George A. Kardomateas

Analysis of Sandwich Beams With a Compliant Core and With In-Plane Rigidity—Extended High-Order Sandwich Panel Theory Versus Elasticity

A new one-dimensional high-order theory for orthotropic elastic sandwich beams is formulated. This new theory is an extension of the high-order sandwich panel theory (HSAPT) and includes the in-plane rigidity of the core. In this theory, in which the compressibility of the soft core in the transverse direction is also considered, the displacement field of the core has the same functional structure as in the high-order sandwich panel theory. Hence, the transverse displacement in the core is of second order in the transverse coordinate and the in-plane displacements are of third order in the transverse coordinate. The novelty of this theory is that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core and the rotation at the centroid of the core) instead of just one (midpoint transverse displacement) commonly adopted in other available theories. It is proven, by comparison to the elasticity solution, that this approach results in superior accuracy, especially for the cases of stiffer cores, for which cases the other available sandwich computational models cannot predict correctly the stress fields involved. Thus, this theory, referred to as the “extended high-order sandwich panel theory” (EHSAPT), can be used with any combinations of core and face sheets and not only the very “soft” cores that the other theories demand. The theory is derived so that all core=face sheet displacement continuity conditions are fulfilled. The governing equations as well as the boundary conditions are derived via a variational principle. The solution procedure is outlined and numerical results for the simply supported case of transverse distributed loading are produced for several typical sandwich configurations. These results are compared with the corresponding ones from the elasticity solution. Furthermore, the results using the classical sandwich model without shear, the first-order shear, and the earlier HSAPT are also presented for completeness. The comparison among these numerical results shows that the solution from the current theory is very close to that of the elasticity in terms of both the displacements and stress or strains, especially the shear stress distributions in the core for a wide range of cores. Finally, it should be noted that the theory is formulated for sandwich panels with a generally asymmetric geometric layout. [DOI: 10.1115/1.4005550]

Buckling and Initial Postbuckling Behavior of Sandwich Beams Including Transverse Shear

An asymptotic solution is presented for the buckling and initial postbuckling behavior of sandwich beams. The effect of transverse shear is included, and the shear correction is calculated from energy equivalency. The asymptotic procedure is based on the nonlinear beam equation (with transverse shear included ), and closed-form solutions are derived for the critical load and for the load and midpoint dee ection and axial shortening vs applied compressiveload during theinitial postbuckling phase.Illustrativeresultsarepresented fora few typical sandwich construction cone gurations, in particular, with regard to the effect of face sheet and core material system. Nomenclature A = total cross-sectional area c = subscript for the core E = Young’ s modulus e = distance of the neutral axis of the section from the core midline .EI/eq = equivalent rigidity f1 = subscript for the top face sheet f2 = subscript for the bottom face sheet G = shear modulus N G = “ effective” shear modulus of the section L = beam length P = axial force Pcr = critical load s = distance along the dee ected beam V = shear force (normal to the dee ected beam axis) v = vertical displacement ® = shear correction coefe cient ¯ = slope of the dee ected beam axis °eq = equivalent for the section shear angle µ = rotation of the cross section due to bending

Growth of internal delaminations under cyclic compression in composite plates

The growth of internal delaminations in composite plates subjected to cyclic compression is investigated. Due to the compressive loading, these structures undergo repeated buckling-unloading of the delaminated layer with a resulting reduction of the interlayer resistance. An important characteristic of the problem is that the state of stress near the delamination tip is of mixed mode, I and II. Equations describing the growth of the delaminations under cyclic loads are obtained on the basis of a combined delamination buckling-post-buckling and fracture mechanics model. The latter is based on a mode-dependent critical fracture energy concept and is expressed in terms of the spread in the energy release rate in the pre- and post-buckling state. It is shown that such a model allows for the accumulation of microdamage at the delamination front. The growth laws developed in this manner are integrated numerically, in order to produce the delamination growth vs number of cycles curves. Furthermore, the investigation includes the possibility of unstable delamination growth. The study does not impose any restrictive assumptions regarding the delamination thickness and plate length (as opposed to the usual thin film assumptions). The results show that for a given value of delamination thickness h, the fatigue delamination growth is strongly affected by the relative location of the delamination through the plate thickness T, the fatigue growth being slower for a smaller value of hT (delaminations located closer to the surface). These theoretical predictions are confirmed by experimental results that are obtained for the growth of delaminations in graphite-epoxy unidirectional specimens under cyclic constant amplitude compressive loading. The test data, which were obtained for several different locations of the delamination through the thickness (hence different degrees of mode mixity), and different applied maximum compressive displacement, seem to be well-correlated with the theory.

Energy release rate and stress intensity factors for delaminated composite laminates

Abstract A procedure of total energy release rate and stress intensity factors is developed for general non-homogeneous laminated composite laminates. The total energy release rate is obtained by using the J -integral for a one dimensional model of plane stress, plane strain and cylindrical bending. Decomposition of it into mode I and mode II, by which the mode mixity calculation is carried out, is based on the assumption of equivalent orthotropic properties through the laminate thickness. The process is straightforward and can be used as a criterion for delamination onset and growth of one dimensional structural model under general loading in the pre- and post-buckling states.

Buckling of long sandwich cylindrical shells under external pressure

The paper deals with the theoretical prediction of buckling loads for sandwich long cylindrical shells with laminated facings and foam core. The loading is a uniform hydrostatic pressure, which means that the loading remains normal to the deflected surface during the buckling process. Several fiber materials are used in the laminated facings. The materials are: Boron/Epoxy, Graphite/Epoxy and Kevlar/Epoxy laminates with 0° orientation with respect to the hoop direction. These various materials are employed to provide comparative data that can be used in design. Shell theory results are generated with and without accounting for the transverse shear effect. Moreover, results based on three-dimensional elasticity are also generated for comparison purposes. The effect of the ratio of radius to thickness is assessed.

Buckling of orthotropic beam-plates with multiple central delaminations

Abstract A closed form solution is developed for predicting the critical load of a composite beamplate with multiple delaminations. The characteristic equation is derived by using non-linear beam theory, performing proper linearization and by imposing the appropriate kinematical continuity and equilibrium conditions. The effects of the dimensions and locations of the delaminations on the critical load are investigated and the results are compared with previously published data.

Nonlinear Response of a Shallow Sandwich Shell With Compressible Core to Blast Loading

This paper investigates the nonlinear dynamic response of a shallow sandwich shell subject to blast loading with consideration of core compressibility. The shallow shell consists of two laminated composite or metallic face sheets and an orthotropic compressible core. Experimental results and finite element simulations in literature have shown that the core exhibits considerable compressibility when a sandwich panel is subjected to impulse loading. To address this issue properly in the analysis, a new nonlinear compressible core model is proposed in the current work. The system of governing equations is derived by means of Hamiltons principle in combination with the Reissner-Hellingers variational principle. The analytical solution for the simply supported shallow shell is formulated using an extended Galerkin procedure combined with the Laplace transform. Numerical results are presented. These results demonstrate that this advanced sandwich model can capture the transient responses such as the stress shock wave effect and the differences in the transient behaviors of the face sheets and the core when a sandwich shadow shell is subjected to a blast loading. However, in the steady state dynamic stage, all the displacements of the face sheets and the core tend to be identical. This model can be further used to study the energy absorption ability of the core and the effects of different material and geometrical parameters on the behaviors of sandwich structures subject to blast loading.

Nonlinear High-Order Core Theory for Sandwich Plates with Orthotropic Phases

case of transversely loaded plates are produced for several typical sandwich configurations. These results are compared with the corresponding ones from the elasticity solution. Furthermore, the results using the classical sandwich model with and without shear are also presented. The comparison among these numerical results shows that the solution from the current theory is very close to that of the elasticity in terms of both the displacements and the transverse stress through the core. Observations in the current work suggest that this new high-order theory could have significant applications in studying the structural and failure behavior of sandwich plates.

The effects of overloads in fatigue crack growth

Abstract Several theories have been proposed to explain the transient fatigue crack growth decelerations and accelerations which follow overloads. The mechanisms that have been proposed to explain retardation after a tensile overload, for example, include residual stress, crack deflection, crack closure, strain hardening, and plastic blunting/resharpening. These mechanisms are reviewed in the light of recent experimental results, and implications with regard to their applicability are examined. It is suggested that no single mechanism can be expected to represent observed effects over the entire range of da/dN versus ΔK; eg, behaviour ranging from the near threshold region to the Paris region.

Effects of compressive load excursions on fatigue crack growth

Abstract The variable-amplitude loading encountered in service often includes compressive excursions. It has been a common practice to ignore these excursions for fatigue crack growth analyses. Recently, experimental data on both smooth bars and cracked specimens with intermittent negative R ratio loadings have indicated that the effects of compressive excursions are not negligible.