Jørgen Asbøll Kepler

Energy partition for ballistic penetration of sandwich panels

Ballistic impact and penetration in sandwich panels at projectile velocities above the ballistic limit are considered. An analytic model is developed that deals with partition of the energy of absorption, allowing for quantitative estimation of the energy fraction consumed via panel elastic response and the one consumed via irreversible damage. The analysis is based on simultaneous solution of two differential equations describing bending and shear deformation of a sandwich panel and taking into account the energy conservation. The solution technique includes the direct and inverse Hankel transformations and results in practical expressions for elastic response and damage energy fractions. Numerical results are corroborated with experimental data obtained from intermediate-velocity impact tests performed for sandwich panels with FRP composite laminate faces and foam cores.

Impact Penetration of Sandwich Panels at Different Velocities - An Experimental Parameter Study: Part I - Parameters and Results

Part I of this article describes a series of tests of localized, penetrating impact on sandwich panels. The sandwich panel size was 500 500 mm2 with a thickness of 46 mm. Three types of panel configuration were tested. Penetration was carried out in quasi-static conditions and at approximately 70 and 93 m/s. Impactor mass was 1 kg with an impactor diameter of 50 mm and with three different impactor tip geometries. For each of the 27 combinations, the total energy absorption was measured, and the damage patterns are described and quantified.

Impact Penetration of Sandwich Panels at Different Velocities – An Experimental Parameter Study: Part II – Interpretation of Results and Modeling

Based on sandwich panel penetration experiments and the observed damage patterns, as described in Part I of this article, the individual energy contributions are estimated from simple physical models. It is shown that the most important contributions are from membrane-state fiber stretching, core compression, and friction between core material and impactor. Lesser contributions are from delaminations, core fracture, and debonding between core and back face-sheet. Addition of the energy absorption contributions generally give smaller total absorption than measured; the most likely reasons for this discrepancy are outlined in the conclusion.

Numerical modeling of sandwich panel response to ballistic loading - energy balance for varying impactor geometries

A sandwich panel is described by an axisymmetric lumped mass— spring model. The panel compliance is simplified, considering only core shear deformation uniformly distributed across the core thickness. Transverse penetrating impact is modeled for impactors of diameters comparable to the panel thickness but significantly smaller than panel length dimensions. Experimental data for the total loss in impactor kinetic energy and momentum and estimated damage energy are described. For a selection of impactor tip shapes, the numerical model is used to evaluate different simplified force histories between the impactor and the panel during penetration. The force histories are selected from a primary criterion of conservation of linear momentum in the impactor—panel system, and evaluated according to agreement with the total measured energy balance.

Equipment for Impact Testing of Sandwich Panels

This article describes test equipment for testing localized, penetrating impact on sandwich panels. The sandwich panels in question are 500 500 mm2 with a typical thickness of 40-55 mm. The impact velocities are in the region 50-130 m/s, with an impactor mass between 0.5 and 1 kg, and an impactor diameter of 50 mm. The above parameters correspond to localized impact on train fronts, airplanes at take-off and landing, cars and similar. A series of 7 impact tests on identical sandwich panels at varying velocities is described.

On application of catenary principles to sandwich structure design—Sandwich/ catenary hybrid beams under uniformly distributed load

Application of catenary principles to sandwich structure design, whereby one face sheet follows the equilibrium shape of a catenary according to the applied load, is investigated. The difference between load transfer through a sandwich beam and through a catenary is outlined. An initial comparison between an inclined elastic string and a sandwich core under shear deformation provides an indication of the potential stiffness advantages of catenary design. A stiffness comparison is made between an ordinary sandwich beam with thin, parallel face sheets, a catenary suspended by the end-points, and a sandwich/catenary hybrid. It is demonstrated that, for mass parity and a uniformly distributed load, and depending on the constituent materials moduli, the sandwich/catenary hybrid may be designed for superior stiffness. A numerical modeling method is outlined for evaluating the deflection of a catenary, and subsequently expanded to predict deflection of a sandwich/catenary hybrid beam. The method is verified through comparison with experimentally measured deflection. It is demonstrated that first-order shear deformable theory, commonly applied to sandwich structures, is inherently unsuited for describing the elastic response of sandwich/catenary hybrids. For a typical range of face-sheet/core moduli, comparisons of relative stiffness for parallel-face sandwich beams and sandwich/catenary hybrid beams are calculated over a range of core heights, for equivalent core height and equivalent core volume.

Concurrent Bending and Localized Impact on Sandwich Panels

The paper describes impact/bending testing of sandwich panels with 10 mm foam core and FRP face-sheets, with emphasis on test procedures, registration of results and description of the specialized test equipment developed. The sandwich panels were subjected to a cylindrical bending load of varying magnitude, while impacted at approximately 500 m/s. The impactor body was a steel sphere, diameter 10mm, with a mass of approximately 4g. The energy absorption and damage morphology of preloaded panels were compared with similar data for impact on specimens without preload. A high-speed camera was used for qualitative registration of panel response.

Numerical Modeling of Sandwich Panel Response to Ballistic Loading

A sandwich panel is described by an axisymmetric lumped mass/spring model. The panel compliance is simplified, considering only core shear deformation. Transverse penetrating impact is modeled; impactor diameter is significantly smaller than panel size. Experimental data for the total loss in impactor kinetic energy and momentum and estimated damage energy are given. For a selection of impactor tip shapes, the numerical model is used to evaluate different force-histories between the impactor and the panel during penetration