Strength of sandwich beams with interface debondings

The adhesive joint bonding the faces to the core material in a sandwich structure ensures that the loads are transferred between the components. However, debondings may arise either during the manufacturing process or due to overloading. These will reduce both the stiffness and the load bearing capacity of the structure. In the present paper, debondings in foam core sandwich beams are investigated assuming that cracks in the interface between the face and core are present. Stress intensity factors are found from an analytical model and compared to solutions from several finite element calculations. Fracture toughness values, determined from simple specimens, are used to predict the fracture loads for beams with simulated debondings subjected to four-point bending.     

横向可压缩电流变夹层梁的振动特性

讨论了电流变夹层梁在考虑电流变材料层横向可压缩时的动力学特性。在建模过程中将电流变材料视为可压缩的粘弹性材料, 假设电流变材料层的横向位移随厚度变化。基于一阶剪切变形理论和能量方法建立了电流变夹层梁的挤压-剪切动力学模型, 并采用有限元方法进行了离散求解。通过对悬臂梁的仿真和实验分析得出:在电流变夹层梁的振动过程中, 上、下约束层的横向位移并不完全相等, 在低频阶段相差不大, 但在高频阶段较为明显; 加大外加电场的强度, 可以减小横向位移的差值; 而电流变层厚度的增加, 将使横向位移的差值加大。      

Shear coupling effects of the core in curved sandwich beams

We consider a composite package formed by two curved external Euler-Bernoulli beams, which sandwich an elastic core with negligible bending strength but providing the shear coupling of the external layers. This coupling considerably affects the gross response of the composite structure. There is an extensive literature on straight sandwich beams of this type, but very little attention has been paid to the effects of curvature. Here, an analytical linear elastic model is proposed for beams with arbitrary variable curvature. Equilibrium equations and boundary conditions are obtained through a variational approach. Useful simplifications are possible for the case of moderately curved beams and beams with constant curvature.     

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.     

Minimum weight design of sandwich beams with honeycomb core of arbitrary density

We consider minimum weight optimization of sandwich beams for a given stiffness. The core consists of regular hexagonal honeycomb structure of arbitrary density. We present a simple algorithm for estimating all design parameters. Concrete examples are also given.     

Vibration and damping analysis of curved sandwich beams with a visoelastic core

The energy method has been used to derive the governing equations of motion for transverse vibrations of curved sandwich beams. Assuming a series solution, the equations are solved for a simply supported curved sandwich beam with viscoelastic cores. The damping effectiveness of the beam is evaluated by application of the correspondence principle of linear viscoelasticity. Theoretical results for resonant frequencies and associated system loss factor for curved sandwich beams have been verified experimentally. The effects of curvature, core thickness, lack of symmetry and modal number on the resonant frequency parameter and associated system loss factor have been studied.     

Free vibration analysis of simply supported sandwich beams with lattice truss core

Free vibration of AISI 304 stainless steel sandwich beams with pyramidal truss core is investigated in the present paper. The lattice truss core is transformed to a continuous homogeneous material. Considering the deformation characteristics of the sandwich beam, the following assumptions are made: (1) the thickness of the sandwich beam remains constant during deformation; (2) for the thin face sheets, only bending deformation is considered, neglecting the effect of transverse shear deformation; (3) for the core, only shear deformation is considered as the core is too weak to provide a significant contribution to the bending stiffness of the sandwich beam. The shear stress is assumed to be constant along the thickness of the core. The governing equation of free vibration is derived from Hamilton's principle, and the natural frequencies are calculated under simply supported boundary conditions. Finally, numerical simulation is carried out to get the mode shapes and natural frequencies. Our results show that the theoretical solutions agree well with the numerical results. It indicates the present method would be useful for free vibration analysis of sandwich beams with lattice truss core.     

FEM analysis of dynamic flexural behaviour of composite sandwich beams with foam core

The dynamic flexural behaviour of sandwich beams, with composite face-sheets and a foam core, was analysed by developing a 3D finite-element model. To model the core behaviour, a crushable foam model was used. The Hou criteria were used to predict the failure of the face-sheets. Dynamic bending tests were performed to validate the numerical model. The comparison between numerical and experimental results in terms of contact-force histories, peak-force values, absorbed energy, and maximum displacement of both face-sheets was satisfactory. It was revealed that the collapse of the foam core under the impact region favoured the failure of the upper face-sheet.     

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.     

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.     

Examination of the failure of sandwich beams with core junctions subjected to in-plane tensile loading

The paper concerns local effects occurring in the vicinity of junctions between different cores in sandwich beams subjected to tensile in-plane loading. It is known from analytical and numerical modelling that these effects display themselves by an increase of the bending stresses in the faces as well as the core shear and transverse normal stresses at the junction. The local effects have been studied experimentally to assess the influence on the failure behaviour both under quasi-static and fatigue loading conditions. Typical sandwich beam configurations with aluminium and glass-fibre reinforced plastic (GFRP) face sheets and core junctions between polymer foams of different densities and rigid plywood or aluminium were investigated. Depending on the material configuration of the sandwich beam, premature failure accumulating at the core junction was observed for quasi-static and/or fatigue loading conditions. Using Aluminium face sheets, quasi-static loading caused failure at the core junction, whereas no significance of the junction was observed for fatigue loading. Using GFRP faces, a shift of the failure mode from premature core failure in quasi-static tests to face failure at the core junction in fatigue tests was observed. In addition to the failure tests, the sandwich configurations have been analysed using finite element modelling (FEM) to elaborate on the experimental results with respect to failure prediction. Both linear modelling and nonlinear modelling including nonlinear material behaviour (plasticity) was used. Comparing the results from finite element modelling with the failure behaviour observed in the quasi-static tests, it was found that a combination of linear finite element modelling and a point stress criterion to evaluate the stresses at the core junction can be used for brittle core material constituents. However, this is generally not sufficient to predict the failure modes and failure loads properly. Using nonlinear material properties in the modelling and a point strain criterion improves the failure prediction especially for ductile materials, but this has to be examined further along with other failure criteria.     

Static and low-velocity impact behavior of sandwich beams with closed-cell aluminum-foam core in three-point bending

In this paper, the response and failure of sandwich beams with aluminum-foam core are investigated. Quasi-static and low-velocity impact bending tests are carried out for sandwich beams with aluminum-foam core. The deformation and failure behavior is explored. It is found that the failure mode and the load history predicted by a modified Gibson's model agree well with the quasi-static experimental data. The failure modes and crash processes of beams under impact loading are similar to those under quasi-static loading, but the force-displacement history is very different. Hence the quasi-static model can also predict the initial dynamic failure modes of sandwich beams when the impact velocity is lower than 5 m/s.     

Experimental investigation of interfacial fracture behavior in foam core sandwich beams with visco-elastic adhesive interface

Interfacial toughness as well as toughness enhancement and long term interfacial fracture behavior in sandwich beams were experimentally examined. The interfacial toughness was enhanced by inserting a chopped glass fiber mat at the interface during the fabrication process. Robust interfacial load capacity and improved toughness were obtained by the method. The long term interfacial fracture behavior presents the characteristics of the three-parameter solid (standard solid) model. The results of the long term fracture tests show a significant increment in crack opening displacement and nominal stress intensity factors. It indicates that during the process of structural design and analysis the interfacial fracture resistance may be overestimated without taking the visco-elastic effect of the materials of the structure into consideration.     

Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method

This paper deals with the vibration analysis of a three layered composite beam with a viscoelastic core. First, the equations of motion that govern the free vibrations of the sandwich beam are derived by applying Hamilton’s principle. Then, these equations are solved by using differential transform method (DTM) in the frequency domain. The variation of modal loss factor with system parameters is evaluated and presented graphically. Also, the results obtained with DTM are checked against the findings of previous studies and a good agreement is observed. It is the first time that DTM is used for the eigenvalue analysis of a sandwich structure.     

Effects of nanoparticle impregnation of polyurethane foam core on the performance of sandwich beams

Polyurethane foam core has been considered for sandwich design due to its high stiffness and toughness. One of the methods of potential improvement of the foam is impregnating it with stiff nanoparticles, increasing its stiffness and collapse strength. In this paper we use the Mori–Tanaka and the self-consistent methods to estimate an increase in the stiffness of closed-cell and open-cell foams impregnated by stiff nanoparticles that do not affect foam geometry. Subsequently, the effect of the impregnation of the foam core on the response of a sandwich beam is demonstrated. The response characteristics considered in the paper include bending deflections in a three-point test, global buckling and wrinkling loads, and the effect of the foam impregnation on its compressive collapse stress associated with local instability of the elements of the foam. Recognizing that the introduction of nanoparticles in the foam material creates local stress concentrations around the inclusions we also examine the local strength of the impregnated foam using the classical Goodier solution for dilute particles and the Mori–Tanaka based stress analysis for a finite particle concentration. In addition, we demonstrate the approach to the evaluation of the resilience of impregnated foam utilizing the dilute approach. While numerical examples concentrate on polyurethane foam, the methodologies and conclusions can be extrapolated to any polymeric foam material reinforced by nanoparticles.     

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.     

Strength evaluations of sinusoidal core for FRP sandwich bridge deck panels

Fiber-reinforced polymer (FRP) sandwich deck panels with sinusoidal core geometry have shown to be successful both in new construction and the rehabilitation of existing bridge decks. This paper is focused on an experimental study of the strength evaluations of a honeycomb sandwich core under out-of-plane compression and transverse shear. The sinusoidal core is made of E-glass Chopped Strand Mat (ChSM) and Polyester resin. The compressive, tensile and shear strengths were first obtained from coupon tests. The out-of-plane compression tests were performed on representative single-cell volume elements of sandwich panels, and the tests included “stabilized” samples to induce compression failure, and “bare” samples to induce local buckling of the core. Finally, four-point bending tests were conducted to study the structural strength behavior under transverse shear. Two types of beam samples were manufactured by orienting the sinusoidal wave either along the length (longitudinal) or along the width (transverse). Both typical shear failure mode of the core material and delamination at the core–facesheet bonding interface were observed for longitudinal samples. The failure for transverse samples was caused by core panel separation. For both single-cell and beam-type specimen tests, the number of bonding layers, i.e., the amount of ChSM contact layer and resin used to embed the core into the facesheet, and the core thickness are varied to study their influence. The experimental results described herein can be subsequently used to develop design guidelines.     

Dynamic wrinkling in sandwich beams

Facings of sandwich structures employed in typical applications are often subject to parametric periodic loading. Such loading can cause local dynamic instability of the facings, i.e. large-amplitude small wavelength lateral vibrations. This phenomenon, called in the paper dynamic wrinkling, may result in fatigue damage or immediate failure. The problem of dynamic wrinkling of the facings is analyzed in the present paper for sandwich beams and for large aspect ratio wide panels that vibrate forming a cylindrical surface. The solution is obtained for the case of a relatively thick or compliant core where the Winkler elastic foundation model of the core is applicable. In addition, the problem is formulated as an extension of the Plantema core model that may be preferable for thinner and stiffer cores. In addition, a new simplified elasticity model is introduced in the paper that is based on the assumption that both facings experience simultaneous and interactive dynamic wrinkling instability. Numerical results shown for the elastic foundation model include the criterion for the onset of dynamic wrinkling and the critical value of the damping coefficient of the facing that is sufficient to prevent such wrinkling. As follows from these results, dynamic wrinkling is unlikely in most engineering applications, except for the case in which the maximum stresses in the facing approach the static wrinkling value.