Localized indentation of sandwich panels with metallic foam core: Analytical models for two types of indenters

Sandwich structures with metallic foam core are sensitive to local indentation because of the low strength of the core and low bending stiffness of the thin face sheets. In this paper, local indentation response of sandwich panels with metallic foam core under a flat/spherical indenter was analyzed. The composite sandwich is modeled as an infinite, isotropic, plastic membrane on a rigid-plastic foundation. For simplicity, a quadratic polynomial displacement field was employed to describe the deformation of the upper face sheet. By using the principle of minimum work, explicit solutions for the indentation force and the sizes of the deformation regions were derived. The analytical results were verified by those from simulation by using the ABAQUS code, and they are in close agreement. Distribution of radial tensile strain of the upper face sheet and the ratio of energy dissipation of foam core to that of the upper face sheet were analyzed.     

Static indentation and unloading response of sandwich beams

This paper deals with analysis of foam core sandwich beams subject to static indentation and subsequent unloading (removal of load). Sandwich beams are assumed continuously supported by a rigid platen to eliminate global bending. An analytical model is presented assuming an elastic-perfectly plastic compressive behaviour of the foam core. An elastic part of indentation response is described using the Winkler foundation model. Upon removal of the load, an elastic unloading response of the foam core is assumed. Also, finite element (FE) analysis of static indentation and unloading of sandwich beams is performed using the FE code ABAQUS. The foam core is modelled using the crushable foam material model. To obtain input data for the analytical model and to calibrate the crushable foam model in FE analysis, the response of the foam core is experimentally characterized in uniaxial compression, up to densification, with subsequent unloading and tension until tensile fracture. Both models can predict load–displacement response of sandwich beams under static indentation and a residual dent magnitude in the face sheet after unloading along with residual strain levels in the foam core at the unloaded equilibrium state. The analytical and FE analyses are experimentally verified through static indentation tests of composite sandwich beams with two different foam cores. The load–displacement response, size of a crushed core zone and the depth of a residual dent are measured in the testing. A digital speckle photography technique is also used in the indentation tests in order to measure the strain levels in the crushed core zone. The experimental results are in good agreement with the analytical and FE analyses.     

Non-linear indentation behavior of foam core sandwich composite materials—A 2D approach

Light weight high performance sandwich composite materials have been used more and more frequently in various load bearing applications in recent decades. However, sandwich materials with thin composite face sheets and a low density foam core are notoriously sensitive to failure by localized external loads. These loads induce significant local deflections of the loaded face sheet into the core of the sandwich composite material, thus causing high stress concentrations. As a result, a complex multiaxial stressed and strained state can be obtained in the area of localized load application. Another important consequence of the highly localized external loads is the formation of a residual dent in the face sheet (a geometrical imperfection) that can reduce significantly the post-indentation load bearing capacity of the sandwich structure.This paper addresses the elastic–plastic response of sandwich composite beams with a foam core to local static loading. The study deals with a 2D configuration, where a sandwich beam is indented by a steel cylinder across the whole width of the specimen. The ABAQUS finite element package is used to model the indentation response of the beams. Both physical and geometrical non-linearities are taken into account. The plastic response of the foam core is modeled by the ¹CRUSHABLE FOAM and the ¹CRUSHABLE FOAM HARDENING option of the ABAQUS code. The purpose of the numerical modeling is to develop correct 2D simulations of the non-linear response in order to further understand the failure modes caused by static indentation. In order to verify the finite element model, indentation tests are performed on sandwich composite beams using a cylindrical indentor. The numerical results show good agreement with experimental test data.     

The influence of correlating material parameters of gradient foam core on free vibration of sandwich panel

For the sandwich panel with mass density gradient (DG) foam core, the Young's modulus of the core varies with the mass density along the thickness direction. To characterize the correlative effect of Young's modulus and mass density of the DG closed-cell foam material, a simplified formula is presented. Subsequently, based on a high-order sandwich plate theory for sandwich panel with homogeneous core, a new gradient sandwich model is developed by introducing a gradient expression of material properties. Finite element (FE) simulation is carried out in order to verify this model. The results show that the proposed model can predict well the free vibration of composite sandwich panel with the gradient core. Finally, the correlating effects of material parameters of the DG foam core on the natural frequencies of sandwich panel are investigated. It is found that the natural frequencies of sandwich panels decrease as the gradient changes of the DG foam cores increase under the condition of that the core masses keep constant.     

Compression strength of sandwich panels with sub-interface damage in the foam core

This paper addresses the effect of a local quasi-static indentation or a low-velocity impact on the residual strength of foam core sandwich panels subjected to edgewise compression. The damage is characterized by a local zone of crushed core accompanied by a residual dent in the face sheet. Experimental studies show that such damage can significantly alter the compressive strength. Theoretical analysis of the face sheet local bending is performed for two typical damage modes (with or without a face–core debonding). The solutions allow estimation of the onset of (a) an unstable dent growth (local buckling) or (b) a compressive failure in the face sheet. The theoretical results are in agreement with the test data for two considered sandwich configurations.     

Response of thin-skinned sandwich panels to contact loading with flat-ended cylindrical punches: Experiments,numerical simulations and neutron diffraction measurements

The response of aluminium foam-cored sandwich panels to localised contact loading was investigated experimentally and numerically using flat-ended cylindrical punch of four varying sizes. ALPORAS and ALULIGHT closed-cell foams of 15 mm thickness with 0.3 mm thick aluminium face sheets (of 236 MPa yield strength) were used to manufacture the sandwich panels. Face sheet fracturing at the perimeter of the indenter, in addition to foam cells collapse beneath the indenter and tearing of the cell walls at the perimeter of the indenter were the major failure mechanisms of the sandwich panels, irrespective of the strength and density of the underlying foam core. The authors employed a 3D model in ABAQUS/Explicit to evaluate the indentation event, the skin failure of the face sheets and carry out a sensitivity study of the panel's response. Using the foam model of Deshpande and Fleck combined with the forming limit diagram (FLD) of the aluminium face sheet, good quantitative and qualitative correlations between experiments and simulations were achieved. The higher plastic compliance of the ALPORAS led to increased bending of the sheet metal and delayed the onset of sheet necking and failure. ALULIGHT-cored panels exhibited higher load bearing and energy absorption capacity, compared with ALPORAS cores, due to their higher foam and cell densities and higher yield strength of the cell walls. Additionally, they exhibited greater propensity for strain hardening as evidenced by mechanical testing and the neutron diffraction measurements, which demonstrated the development of macroscopically measurable stresses at higher strains. At these conditions the ALULIGHT response upon compaction becomes akin to the response of bulk material with measurable elastic modulus and evident Poisson effect.     

Dynamic response of clamped sandwich beam with aluminium alloy foam core subjected to impact loading

The dynamic response of clamped sandwich beam with aluminium alloy open-cell foam core subjected to impact loading is investigated in the paper. The face sheet and the core of the sandwich beam have the different thickness. And the sandwich beam is impacted by a steel projectile in the mid-span. The impact force is recorded by using accelerometer. The results show that tensile crack and core shear are the dominant failure modes. And the impact velocity and the thickness of the face sheet and the foam core have a significant influence on the failure modes and the impact forces. Combining with the inertia effect and experimental results, the failure mechanisms of the sandwich beams are discussed. The thickness of the foam core plays an important role in the failure mechanism of the sandwich beam. In present paper, the failure of the sandwich beam with a thin core is dominated by the bending moment, while the sandwich beam with a thick core fails by bending deformation in the front face sheet and the bottom face sheet in opposite direction due to the plastic hinges in the front face sheet.     

Compressive strength after impact of CFRP-foam core sandwich panels in marine applications

A plastic micro buckling approach is investigated in order to see whether it can be used to analytically predict the residual strength of carbon fiber sandwich structures.

A parametric study on impact damage resistance and residual strength of sandwich panels with carbon fiber-vinylester faces and PVC foam core is conducted. Two sandwich configurations are studied. The first configuration consists of thin faces and an intermediate density core, representative of a panel from a superstructure. The second configuration consists of thick faces and a high density core, representative of a panel from a hull. Two different impactor geometries are used. One spherical impactor and one pyramid shaped impactor are used in a drop weight rig to inflict low velocity impact damage of different energy levels in the face of the sandwich.

The damages achieved ranges from barely visible damages to penetration of one face. Residual strength is tested using in-plane compression of the sandwich plates either instrumented with strain gauges or monitored with digital speckle photography.     

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。      

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.     

Moisture diffusion in composite sandwich structures

The mechanical properties of polymer core materials in sandwich structures are often degraded by moisture that is absorbed during storage. To date, there is no reliable model to predict the amount of moisture that is present in these sandwich core materials. A multi-layer diffusion model applicable to these sandwich structures is described in this report. Inputs to this model are: (1) diffusivities of core and face sheet materials as functions of temperature, (2) moisture saturation data as a function of relative humidity, and (3) sandwich structure exposure history. The output is a prediction of the amounts of moisture in the core material and face sheets as a function of time.

In order to validate this model, moisture diffusion experiments were performed on a sandwich material consisting of graphite–epoxy face sheets and a core of Rohacell^® polymethacrylimide 200WF foam. Samples of this material were dried, and then hydrated at either 32 °C or 65 °C at either 83% or 100% relative humidity. The face sheets were separated from the core and each component was weighed, dried, and weighed again in order to determine the moisture distribution in the sandwich structure. The results were then compared with the model predictions.     

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.     

Buckling,collapse and failure analysis of FRP sandwich panels

Rectangular orthotropic fiber-reinforced plastic (FRP) sandwich panels were tested for buckling in uni-axial compression. The panels, with 0.32 cm (0.125 in.) face sheets and a 1.27 cm (0.5 in.) core of either balsa or linear poly(vinyl chloride) (PVC) foam, were tested in two sizes: 154×77 cm² (72×36 in.²) and 102×77 cm² (48×36 in.²). The sandwich panels were fabricated using the vacuum-assisted resin transfer molding process. The two short edges of the sandwich panels were clamped, while the two long edges were simply supported for testing. The clamped panel ends were potted into a steel frame. The experimental elastic buckling loads were then measured using strain gauges fixed to both sides of the panels. A total of 12 panels were tested under uni-axial compression. Bifurcation in the load versus engineering strain curve was noted in all cases. For all six sandwich panels tested using balsa core, the type of failure was easily identified as face sheet delamination followed by core shear failure. For all six PVC foam core sandwich panels tested, the type of failure consisted of core shear failure with little or no face sheet delamination. In the failed balsa core panels there was little or no evidence of balsa remaining on the FRP face sheet, however, in the PVC foam core panels there were ample amounts of foam left on the FRP face sheet. It was concluded that although the buckling loads for the foam core panels were not as high as those for the balsa core panels, PVC foam core bonding to the FRP face sheets was superior to balsa core bonding.     

Effect of core thickness on wave number and damping properties in sandwich composites

Due to their higher strength-to-weight and stiffness-to-weight ratios compared to metals, fiber reinforced composite materials are a great alternative for use in many structural applications. However these properties lead to poor acoustic performance as composite materials are excellent noise radiators. This is particularly true for sandwich composite structures. Therefore the focus of this study is to investigate the effect of a core thickness change on the vibrational properties of Rohacell foam/carbon-fiber face sheet sandwich composite beams. Four different foam core thicknesses were explored, using a combination of experimental and analytical methods to characterize sound and vibrational properties of the sandwich beams. First, the wave number responses of the beams were obtained, from which coincidence frequencies were identified. Second, from the frequency response functions the structural damping loss factor, η, was determined using the half-power bandwidth method. Experimental and analytical results show that the relationship between core thickness and coincidence frequency is non-linear. A drastic increase in coincidence frequency was observed for the sandwich beam with the thinnest core thickness due to the low bending stiffness. Moreover this low bending stiffness results in low damping values, and consequently high wave number amplitude responses at low frequency ranges (<1000 Hz).     

Experimental investigation of compression failure of sandwich specimens with face/core debond

An experimental study of the in-plane compressive failure mechanism of foam cored sandwich specimens with an implanted through-width face/core debond is presented. Tests were conducted on sandwich specimens with glass/vinylester and carbon/epoxy face sheets over various PVC foam cores. Observation of the response of the specimens during testing showed that failure occurred by buckling of the debonded face sheet, followed by rapid debond growth towards the ends of the specimen. The compression strength of the sandwich specimens containing a debond decreased quite substantially with increasing debond size. A high-density core resulted in less strength decrease at any given debond size. Examination of the failure surfaces after separation of the face sheet and core revealed traces of core material deposited on the face sheet evidencing cohesive core failure. The amount of core material adhered to the face sheet decreased with increasing foam density indicating increasing tendency for core/resin interfacial failure.     

面板材料对泡沫铝夹芯梁抗冲击性能的影响

为考查泡沫铝夹芯梁面板材料对其抗冲击性能的影响,运用数值模拟方法计算了相同重量下面板材料分别为304#不锈钢、工业纯铝和HRB335级钢三种泡沫铝夹芯梁在不同冲量作用下的动力响应;分析了面板材料对泡沫铝夹芯梁跨中变形及芯材压缩应变的影响.结果显示,在冲量相同的情况下,面板材料对泡沫铝夹芯梁的抗冲击性能有一定的影响;爆炸...     

泡沫铝夹芯板抗冲击性能分析

试验设计了3块钢板夹泡沫铝夹芯板,厚度分别为50 mm、70 mm和100 mm。对每种厚度夹芯板进行七组不同落锤高度的冲击试验,测得了上、下面板变形值,记录了夹芯板的破坏情况。应用数值模拟软件ANSYS/LS-DYNA进一步还原夹芯板冲击过程,导出了面板与芯材的吸能占比。基于假设的夹芯板理论模型,给出了平均冲击荷载、局部变形和整体变形最大值的估算公式。结果表明:当夹芯板尺寸和材料强度一定时,局部变形值与落锤高度的平方根成正比,整体变形最大值、平均冲击力均与落锤高度的平方根成线性关系。夹芯板的抗冲击性能主要依靠增大泡沫铝芯层的变形进行耗能,芯层越厚,泡沫铝吸能占比越大,局部变形越小,夹芯板受到的冲击力越大。     

Compression-after-Impact Strength of Sandwich Panels with Core Crushing Damage

Compression-after-impact (CAI) strength of foam-cored sandwich panels with composite face sheets is investigated experimentally. The low-velocity impact by a semi-spherical (blunt) projectile is considered, producing a damage mainly in a form of core crushing accompanied by a permanent indentation (residual dent) in the face sheet. Instrumentation of the panels by strain gauges and digital speckle photography analysis are used to study the effect of damage on failure mechanisms in the panel. Residual dent growth inwards toward the mid-plane of a sandwich panel followed by a complete separation of the face sheet is identified as the failure mode. CAI strength of sandwich panels is shown to decrease with increasing impact damage size. Destructive sectioning of sandwich panels is used to characterise damage parameters and morphology for implementation in a finite element model. The finite element model that accounts for relevant details of impact damage morphology is developed and proposed for failure analysis and CAI strength predictions of damaged panels demonstrating a good correlation with experimental results.