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。     

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.     

The dynamic response of composite sandwich beams to transverse impact

The dynamic response of glass fibre–vinylester composite beams is measured by impacting the beams at mid-span with metal foam projectiles. The beams exist in composite monolithic form, and in sandwich configuration with composite face-sheets and a core made from PVC foam or end-grain balsa wood. High-speed photography is used to measure the transient transverse deflection of the beams and to record the dynamic modes of deformation and failure. For both monolithic and sandwich configurations, a flexural wave travels from the impact site towards the supports. Ultimate failure of the monolithic and sandwich beams is by tensile tearing of the faces. The sandwich beams also exhibit cracking of the core, and face-sheet delamination. The dynamic strength of the beams is quantified by the maximum transient transverse deflection at mid-span of the beams as a function of projectile momentum. It is demonstrated that sandwich beams can outperform monolithic beams of equal mass. The trade-off between core strength and core thickness is such that a low density PVC foam core outperforms a higher density PVC foam core. End-grain balsa wood has a superior stiffness and strength to that of PVC foam in compression and in shear. Consequently, sandwich beams with a balsa core outperform beams with a PVC foam core for projectiles of low momentum. The order reverses at high values of projectile momentum: the sandwich beams with a balsa wood core fail prematurely in longitudinal shear by splitting along the grain.     

嵌锁式CFRP方形蜂窝夹芯梁低速冲击响应及失效机理

采用嵌锁组装工艺制备了碳纤维/树脂基复合材料方形蜂窝夹芯梁,实验研究了低速冲击载荷下简支和固支夹芯梁的动态响应及失效机理,获得了不同冲击速度下夹芯梁的失效模式,分析了其损伤演化过程和失效机理,探讨了冲击速度、边界条件、面板质量分布以及槽口方向等因素对夹芯梁破坏模式及承载能力的影响。研究结果表明,芯材长肋板槽口方向对夹芯梁的失效模式有较大影响,槽口向上的芯材跨中部分产生了挤压变形,而槽口向下的芯材跨中部分槽口在拉伸作用下出现了沿槽口开裂失效,继而引起面板脱粘和肋板断裂;同等质量下,较厚的上面板设计可以提高夹芯梁的抗冲击能力,冲击速度越大,夹芯梁的峰值载荷和承载能力越高;固支边界使得夹芯梁的后失效行为呈现出明显的强化效应,在夹芯梁跨中部分发生初始失效后出现了后继的固支端芯材和面板断裂失效模式。     

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.     

High order behavior of sandwich plates with free edges––edge effects

The edge effects of a sandwich plate with a “soft” core and free edges, i.e. the plate is supported only at the lower face-sheet, and the upper face-sheet and the core are free of stresses at their edges, using the high order approach (HSAPT), are presented. The two-dimensional analysis consists of a mathematical formulation that uses the classical thin plate theory for the face-sheets and a three-dimensional elasticity theory for the core. The governing equations and the required boundary conditions are derived explicitly through variational principals, yielding a system of eight partial differential equations. The non-homogeneous differential equations system is numerically solved using a modification of the extended Kantorovich method (MEKM). The model presented enables a two-dimensional solution of the stress and displacement fields when subjected to a general scheme of loads. It is applicable to any type of boundary conditions that can be applied separately on each face-sheet and on the core. A numerical study is presented, and it examines the behavior and the two-dimensional stress field of a sandwich plate with free edges, at the upper face-sheet and core, subjected to thermal and uniformly distributed loads, for various boundary conditions at the lower face-sheet. For completeness, the MEKM solution of the two-dimensional high order model is verified through comparison with a three-dimensional Finite Element model revealing good correlation. Furthermore, the problems involved in the construction of an appropriate three-dimensional FE model of a full scale sandwich plate that require large computer resources are discussed.The numerical study yields that the peeling (normal) stresses, which reach their maximum values at the edges of the sandwich plate, using a one-dimensional analysis, varies also in the transverse direction from a maximum value in the middle of the edge, descending towards the corners. Moreover, the nature of variation along the boundaries strongly depends on the type of loading and the transverse boundary conditions. The substantial variation of the stress field in the transverse direction clearly shows the necessity of a two-dimensional analysis and the inefficiencies of the one-dimensional model.     

ELASTIC-PLASTIC DYNAMIC RESPONSE OF FULLY BACKED SANDWICH PLATES UNDER LOCALIZED IMPULSIVE LOADING

An analytical model is developed to assess the elastic-plastic dynamic response of fully backed sandwich plates under localized impulse load.The core is modeled as an elastic-perfectly plastic foundation.The top face sheet is treated as an individual plate resting on the foundation.The elastic-plastic analysis for the top face sheet is based on a minimum principle in dynamic plasticity associated with the finite difference technique.The effects of spatial and temporal distributions of the impulsive loading on the dynamic response of sandwich plates are discussed.The model can be used to predict the impulse-induced local effect on fully backed sandwich plates.     

Effects of Seawater and Low Temperatures on Polymeric Foam Core Material

Polymeric composite sandwich structures, often manufactured using a thick foam core material and thin composite facings, are of significant interest in naval applications. This paper summarizes the coupled effect of sea water and low temperature on the mechanical properties of closed cell polymeric H100 foam core material. The study considers the effects of harsh sea environmental conditions on the fracture and deformation behavior of such a foam material under complex loading conditions that include tension, torsion, compression, and true-triaxial stress paths. Mechanical testing techniques are developed using coupon samples of suitable geometry that minimize grip effects on these low density complex foam materials, along with information associated with the observed cross-anisotropic behavior. Interfacial delamination fracture response for the sandwich structures due to the combined effects of sea water and low temperature are evaluated and the associated degradation in critical energy release rate for delamination is found to be substantial. Experimental data for H100 foam cores associated with moisture induced expansional strains are also included.     

高速颗粒流冲击下负泊松比力学超材料夹芯梁的动态响应及缓冲吸能机理

建立了颗粒流子弹发射有限元模型,利用离散元和有限元的联合模拟方法,研究了高速颗粒流冲击负泊松比内凹蜂窝夹芯梁的动态响应及缓冲吸能机理。分析了加载冲量、冲击角、芯材强度以及颗粒流子弹与面板间的摩擦力等因素对夹芯梁动态响应的影响。研究结果表明:夹芯梁在正向颗粒流子弹冲击载荷作用下表现为局部凹陷和整体弯曲的耦合变形模式,面内设计芯材因胞壁弯曲呈现局部内凹的变形模式,面外设计芯材因胞壁屈曲呈现局部褶皱的变形模式。在等面密度的条件下,采用面外设计的硬芯夹芯梁面板的跨中最大挠度比采用面内设计的软芯夹芯梁小,但初始冲击力峰值和冲击力整体水平较高,冲击力响应时间较短。夹芯梁前后面板的跨中最大挠度与冲击载荷近似呈对数线性递增关系。与正向冲击相比,斜冲击下夹芯梁的变形模式具有非对称性,局部凹陷程度减小;在颗粒流子弹不同冲击角度作用下,夹芯梁前后面板的跨中最大挠度、初始冲击力峰值以及传递到夹芯梁的动能和动量占比随冲击角度的增大而减小,而颗粒流子弹与夹芯梁面板间的摩擦因数对夹芯梁的动态响应无显著影响。     

Suggestion of a new dimensionless number for dynamic plastic response of beams and plates

Summary A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is defined as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are reflected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical influence of the structure on the dynamic response. For an impulsively loaded beam or plate, the final dimensionless deflection is solely dependent upon the response number. When the secondary effects of finite deflections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape. Received 17 October 1997; accepted for publication 19 March 1998     

复合夹层梁瞬态响应的谱有限元法

采用谱有限元法进行复合夹层梁的瞬态响应分析．该方法基于复合夹层梁的六阶运动微分方程,以其波动解作为动力位移形函数,根据标准有限元策略来构建复合夹层梁的动刚度矩阵．在频域内,夹心粘弹性材料的频率相关性采用复模量模型来模拟,进而利用快速傅立叶变换技术(FFT),得到时域内复合夹层梁的瞬态响应分析结果．最后以两端固支夹层梁为例,对其进行了矩形脉冲荷载下的动力响应分析,并与通用有限元程序NASTRAN的计算结果进行了对比,两者吻合良好．     

Imperfection sensitivity of axially compressed stringer reinforced cylindrical sandwich panels

This paper presents some numerical results of the effects of several nondimensional parameters on the buckling and initial post buckling behaviors of shallow sandwich panels under axial compression. Results are presented that show these effects due to transverse shearing resistance of the core material, different face-sheet thicknesses, and different core thicknesses. Further effects on the buckling and initial postbuckling behaviors of sandwich panels are presented due to the torsional resistance of longitudinal edge stiffeners.The results show that the range of flatness parameter, δ/d, for which sandwich panels remain imperfection-insensitive increases with increases in transverse shearing resistance of the core material and with larger core thicknesses. These results also indicate that this range of δ/d is smallest when the face-sheet thicknesses are equal. Finally, as in the case of homogeneous panels, torsional resistance of the longitudinal edge stiffeners has the effect of making the sandwich panel less imperfection-sensitive.     

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.     

Underwater blast loading of sandwich beams: Regimes of behaviour

Finite element (FE) calculations are used to develop a comprehensive understanding of the dynamic response of sandwich beams subjected to underwater blast loading, including the effects of fluid–structure interaction. Design maps are constructed to show the regimes of behaviour over a broad range of loading intensity, sandwich panel geometry and material strength. Over the entire range of parameters investigated, the time-scale associated with the initial fluid–structure interaction phase up to the instant of first cavitation in the fluid is much smaller than the time-scales associated with the core compression and the bending/stretching responses of the sandwich beam. Consequently, this initial fluid–structure interaction phase decouples from the subsequent phases of response. Four regimes of behaviour exist: the period of sandwich core compression either couples or decouples with the period of the beam bending, and the core either densifies partially or fully. These regimes of behaviour are charted on maps using axes of blast impulse and core strength. The simulations indicate that continued loading by the fluid during the core compression phase and the beam bending/stretching phase cannot be neglected. Consequently, analyses that neglect full fluid–structure interaction during the structural responses provide only estimates of performance metrics such as back face deflection and reaction forces at the supports. The calculations here also indicate that appropriately designed sandwich beams undergo significantly smaller back face deflections and exert smaller support forces than monolithic beams of equal mass. The optimum transverse core strength is determined for minimizing the back face deflection or support reactions at a given blast impulse. Typically, the transverse core strength that minimizes back face deflection is 40% below the value that minimizes the support reaction. Moreover, the optimal core strength depends upon the level of blast impulse, with higher strength cores required for higher intensity blasts.     

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.     

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.     

Metallic sandwich panels subjected to multiple intense shocks

The mechanical response and fracture of metal sandwich panels subjected to multiple impulsive pressure loads (shocks) were investigated for panels with honeycomb and folded plate core constructions. The structural performance of panels with specific core configurations under multiple impulsive pressure loads is quantified by the maximum transverse deflection of the face sheets and the core crushing strain at mid-span of the panels. A limited set of simulations was carried out to find the optimum core density of a square honeycomb core sandwich panels under two shocks. The panels with a relative core density of 4%–5% are shown to have minimum face sheet deflection for the loading conditions considered here. This was consistent with the findings related to the sandwich panel response subjected to a single intense shock. Comparison of these results showed that optimized sandwich panels outperform solid plates under shock loading. An empirical method for prediction of the deflection and fracture of sandwich panels under two consecutive shocks – based on finding an effective peak over-pressure – was provided. Moreover, a limited number of simulations related to response and fracture of sandwich panels under multiple shocks with different material properties were performed to highlight the role of metal strength and ductility. In this set of simulations, square honeycomb sandwich panels made of four steels representing a relatively wide range of strength, strain hardening and ductility values were studied. For panels clamped at their edge, the observed failure mechanisms are core failure, top face failure and tearing at or close to the clamped edge. Failure diagrams for sandwich panels were constructed which reveal the fracture and failure mechanisms under various shock intensities for panels subjected to up to three consecutive shocks. The results complement previous studies on the behavior and fracture of these panels under high intensity dynamic loading and further highlights the potential of these panels for development of threat-resistant structural systems.     

Higher-order dynamic response of composite sandwich panels with flexible core under simultaneous low-velocity impacts of multiple small masses

Small mass impactors, such as runway debris and hailstones may result in a wave controlled local response, which is essentially independent of boundary conditions. The higher-order impact model of sandwich beams presented by Mijia and Pizhong [Mijia, Y., Pizhong, Q., 2005. Higher-order impact modeling of sandwich structures with flexible core. International Journal of Solids and Structures 42 (10), 5460–5490] is developed and enhanced to impact analysis of sandwich panels with transversely flexible cores. Therefore, an improved fully dynamic higher-order impact theory is developed to analyze the low-velocity impact dynamic of a system which consists of a composite sandwich panel with transversely flexible core and multiple small impactors with small masses. Impacts are assumed to occur normally and simultaneously over the top face-sheet with arbitrary different masses and initial velocities of impactors. The contact forces between the panel and the impactors are treated as the internal forces of the system. First shear deformation theory (FSDT) is used for the face-sheets while three-dimensional elasticity is used for the soft core. The fully dynamic effects of the core layer and the face-sheets are considered in this study. Contact area can be varied with contact duration. The results in multiple mass impacts over sandwich panels that are hitherto not reported in the literature are presented based on proposed improved higher-order sandwich plate theory (IHSAPT). Finally, for the case study of the single mass impact, the numerical results of the analysis have been compared either with the available experimental results or with some theoretical results. As no literature could be found on the impact of multiple impactors over sandwich panels, the present formulation is validated indirectly by comparing the response of two cases of double small masses and single small mass impacts. Also, in order to demonstrate the applicability of the validation, the analytical relation of minimum distance between two impactors is derived based on Olsson’s wave control principle in this paper.     

爆炸载荷作用下具有可折叠芯层夹芯梁的动态响应

基于目前研究最广泛的刚性折纸(Tachi-origami)样式,通过改变其初始折叠角度构建出4种不同的蜂窝胞元,并且通过排列分布将其组成夹芯梁。采用商用有限元软件Abaqus/explicit对准静态和爆炸载荷作用下可折叠芯层夹芯梁的力学响应进行研究,分析可折叠芯层的泊松比变化规律、夹芯梁背板挠度以及能量吸收机理;并将夹芯梁与等质量的实体梁进行对比。采用后面板最大挠度作为抗爆性能的评价,结果发现:可折叠芯层在准静态载荷下具有一定的负泊松比效应;夹芯梁的抗爆性能优于实体梁,曲边蜂窝的初始折角对其作为芯层夹芯梁的抗爆性能有较大影响,随着初始折角的逐渐增大,其抗爆性能逐渐下降;当初始折角为直角时对应于方孔直边蜂窝,其抗爆性能最差。     

在有限变形条件下损伤粘弹性梁的动力学行为

本文在有限变形条件下，根据损伤粘弹性材料的一种卷积型本构关系和温克列假设，建立了粘弹性基础上损伤粘弹性Timoshenko梁的控制方程。这是一组非线性积分——偏微分方程。为了便于分析，首先利用Galerkin方法对该方程组进行简化，得到一组非线性积分一常微分方程。然后应用非线性动力学中的数值方法，分析了粘弹性地基上损伤粘弹性Timoshenko梁的非线性动力学行为，得到了简化系统的相平面图、Poincare截面和分叉图等。考察了材料参数和载荷参数等对梁的动力学行为的影响。特别，考察了基础和损伤对粘弹性梁的动力学行为的影响。