Angle-ply Composite Laminates Research Articles

Swarm intelligence hybridized with genetic search in multi-objective design optimization under constrained-Pareto dominance

The inclusion of uncertainty in structural design optimization led to more complex design optimization formulations, where uncertainty quantification has significant influence on solution methods and computing times. Designs maintaining steady levels of performance, under uncertainty, are called robust and the combination of both robustness and performance optimality leads to a methodology called Robust Design Optimization (RDO). In this work a new approach to the RDO of angle-ply composite laminate structures is proposed. The key concept of this methodology is the hybridization between the principles of Particle Swarm Optimization and Genetic Algorithms, through the evolution of multiple populations based on local and global constrain-dominance. The RDO problem is here defined as the bi-objective minimization of the structural weight (optimality) and the determinant of the variance–covariance matrix (robustness) of the system’s response functionals, subject to stress and displacement constraints. A numerical structural design problem, representing a composite laminate engine hood shell, shows the capabilities of the proposed approach. Results display the good convergence properties of the proposed hybridizations both in the search and objective spaces.

Auxetic Composite Laminates with Through-Thickness Negative Poisson's Ratio for Mitigating Low Velocity Impact Damage: A Numerical Study.

Auxetic materials are those that exhibit negative Poisson’s ratios. Such a unique property was shown to improve the indentation and impact resistances. Angle-ply composite laminates can be designed to produce negative Poisson’s ratio at the laminate level due to the large anisotropicity of the individual layer and the strain mismatch between adjacent layers. This paper investigates the effect of through-thickness negative Poisson’s ratio on the low velocity impact behaviors of carbon fiber reinforced polymer matrix composite laminates, including the global impact behaviors, as well as the delamination, and the fiber and matrix damage. Results from numerical investigations show consistently reduced fiber and matrix tensile damage in the auxetic laminate in all plies, in comparison to the non-auxetic counterpart laminates (up to 40% on average). However, the auxetic laminate does not present a clear advantage on mitigating the delamination damage or the matrix compressive damage.

Modelling damage in half-hole pin bearing cross-ply and angle-ply composite laminates

This paper presents the development and validation of a mesoscale numerical model to predict the bearing failure of composite laminates reinforced by unidirectional continuous fibers, focusing on specimens that show a significant non-linear response prior to failure. Half-hole pin bearing tests were carried out with multiple instrumentation for the comprehensive characterization of the failure process. Three-dimensional finite element models were used for the simulation of plastic deformation and damage of the cross- and angle-ply specimens using fiber-aligned mesh for the composite plies. To consider the non-linear material behavior prior to crack propagation, the constitutive model proposed includes a bi-linear elastoplastic model to represent the non-linear response under longitudinal shear. For the prediction of the peak and post-peak behavior, 3D invariant-based failure criteria and mechanism-based continuum damage models were used for intralaminar damage, together with a discrete cohesive zone model for delamination. Thorough analyses and comparisons of the experimental and numerical results show a good correlation of the bearing strengths and overall deformation, as well as good agreement in terms of damage size and damage shape. Relevant limitations include difficulties in predicting the post-peak plateau stresses and the loading displacements in some configurations, setting the stage for additional future research.

Correction factors for in-plane shear strength and stiffness testing of flat angle-ply composite laminates with high Poisson’s ratios

In this paper, a method to obtain correction factors for in-plane shear properties in fibre-reinforced polymers with high Poisson’s ratio under biaxial load conditions and at high loads is presented. Experimental testing shows the deviations from classical laminate theory for such cases. The transverse deformation ratio is a general form of Poisson’s ratio and, for a ±45° angle-ply laminate, increases with strain. This effect is shown to exist for long and short test specimens, where significant biaxiality in the stress state is present. Reasons for this include fibre rotation at higher loads in tensile load conditions, and matrix plasticity and damage initiation. Test results show that the expanded formulas compensate errors in shear strength calculation of angle-ply laminates which arise from using nominal parameters with standard formulas. The results are also applicable to structures under biaxial load and when transverse contraction is inhibited, e.g. in shear panels. Further potential uses are in the presence of high shear strains and to detect the onset of damage under shear loading.

Investigation of RC Beams Rehabilitated with Angle-Ply Composite Laminate Plate

Investigation of RC Beams Rehabilitated with Angle-Ply Composite Laminate Plate

Simulation-based design: a case study in combining optimization methodologies for angle-ply composite laminates

Over the last decades, the intense need for more robust and lightweight structures, together with the dramatic improvement of computational power, had, as a result, the introduction of simulations in the traditional product development. As a simulation, it is considered any computer process that imitates a real system by generating similar responses over time. Simulations allow the designers to create virtual prototypes that can speed up the design phase and, thus, the product development time in total. This design paradigm shift is called simulation-based design (SBD) and includes several simulations and optimization techniques. The most notable of these techniques are; computer-aided design (CAD), finite element analysis (FEA), topology optimization (TO), and parametric optimization (PO). A combined SBD methodology, including these techniques, is presented here. This methodology is a two-stage optimization process. During the first stage, traditional compliance TO using the SIMP approach was conducted, while at the second, a PO with an evolutionary algorithm was applied. The presented methodology is focused on the optimization of composite laminates. In particular, an angle-ply laminated beam made by carbon fiber reinforced polymer (FRP) was used as a case study and optimized both for its topology and fibers’ direction. The results of this research are presented and tested using a commercial example. The suggested methodology resulted in a lighter and more robust design solution. These design solutions can be constructed either by conventional manufacturing processes (CMP) or by additive manufacturing (AM). Designers looking for interesting and lightweight composited structures can exploit the results found in this paper. The implemented process can easily be modified in order to cover any possible optimization of FRP products.

A meshless study of antisymmetric angle-ply laminates using high-order shear deformation theories

Composite laminated plates have found several applications in engineering field. For instance, aerospace and automotive industry use these structures in several components of their products due to their exceptional specific properties along the direction of the fibres. There are several two-dimensional plate models that aim to more accurately and more efficiently predict the kinematics of those structures. Unlike the Classical Plate Theory (CLPT), which can only be applied to thin laminates, the First-Order Shear Deformation Theory (FSDT), developed by Reissner and Mindlin, already accounts shear effects and, due to that, it can describe in a satisfactory way the kinematic of a generic thick laminated plate. Nevertheless, the FSDT considers linear shape functions to describe the in-plane displacements through the plate thickness, which results in constant shear strains. Thus, the traction boundary conditions on the top and bottom surface of plate are violated. Additionally, the FSDT needs shear correction factors, which are not easily obtained for a generic problem. Equivalent single layer (ESL) theories following high-order shear deformation theories (HSDTs) have been proposed and more efficiently applied to composite laminated plates. These theories allow to represent the nonlinear variation of transverse shear stresses through thickness of plate because they possess nonlinear shape functions interpolating the in-plane displacements. Thus, the kinematics of these structural elements can be better described and more accurate stress fields can be obtained for problems that cannot be handled with the FSDT.These structures have been analysed for several years using the Finite Element Method (FEM), which is the most popular numerical tool in structural analysis. However, several other advanced numerical techniques, such as meshless methods, can also handle this kind of problems and, in some cases, in a more efficient way. This work makes use of a recently developed meshless method – the Natural Neighbour Radial Point Interpolation Method (NNRPIM) (Belinha, 2014) – to study the bending of antisymmetric angle-ply composite laminates using distinct HSDTs.

Tensile strength of multi-angle composite laminate scarf joints with FEM

This study focus on the tensile strength of angle-ply composite laminate scarf joints and corresponding finite element modelling (FEM) methods. Tensile tests are performed at 25°C and 75°C on scarf joint specimens with unidirectional laminate stacking sequences. The joint tensile strength result values at 75°C represent around 86% of those obtained at 25°C. The tensile test is simulated with finite element modelling including cohesive elements to model failure. The joint adhesive film is represented either with only full thickness cohesive elements, or with thin or zero-thickness cohesive elements combined with solid elements having a plastic adhesive material model. Simulations results show that in the case of a unidirectional laminate, the adhesive modelling method had less than 1% effect on the simulated tensile failure strength. For quasi-isotropic laminates with a given ply angle count but of varying ply order, the simulated tensile failure strength varies up to 15%, which confirms tendencies reported in the literature.

Reliability-based Robust Design Optimization with the Reliability Index Approach applied to composite laminate structures

In this paper a new approach to the Reliability-based Robust Design Optimization (RBRDO) of angle-ply composite laminate structures is presented. The problem is defined as a bi-objective Robust Design Optimization (RDO) problem, with deterministic and probabilistic constraints. Design optimization is considered as the minimization problem of the weight (optimality) and the determinant of the variance-covariance matrix of the response functionals of the system (robustness). Reliability assessment is executed by the Reliability Index Approach (RIA), as an inner cycle. The key concept of this methodology is the exclusive use of evolutionary algorithms with elitist strategy, allowing for global convergence in the two optimization cycles. The RIA problem was reformulated and a set of new evolutionary operators were developed. A numerical example is presented and the results compared with other RBRDO and RDO formulations. Results show that deterministic and probabilistic structural integrity measures are quite sensitive to uncertainty, for multi-component composite structures.

Damping of carbon fibre and flax fibre angle-ply composite laminates

The damping behaviour of continuous carbon fibre and flax fibre reinforced polymer (CFRP and FFRP) composites was studied by comparing angle-ply laminates. Using logarithmic decrement measurements, dynamic mechanical analysis and vibration beam measurements, the damping was described as the specific damping capacity ψ in order to compare data using the different methods.Our results show approximately 2–3 times better damping of FFRP compared to CFRP at low frequency and low strain. We show that the damping of both materials increases with increasing angle-ply orientation below 300Hz. While the matrix and interface seems to contribute mainly to damping at lower frequencies, the fibre shows an increasing contribution with ψ = 64.4% for unidirectional FFRP at 1259Hz in the 5th mode of vibration, without a notable change in the elastic modulus. This work demonstrates that the FFRP may be simultaneously stiff and efficient at damping.

Failure analysis of fiber-reinforced composite laminates subjected to biaxial loads

A nonlinear constitutive model for a single lamina is proposed for the failure analysis of composite laminates. In the material model, both fiber and matrix are assumed to behave as elastic-plastic and the in-plane shear is assumed to behave nonlinearly with a variable shear parameter. The damage onset for individual lamina is detected by a mixed failure criterion, composed of the Tsai-Wu criterion and the maximum stress criterion. After damage takes place within the lamina, the fiber and in-plane shear are assumed to exhibit brittle behavior, and the matrix is assumed to exhibit degrading behavior. The proposed nonlinear constitutive model is tested against experimental data and good agreement is obtained. Then, numerical analyses are carried out to study the failure behavior of symmetric angle-ply composite laminates and symmetric cross-ply composite laminates subjected to biaxial loads. Finally, the conclusions obtained from the numerical analysis are given.

A criterion for failure mode prediction of angle-ply composite laminates under in-plane tension

As the failure of fibre-reinforced angle-ply composite laminates involves basic features of failure of general laminates, its understanding and prediction are of fundamental importance. In this paper, a criterion for predicting the failure mode of angle-ply laminates under in-plane tension is presented. The criterion is able to predict the two different modes of the final failure of angle-ply laminates found in previous experiments: the pull-out of the internal layer due to transverse cracks and delaminations with no fibre breakage, and a single crack across the width of the laminate. The theoretical results demonstrate that the final failure mode of an angle-ply laminate is determined by the value of a failure factor which is related to the thickness and strength of the lamina, the width and ply angle of the laminate, and the interface strength. The pull-out failure occurs when the failure factor is greater than one, and the single cracking occurs when it is less than one. The criterion also shows that the final failure of angle-ply laminates exhibits size effects both in the thickness direction and the width direction. Moreover, the criterion is extended and applied to general angle-ply laminates. The theoretical predictions agree with experimental results.

Interlaminar Stresses in Composite Laminates Subjected to Anticlastic Bending Deformation

Approximate elasticity solutions for prediction of the displacement, stress, and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width and subjected to uniform axial extension and uniform temperature change were developed earlier by the authors. In the present paper, the authors have extended these solutions to treat bending deformation. Bending and torsion moments are combined to yield a deformation state without twisting curvature and with transverse curvature due only to the laminate Poisson effect. This state of deformation is termed anticlastic bending. The approximate elasticity solution for this bending deformation is shown to recover laminated plate theory predictions at interior regions of the laminate and thereby illustrates the boundary layer character of this interlaminar phenomenon. The results exhibit the anticipated response in congruence with the solutions for uniform axial extension and uniform temperature change, where divergence of the interlaminar shearing stress is seen to occur at the intersection of the free edge and planes between lamina of +θ and –θ orientation. The analytical results show excellent agreement with the finite-element predictions for the same boundary-value problem and thereby provide an efficient and compact solution available for parametric studies of the influence of geometry and material properties. Finally, the solution was exercised to determine the dimensions of the boundary layer in bending for very large numbers of layers.

Application of the submodeling technique to the analysis of the edge effects of composite laminates

This study deals with the edge effects in angle-ply composite laminates subjected to tensile test. The submodeling technique is used to achieve the numerical results. In a first step, a [45/–45]s laminated strip is studied, comparing the results with the previous approaches. The fulfilment of equilibrium equations by the stresses obtained numerically is studied to delimit the zone with inaccurate results due to the singularity of the problem. Antisymmetric configurations are analyzed enclosing the validity of the numerical results near the edges to the limits previously obtained. The aspect ratio and the orientation angle have been varied to analyze their effect.

Delaminated multilayered plates under uniaxial extension. Part II: Efficient layerwise mesh strategy for the prediction of delamination onset

In the first part (Saeedi et al., 2011) of this two-part paper, a layerwise stress model, called the LS1 model, has been extended to the analysis of delaminated multilayered plates subjected to uniaxial extension. The LS1 analytical solutions of general delaminated multilayered plates have been derived and compared to three-dimensional finite element method (3D-FEM) solutions. It has been proved that there is a good agreement between the LS1 and 3D-FEM models except very near singularities (free edges, crack tips,…). In order to overcome the drawback of the LS1 model in the vicinity of singularities, a refinement approach, called the refined LS1 is proposed in this part. Based on an irregular layerwise mesh, the refined LS1 model is applied to the prediction of the delamination onset in angle-ply composite laminates. The comparison between the refined LS1 and 3D-FE models reveals an excellent agreement in terms of interlaminar stresses and strain energy release rate, even very close to singularities. The proposed refined LS1 model can be used as an accurate and very efficient model for the prediction of initiation and propagation of delamination in multilayered plates under uniaxial extension using stress based or energy release rate based criteria.

A novel semi energy finite strip method for post-buckling analysis of relatively thick anti-symmetric laminated plates

In the current paper, a novel semi-energy FSM is developed based on the concept of first order shear deformation theory (FSDT) in order to attempt the post-buckling solution for thin and relatively thick anti-symmetric angle-ply composite laminates subjected to uniform end-shortening. The laminated plates are assumed to be simply supported at their boundaries. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. The study of the results has provided confidence in the validity and capability of the developed FSM in handling the post buckling problem of anti-symmetric angle-ply laminates.

Interlaminar stresses in composite laminates: Thermoelastic deformation

An approximate elasticity solution for prediction of the displacement, stress and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width and subjected to uniform axial extension was developed earlier [4]. In the present paper, the authors have extended that solution to treat thermal stresses and deformations induced by a uniform change in laminate temperature. The results have revealed not only the complex fields within the laminate, but also inter-relationships between the lamina axial and shearing coefficients of thermal expansion and the effective laminate coefficients of thermal expansion. Further, the solution is shown to recover laminated plate theory predictions for thermally induced fields at interior regions of the laminate, thereby confirming the boundary layer nature of the interlaminar phenomena for the thermoelastic case. Finally, the results exhibit the anticipated response in congruence with the mechanical solution of Ref. [4] and the thermoelastic results satisfy the conditions of self-equilibration necessary for the finite-width laminate subjected to free thermal deformation. Integration of the stress σ x over the laminate cross-section in the y– z plane is shown to converge to zero as the number of Fourier terms is increased. While the exact solution for mechanical loading is known to exhibit singular behavior, non-convergence of the interlaminar shearing strain is also seen to occur at the intersection of the free edge and planes between lamina of + θ and − θ orientation under thermal loading. The analytical results show excellent agreement with the finite-element predictions for the same boundary-value problem.

Failure analysis of laminates by implementation of continuum damage mechanics in layer-wise finite element theory

In this paper a 3-D continuum damage mechanics formulation for composite laminates and its implementation into a finite element model that is based on the layer-wise laminate plate theory are described. In the damage formulation, each composite ply is treated as a homogeneous orthotropic material exhibiting orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. The progressive damage of different angle ply composite laminates under quasi-static loading that exhibit the free edge effects are investigated. The effects of various numerical modeling parameters on the progressive damage response are investigated. It will be shown that the dominant damage mechanism in the lay-ups of [+30/-30]s and [+45/-45]s is matrix cracking. However, the lay-up of [+15/-15] may be delaminated in the vicinity of the edges and at <TEX>$+{\theta}/-{\theta}$</TEX> layers interfaces.

Numerical elastic-plastic simulation of interlaminar stresses in a notched angle-ply thermoplastic composite laminate

A thermoplastic angle-ply AS4/PEEK laminate with a hole is considered. The interlaminar stresses along the hole edge at different interfaces under uniaxial extension are investigated. According to the symmetries of the structure and loading, a suitable finite-element model is developed. Utilizing a three-dimensional elastic-plastic finite-element procedure elaborated previously, a finite-element modeling of the interlaminar stresses in a thick angle-ply composite laminate is carried out. Based on the interlaminar stresses obtained, the dangerous locations of delamination initiation are predicted. The results obtained indicate that there is some relationship between the dangerous locations and fiber orientations in the adjacent layers, and it maybe inferred that the critical locations are near the regions where the hole edge is tangent to the fiber orientation in the layers adjacent to the interface. The interlaminar stresses at the same interfaces are not sensible to distances from the midplane of the laminate. Very high interlaminar tensile stresses are found to exist on the hole edge at the +25°/+25° or -25°/-25° interfaces, and delaminations can initiate there first.

Energy absorption and bending stiffness in CFRP laminates: The effect of 45° plies

The impact characteristics of cross-ply and angle-ply composite laminates were investigated, with an instrumented impact drop tester by performing gravity-assisted drop tests on [0/90] 6s and [0/45/90] 4s laminates. The impact energy was kept constant at 12 J for all the tests. From the dynamic responses presented here as force history, energy history and force–displacement plots, relevant characteristics such as contact time, delamination load, absorbed energy, bending stiffness, after impact deflection, etc. were obtained. The plots were non-smooth, disclosing the salient features of the composites. It was important to note that the [0/45/90] 4s was more resistant to impact bending, but incurred more damage as exhibited by its higher contact time and absorbed energy. The laminates were sectioned through the impact point and magnified macro- and micro-photographs were taken to show the failure modes, which include delamination, matrix cracking, etc.