Low-velocity heavy-mass impact response of slender metal foam core sandwich beam

The objective of this work is to investigate the dynamic large deflection response of fully clamped metal foam core sandwich beam struck by a low-velocity heavy mass. Analytical solution and ‘bounds’ of dynamic solutions are derived, respectively. Also, finite element analysis is carried out to obtain the numerical solution of the problem. Comparisons of the dynamic, the quasi-static and numerical solutions for the non-dimensional maximum deflection of the sandwich beam with non-dimensional initial kinetic energy of the striker are presented for different cases of mass ratio, impact velocity and location. It is seen that the dynamic solution approaches the quasi-static one as the mass ratio of the striker to the beam is large enough, the quasi-static solution is in good agreement with the numerical results and both solutions lie in the ‘bounds’ of dynamic solutions. The quasi-static and numerical results for the impact force against the maximum deflection of the sandwich beam are obtained. It shows that the quasi-static solution can offer adequate accuracy to predict the low-velocity heavy-mass impact response of fully clamped sandwich beam.     

Numerical simulations of low-velocity impact on an aircraft sandwich panel

The potential hazards resulting from a low-velocity impact (bird-strike, tool drop, runway debris, etc.) on aircraft structures, such as engine nacelle or a leading edge, has been a long-term concern to the aircraft industry. Certification authorities require that exposed aircraft components must be tested to prove their capability to withstand low-velocity impact without suffering critical damage.

This paper describes the results from experimental and numerical simulation studies on the impact and penetration damage of a sandwich panel by a solid, round-shaped impactor. The main aim was to prove that a correct mathematical model can yield significant information for the designer to understand the mechanism involved in the low-velocity impact event, prior to conducting tests, and therefore to design an impact-resistant aircraft structure.

Part of this work presented is focused on the recent progress on the materials modelling and numerical simulation of low-velocity impact response onto a composite aircraft sandwich panel. It is based on the application of explicit finite element (FE) analysis codes to study aircraft sandwich structures behaviour under low-velocity impact conditions. Good agreement was obtained between numerical and experimental results, in particular, the numerical simulation was able to predict impact damage and impact energy absorbed by the structure.     

Nano-structured sandwich composites response to low-velocity impact

This paper investigates the influence of exfoliated nano-structures on sandwich composites under impact loadings. A set of sandwich composites plates made of fiberglass/nano-modified epoxy face sheets and polystyrene foams was prepared. The core was 25 mm thick and the face sheets were made of eight layers of woven fabric glass fibers and nano-modified epoxy (≈0.8 mm of thickness). The epoxy system was bisphenol A resin and an amine hardener. The fiber volume fraction used was around 65%, while the nanoclay content varied from 0 wt.% to 10 wt.%. The nanoclay used was Cloisite 30B from Southern Clay. The sandwich panels were submitted to low-velocity impact tests with energies from 5 J to 75 J. Two sets of experiments were performed, i.e. high velocity + low mass and low velocity + high mass. Damage caused by the two groups of experiments and peak forces measured were dissimilar. The results show that the addition of 5 wt.% of nanoclay lead to a more efficient energy absorption. The failure modes were also analyzed, and they seems to be affected by the nanoclay addition to face sheets.     

Effect of physical and geometrical parameters on transverse low-velocity impact response of sandwich panels with a transversely flexible core

The effects of important physical and geometrical parameters on transverse low-velocity impact response of composite sandwich panels have been studied in this paper. Impacts are assumed to occur normally over the top and/or the bottom face sheets, at arbitrary locations and with different impactor masses and initial velocities. For deriving closed-form solutions for the contact force, displacements of the impactor and the panel in the transverse direction, the sandwich panel has been modeled as a discrete three-degrees-of-freedom dynamic system with equivalent masses and springs (SM). The dynamic response of the panel is based on the improved higher-order sandwich plate theory (IHSAPT) and both thick and thin panels have been analyzed. The effects of transverse flexibility of the core, and boundary conditions are considered. Also, the area of the contact patch between the impactor and the panel can be varied as it changes with contact duration. The numerical results of the analysis have been compared either with the available experimental results or with some theoretical results. It is established that the dynamic behavior of the sandwich panel depends on various parameters, such as the aspect ratio and the length-to-thickness ratio of the panel, core thickness, boundary conditions of the panel and impactor parameters like its potential energy, velocity and the location of contact point, etc.     

Response of composite sandwich panels with transversely flexible core to low-velocity transverse impact: A new dynamic model

A new computational procedure based on improved higher order sandwich plate theory (IHSAPT) and two models representing contact behavior between the impactor and the panel are adopted to study the low velocity impact phenomenon of sandwich panels comprising of a transversely flexible core and laminated composite face-sheets. The interaction between the impactor and the panel is modeled with the help of a new system having three-degrees-of-freedom, consisting of spring–mass–damper–dashpot (SMDD) or spring–mass–damper (SMD). The effects of transverse flexibility of the core, and structural damping are considered. The present analysis yields analytic functions describing the history of contact force as well as the deflections of the impactor and the panel in the transverse direction. In order to determine all components of the displacements, stresses and strains in the face-sheets and the core, a numerical procedure based on improved higher order sandwich plate theory (IHSAPT) and Galerkin's method is employed for modeling the layered sandwich panel (without the impactor), while the analytic force function developed on the basis of SMDD or SMD model, can be used for the contact force between the impactor and the panel. The contact force is considered to be distributed uniformly over a contact patch whose size depends on the magnitude of the impact load as well as the elastic properties and geometry of the impactor. Various boundary conditions for the sandwich panel have also been considered. Finally, the numerical results of the analysis have been compared either with the available experimental results or with some theoretical results.     

Three-point bending of sandwich beams with aluminum foam-filled corrugated cores

Sandwich panels having metallic corrugated cores had distinctly different attributes from those having metal foam cores, the former with high specific stiffness/strength and the latter with superior specific energy absorption capacity. To explore the attribute diversity, all-metallic hybrid-cored sandwich constructions with aluminum foam blocks inserted into the interstices of steel corrugated plates were fabricated and tested under three-point bending. Analytical predictions of the bending stiffness, initial failure load, peak load, and failure modes were obtained and compared with those measured. Good agreement between analysis and experiment was achieved. Failure maps were also constructed to reveal the mechanisms of initial failure. Foam insertions altered not only the failure mode of the corrugated sandwich but also increased dramatically its bending resistance. All-metallic sandwich constructions with foam-filled corrugated cores hold great potential as novel lightweight structural materials for a wide range of structural and crushing/impulsive loading applications.     

Modelling of low-energy/low-velocity impact on Nomex honeycomb sandwich structures with metallic skins

In the aircraft industry, manufacturers have to decide quickly whether an impacted sandwich needs repairing or not. Certain computation tools exist at present but they are very time-consuming and they also fail to perfectly model the physical phenomena involved in an impact. In a previous publication, the authors demonstrated the possibility of representing the Nomex™ honeycomb core by a grid of nonlinear springs and have pointed out both the structural behaviour of the honeycomb and the influence of core-skin boundary conditions. This discrete approach accurately predicts the static indentation on honeycomb core alone and the indentation on sandwich structure with metal skins supported on rigid flat support. In this study, the domain of validity of this approach is investigated. It is found that the approach is not valid for sharp projectiles on thin skins. In any case, the spring elements used to model the honeycomb cannot take into account the transverse shear that occurs in the core during the bending of a sandwich. To overcome this strong limitation, a multi-level approach is proposed in the present article. In this approach, the sandwich structure is modelled by Mindlin plate elements and the computed static contact law is implemented in a nonlinear spring located between the impactor and the structure. Thus, it is possible to predict the dynamic structural response in the case of low-velocity/low-energy impact on metal-skinned sandwich structures. A good correlation with dynamic experimental tests is achieved.     

Stability of the face layer of sandwich beams with sub-interface damage in the foam core

This paper addresses the effect of local indentation/impact damage on the bearing capacity of foam core sandwich beams subjected to edgewise compression. The considered damage is in a form of through-width zone of crushed core accompanied by a residual dent in the face sheet. It is shown that such damage causes a significant reduction of compressive strength and stiffness of sandwich beams. Analytical solutions estimating the Euler’s local buckling load are obtained for two typical modes of damage. These solutions are validated through experimental investigation of three sandwich configurations. The results of the analytical analysis are in agreement with the experimental data.     

球形孔泡沫铝合金三明治梁的三点弯曲变形

研究了球形孔泡沫铝合金的单轴压缩性能,得到了抗压强度与相对密度的关系;与多边形孔泡沫铝合金和泡沫纯铝作了对比,发现球形孔使力学性能有了较大的提高.根据球形孔泡沫铝合金三明治梁三点弯曲的载荷(P)位移(δ)曲线研究了四种常见破坏模式并建立了破坏模式图.用极限载荷公式得到的计算值与极限载荷的实验值吻合良好.球形孔泡沫铝合金力学性能高于多边形孔泡沫铝合金及泡沫纯铝,因而其三明治梁的力学性能最好.     

Collapse of clamped and simply supported composite sandwich beams in three-point bending

Composite sandwich beams, comprising glass–vinylester face sheets and a PVC foam core, have been manufactured and tested quasi-statically. Clamped and simply supported beams were tested in three-point bending in order to investigate the initial collapse modes, the mechanisms that govern the post-yield deformation and parameters that set the ultimate strength of these beams. Initial collapse is by three competing mechanisms: face microbuckling, core shear and indentation. Simple formulae for the initial collapse loads of clamped and simply supported beams along with analytical expressions for the finite deflection behaviour of clamped beams are presented. The simply supported beams display a softening post-yield response, while the clamped beams exhibit hardening behaviour due to membrane stretching of the face sheets. Good agreement is found between the measured, analytical and finite element predictions of the load versus deflection response of the simply supported and clamped beams. Collapse mechanism maps with contours of initial collapse load and energy absorption are plotted. These maps are used to determine the minimum mass designs of sandwich beams comprising woven glass face sheets and a PVC foam core.     

Ballistic impact experiments of metallic sandwich panels with aluminium foam core

Metallic sandwich structures with aluminium foam core are good energy absorbers for impact protection. To study their ballistic performance, quasi-static and impact perforation tests were carried out and the results are reported and analysed in this paper. In the experiments, effects of several key parameters, i.e. impact velocity, skin thickness, thickness and density of foam core and projectile shapes, on the ballistic limit and energy absorption of the panels during perforation are identified and discussed in detail.     

The dynamic response of end-clamped sandwich beams with a Y-frame or corrugated core

The dynamic response of end-clamped monolithic beams and sandwich beams has been measured by loading the beams at mid-span using metal foam projectiles. The AISI 304 stainless-steel sandwich beams comprise two identical face sheets and either prismatic Y-frame or corrugated cores. The resistance to shock loading is quantified by the permanent transverse deflection at mid-span of the beams as a function of projectile momentum. The prismatic cores are aligned either longitudinally along the beam length or transversely. It is found that the sandwich beams with a longitudinal core orientation have a higher shock resistance than the monolithic beams of equal mass. In contrast, the performance of the sandwich beams with a transverse core orientation is very similar to that of the monolithic beams. Three-dimensional finite element (FE) simulations are in good agreement with the measured responses. The FE calculations indicate that strain concentrations in the sandwich beams occur at joints within the cores and between the core and face sheets; the level of maximum strain is similar for the Y-frame and corrugated core beams for a given value of projectile momentum. The experimental and FE results taken together reveal that Y-frame and corrugated core sandwich beams of equal mass have similar dynamic performances in terms of rear-face deflection, degree of core compression and level of strain within the beam.     

Three-dimensional solution of low-velocity impact on sandwich panels with hybrid nanocomposite face sheets

In this article, a three-dimensional solution based on Fourier's series and the generalized differential quadrature method is presented to model the low-velocity impact on sandwich panels with hybrid nanocomposite face sheets. Navier's equations are derived and displacements are substituted by their corresponding Fourier's series. The contact force is considered as a Fourier's series of impactor displacement and deflection of contact point. To verify the theoretical model, experiments are performed on a polyurethane foam-cored sandwich panel with epoxy/woven-fiberglass/nanosilica hybrid nanocomposite face sheets. Contact force and lateral displacement of contact point histories are compared with the theoretical model.     

齿板-玻璃纤维/聚氨酯泡沫芯夹层梁的低速冲击性能

提出了一种由齿板-玻璃纤维（TP-GF）混合面板和聚氨酯（PU）泡沫芯材组成的新型TP-GF/PU泡沫夹层梁,结构中金属板通过齿钉压入GF与内部芯材连接,该夹层梁采用真空导入模压工艺制作。通过低速冲击试验,研究了不同冲击能量、纤维厚度和泡沫密度下TP-GF/PU泡沫夹层梁的冲击响应和损伤模式,并与普通的夹层梁进行了对比分析;通过双悬臂梁试验研究了混合夹层梁的界面性能,计算了夹层梁的应变能释放率。结果表明:在22 J、33 J、44 J能量冲击下,泡沫芯材密度为150 kg/m3的TP-GF/PU泡沫夹层梁的最大接触力较普通夹层梁分别提高了31.2%、48.6%、33.3%,冲击能量吸收分别增加了17.2%、11.3%、15.5%;随着冲击能量、面板纤维层数及芯材密度的增加,TP-GF/PU泡沫夹层梁最大接触力增大,密度较低的TP-GF/PU泡沫夹层梁损伤形式主要为面板的局部弯曲,而芯材密度较高的TP-GF/PU泡沫夹层梁则以穿透损伤为主;增加泡沫芯材密度和面板纤维厚度能够提高TP-GF/PU泡沫夹层梁的抗冲击性能,随着芯材密度的增大TP-GF/PU泡沫夹层梁的应变能释放率峰值越高,界面性能越好。      

Contact force history analysis of composite sandwich plates subjected to low-velocity impact

Usually the modified Hertzian contact law or experimental static indentation law has been used to analyze low-velocity impact response of composite laminates. In composite laminated plates subjected to low-velocity impact, usually indentation by impact is very small and also energy absorption by indentation is negligible, so ‘spring element method’, which proposed by author recently, can be well applied to investigate impact response. In the present study ‘lumped mass method’ also had been proposed by author to approximately calculate contact force history of composite laminates will be conceptually described as well as the spring element method. And it will be discussed that how the spring element method can be applied to composite sandwich plates. Finally numerical results easily obtained from finite element analysis based on the spring element method using general-purpose commercial FEM software is compared with experimental results. The comparison shows overall agreement.     

Dynamic analysis of an axially moving sandwich beam with viscoelastic core

A development of the beam model of the axially moving sandwich continua with elastic faces and the core characterized by viscoelastic properties is presented in this paper. Two-parameter Kelvin–Voigt rheological model is used to describe material properties of the core. The Galerkin method is used to solve the governing partial differential equation. Dynamic analysis of the composite with two aluminum facings and a polyurethane core is carried out. The effect of the transport speed, the core thickness and the internal damping of the core material on the dynamic behavior of the system is investigated in undercrtitical and supercritical range of transport speed.     

High-order free vibration analysis of sandwich beams with a flexible core using dynamic stiffness method

In this paper, high-order free vibration of three-layered symmetric sandwich beam is investigated using dynamic stiffness method. The governing partial differential equations of motion for one element are derived using Hamilton’s principle. This formulation leads to seven partial differential equations which are coupled in axial and bending deformations. For the harmonic motion, these equations are divided into two ordinary differential equations by considering the symmetrical sandwich beam. Closed form analytical solutions of these equations are determined. By applying the boundary conditions, the element dynamic stiffness matrix is developed. The element dynamic stiffness matrices are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by use of numerical techniques and the known Wittrick–Williams algorithm. Finally, some numerical examples are discussed using dynamic stiffness method.     

Bending response of web-core sandwich beams

This paper presents a new analytical solution for the bending response of a web-core sandwich beam. The beam is a transverse cut from the sandwich plate. The method is based on the plane frame analysis, where the response of the beam is divided into local and global components. The Clebsch’s method is used to calculate the deflection of the face plates. The validation of the plane frame method is carried out with FE-analyses based on the shell element formulation. Also a comparison is made with the method based on homogenized beam. Periodic stress distributions in the face plates are revealed with the plane frame analysis and are supported by the FE-analysis. The existing methods based on homogenized beam are not able to predict these stresses. The plane frame analysis can benefit the development of the theory related to web-core sandwich plate.     

Limits of asymptotic solutions in low-velocity impact of composite plates

This paper presents a study of the low velocity impact response of composite plates by using dimensional analysis and lumped-parameter models. Simple analytical expressions are obtained and used to construct a characterization diagram that shows the relationship between the maximum normalized impact force and two non-dimensional parameters. For a given impact event, it is shown that the non-dimensional parameters can be obtained by analytical, computational or experimental methods. Once these parameters are determined, the characterization diagram can be used to estimate the type of response, and maximum impact force. Furthermore, the diagram can be used to select adequate simple models for a given impact situation. It is shown that these simple models provide very good approximations of the impact response for a pre-determined wide range of impact parameters.     

Modelling of composite sandwich structures with honeycomb core subjected to high-velocity impact

In this study the perforation of composite sandwich structures subjected to high-velocity impact was analysed. Sandwich panels with carbon/epoxy skins and an aluminium honeycomb core were modelled by a three-dimensional finite element model implemented in ABAQUS/Explicit. The model was validated with experimental tests by comparing numerical and experimental residual velocity, ballistic limit, and contact time. By this model the influence of the components on the behaviour of the sandwich panel under impact load was evaluated; also, the contribution of the failure mechanisms to the energy-absorption of the projectile kinetic energy was determined.