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.     

轻质金属泡沫夹芯曲板的抗爆炸冲击响应研究

夹芯结构具有高比强度、高比刚度和优异的吸能能力,已经被广泛应用于工程结构用来抵御高强度的爆炸冲击载荷。本文采用有限元数值模拟方法研究了爆炸载荷作用下四边固支夹芯曲板的动力响应。比较了同等质量下夹芯曲板、夹芯平板、实体曲板和实体平板四种结构的抗爆炸冲击性能,讨论了不同曲率和非对称因子对结构动力响应的影响,得到了使得夹芯曲板抗爆炸性能最佳的非对称因子。研究结果表明：夹芯曲板的抗爆炸冲击性能优于等质量的夹芯平板、实体曲板和实体平板结构,增大夹芯曲板的曲率能够提高结构的抗爆炸冲击性能。     

冲击波与破片对波纹杂交夹层板的联合毁伤数值研究

通过有限元软件LS-DYNA模拟了波纹杂交夹层板在冲击波与破片联合作用下的响应过程,研究了炸药当量、载荷类型和填充方式对波纹杂交夹层板变形与失效模式的影响,并与实体板、间隔板和波纹夹层板的抗联合毁伤性能进行了对比,讨论了波纹杂交夹层板的能量吸收特性。数值计算结果表明:与冲击波单独作用相比,破片群单独作用和冲击波与破片联合作用对结构造成的毁伤更为严重;当药量较小时,波纹夹层板和波纹杂交夹层板的抗联合毁伤性能优于实体板与间隔板,波纹杂交夹层板的抗联合毁伤性能从全填充、迎爆面填充到背爆面填充逐渐降低;当药量较大时,所有结构均产生破口失效;在能量耗散方面,冲击波单独作用时以波纹芯层吸能为主,破片群单独作用和冲击波与破片联合作用时以上面板吸能为主。     

Assessment of Non-adiabatic Behaviour in Thermoelastic Stress Analysis of Composite Sandwich Panels

Thermoelastic stress analysis (TSA) is used to derive the surface stresses in large sandwich structure panels with honeycomb core and carbon fibre face sheets. The sandwich panels are representative of those used for secondary aircraft structure. The panels were subjected to a pressure load, similar to that experienced in-service, using a custom designed test rig. To achieve the necessary adiabatic conditions for TSA, cyclic loading is regarded as an essential feature. As the panels were full-scale, the maximum loading frequency that could be imparted to the panels by the rig was 1 Hz, which is below the usual range recommended to achieve adiabatic behaviour. To assess the effectiveness of TSA at low frequencies two approaches to calibration are investigated and compared with the stress distribution obtained from independently validated FE models. The thermoelastic response was calibrated into stress data using thermoelastic constants derived experimentally from tensile strips of the sandwich panel face sheet material. It is shown that by using thermoelastic constants obtained from the tensile strips manufactured with the same lay-up as the sandwich panel face sheets, and at the same cyclic load frequency used in the full-scale tests, quantitative stress metrics can be derived from the TSA data. More significantly, a deeper insight into the importance of the thermal characteristics in TSA of laminated materials is provided. It is demonstrated that, for the material used in this work, it is possible to use the global material behaviour to obtain quantitative results when adiabatic conditions do not prevail.     

爆炸载荷下正弦曲边三维负泊松比夹芯板的动态响应和吸能特性

具有优异能量吸收特性的负泊松比结构在抗爆炸冲击防护领域有广阔的应用前景。为进一步提升夹芯板的抗爆性能,提出了一种在X、Y方向力学特性相同的正弦曲边三维负泊松比夹芯板用于防爆保护。采用数值模拟方法,对夹芯板在空爆载荷下的动态响应和吸能特性进行了研究,分析了夹芯板塑性拉伸和弯曲对背面板变形模式和轴向偏转分布的影响,并探究了爆炸距离、炸药质量、面板厚度和芯层关键结构参数对夹芯板变形和能量吸收的影响。结果表明,在空爆载荷下,夹芯板的动态响应过程可分为芯层压缩、整体变形和自由振动3个阶段。后面板在纵向（X方向）和横向（Y方向）上的抗变形能力无明显差异。随着炸药质量增加和爆炸距离减小,夹芯板的后面板中心位移增加,芯层吸能占比减小。此外,采用薄前面板和厚后面板的夹芯板可以提高芯层的吸能占比。当分别增加相同的前、后面板厚度时,前面板厚度对减小后面板中心位移的影响更显著。当芯层厚度从0.6 mm减小至0.2 mm时,后面板中心位移减小49.0%,总能量吸收增加86.7%;芯层振幅从0.2 mm增大至1.0 mm时,后面板中心位移减小20.7%,总能量吸收大致不变;芯层高度从10 mm增大至18 mm时,后面板中心位移减小88.3%,总能量吸收增加56.9%;芯层宽长比从0.56减小至0.2时,后面板中心位移减小39%,总能量吸收增加47.4%。

     

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.     

Nonlinear Transient Response of Functionally Graded Material Sandwich Doubly Curved Shallow Shell Using New Displacement Field

In this paper, the nonlinear transient dynamic response of functionally graded material(FGM) sandwich doubly curved shell with homogenous isotropic material core and functionally graded face sheet is analyzed using a new displacement field on the basis of Reddy's third-order shear theory for the first time. The equivalent material properties for the FGM face sheet are assumed to obey the rule of simple power law function in the thickness direction.Based on Reddy'stheory of higher shear deformation, a new displacement field is developed by introducing the secant function into transverse displacement. Four coupled nonlinear differential equations are obtained by applying Hamilton's principle and Galerkin method. It is assumed that the FGM sandwich doubly curved shell is subjected to step loading, air-blast loading,triangular loading, and sinusoidal loading, respectively. On the basis of double-precision variablecoefficient ordinary differential equation solver, a new program code in FORTRAN software is developed to solve the nonlinear transient dynamics of the system. The influences of core thickness, volume fraction, core-to-face sheet thickness ratio, width-to-thickness ratio and blast type on the transient response of the shell are discussed in detail through numerical simulation.     

Special behavior of unidirectional sandwich panels with transversely flexible core under statical loading

Special features inherent in the response of ordinary (fully bonded) and delaminated sandwich panels with a transversely flexible (“soft”) core subjected to external in-plane and vertical statical loads are analyzed. The analytical formulation is based on a higher-order theory for sandwich panels with non-rigid bond layers between the face sheets and the core. The central finite difference scheme is used for discretizing the continuous formulation. The deflated iterative Arnoldi scheme for solution of a large-scale generalized eigenvalue problem is employed, as well as the quasi-Newton global framework for the natural parameter and the arc-length continuation procedures. The numerical higher-order analysis reveals that the ordinary sandwich panel behaves as a compound structure in which the local/localized, overall or interactive forms of the response can take place depending on the geometry, mechanical properties, and boundary conditions of the structure. The non-sinusoidal modes confined to the support zones of the panel may occur at critical loads much lower than those predicted on the basis of presumed sinusoidal modes. Soft-core sandwich panels possess a complex branching behavior with limit points and secondary bifurcations. The thin-film-delamination approach used in the field of the composite plates is unsuitable for the analysis of delaminated sandwich panels and consideration of the interaction between the face sheets and the core is required. The complex response of the soft-core sandwich panels can be predicted only with the aid of the enhanced higher-order theory.     

Elastica of sandwich panels with a transversely flexible core—A high-order theory approach

The elastica behavior of an extensional sandwich panel with a “soft” core when subjected to in-plane compressive loads is presented and it is compared with the response of its extensional equivalent single layer (ESL) with shear deformations model. The field equations along with the appropriate boundary conditions for the sandwich and the ESL panels have been derived through a variational approach following the High-order SAndwich Panel Theory (HSAPT) approach that takes into account the vertical flexibility of the core. The governing equations include the effects of the extension of the mid-surfaces of the face sheets of the sandwich panel or the mid-plane of the ESL model which the classical elastica approach misses. The results of the elastica response of a clamped-simply-supported sandwich panel and its ESL counterpart are presented and compared. They include the response along the panel, deformed shapes and equilibrium curves of in-plane loads versus structural quantities such as displacements and internal stress resultants and stresses. These results reveal that the predicted buckling load of the ESL panel is larger than that of the sandwich panel and that deep in the non-linear range the upper face sheet wrinkles with increasing overall and edge displacements and a release of the load. Hence, the use of an equivalent single layer panel especially when a sandwich panel with a compliant core is considered may lead to unsafe and unreliable predictions when large displacements and large rotations are considered.     

Plasticity of formable all-metal sandwich sheets: Virtual experiments and constitutive modeling

The mechanical behavior of a metallic sandwich sheet material composed of two flat face sheets and two bi-directionally corrugated core layers is analyzed in detail. The manufacturing of the sandwich material is simulated to obtain a detailed unit cell model which accounts for the non-uniform thickness distribution and residual stresses associated with the stamping of the core layers. Virtual experiments are performed by subjecting the unit cell model to various combinations of bi-axial in-plane loading including the special cases of uniaxial tension, uniaxial compression, equi-biaxial tension and shear. The results demonstrate that the core structure’s contribution to the in-plane load carrying capacity of the sandwich sheet material is similar to that of the face sheets. The numerical results are also used to identify the effective yield surface and hardening response of both the core layer and the face sheets. An anisotropic yield function with linear pressure dependency is proposed to approximate the equal-plastic work surfaces for the core structure and face sheets. Furthermore, a new two-surface model with non-linear interpolation based on plastic work density is presented to describe the observed combined isotropic-distortional hardening of the core structure.     

Non-linear response of curved sandwich panels – extended high-order approach

The geometrical non-linear behavior a curved sandwich panel with a stiff or compliant core when subjected to a pressure load using the Extended High-Order Sandwich Panel theory (EHSAPT), is presented. The formulation follows the EHSAPT procedure where the in-plane. i.e circumferential rigidity of the core is considered and the distribution of the displacements through the depth of the core are presumed. These displacement distributions are the closed-form solutions of the 2D governing equations of the curved core without circumferential rigidity that appear in the HSAPT curved sandwich panel model. The mathematical formulation includes the field equations along with the appropriate boundary and continuity conditions that take into account the high-order stress resultants in the core due to the presumed distributions. Finally a numerical study is conducted for a panel loaded by a distributed pressure at the upper face sheet. It reveals that the post-buckling response of a curved sandwich panels is associated with shallow to deep wrinkling deformations of the upper face sheet in the case of a simply-supported panel or a general non-linear pattern without wrinkles in the case of pinned supports with a short span. In both cases a stable post-buckling response is observed similar to that of a plate one.     

Failure mechanisms in composite panels subjected to underwater impulsive loads

This work examines the performance of composite panels when subjected to underwater impulsive loads. The scaled fluid-structure experimental methodology developed by Espinosa and co-workers was employed. Failure modes, damage mechanisms and their distributions were identified and quantified for composite monolithic and sandwich panels subjected to typical blast loadings. The temporal evolutions of panel deflection and center deflection histories were obtained from shadow Moiré fringes acquired in real time by means of high speed photography. A linear relationship of zero intercept between peak center deflections versus applied impulse per areal mass was obtained for composite monolithic panels. For composite sandwich panels, the relationship between maximum center deflection versus applied impulse per areal mass was found to be approximately bilinear but with a higher slope. Performance improvement of sandwich versus monolithic composite panels was, therefore, established specially at sufficiently high impulses per areal mass (I₀/M¯>170 m s⁻¹). Severe failure was observed in solid panels subjected to impulses per areal mass larger than 300 m s⁻¹. Extensive fiber fracture occurred in the center of the panels, where cracks formed a cross pattern through the plate thickness and delamination was very extensive on the sample edges due to bending effects. Similar levels of damage were observed in sandwich panels but at much higher impulses per areal mass. The experimental work reported in this paper encompasses not only characterization of the dynamic performance of monolithic and sandwich panels but also post-mortem characterization by means of both non-destructive and microscopy techniques. The spatial distribution of delamination and matrix cracking were quantified, as a function of applied impulse, in both monolithic and sandwich panels. The extent of core crushing was also quantified in the case of sandwich panels. The quantified variables represent ideal metrics against which model predictive capabilities can be assessed.     

Effect of Facesheet Thickness on Dynamic Response of Composite Sandwich Plates to Underwater Impulsive Loading

The response of sandwich structures to underwater blast loading is analyzed. The analysis focuses on the effect of varying structural attributes on energy dissipation and deformation. The structures analyzed are planar sandwich plates with polymer foam cores and fiber-reinforced polymer composite facesheets. The thickness of the facesheets is varied under the conditions of constant material properties and core dimensions. The fully three-dimensional finite-element simulations carried out account for underwater blast loading through the use of the Mie-Gruneisen equation-of-state of a linear Hugoniot form and a modified Drucker-Prager core crushing model. The impulse imparted to the panels is varied from 4 to 42 kPa·s. The results show that there exists an optimal thickness of the facesheets which maximizes energy absorption in the core and minimizes the overall deflection of the structure.     

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.     

Three-dimensional thermoelastic analysis of finite length laminated cylindrical panels with functionally graded layers

Based on the 3D thermoelasticity theory, the thermoelastic analysis of laminated cylindrical panels with finite length and functionally graded (FG) layers subjected to three-dimensional (3D) thermal loading are presented. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The variations of the field variables across the panel thickness are accurately modeled by using a layerwise differential quadrature (DQ) approach. After validating the approach, as an important application, two common types of FG sandwich cylindrical panels, namely, the sandwich panels with FG face sheets and homogeneous core and the sandwich panels with homogeneous face sheets and FG core are analyzed. The effect of micromechanical modeling of the material properties on the thermoelastic behavior of the panels is studied by comparing the results obtained using the rule of mixture and Mori–Tanaka scheme. The comparison studies reveal that the difference between the results of the two micromechanical models is very small and can be neglected. Then, the effects of different geometrical parameters, material graded index and also the temperature dependence of the material properties on the thermoelastic behavior of the FG sandwich cylindrical panels are carried out.     

Point-wise impulse (blast) response of a composite sandwich plate including core compressibility effects

This work analyzes the nonlinear impulse response of a composite sandwich plate exposed to a sudden point-wise transverse loading on the top face sheet. The nonlinearity arising from the core compressibility in the thickness direction is modeled and incorporated into the constitutive relations explicitly. As such, one can have a deep insight regarding the stress, strain and displacement profiles into the sandwich plate. The sandwich plate is assumed to be perfectly bonded at the face sheet/core interfaces. The equations of motion are formulated using Hamilton’s principle. The simply supported case is used to illustrate the procedure for solving the nonlinear equations. Numerical results are presented to demonstrate the response in terms of the transverse deformation and stresses in the composite sandwich plate. The effects of the variation of the geometrical parameters of the structure on the blast impulse response are also studied. Some conclusions are suggested regarding the associated optimal design of sandwich plates.     

孔结构金属复合夹芯板抗爆炸冲击响应及吸能特性研究

采用有限元方法研究爆炸载荷下四边固支孔结构金属复合夹芯板的动力响应及吸能特性,给出了孔结构金属复合夹芯板的动力响应过程,得到夹芯板的变形模式,比较了孔结构金属复合夹芯板与非孔结构金属复合夹芯板的抗爆炸冲击性能,同时讨论了孔大小、间距、排布方式和面板质量分布等因素对孔结构金属复合夹芯板抗爆炸冲击性能的影响。研究结果表明,迎爆面外面板的孔设计使爆炸冲击波穿过孔洞直接作用在芯材上,增强了芯材的压缩,从而提高了夹芯板的能量吸收能力。同等面密度情况下,内外面板厚度比大于1的孔结构金属复合夹芯板变形挠度小于内外面板厚度比小于1的孔结构金属复合夹芯板。进一步研究发现,通过合理设计内外面板的质量分布,可以使孔结构金属复合夹芯板的抗爆炸冲击性能最优。     

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.     

The Effects of Air and Underwater Blast on Composite Sandwich Panels and Tubular Laminate Structures

The resistance of glass-fibre reinforced polymer (GFRP) sandwich panels and laminate tubes to blast in air and underwater environments has been studied. Procedures for monitoring the structural response of such materials during blast events have been devised. High-speed photography was employed during the air-blast loading of GFRP sandwich panels, in conjunction with digital image correlation (DIC), to monitor the deformation of these structures under shock loading. Failure mechanisms have been revealed by using DIC and confirmed in post-test sectioning. Strain gauges were used to monitor the structural response of similar sandwich materials and GFRP tubular laminates during underwater shocks. The effect of the backing medium (air or water) of the target facing the shock has been identified during these studies. Mechanisms of failure have been established such as core crushing, skin/core cracking, delamination and fibre breakage. Strain gauge data supported the mechanisms for such damage. These studies were part of a research programme sponsored by the Office of Naval Research (ONR) investigating blast loading of composite naval structures. The full-scale experimental results presented here will aid and assist in the development of analytical and computational models. Furthermore, it highlights the importance of support and boundary conditions with regards to blast resistant design.     

爆炸载荷下双向梯度仿生夹芯圆板的力学行为

基于王莲仿生面内梯度芯层,通过引入面外梯度,设计了一种双向梯度仿生夹芯圆板。在此基础上,运用ABAQUS有限元软件,对不同排列方式的双向梯度夹芯圆板在不同爆炸载荷作用下的响应进行了数值仿真,着重分析了不同仿生夹芯圆板的前后面板挠度、芯层压缩量、变形模式和能量吸收等特性,得到了一种抗爆性能较好的芯层排列方式。结果表明:相较于单一的面外梯度夹芯圆板,合理设计的双向梯度仿生夹芯圆板可以有效降低后面板挠度,并提高芯层的能量吸收。