Layerwise Stress Research Articles

Failure Mechanisms of GFRP Scarf Joints under Tensile Load.

A potential repair alternative to restoring the mechanical properties of lightweight fiber-reinforced polymer (FRP) structures is to locally patch these areas with scarf joints. The effects of such repair methods on the structural integrity, however, are still largely unknown. In this paper, the mechanical property restoration, failure mechanism, and influence of fiber orientation mismatch between parent and repair materials of 1:50 scarf joints are studied on monolithic glass fiber-reinforced polymer (GFRP) specimens under tensile load. Two different parent orientations of [−45/+45]2S and [0/90]2S are exemplarily examined, and control specimens are taken as a baseline for the tensile strength and stiffness property recovery assessment. Using a layer-wise stress analysis with finite element simulations conducted with ANSYS Composite PrepPost to support the experimental investigation, the fiber orientation with respect to load direction is shown to affect the critical regions and thereby failure mechanism of the scarf joint specimens.

Determination of stresses, strains and failure types in multidirectional laminates under pure bending

Curved structures made of fibre-reinforced plastics tend to show an out-of-plane failure type, when loaded under bending. One method to determine the related tensile strength in thickness direction, is the standardised unfolding test related to ASTM D6415 with L-profile specimens. However, the standard shall be used for unidirectional materials only, which is not the case for multidirectional laminates. Therefore, this publication presents methods to determine the layer-wise stress and strain state as well as occurring failure types of multidirectional laminates. An extension of the Lekhnitski formulae is presented and its results are validated by comparison with high resolution strain measurements by Digital Image Correlation. Based on the analytical solution, a failure analysis using Cuntze’s Failure Mode Concept is conducted. It was revealed, that the failure load and position can be predicted accurately, if a failure type related strength –in-plane or out-of-plane failure– is used. In the presence of [Formula: see text]-layers higher deviations occur between test and prediction and therefore limits the validity of the presented analytical failure analysis.

Analytical layerwise stress and deformation analysis of laminated composite plates with arbitrary shapes of interfacial imperfections and discontinuous lateral deflections

In the present article, a double power series analytical layerwise model is proposed for analysis of multilayer orthotropic plates with arbitrary shapes of interfacial bond defects. In contrast to the previous models, the discontinuity in the lateral deflections of the successive layers is also considered. The adhesive bonding layers are modeled by elastic elements with normal and shear stiffness coefficients; so that, the continuity conditions of the transverse shear and normal stresses are met at the layer interfaces. It is the first time that an analytical solution rather than the data-dependent finite element method is proposed for stress and displacement analysis of multilayer rectangular plates with arbitrary shapes of interfacial bond damages, including the discontinuity in the transverse displacements of the successive layers. Results of the transverse displacement and stresses are then refined according to the 3D theory of elasticity. Results reveal that even small violations in the bonding between layers, may increase the resulting stresses, lateral deflections, and the differences between lateral deflections of the successive layers to more than twice, thrice, and five times, respectively. Moreover, in contrast to the growth of the in-plane stresses, redistribution of the transverse shear stress is governed by the equilibrium rather than the constitutive-law-based conditions.

A statically compatible layerwise stress model for the analysis of multilayered plates

This paper proposes a new layerwise model for multilayered plates. The model, called SCLS1 for Statically Compatible Layerwise Stresses with first-order membrane stress approximations per layer in thickness direction, complies exactly with the 3D equilibrium equations and with the free-edge boundary conditions. As in the LS1 model initially proposed by Naciri et al. (1998), the laminated plate is considered as a superposition of Reissner plates coupled by interfacial stresses which are considered as generalized stresses. However, the divergences of the interlaminar transverse shears are introduced as additional generalized stresses in the SCLS1 model. Also, a refined version of the new model is obtained by introducing several mathematical layers per physical layer. Contrary to the LS1 model which is derived by means of the Hellinger–Reissner principle, the new model is derived by means of the minimum of the complementary energy principle. This ensures the convergence of the refined SCLS1 solution to the exact 3D solution as the number of mathematical layers per physical layer increases. The new model has been implemented in a new version of the in-house finite element code MPFEAP . Several comparisons are made between LS1, SCLS1 and full 3D FE models in order to assess the performances of the new model which shows itself very effective.

The LS1 model for delamination propagation in multilayered materials at [formula omitted] interfaces: A comparison between experimental and finite elements strain energy release rates

The aim of this paper is to analyze delaminated multilayered plates under classical loads using an alternative model to the existing three-dimensional finite element methods (3D-FEM). The proposed alternative model, named LS1, is a layerwise stress model proving significantly less computationally expensive while accurate and efficient. In particular this paper uses experimental data from different simple test specimens in a finite element code, which is based on LS1, in order to calculate strain energy release rates (SERR) in different modes of delamination. The focus is on two types of delaminated interfaces 0°/0° and 0°/45°. The obtained SERR results are in very good agreement with the experimental values and, in the case of mixed-mode delamination, they are as accurate as the SERR obtained by 3D-FE models. The other interesting property of the LS1 model is the very fast calculation speed as the SERR can be analytically deduced from interfacial stresses. This relation which only depends on the stacking sequence and the position of delamination is presented.

Stress analysis of long multilayered plates subjected to invariant loading: Analytical solutions by a layerwise stress model

This paper deals with the analysis of long multilayered plates subjected to invariant loading along the longitudinal direction. By assuming that the strain field is independent of the longitudinal coordinate, the general form of the displacement field is obtained for a rectangular plate. It is shown that there are only four types of loading which can be applied at the longitudinal ends of the plate: traction, out-of-plane bending, torsion and in-plane bending. In addition to these loads, the plate can be subjected to any loading on its top/bottom surfaces and any force/displacement boundary conditions at its lateral edges provided that these loads and boundary conditions are invariant along the longitudinal direction. Based on the obtained displacement field, a layerwise stress model, called the LS1 model, is used to solve the problem. The analytical LS1 solutions are obtained for general long multilayered plates with arbitrary lateral boundary conditions subjected to all types of invariant loads. Various numerical examples, related to different load conditions, are investigated and the LS1 results are compared to those obtained by a three-dimensional finite element (3D-FE) analysis. Excellent agreements in terms of overall stiffness matrix and free-edge interlaminar stresses are found between the LS1 and 3D-FE models.

Robust [formula omitted] generalized FEM approximations for higher-order conformity requirements: Application to Reddy’s HSDT model for anisotropic laminated plates

The Third-order Plate Theory proposed by Reddy for modeling laminated composite plates has earned wide acceptance in the engineering community. It involves the same five generalized displacement components (uo,vo,wo,ψx,ψy) as the first-order models (e.g. Mindlin’s) and, at the same time, its higher-order expansion across the thickness enables it to provide more accurate displacements and layer-wise stress estimates. However, its FEM implementation is somewhat hindered by the need to employ a C1(Ω) continuous basis for the transverse displacement wo.In this paper, an instance of the Generalized Finite Element Method, GFEM, which allows an arbitrary Ck continuity, is used to solve arbitrary anisotropic laminated composite plate bending problems.The resultant basis functions naturally exhibit inter-element continuity and can be easily enriched to generate arbitrary p-enriched basis functions. These characteristics result in excellent abilities in terms of approximating the layer stresses. In particular, the high degree of the basis, combined with its continuity, enables the transverse shear stresses to be integrated from the local equilibrium equations, and also post-processed in a scaling operation explored by the authors to provide additional accuracy of the estimates across the thickness. Additionally, all of the estimated strain and stress fields are naturally continuous, without the need for any heuristic averaging or smoothing operation. The procedure is robust enough to allow for Partition of Unity (PoU) construction free of geometrical restrictions on the elements and it is suitable for mixed Ck/C0 formulations, using continuous functions only for those variables which require such continuity, in order to reduce the computational cost.The method is implemented with three-node triangular elements, and its performance is illustrated through comparisons with analytic solutions, with special emphasis on the computation of the transverse stress field for thick laminates.

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.

Cylindrical bending of multilayered plates with multi-delamination via a layerwise stress approach

Three-dimensional finite element simulations of delamination propagation in multilayered plates are usually expensive in computational time and memory. In this paper, a two-dimensional layerwise model, called the LS1 model, is introduced as an accurate and effective alternative to the finite element method. The LS1 model is extended to the analysis of delamination growth in multilayered plates subjected to cylindrical bending loading. To this end, a general multilayered plate with arbitrary boundary conditions is investigated. By imposing the unilateral contact conditions at delaminated interfaces, analytical LS1 solutions to a general multi-delamination problem are obtained. As application examples, two classical mode I (Double Cantilever) and mode II (End Notched Flexure) delamination tests are investigated. By considering two types of crack resistance curve, the delamination propagation in composite laminates is studied. The LS1 results are found and compared to those of a finite element model. Very good agreements between the results of the two models prove the efficiency and accuracy of the LS1 model for the simulation of delamination propagation in laminates subjected to cylindrical bending.

Bending analysis of laminated and sandwich plates using a layer-wise stress model

In this paper, the behavior of laminated composites is investigated using several high order or layer-wise finite element calculations. A layer-wise model and its dedicated C0 eight-node finite element have been originally specifically developed for interlaminar stresses analysis in free edge problem [1,2] or recently for bonding study [3]. This model is the core of the present comparisons. It is based on a typical layer-wise description which represents the laminate as a superposition of Reissner plates coupled by interfacial stresses. This element has 5n degrees of freedom per node (n is the layers number) and is able to predict interlaminar stresses. These out-of-plane stresses are deduced directly from constitutive equations without post-processing steps. While previous papers dealt with the accuracy of these interface stresses, in the present paper the accuracy and validity of displacements and stresses are established on classical benchmark bending examples for composites and sandwich plates. The aim is also a better positioning and promoting of this stress approach deriving from the work of Pagano [4], which is not usually studied in this way.

Delaminated multilayered plates under uniaxial extension. Part I: Analytical analysis using a layerwise stress approach

The aim of this two-part paper is to propose an efficient and accurate alternative to the computationally expensive three-dimensional finite element method (3D-FEM), for analyzing delaminated multilayered plates under uniaxial extension. Many of the existing models deal with the analysis of multilayered structures only in the non-delaminated state. The first part of the present study extends the application of a layerwise stress model, called the LS1 model, to delaminated multilayered plates subjected to uniaxial extension. The analytical LS1 solutions are derived for general non-delaminated and delaminated multilayers and compared to 3D finite element solutions. The comparison gives a good agreement between the LS1 and 3D-FE models except near singularities (free edges, crack tips,…). In order to overcome this drawback, a refinement approach, called the refined LS1, is presented in Part II and applied to angle-ply rectangular composite laminates. The comparison between the refined LS1 and 3D-FE models reveals an excellent agreement, even in the vicinity of singularities, in terms of interlaminar stresses and strain energy release rate. The main conclusion of the second part is that the proposed refined LS1 model can be used as an accurate and very efficient model for evaluating the interfacial stress fields as well as the strain energy release rate in multi-delamination problems.

Flexure analysis of unsymmetric orthotropic beams with an interlayer

This paper presents a layer-wise stress and deformation analysis of a three-layer beam configuration consisting of two dissimilar orthotropic adherends of different thicknesses that are joined together by a deformable interlayer of finite thickness. Analytical solutions for the case of three-point flexure loading are presented for both compressible and incompressible interlayers. Parametric analysis reveals the influences of asymmetry of moduli and adherend thicknesses, interlayer thickness, and overhang of the beams on the beam compliance. Analytical predictions of beam compliance show very good agreement with finite element results. Experimental measurements of compliance of various unsymmetric beams consisting of aluminum adherends separated by a rubber interlayer were performed in order to validate the analysis. Excellent agreement between measured and predicted compliance values was observed.

Some studies on static analysis of composite thin-walled box beam

Long hollow rectangular composite box beam configurations are used quite commonly in engineering structures especially in aerospace, ship building and civil engineering construction. In the present study a finite element method is presented for the determination of transverse displacement and layer-wise stress distribution of thin-walled plate structure assembled from flat plates. The finite element formulation is based on Mindlin plate theory which takes shear deformation of the beam into consideration. Effect of material and lay-up sequence on the structural behavior of rectangular cross-section thin-walled composite box beam under uniformly distributed load on the top face with end supports is studied.