Anisotropic Lay-up Research Articles

Four-point bending behaviors of CFRP trapezoidal corrugated sandwich plates

The stiffness, failure load and failure mechanism of carbon fibre reinforced plastic (CFRP) composite trapezoidal corrugated sandwich plates (CTCSPs) subjected to four-point bending load were studied by experiment, modelling prediction and parametric analysis. With orthogonal anisotropic lay-ups containing ± θ plies (θ = 15°, 45° and 90°), three all-CFRP specimens were fabricated by mold hot pressing and secondary bonding. The four-point bending behaviors of specimens were tested and compared, and the analytical expressions of stiffness and failure load were provided. Four buckling failure modes and four strength failure modes were analytically considered. The spatial location and time sequence of eight failure modes were revealed by numerical linear buckling and progressive damage models established in ABAQUS. The modelling stiffness, failure load and failure process agreed with the four-bending experimental results. By increasing θ, the limit load of the specimens first increases and then decreases while the stiffness decrease. Correspondingly, the initial failure modes are shear corrugation fracture, debonding and face fracture. The variations in stiffness parameters and failure mechanism maps were presented; the latter can simultaneously predict the limit load and failure mode. The limit load and stiffness of CTCSPs can be improved more obviously by increasing the number of the face plies than by expanding the core plies.

Exploration of the effect of wing component post-buckling on bending-twist coupling for nonlinear wing twist

A new investigated concept for passive load alleviation is to exploit the nonlinear behavior of wing design components to trigger a deformation which reduce loads once a critical load level is reached. The necessary deformation is a torsional rotation which is supposed to reduce the angle of attack. For this target, wingbox sections are investigated regarding their nonlinear behavior with finite element analysis. Parameter studies feature anisotropic carbon fiber reinforced polymer (CFRP) layups for the skins, layups and thicknesses for spars and the presence of stringers. Results show a desired nonlinear progressive bending-torsion coupling for an unstiffened wingbox section, when the upper skin and the rear spar are modified. After modification they are allowed to buckle within the load envelope. The skin has an anisotropic layup. The rear spar needs to be thinner than the front spar. Both modifications result in progressively increasing torsional rotation of the wingbox with increasing load. Stringers are not applied because they limit the nonlinearity which is not desired for the envisioned load alleviation technique.

Geometrically nonlinear vibration of anisotropic composite beams using isogeometric third-order shear deformation theory

Due to broad usage of anisotropic composite beams in modern engineering structures, the main goal of the present work is to examine their geometrically nonlinear vibration. To this end, a third-order shear deformation theory with a nonlinear von-Kármán strain field is used for anisotropic beams and combined with the advantages of the isogeometric framework. The layup properties are assumed to be anisotropic in the depth direction and a transient tip follower force is considered. The governing nonlinear equations of vibration are integrated by means of the Newmark approach and solved with the Newton–Raphson method. Flutter loads as well as natural frequencies are obtained by eigenvalue analysis. The effects of various important factors such as non-prismatic shape, orientation of the composite fibers, critical follower force and bifurcation point are studied, using both h- and p-refinements. The results show that the nonlinear vibration and flutter characteristics of the anisotropic composite beams are completely different from those for orthotropic and isotropic ones. Thick beams with anisotropic layups are more sensitive to the shear parameter than conventional ones and deform primarily in shear mode rather than in bending. Anisotropic beams reveal a higher flutter instability force than other cases for a given shear parameter value. Another important phenomenon is that the stress distribution in anisotropic layups shows irregular patterns both in depth and time. Anisotropic layups with ply angles between 15° and 45° seem to present enhanced nonlinear performance with respect to other layup choices. A coarse mesh of quartic C3 B-splines is observed to provide high accuracy for nonlinear deflections in anisotropic cases even for rather low shear parameters.

Buckling solutions of clamped-pinned anisotropic laminated composite columns under axial compression using bifurcation approach and finite elements

Following the bifurcation approach, a generalized closed form buckling solution for clamped-pinned anisotropic laminated composite columns under axial compression is developed using the energy method. The effective axial, coupling, and flexural rigidity coefficients of the anisotropic layups are determined following the generalized constitutive relationship using dimensional reduction by static condensation of 6×6 rigidity matrix. The presented analytical explicit formula reproduces Euler buckling expression in the case of isotropic or specially-orthotropic materials once the effective coupling term vanishes. On the other hand, the analytical formula furnishes two extra terms which are functions of the effective coupling, flexural and axial rigidity. The analytical buckling formula is confirmed against finite element Eigen value solutions for different anisotropic laminated layups yielding high accuracy for a wide range of stacking sequences. A parametric study is then conducted to examine the effect of ply orientations, material properties including hybrid carbon/glass fiber composites, FE element type, and column size. Relevance of the numerical and analytical results is discussed in comparison to previous results in literature for cross ply laminates.

Analytical and Finite Element Buckling Solutions of Fixed–Fixed Anisotropic Laminated Composite Columns Under Axial Compression

A generalized analytical formula is developed to predict buckling of anisotropic laminated composite fixed–fixed thin columns by using the Rayleigh–Ritz displacement field approximation. Based on the generalized constitutive relationship, the effective extensional, coupling and flexural stiffness coefficients of the anisotropic layup are determined using dimensional reduction by static condensation of the 6[Formula: see text][Formula: see text][Formula: see text]6 composite stiffness matrix. The resulting explicit formula is expressed in terms of the flexural stiffness since the coupling and extensional stiffness coefficients drop out of the formulation for this boundary condition when following the standard Rayleigh–Ritz formulation steps. This formula is similar to the Euler buckling formula in which the flexural rigidity is expressed in terms of the flexural stiffness coefficient of laminated composites. Motivated by reducing some of the discrepancy with the finite element results, the pre-buckling solution was substituted into the bifurcation expression to yield an updated formula that includes the coupling and extensional stiffness coefficients. The analytical results are verified against finite element Eigen value solutions for a wide range of anisotropic laminated layups yielding high accuracy. A parametric study is then conducted to examine the effect of ply orientation and material properties including hybrid carbon/glass fiber composites. Relevance of the numerical and analytical results is discussed for all these cases. In addition, comparisons with an earlier buckling solution for cross-ply laminated columns are made.

Closed form stability solution of simply supported anisotropic laminated composite plates under axial compression compared with experiments

Closed form expression for the buckling load of generally anisotropic laminated composite simply supported thin plates is derived. The Rayleigh-Ritz displacement field approximation based on the energy approach introduced an upper bound solution compared to the FE results. Therefore, the critical stability matrix is used to obtain an accurate buckling formula. The effective axial, coupling and flexural stiffness coefficients of the anisotropic layup is determined from the generalized constitutive relationship using dimensional reduction by static condensation of the 6×6 composite stiffness matrix. The resulting explicit formula has an additional term, which is a function of the effective coupling and axial stiffness. This formula reduces down to Euler buckling formula once the effective coupling stiffness term vanishes for isotropic and certain classes of laminated composites. The closed form results are verified against finite element Eigenvalue solutions for a wide range of anisotropic laminated layups yielding high accuracy. Comparisons with a limited number of experiments are also performed showing good correspondence. A brief parametric study is then conducted to examine the effect of ply orientations and material properties including hybrid carbon/glass fiber composites. Relevance of the numerical and closed form results is discussed for all these cases.

The response of layered anisotropic tubes to centrifugal loading

The displacement-based elastic solution for layered anisotropic tubes is extended to allow for the presence of centrifugal loading. The additional terms in the stress–strain equations derived in this work are validated by comparing the results obtained using the current solution against those determined using finite element simulation of rotating thin and thick-walled glass fibre reinforced plastic tubes of arbitrary anisotropic lay-up. The solution is presented in such a form that it can be utilised to determine the linear thermo-mechanical behaviour of rotating tubes with anisotropic lay-up, subjected to any combination of internal and external axisymmetric pressure, axial loading, torsional loading, and constant temperature change.

On the propensity of laminates to delaminate

Laminates have a propensity to delaminate; the mathematical plane between adjacent plies offers a preferred path for crack propagation, irrespective of the nature of the stress field that gives rise to the elastic strain energy released. This is because the plane between plies is characterised by a specific fracture surface energy significantly lower than those for internal surfaces that intersect fibres. In the second of his two classical publications on fracture, A.A. Griffith showed how crack rotation in two-dimensional stress fields occurs. This suggests how, in a laminate, pre-existing flaws are able to seek out the plane of lamination; here, crack rotation under the influence of, for example, shear stress is examined in the context of laminates designed for use in aerospace. One physical consequence of Griffith’s calculation is the prediction of crack propagation in elastic solids subjected to bidimensional compression with strongly unequal principal stresses. A simple bidimensional compression rig has been devised to investigate this prediction. To obviate the risk of delamination, it will be necessary to move away from anisotropic lay-ups, and further develop three-dimensional weaves and methods for weaving three-dimensional weaves. A method whereby a three-dimensional fibre weave, which has cubic symmetry and no zero-valued shear moduli, might be weaved is outlined.

Natural boundary conditions in the bending of anisotropic laminated plates

Natural boundary conditions in the bending of anisotropic plates can never be exactly satisfied by a solution in a variables separable form. This creates difficulties for classic solution methods such as Ritz and finite elements, both of which are based on a variables separable approach. Solutions utilizing both of these methods are obtained for deflection, moment resultant , and shear force resultants for simply supported, clamped, and mixed (clamped-simply supported) boundary conditions. A comparison is made between the solutions from these two approaches with emphasis on convergence and how closely each method satisfies natural boundary conditions. Balanced-symmetric angle-ply, special orthotropic, and general anisotropic lay-ups are considered.

Moving away from anisotropic lay-ups; modelling of 3D preforms & weaves

Six is the number of fibre orientations necessary and sufficient to remove all zero-valued shear moduli from fibre arrays that have cubic symmetry. Of particular interest is a weave, of just four families of flexible fibres, that has equal numbers of equal fibre lengths parallel to the six face diagonals of a cube. The relative positions of fibre lengths in this weave can be visualised as the edges of space-filling equilateral truncated octahedra.

Anisotropic effects in the compression buckling of laminated composite cylindrical shells

This paper addresses two aspects of buckling relevant to design. The first describes the preliminary experimental results that validate the presence of a newly reported spiral buckling mode; whilst the second concerned the effects of extension/twist anisotropy on the buckling loads of cylindrical shells under compression. The influence of designing laminates with antisymmetric lay-ups in comparison with a symmetrical lay-up is also investigated. Antisymmetric quasi-isotropic laminates, based on 0, 90 and ±45° angles produces greater buckling loads than the equivalent symmetric lay-up. Whilst all anisotropic coupling effects appear to lower the buckling loads, a laminate that is 48 plies thick is necessary to eliminate them in thin-walled shells. Such a laminate is at least 6 mm thick. Many designs require thinner laminates, and in so doing, mitigate the need for guidelines on efficient anisotropic lay-ups. Neglecting the effect of prebuckling deformation, it is found that extension/twist coupling is less deleterious than flexural/twist coupling in this respect. Therefore, antisymmetric laminates appear preferable for initial buckling of quasi-isotropic laminates.

Stress Determination at Skin-Stiffener Interfaces of Composite Stiffened Panels Under Generalized Loading

An approach is presented to calculate stresses at the skin-stiffener inter faces of composite stiffened panels. The skin and stiffener can have general anisotropic layup and the loading can be in-plane or out-of-plane as long as the in-plane stresses far from the flange edge can be at most linear in the out-of-plane direction. A stress-based en ergy minimization is used with a variational calculus derivation of the governing equa tions. All six stresses are determined at the skin-stiffener interface. Comparison of the present closed form solution with a finite element solution shows good agreement. The stresses determined with the present method are used in a failure criterion to predict onset of delamination. The effects of geometry and layup on the onset of delamination for various loadings are investigated and several trend curves useful for design applications are presented.