at the hole edge. Thus, the interlaminar stress distribution phenomena may lead to delamination initiation in the laminate near the periphery of the bolt head, and should be considered in composite bolted joint design.

Three-dimensional stresses analysis in rotating thin laminated composite cylindrical shells

In this paper, the 3D stress state and inter-laminar stresses in a rotating thin laminated cylinder shell are studied. The thickness of the cylinder is supposed to be thin and it is made of laminated composite material and can have general layer stacking. The governing equations of the cylindrical shell are obtained by employing the Layerwise theory (LWT). The effect of rotation is considered as rotational body force which is induced due to the rotation of the cylinder about its axis. The Layerwise theory (LWT), is used to discrete the partial differential equations of the problem to ordinary ones, in terms of the displacements of the mathematical layers. By applying the Free boundary conditions the solution of the governing equations is completed and the stress state, the inter-laminar stresses, and the edge effect in the rotating cylindrical shells are investigated in the numerical results. To verify the results, LWT solution is compared with the results of the FEM solution and good agreements are achieved. The inter-laminar normal and shear stresses in rotating cylinder are studied and effects of layer stacking and angular velocity is investigated in the numerical results.

Interlaminar stresses in thick cylindrical shell with arbitrary laminations and boundary conditions under transverse loads

Abstract In this study, based on three-dimensional multi-term extended Kantorovich method (3DMTEKM), an analytical method is established to obtain the interlaminar stresses resulting from bending of thick cylindrical laminated shells with arbitrary laminations and boundary conditions. Numerical results show that this approach can accurately predict the 3D behavior of interlaminar stresses. Also, they clearly indicate the singular behavior of interlaminar normal and shear stresses in the boundary-layer regions near the edges of the shells. The results obtained from this theory are compared with numerical or analytical results of the existing solutions in simplified cases or with those of ABAQUS finite element software for the cases which there exist no results in the literature. Finally, the power of the present approach in obtaining the interlaminar stresses in thick cylindrical laminated shells with general lay-ups, boundary conditions and finite dimensions is examined.

Edge stresses analysis in thick composite panels subjected to axial loading using layerwise formulation

Based on a reduced displacement field, a layer-wise (LW) formulation is developed for analysis of thick shell panels which is subjected to axial tension. Employing the principle of minimum total potential energy, the local governing equations of thick panel which is subjected to axial extension are obtained. An analytical method is developed for solution of the governing equations for various edge conditions. The governing equations are solved for free and simply supported edge conditions. The interlaminar stresses in the panel are investigated by means of Hooke's law and also by means of integration of the equilibrium equations of elasticity. Dependency of the result upon the number of numerical layers in the layerwise theory (LWT) is studied. The accuracy of the numerical results is validated by comparison with the results of the finite element method and with other available results in the open literature and good agreement is seen between the results. Numerical results are then presented for the distribution of interlaminar normal and shear stresses within the symmetric and un-symmetric cross-ply thick panels with free and simply supported boundaries. The effects of the geometrical parameters such as radius to thickness and width to thickness ratio are investigated on the distribution of the interlaminar stresses in thick panels.

Free Edge Mixed Mode Delamination Analysis of Laminated Composites with Wrap-Around Configuration: A Finite Element Study

Finite element analyses of laminated composites were done in the present study with respect to suppression of free edge delamination by an innovative technique. Wrap-around configuration was considered to determine its effectiveness over the wrapper-less laminated configuration on laminated composites. Nodal stresses were generated ahead of the crack tip through finite element analysis. This was used for determining interlaminar normal stress and inter laminar shear stress distributions at the critical interface. Later virtual crack closure technique was used to estimate the strain energy release rate components for several sizes of virtual crack extensions through a single finite element analysis. Computational analysis predicts Mode-I delamination as dominant mode of failure. This mode of delamination was significantly suppressed with wrap-around configuration on laminated composites.

Interlaminar stresses of laminated composite beams resting on elastic foundation subjected to transverse loading

In the present study, static analysis of the interlaminar stresses and free edge effects in a laminated composite beam resting on the Winkler-type elastic foundation is discussed. Equilibrium equations under transverse load along with the appropriate boundary conditions are obtained by using the Reddy’s layerwise theory. An approximate elasticity solution for a special case of the boundary conditions is developed to verify the validity and accuracy of the present theory. Various examples are presented for the interlaminar normal and shear stresses along the interface and through the thickness of the beam and numerical results for the free edge-clamped boundary conditions are obtained. Finally, the effect of various parameters containing the concentration of the load, stiffness of the elastic foundation and dimension aspect ratio on the interlaminar stresses is studied. Results show an excellent agreement between the layerwise theory and approximate elasticity solution and demonstrate that the magnitude of interlaminar stresses in this problem are significant and should be considered in the structural design.

Dynamic delamination in curved composite laminates under quasi-static loading

In the wind energy industry, new advances in composite manufacturing technology and high demand for lightweight structures are fostering the use of composite laminates in a wide variety of shapes as primary load carrying elements. However, once a moderately thick laminate takes highly curved shape, such as an L-shape, Interlaminar Normal Stresses (ILNS) are induced together with typical Interlaminar Shear Stresses (ILSS) on the interfaces between the laminas. The development of ILNS promotes mode-I type of delamination propagation in the curved part of the L-shaped structure, which is a problem that has recently raised to the forefront in in-service new composite wind turbines. Delamination propagation in L-shaped laminates can be highly dynamic even though the loading is quasistatic. An experimental study to investigate dynamic delamination under quasi-static loading is carried out using a million fps high speed camera. Simulations of the experiments are conducted with a bilinear cohesive zone model implemented in user subroutine of the commercial FEA code ABAQUS/explicit. The experiments were conducted on a 12-layered woven L-shaped CFRP laminates subjected to shear loading perpendicular to the arm of the specimen with a free-sliding fixture to match the boundary conditions used in the FEA. A single delamination is found to initiate at the 5th interface during a single drop in the load. The delamination is then observed to propagate to the arms at intersonic speed of 2200m/s. The results obtained using cohesive zone models in the numerical simulations were found to be in good agreement with experimental results in terms of load displacement behavior and delamination history.

Flexural behavior of composite curved beams on an elastic foundation

The effects of the inner outer radius ratio on the through-thickness tensile stress and the in-plane tension stress are discussed with a focus on the curved beam based on an elastic foundation. The curved beam composed of two different materials was analyzed,and the location of the neutral axis for the in-plane tension stress was determined. Combining the boundary conditions of the zero internal and external surface stress,interlaminar normal stress,and continuous displacement in the thickness direction,the analytical solutions of the through-thickness tensile stress of the composite curved beam and in-plane normal stress were obtained under pure bending. Furthermore,the effects of volume fraction,material parameters and the placed position of the two kinds of materials on the stress of the composite curved beam were investigated. As a convenient and effective calculation strategy,the method could be extended to the application of curved beams with multiple layers of different materials for solving the strength of rectangular composite curved beams,especially the interlaminar strength in practical engineering.