Analytical modeling and finite element simulation of the plastic collapse of sandwich beams with pin-reinforced foam cores

Analytical predictions are presented for the plastic collapse strength of lightweight sandwich beams having pin-reinforced foam cores that are loaded in 3-point bending. Both polymer and aluminum foam cores are considered, whilst the facesheet and the pins are made of either composite or metal. Four different failure modes are account for: metal facesheet yield or composite facesheet microbuckling, facesheet wrinkling, plastic shear of the core, and facesheet indentation beneath the loading rollers. A micromechanics-based model is developed and combined with the homogenization approach to calculate the effective properties of pin-reinforced foam cores. To calculate the elastic buckling strength of pin reinforcements, the pin-reinforced foam core is treated as assemblies of simply supported columns resting upon an elastic foundation. Minimum mass design of the sandwich is then obtained as a function of the prescribed structural load index, subjected to the constraint that none of the above failure modes occurs. Collapse mechanism maps are constructed and compared with the failure maps of foam-cored sandwich beams without pin reinforcements. Finite element simulations are carried out to verify the analytical model and to study the performance and failure mechanisms of the sandwich subject to loading types other than 3-point bending. The results demonstrate that the weaker the foam is, the more optimal the pin-reinforced foam core becomes, and that sandwich beams with pin-reinforced polymer foam cores are structurally more efficient than foam- or truss-cored sandwich beams.     

Investigation of the Sandwich Plate Twist Test

Analysis and test results for the compliance of the sandwich plate twist test are presented. The analysis utilizes classical laminated plate theory (CLPT) and finite element analysis (FEA). It is shown that CLPT greatly underestimates the plate compliance, except when very stiff cores and compliant face sheets are used, as a result of transverse core shear deformation, not accounted for in this theory. Parametric studies are conducted using FEA to examine the influence of transverse shear moduli of the core and specimen dimensions on the plate compliance. The influences of indentation at load introduction and support locations, and overhang (oversized panel) are also examined. A test fixture is designed where two diagonally opposite corners of the panel are loaded, while the other two corners are supported to provide twisting deformation of the panel. Tests were conducted on square sandwich panels consisting of aluminum face sheets over various PVC foam cores. CLPT was found to greatly underestimate the experimental plate compliance. Finite element predictions of the plate compliance were in much closer agreement with the experimental data.     

Test method for measuring strength of a curved sandwich beam

A fixture for testing curved sandwich beams in flexure was designed and evaluated. The test specimen is a continuous sandwich beam consisting of a central circular 90° region connected by two straight legs. The fixture was designed according to the four-point flexure principle to produce a pure bending moment in the curved region. The validity of the test fixture in producing the desired loading was examined by fitting a curved aluminum bar of similar bending stiffness as the sandwich beams considered. Strain gage readings were successfully compared to predictions from curved homogeneous beam theory. In addition, the deflection of the beam at the loading points was analyzed using straight and curved beam theory for the various sections of the beam, and predictions were compared to measured load-displacement response. Good agreement was achieved between experimental and analytical results lending confidence to the test principle. Curved sandwich beams consisting of glass/polyester face sheets over a PVC foam core were tested to failure and the loading response of the beams and their failure behavior are discussed. It was found that the beams failed at the upper face/core interface due to radial tension stress.     

夹芯板结构局部压入力学响应研究

利用材料试验机(MTS)实验研究了复合材料面板、闭孔泡沫铝芯层夹芯板结构在准静态压入时的变形和破坏特征。实验结果表明,夹芯板的破坏主要集中在压头作用的局部区域内;同时,根据最小势能原理建立了泡沫铝夹芯板在半球形压头作用下的压入力学响应理论预测模型。通过引入无量纲参数分析了夹芯板压入载荷-位移响应,并在不同面板厚度、芯层厚度和芯层相对密度情况下,对夹芯板压入响应理论解的有效性和适用性进行了讨论。     

Failure behavior of composite sandwich structures under local loading

Usually when analyzing the mechanical response of foam-cored fiber-reinforced composite sandwich structures to localized static loading, the face sheets are treated as a linear-elastic material and no damage initiation and growth is considered. However, practice shows that at higher indentation magnitudes damage develops in the face sheet in the area of contact with the indentor, which could lead to local failure of the face laminate due to the loss of bending stiffness and strength. Therefore, the main objective of the present study is to develop a damage model for predicting the local failure in the composite face sheet and its influence on the load–displacement behavior of sandwich structures under local loading. For this purpose, the Hoffman failure criterion is incorporated into a finite element modeling procedure using the ABAQUS program system. Results deducted from the modeling procedure are compared with experimental data obtained in the case of static indentation tests performed on sandwich beam specimens using steel cylindrical indentors. It is shown that taking into account the damage in the face sheet leads to a substantial improvement in the performance of the model when simulating the mechanical behavior of the sandwich structures at higher indentation values.     

泡沫铝夹芯梁四点弯曲性能试验研究

通过准静态四点弯曲试验对泡沫铝夹芯梁的弯曲力学性能进行了测试,研究了它的破坏过程、破坏形态和典型荷载-位移曲线,分析了芯层厚度和面层厚度等参数对其弯曲力学性能的影响。结果表明,泡沫铝夹芯梁四点弯曲破坏过程历经三个阶段,呈现三种失效模式:整体弯曲破坏、局部屈曲破坏以及整体屈曲破坏;芯层厚度和面层厚度对夹芯梁的弯曲承载力和吸能效果有明显影响;在本试验参数范围内,芯层厚度为25mm,面层厚度为0.4mm时,夹芯梁具有最优弯曲力学性能。     

Strength and stiffness of sandwich beams in bending

This investigation is concerned with the experimental versus analytical correlation of the mechanical properties of sandwich-beam specimens. Such sandwich structures are commonly employed in the aircraft industry. Four-point and three-point load tests were conducted on a large number of sandwich-beam specimens, fabricated by using fiber-glass reinforced plastics (both unidirectional and woven-glass cloth) and DTD 685 aluminum alloy for the facings with aluminum honeycomb core and polyurethane foam cores and the indigenously available Araldite as the bonding medium between the core and the facings.The flexural stiffness of the composite sandwich specimens used in this investigation compared favorably with theoretical predictions. The shear stiffness was found to be about 55 percent and 45 percent of the theoretically predicted values for FRP (fiberglass-reinforced-plastic) cloth and FRP unidirectional laminates with aluminum honeycomb core sandwich, respectively. The failure load as determined by experiments was less than the theoretically predicted safe load. There was a loss of strength as well as a steep decrease in the failure load in the case of low density foam core.It was concluded that FRP facing plates with aluminum honeycomb core sandwich structure may be preferred to similar aluminum-alloy facing sandwich construction if high flexural stiffness and shear stiffness properties are required at less cost and weight. Indigenously available Araldite was quite satisfactory for bonding the core to the facings.This investigation has confirmed the importance of experiments in the field of sandwich structures which can effectively replace other conventional uneconomical structural or machine members which are currently in use.     

环氧树脂/泡沫铝一体型复合夹层板压缩及弯曲试验研究

提出了一种环氧树脂/泡沫铝一体型复合夹层板,通过准静态试验以及与纯泡沫铝、传统蒙皮夹层板的对比研究了其破坏过程、破坏形貌、破坏机理及压缩和弯曲力学性能。分别通过压缩应力-应变曲线和弯曲荷载-挠度曲线分析了复合层厚度对压缩及弯曲力学性能的影响,并与传统夹层板的力学性能进行了比较。结果表明,随着夹层板中环氧树脂/泡沫铝复合层厚度增加,其压缩弹性模量和抗压强度增加,弯曲承载力提高。相比传统蒙皮夹层板,由于表层和芯层之间没有明显界面,大大提高了夹芯板的整体性,在受力过程中不会出现表层剥离等现象。     

泡沫铝子弹高速撞击下铝基复合泡沫夹层板的动态响应

应用一级轻气炮驱动泡沫铝弹丸高速撞击加载技术,对实心钢板以及前/后面板为Q235钢板、芯层分别为铝基复合泡沫和普通泡沫铝的夹层板结构,在脉冲载荷作用下的动态力学响应进行实验研究。结果表明:泡沫铝子弹高速撞击靶板可近似模拟爆炸载荷效果;铝基复合泡沫夹层板的变形分为芯层压缩和整体变形两个阶段;与其他靶板相比,铝基复合泡沫夹层板的抗冲击性能最优。基于实验研究,应用LS-DYNA非线性动力有限元软件,对泡沫铝夹层板的动态响应进行数值模拟。结果表明:泡沫铝子弹的长度和初始速度对子弹与夹层板之间的接触作用力影响显著,并且呈线性关系。泡沫芯层强度对等质量及等厚度夹层板的抗冲击性能均有显著影响,夹层板中心挠度对前、后面板的厚度匹配较为敏感,在临界范围内,若背板厚度大于面板厚度,可减小夹层板的最终挠度。夹层板面板宜采用刚度较低、延性好、拉伸破坏应变较大的金属材料。     

泡沫铝夹层结构抗冲击性能的近场动力学模拟分析

针对某光学舱所采用的泡沫铝夹层防护结构在破片冲击下的抗冲击性能问题,采用Monte-Carlo方法创建了泡沫铝结构的二维细观模型,在常规态型近场动力学理论中引入了Mises屈服准则和线性各向同性强化模型,建立了近场动力学塑性本构的数值计算框架。基于近场动力学计算程序模拟了低速冲击作用下泡沫铝夹层结构的塑性变形以及有机玻璃背板的裂纹扩展形态,分析了泡沫铝芯材孔隙率对该夹层结构抗冲击性能和损伤模式的影响规律。结果表明：泡沫铝夹层结构良好的塑性变形能力是其发挥缓冲与防护作用的主要因素,并且在一定范围内,泡沫铝芯材孔隙率越高,则夹层结构具有更好的抗冲击性能;当泡沫铝孔隙率从0.4提升到0.7时,泡沫铝对冲击物的动能吸收率从90%提高到99%;模拟结果与实验结果具有较好的一致性,验证了模拟结果的准确性和分析结论的有效性。通过数值模拟,预测了有机玻璃背板的裂纹扩展形态,发现提高泡沫铝的孔隙率能获得更好的防护效果。     

泡沫金属固支夹芯圆板的大挠度变形分析

论文分析了大挠度情况下固支夹芯圆板在准静态中心荷载作用下的承载能力.提出了考虑芯层强度影响的夹芯结构屈服条件,应用该条件,并基于边界条件和平板的初始变形机制假设夹芯板的速度场,推导了夹芯圆板考虑弯曲和膜力联合作用的大挠度响应,并应用数值算例验证了分析模型的合理性,在此基础上,分析和讨论了面板厚度、芯层厚度和芯层强度对夹芯圆板承载能力的影响.     

Low-velocity impact response of sandwich beams with functionally graded core

The problem of low-speed impact of a one-dimensional sandwich panel by a rigid cylindrical projectile is considered. The core of the sandwich panel is functionally graded such that the density, and hence its stiffness, vary through the thickness. The problem is a combination of static contact problem and dynamic response of the sandwich panel obtained via a simple nonlinear spring-mass model (quasi-static approximation). The variation of core Young’s modulus is represented by a polynomial in the thickness coordinate, but the Poisson’s ratio is kept constant. The two-dimensional elasticity equations for the plane sandwich structure are solved using a combination of Fourier series and Galerkin method. The contact problem is solved using the assumed contact stress distribution method. For the impact problem we used a simple dynamic model based on quasi-static behavior of the panel—the sandwich beam was modeled as a combination of two springs, a linear spring to account for the global deflection and a nonlinear spring to represent the local indentation effects. Results indicate that the contact stiffness of the beam with graded core increases causing the contact stresses and other stress components in the vicinity of contact to increase. However, the values of maximum strains corresponding to the maximum impact load are reduced considerably due to grading of the core properties. For a better comparison, the thickness of the functionally graded cores was chosen such that the flexural stiffness was equal to that of a beam with homogeneous core. The results indicate that functionally graded cores can be used effectively to mitigate or completely prevent impact damage in sandwich composites.     

Response and collapse of foam-supported sheet metal beams and shallow arches

This paper considers the response and failure characteristics of beams and arches constructed by bonding a layer of foam to a single metal sheet, thus creating a “Foam-Supported Sheet Metal,” or FSSM composite. The investigation was conducted from experimental and analytical/numerical perspectives. In the experiments, strips of Rohacell foam were bonded to straight or curved aluminum 2024 strips to construct the composites. The specimens were then supported at the ends and bent under a central load such that the foam was in tension. The results showed that significant increases in stiffness and failure loads could be achieved using this concept with relatively small weight penalty. Catastrophic failure occurred when the foam reached its tensile failure stress. Formulas to predict the bending stiffness and moment at failure of the composite sections were derived from beam theory and are presented. To predict the response of arches, a nonlinear finite element model was developed. The numerical results showed good agreement with the load-deflection responses and failure loads measured experimentally.     

爆炸载荷下分层梯度泡沫铝夹芯板的失效模式与抗冲击性能

采用弹道冲击摆系统开展了爆炸载荷下分层梯度泡沫铝夹芯板的变形/失效模式和抗冲击性能实验研究,并配合激光位移传感器得到试件后面板中心点的挠度-时程响应曲线。研究了炸药当量和芯层组合方式对夹芯板试件变形/失效模式和抗冲击性能的影响。实验结果表明,泡沫铝夹芯板的变形/失效模式主要表现为面板的非弹性大变形,芯层压缩变形、芯层拉伸断裂以及芯层剪切失效。在研究爆炸冲量范围内,非梯度芯层夹芯板的抗冲击性能明显优越于所有分层梯度芯层夹芯板。对于分层梯度夹芯板试件,爆炸冲量较小时芯层组合形式对分层梯度芯层夹芯板的抗冲击性能的影响不大,而爆炸冲量较大时,最大相对密度芯层靠近前面板组合形式的分层梯度夹芯板试件抗冲击性能较好。研究结果可为泡沫金属夹芯结构的优化设计提供参考。     

Response and Damage Tolerance of Composite Sandwich Structures under Low Velocity Impact

The deformation and failure response of composite sandwich beams and panels under low velocity impact was reviewed and discussed. Sandwich facesheet materials discussed are unidirectional and woven carbon/epoxy, and woven glass/vinylester composite laminates; sandwich core materials investigated include four types of closed cell PVC foams of various densities, and balsa wood. Sandwich beams were tested in an instrumented drop tower system under various energy levels, where load and strain histories and failure modes were recorded for the various types of beams. Peak loads predicted by spring-mass and energy balance models were in satisfactory agreement with experimental measurements. Failure patterns depend strongly on the impact energy levels and core properties. Failure modes observed include core indentation/cracking, facesheet buckling, delamination within the facesheet, and debonding between the facesheet and core. In the case of sandwich panels, it was shown that static and impact loads of the same magnitude produce very similar far-field deformations. The induced damage is localized and is lower for impact loading than for an equivalent static loading. The load history, predicted by a model based on the sinusoidal shape of the impact load pulse, was in agreement with experimental results. A finite element model was implemented to capture the full response of the panel indentation. The investigation of post impact behavior of sandwich structures shows that, although impact damage may not be readily visible, its effects on the residual mechanical properties of the structure can be quite detrimental.     

Sandwich Panel Cores for Blast Applications: Materials and Graded Density

Sandwich composites are of interest in marine applications due to their high strength-to-weight ratio and tailorable mechanical properties, but their resistance to air blast loading is not well understood. Full-scale 100 kg TNT equivalent air blast testing at a 15 m stand-off distance was performed on glass-fibre reinforced polymer (GFRP) sandwich panels with polyvinyl chloride (PVC); polymethacrylimid (PMI); and styrene acrylonitrile (SAN) foam cores, all possessing the same thickness and density. Further testing was performed to assess the blast resistance of a sandwich panel containing a stepwise graded density SAN foam core, increasing in density away from the blast facing side. Finally a sandwich panel containing compliant polypropylene (PP) fibres within the GFRP front face-sheet, was subjected to blast loading with the intention of preventing front face-sheet cracking during blast. Measurements of the sandwich panel responses were made using high-speed digital image correlation (DIC), and post-blast damage was assessed by sectioning the sandwich panels and mapping the damage observed. It was concluded that all cores are effective in improving blast tolerance and that the SAN core was the most blast tolerant out of the three foam polymer types, with the DIC results showing a lower deflection measured during blast, and post-blast visual inspections showing less damage suffered. By grading the density of the core it was found that through thickness crack propagation was mitigated, as well as damage in the higher density foam layers, thus resulting in a smoother back face-sheet deflection profile. By incorporating compliant PP fibres into the front face-sheet, cracking was prevented in the GFRP, despite damage being present in the core and the interfaces between the core and face-sheets.     

Study on the Collapse of Pin-Reinforced Foam Sandwich Panel Cores

New fabrication technologies now allow for hybrid sandwich structures, known as X-core, to be manufactured. The X-core panels consist of a pin reinforced polymer foam core with carbon fiber face sheets. Carbon fiber or metallic (Titanium/Steel) pins are inserted into the foam core in the out-of-plane direction and extend from face sheet to face sheet. The through thickness three-point simply supported bending behavior of these panels is used to evaluate the collapse characteristics of the panels. Explicit experimental observations are used to calibrate analytical energy balance models describing the panel collapse as a function of geometry and properties. The mechanical response of X-core sandwich panels is compared to current sandwich materials for material selection.     

Impulsive loading of clamped monolithic and sandwich beams over a central patch

An analytical model is developed for the response of clamped monolithic and sandwich beams subjected to impulse loading over a central loading patch. A number of topologies of sandwich core are investigated, including the honeycomb core, pyramidal core, prismatic diamond core and metal foam. The various cores are characterised by their dependencies of through-thickness compressive strength and longitudinal tensile strength upon relative density. Closed-form expressions are derived for the deflection of the beam when the ratio r of length of loading patch to the beam span exceeds 0.5. In contrast, an ordinary differential equation needs to be solved numerically for the choice r<0.5. Explicit finite element calculations show that most practical shock loadings can be treated as impulsive and the accuracy of the impulsive analytical predictions is confirmed. The analytical formulae are employed to determine optimal geometries of the sandwich beams that maximise the shock resistance of the beams for a given mass. The optimisation reveals that sandwich beams have a superior shock resistance relative to monolithic beams of the same mass, with the prismatic diamond core sandwich beam providing the best performance. Further, the optimal sandwich beam designs are only mildly sensitive to the length of the loading patch.     

撞击载荷下泡沫铝夹芯梁的塑性动力响应

应用泡沫金属子弹撞击加载的方式研究了固支泡沫铝夹芯梁和等质量实体梁的塑性动力响应。 采用激光测速装置和位移传感器测量了泡沫子弹的撞击速度和后面板中心点的位移-时间曲线,研究了加载 冲量、面板厚度和芯层厚度对夹芯梁抗冲击性能的影响。给出了泡沫铝夹芯梁的变形与失效模式,实验结果 表明结构响应对夹芯结构配置比较敏感,后面板中心点的残余变形与加载冲量、面板厚度呈线性关系。与等 质量实体梁的比较表明,泡沫铝夹芯梁具有更好的抗冲击能力。实验结果对多孔金属夹芯结构的优化设计具 有一定的参考价值。     

铝面板PMI泡沫芯夹层梁弹性弯曲的二维模型

将面板PMI泡沫芯夹层梁的弯曲问题按平面应力问题研究,采用弹性理论建立了铝面板PMI泡沫芯夹层梁弯曲变形的微分方程,利用奇异函数把作用在梁上的外载荷表示为分布载荷,推导出了铝面板PMI泡沫芯夹层梁弯曲变形时的挠曲线表达式．采用该方法对面板PMI泡沫芯夹层梁弯曲挠度进行计算,将求得的计算结果与有限元法结果及实验数据进行对比,发现该方法求得的梁中点挠度更接近实验值,这说明该方法可靠的．该方法给出了铝面板PMI泡沫芯夹层梁弯曲时的挠度计算通式,而且梁中点挠度计算公式的表达形式也较为简便,可方便工程设计人员在工程实际中推广应用．