Stresses In Composite Laminates Research Articles

Tikhonov Regularization for the Fully Coupled Integral Method of Incremental Hole-Drilling

BackgroundThe unit pulse integral method is used extensively with the incremental hole-drilling residual stress measurement technique. The ASTM E837 standard, which applies only to isotropic materials, recommends the use of Tikhonov regularization to reduce instability when many depth increments are used. In its current formulation, Tikhonov regularization requires the decoupling of stress, as is possible for isotropic materials. The fully coupled integral method is needed for residual stress determination in layered composite laminates and is currently employed without Tikhonov regularization. This causes greater sensitivity to measurement errors and consequently large stress uncertainties. An approximate method of applying Tikhonov regularization exists for biaxial composites, but is not applicable to more complex laminates.ObjectiveExtend Tikhonov regularization to the fully coupled integral method to improve residual stress determination in composite laminates.MethodsThis work investigates the use of the approximate and fully coupled regularization approaches in an angle ply composite laminate of [+45/-45/0/90]s construction. Experimental validation in a [0/+45/90/-45]s laminate is also presented where the regularized fully coupled integral method is compared to the series expansion method that includes all in-plane stress and strain directions simultaneously in a least-squares solution.ResultsThe regularized integral method produces comparable results to those of series expansion while requiring twelve times less FE computation to calculate the compliances. The optimal degree of regularization is also more convenient to determine than the optimal combination of series order required by series expansion.ConclusionsThe new method is easily applied and should find wide application in the measurement of residual stresses in composite laminates.

Interlaminar Stress Calculation in Composite Laminates Using an 8-noded Brick Element Based on Mixed Finite Element Formulation

An eight-noded brick element is developed for accurate estimation of interlaminar stresses in composite laminates. This element incorporates the three transverse stresses σz, σyz and σxz as the degree of freedoms apart from the three displacements (u, v and w). The displacements are calculated as usual from the principle of virtual work, and the stresses are interpolated independently in the constitutive equation. In composite laminates the shear and normal stresses are continuous across the laminates. This stress continuity can be imposed using continuous shape functions for stress components. Studies are done for various laminates and results are compared with available solutions from the literature.

A New Shear Deformation Theory in Axiomatic Framework for Bending and Buckling Analysis of Cross-Ply and Angle-Ply Laminated Composite Plates

Abstract In this study, a new higher order hyperbolic shear deformation theory for mechanical analysis of cross-ply and angle-ply multilayered plates is developed. Analytical solution to the static and buckling responses of symmetric and anti-symmetric composite laminates is presented. The proposed theory considers secant hyperbolic function of thickness coordinate in the displacement field. Also the developed theory assumes non-linear distribution of displacements and ensures that the top and lower surfaces of the plates have zero shear stresses. The equilibrium equations are obtained by applying the principle of virtual work. The stiffness characteristics of cross-ply and angle-ply laminates are taken into account when solving these governing equations. The closed-form Navier solution satisfying the corresponding boundary conditions is derived for simply supported (SS) composite plates. The results for non-dimensional deflections, and stresses of composite laminates under the effect of sinusoidal and uniform distributed load are thus obtained. The uni-axial and bi-axial loading force are used to evaluate critical buckling loads. Furthermore, the impact of span thickness ratio, aspect ratios, fiber orientation, modulus ratio, etc. on static and buckling analysis plates is also studied. The validity of present formulation is demonstrated by comparing our results with some of the available results in the literature.

Analisys of interlaminar stresses in composite laminates by finite difference method

In this work, full stress tensor components regarding stress state for a simmetrical composite laminate under uniform uniaxial extension have been determined. Off-plane stresses are specially meaningful due to the fact that they are responsible for failure mechanisms such as delamination and shear stress cracking. A finite difference scheme has been used to solve internal equilibrium equations subjected to stress-free boundary conditions along boundary lines; moreover symmetry considerations have been made. In such way, we get an improvement in solutions in contrast with results obtained following bidimensional reasoning and using laminate based elements. Off-plane stresses for differents ply-sequences have been evaluated and maximum and minimum values for different fibers orientations were explored.

A Two-Stage Genetic Algorithm for Molding Parameters Optimization for Minimized Residual Stresses in Composite Laminates During Curing

A Two-Stage Genetic Algorithm for Molding Parameters Optimization for Minimized Residual Stresses in Composite Laminates During Curing

3D Thermal Stresses in Composite Laminates Under Steady-State Through-Thickness Thermal Conduction

In this study, 3D thermal stresses in composite laminates under steady-state through thickness thermal conduction are investigated by means of a stress function-based approach. One-dimensional thermal conduction is solved for composite laminate and the layerwise temperature distribution is calculated first. The principle of complementary virtual work is employed to develop the governing equations. Their solutions are obtained by using the stress function-based approach, where the stress functions are taken from the Lekhnitskii stress functions in terms of in-plane stress functions and out-of-plane stress functions. With the Rayleigh–Ritz method, the stress fields can be solved by first solving a standard eigenvalue problem. The proposed method is not merely computationally efficient and accurate. The stress fields also strictly satisfy the prescribed boundary conditions validated by the results of finite element method (FEM) results. Finally, some of the results will be given for discussion considering different layup stacking sequences, thermal conductivities and overall temperature differences. From the results, we find that the thermal conductivity greatly affects the stress distributions and peak values of stresses increase linearly for the present model. The proposed method can be used for predicting 3D thermal stresses in composite laminates when subjected to thermal loading.

A stress function based viscoelastic model for relaxation of free edge stresses in composite laminates

In this study, the relaxation of free edge stresses in viscoelastic composite laminates is investigated by means of a stress function based viscoelastic model. A linear viscoelastic model using Prony series is adopted for time-dependent material behavior. The stress functions are taken from the Lekhnitskii stress functions and expressed in terms of in-plane stress functions and out-of-plane stress functions, where the out-of-plane stress functions are assumed as a combination of harmonic and hyperbolic functions for developing a Ritz-type solution procedure. By enforcing the complementary virtual work, the fourth order and second order coupled differential equations are obtained and further solved by a standard eigenvalue problem. The benefit of stress function based approach is not merely computationally efficient and accurate. The stress boundary conditions can also be strictly satisfied at the free edges since they are prescribed in the assumed functions. Finally, some of the results will be given for discussion considering different layup stacking sequences. It can be found that by using the present method and Prony series, the relaxation effect on the free edge stresses can be clearly observed and well simulated for the viscoelastic laminates under uniaxial tensile load.

Impact of process induced residual stresses on interlaminar fracture toughness in carbon epoxy composites

Residual stresses are induced in composite laminates during the process of manufacturing due to thermal mismatch between composite constituents during curing. Processes induced residual stresses effects the safety of structural components and can play a main role in matrix cracking, crack initiation and propagation. The objective of this research is to study the influence induced residual stresses on interlaminar fracture toughness (GI) of Carbon/Epoxy laminates. Initially laminates were cured under room temperature followed by post curing at various temperatures using a chosen cure cycle. Slitting method was employed to determine the residual stress distribution in post cured laminates and its effects on GI was estimated using Double Cantilever beam (DCB) test. The results show a gradual increase in GI with increase in compressive residual stresses in composite laminate. Further, the fracture surfaces of laminates were carefully studied using scanning electron microscope to know the interfacial adhesion of matrix and fiber.

Accurate Evaluation of Interlaminar Stresses in Composite Laminates via Mixed One-Dimensional Formulation

This paper presents a novel mixed one-dimensional formulation based upon Reissner’s mixed variational theorem for the accurate stress analysis of general multilayered beam problems. Carrera’s unified formulation is recalled to generate a class of theory of structure that assumes both displacements and stresses over the cross section of the beam. On the other hand, the finite element method is employed to obtain the governing equations in weak form using standard Lagrangian interpolation. Independent assumptions are taken for each layer of the laminated beam through a layerwise distribution of the unknowns, and the interlaminar continuity of the transverse stresses is imposed a priori by ensuring piecewise continuous fields in the thickness direction. A set of locally defined, hierarchical Legendre polynomials is chosen for the expansion of the variables over the cross-section surface, enabling the user to refine the model in particular zones of interest and to control the accuracy of the stress analysis through the polynomial order of the theory of structure. The numerical assessment of the proposed mixed elements for multilayered problems is carried out by comparison against benchmark solutions of the literature, including plate formulations and elasticity solutions. The free-edge problem is also addressed to show the three-dimensional capabilities of the model.

Numerical analysis and fiber Bragg grating monitoring of thermocuring processes of carbon fiber/epoxy laminates

A three-dimensional differential viscoelastic model combining the effects of curing degree, thermal expansion, chemical shrinkage and stress relaxation for composite laminates was established and well verified. The evolution of strain and stress of composite laminates during cure was numerically simulated using the validated model. Also, fiber Bragg grating temperature and strain sensors were adjacently embedded in the composite laminate to in situ monitor the temperature and strain evolution. The monitored strain was evaluated by comparison with the corresponding simulated strain. The results reveal that the monitored temperature can reflect the actual temperature evolution in composite laminates, whereas the monitored strain cannot accurately characterize the actual strain evolution in composite laminates at the early stage of cure. However, when the resin/grating interfacial bond strength increases enough to transfer resin strain effectively, the changes in the monitored strain can match well with the actual strain changes.

A multi-scale moisture diffusion coupled with stress model for composite materials

In this paper, an equivalent model on coefficient of hygrothermal expansion for composite layer and a multi-scale model for calculating the strain and stress of composite plates are proposed. These two models also can be applied to thermal expansion problems and guide the structure design of the composite materials. A model descripting the coupling behavior of moisture diffusion and stress in composite laminates is proposed based on the second Fick’s law. Compared to other models, this model can accurately predict the anomalous behavior in the process of moisture absorption. A number of experiments and finite-element simulations are conducted to validate this model. A comparison of the model’s predictions with experimental data shows a good agreement.

Modeling framework for free edge effects in laminates under thermo-mechanical loading

Abstract In this paper, a novel Quasi-2D (Q-2D) plane strain formulation for predicting interlaminar stresses in multi-directional laminates is developed and implemented within the finite element method framework. In particular, analyses of free edge stresses in composite laminates subjected to uniform axial and/or thermal loading are conducted. The Q-2D modeling approach presented here is validated by comparing the predicted interlaminar stresses with corresponding 3D models and previously published data. Computational time required for determining the interlaminar stresses using Q-2D model is approximately 30 times lower than the 3D analysis of the same laminate. Also, the Q-2D model is implemented within a commercially available software by modifying a 3D model to behave like a 2D model. This is particularly advantageous over developing an in-house finite element method code to capture the complex free edge stress states in multi-directional composites. Hence, the current framework can potentially be used as a computational tool for efficiently predicting the interlaminar stresses in different laminates subjected to thermo-mechanical loading, which can assist in determining interlaminar regions susceptible to free edge delamination.

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.

Evaluation of curing residual stresses in three-phase thin composite laminates considering micro-scale effects

Generally, in thin laminates, residual stresses are studied in two scales; micro mechanics and macro-mechanics. So far, no study has included both the micro- and macro-scale analysis for predicting the thermal residual stresses of composite laminates. In other words, no literature model is proper for both the micro and macro scale at the same time. This paper presents a procedure to integrate micro and macro thermal residual stresses in composite laminates. The combination of micromechanics-based analytical results and hole-drilling calibration factors leads to predict the macro thermal residual stresses of a unidirectional laminate. Classical lamination theory (CLT) is then employed to predict macroscopic thermal residual stress of each layer in laminated composites (with different orientations). Comparison of longitudinal, transverse and in-plane shear stresses between the proposed approach and published experimental results is made for glass/epoxy laminates in cross-ply and quasi-isotropic configurations. Available experimental data from incremental hole-drilling method show that the present combination procedure yields more precise residual stresses predictions in comparison with the state that the CLT is used only. In other words, the presented procedure which adds the micro residual scale results to the CLT, gives rise to a better prediction of residual stress fields. Consequently, ignoring the micro-mechanical effects may result in some uncertainties in thermal residual stress evaluation of thin composite laminates. Furthermore, while the CLT is not able to take into account the in-plane shear residual stresses for the cross-ply composites, the present procedure can provide an estimation of shear residual stress field.

Extended Kantorovich method for local stresses in composite laminates upon polynomial stress functions

The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work, the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is established to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method (FEM). The convergent stresses have good agreements with those results obtained by three dimensional (3D) FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kantorovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.

Free edge stresses in composite laminates with imperfect interfaces under extension, bending and twisting loading

An accurate analytical three-dimensional elasticity solution is presented for the free edge stresses in composite laminates under extension, bending and twisting loading, accounting for possible bonding imperfections at the layer interfaces. The bonding imperfection is modeled using the linear spring-layer model. A mixed formulation with both displacements and stresses as primary variables is developed using the Reissner-type variational principle and the solution is obtained using the recently developed mixed-field multiterm extended Kantorovich method (MMEKM). The method ensures exact and point-wise satisfaction of the traction-free edge boundary conditions and interlaminar stress continuity conditions, which is key to the accurate solution of free edge stresses. A detailed numerical study established excellent convergence characteristics of iterative series solution. The presence of bonding imperfection at an interface leads to nonsingular free edge interlaminar stresses at that interface, in contrast with the singular stress field occurring at a classical perfect interface. The effect of loading type on the relative reduction of free edge stresses with the increase in imperfection compliance is investigated for cross-ply and angle-ply laminates. The effect of ply-angle of angle-ply laminates on the same is also ascertained.

Chemical and thermal shrinkage in thermosetting prepreg

A methodology for predicting residual cure deformation and stresses in composite laminates during cure is proposed. The technique employs an unbalanced cross-ply strip denoted as a “bi-lamina” strip to measure the in situ development of chemical and thermal shrinkage deformation during a specified thermal cycle. The constitutive model of the composite material was developed based on self-consistent micro-mechanical homogenization with variable resin thermo-mechanical material properties during the cure cycle. The resin properties were determined as a function of cure and temperature using different experimental techniques, including differential scanning calorimetry, digital image correlation, rheometry and dynamic mechanical analysis. The predicted bending deflection profiles of the strip agreed closely with experimental observations. The proposed methodology can be used to validate the material model of the resin and composite during the cure cycle.

Reduction of Free Edge Peeling Stress in Composite Laminates under Bending Load

In this paper, a stress function-based approach was proposed to analyze the reduction of free-edge peeling stress in smart composite laminates using piezoelectric actuator under bending load. Electro-mechanically coupled governing equation was obtained by complimentary virtual work principle. The stress state was solved by the generalized eigenvalue procedure. The free-edge peeling stress of smart composite laminates was reduced by the piezoelectric actuation. The reduction rate of peeling stress in cross-ply composite laminate is larger than that in angle ply composite laminate.

Influence of Residual Stresses on the Damage of Composite Laminates under Tensile Loading

This work investigates the effect of residual stresses on the damage of composite laminate. The incremental hole-drilling method is applied to determine residual stresses in composite laminates [02/θ2]s and then acoustic emission technique is used for the identification of damage appearance during the tensile testing. The samples with different residual stress distribution are prepared through curing and post curing in order to study the role of residual stress on the damage of composite laminates. Besides the experimental method, the theoretical approach is applied to illustrate the role of residual stress on the damage of composite laminates.

A three-dimensional thermo-viscoelastic analysis of process-induced residual stress in composite laminates

A three-dimensional thermo-viscoelastic model to simulate the residual stress in composite laminates during curing was proposed using the differential constitutive law. Based on a generalized Maxwell model with n Maxwell elements, a three-dimensional differential thermo-viscoelastic constitutive law was developed and corresponding differential finite element codes were incorporated into commercial software ABAQUS with an UMAT subroutine. In the present thermo-viscoelastic model the changes in thermal expansion, chemical shrinkage and stress relaxation were taken into account. The differential thermo-viscoelastic model and its finite element analysis were numerically validated in comparison to those presented by White and Kim (1998). Furthermore, the influence of aluminum skins on residual stress development for autoclaved composite laminates was evaluated with the present differential thermo-viscoelastic model. The results indicate that the aluminum skins have negligible effects on the cure of composite laminates and significant effects on the residual stress development during curing.