Energy absorption of double-layer foam cladding for blast alleviation

In the present study, a double-layer foam cladding is proposed to fulfill different structural protection purposes. The energy absorption capacity of the double-layer foam cladding under blast load is analytically derived based on a rigid-perfectly plastic-locking foam model. Different configurations of the layered foam cladding are studied. The maximum absorbed energy and the maximum blast impulse that can be resisted by the cladding are calculated. Numerical simulation with finite element method is also carried out. Good agreement is found between the analytical and the numerical results. The present analytical solution of the energy absorption capacity of the double-layer foam cladding can be effectively used for sacrificial foam cladding design.     

方孔蜂窝夹层板在爆炸载荷下的吸能特性

通过有限元数值模拟方法,对方孔蜂窝夹层板在爆炸冲击载荷下的变形机理和吸能特性进行了分析。在单位面积质量以及夹层板芯层薄壁间距、高度给定的情况下,通过对不同夹芯层相对密度下夹层板的吸能率以及上、下面板最大变形的比较,得出了最优的夹芯层相对密度。在此相对密度下,夹芯层吸能率最高,下面板变形最小,夹层板的抗冲击性能最优。同时还讨论了夹层板芯层薄壁间距、厚度、高度以及面板厚度对其各部分吸能率的影响,以得到最优化的夹层板结构。     

A numerical model for bird strike of aluminium foam-based sandwich panels

Experimental bird-strike tests have been carried out on double sandwich panels made from AlSi7Mg0.5 aluminium foam core and aluminium AA2024 T3 cover plates. The bird-strike velocity varied from 140 to 190 m/s. The test specimens were instrumented with strain gauges in the impacted area to measure the local strains of the rear sandwich plate. A numerical model of this problem has been developed with the non-linear, finite element program LS-DYNA. A continuum damage-mechanics-based constitutive model was used to describe the behaviour and failure of the aluminium cover plates. The foam core was modelled by a pressure sensitive constitutive model coupled by a failure criterion on maximum volumetric strains. The bird was represented by an idealised geometry and the material model was defined by a linear equation-of-state. A multi-material arbitrary Lagrangian Eulerian (ALE) element formulation was used to represent the motion of the bird, whereas the sandwich panel was described by a Lagrangian reference configuration. A fluid–structure interface ensured proper coupling between the motion of the bird and the solid materials of the sandwich panel. It was found that the model was able to represent failure of both the aluminium cover plates as well as the aluminium foam core.     

泡沫铝衰减冲击波压力的理论分析

由于泡沫铝具有良好的缓冲与吸收撞击或爆炸能量性能,常被粘贴在主结构可能遭受撞击面或迎爆面,用于降低撞击或爆炸冲击波对主结构的破坏作用。目前关于泡沫铝缓冲层衰减主结构上冲击波压力的理论计算没有得到很好的解决。为考查泡沫铝相对密度、孔洞形式及厚度对其衰减主结构上冲击波压力的影响,运用一维冲击波理论,考虑冲击波在压缩泡沫铝材料过程中的能量损耗,提出一种简化计算泡沫铝缓冲层衰减结构物上冲击波压力的方法。运用该方法分析了结构物上包覆一层泡沫铝缓冲层对飞片撞击结构所产生冲击波压力的衰减情况。并通过实例给出计算泡沫铝缓冲层衰减飞片冲击结构上冲击波压力的计算步骤及其影响因素。     

Analysis of foam claddings for blast alleviation

An analytical Load-Cladding-Structure (LCS) model is proposed to investigate the blast alleviation behavior of sacrificial foam claddings. The deformation of the foam subjected to blast loading is derived based on shock wave propagation theory. The coupled global response of the protected main structure is taken into consideration in the study. Two non-dimensional parameters for the foam cladding are introduced. It is seen that the maximum deflection of the protected structure subjected to a certain explosive load varies with the two non-dimensional parameters of the foam cladding. Based on the LCS model, the foam cladding can be appropriately designed to achieve structural retrofit against blast loads. The maximum allowable blast load for the structure with the protection of a particular foam cladding can be predicted. It is concluded that the efficiency of the structural retrofit based on foam materials depends on the properties of the blast load, the foam cladding as well as the protected structure.     

车用高强钢厚板模内淬火组织演变研究

目的 揭示高强钢厚板在热冲压模内淬火过程中的马氏体组织演变特征和规律。方法 建立了6 mm厚硼钢板热冲压模内淬火过程马氏体相变有限元预测模型,分析了马氏体分布情况及演变特征,阐明了保压力等关键淬火参数对组织演变的影响规律。结果 沿板面方向,马氏体从角部开始转化,逐渐由边缘向内部扩展,呈现出“边缘高、中部低”的分布特征。沿板厚方向,马氏体呈现出“表层高、心部低”的分布特征;随淬火过程的进行,这种厚向梯度分布特征逐渐弱化。与薄板相比,厚板的马氏体相变启动和结束时刻均较晚,且马氏体转化率明显较低,马氏体沿厚向分布的不均匀性也更明显。随保压力的增大,马氏体转化结束时刻前移,马氏体转化率增大且沿厚向分布更均匀,抗拉强度增大,延伸率减小;当保压力超过40 MPa时,上述影响逐渐减弱。结论 与薄板相比,厚板组织沿板面和板厚方向均呈现更明显的梯度分布特征。保压力对厚板组织演变和力学性能有较大影响,但这种影响随保压力的增大而逐渐减弱。     

Blast resistance and energy absorption of foam-core cylindrical sandwich shells under external blast

The early time, through-thickness stress wave response of a foam-core, composite sandwich cylindrical shell under external blast is examined in this paper. Solutions for the transient response of the facesheets were derived as stress waves propagated through an elastic–plastic, crushable foam core. These solutions were found to be in good agreement with results from finite element analysis. The blast response of the composite sandwich cylindrical shell was shown to be affected by the magnitude and duration of the pressure pulse. High amplitude, low duration (impulsive) pressure pulses induced the greatest energy absorption. Low amplitude, long duration pressure pulses caused minimal energy absorption. The amount of energy absorbed increased and the failure load decreased with increasing core thickness. Sandwich shells with foams of varying density, compressive modulus and crushing resistance were also examined. The sandwich shells with the foam of the highest density, compressive modulus and crushing resistance (Divinycell HCP100) were found to be the most blast resistant to failure even though no energy was absorbed by them. Per unit weight, however, the shells with a lighter, less stiff and strong, Divinycell H200 foam core were more blast resistant to failure than shells with a Divinycell HCP100 foam core.     

Effect of distance from the support on the penetration mechanism of clamped circular polycarbonate armor plates

A 1.91-mm thick circular polycarbonate plate of 115 mm diameter was impacted by a spherical steel projectile of 6.98 mm diameter at its center. Subsequent impacts were made at 10, 20, 30, 40, and 50 mm radii of the plate. Dent dimensions for the damaged plate were measured using optical microscope. For a constant projectile velocity of 138 m s⁻¹ which was below the perforation limit of the plate under investigation, a maximum thickness reduction close to the edge support was observed. The experimental work was modeled into explicit finite-element analysis program LSDYNA for simulations. LSDYNA was able to predict the dent depth and reduction in plate thickness at impact points precisely. In this research, the effect of the impact location distance from the supports on the damage mechanism of circular polycarbonate armor plates is investigated. The target plate was subjected to constant velocity projectile impacts starting at the plate midpoint and varying the impact distance from midpoint towards the clamped edge. Failure of plate is predicted close to the constrained boundary under uniform conditions.     

The fracture of concentrically loaded square ceramic plates

A testing system is described which measures the fracture stress of square plates. The loading is concentric and the plate is simply supported at the corners. The effective stressed volume can conveniently be changed by varying the diameter of the loading circle. The test is used to measure the fracture characteristics of square alumina plates 103 mm square and 1 mm thick. The displacement of the centre of the plate at fracture is about 3 mm, so the elastic system is geometrically non-linear. A non-linear finite element analysis using the ABAQUS program gave a stress distribution that was found to be in very good agreement with measured stress. The finite element solution was used to calculate stress-volume and stress-area integrals, which are tabulated, and these give the effective volumes and areas, for loading circles of 25 and 7.5 mm diameter. Two batches of plates were fractured, one with a loading circle of 25 mm diameter and the other 7.5 mm. Weibull plots were made assuming zero threshold stress. The first plots used the maximum tensile stress in the plate derived from the measured load using the finite element solution. This stress occurs at the intersection of the plate diagonal with the loading circle. Different values ofm (19.58 and 15.48) were given for the two loading circle diameters. Plots based on the stress determined at the fracture origin gave nearly identical values ofm (13.92 and 13.72). Weibull statistics and the values of the stress-volume or the stress-area integrals were used to predict the ratio of the average fracture stress for the two loading circle diameters. The predictions showed good agreement with the measured values. The stress-area integrals, which are simpler to calculate, gave almost as good predictions as did the stress-volume integrals.     

Ballistic Limit of Single and Layered Aluminium Plates

Abstract: This paper presents an experimental and finite‐element investigation of ballistic limit of thin single and layered aluminium target plates. Blunt‐, ogive‐ and hemispherical‐nosed steel projectiles of 19 mm diameter were impacted on single and layered aluminium target plates of thicknesses 0.5, 0.71, 1.0, 1.5, 2.0, 2.5 and 3 mm with the help of a pressure gun to obtain the ballistic limit in each case. The ballistic limit of target plate was found to be considerably affected by the projectile nose shape. Thin monolithic target plates as well as layered in‐contact plates offered lowest ballistic resistance against the impact of ogive‐nosed projectiles. Thicker monolithic plates on the other hand, offered lowest resistance against the impact of blunt‐nosed projectiles. The ballistic resistance of the layered targets decreased with increase in the number of layers for constant overall target thickness. Axi‐symmetric numerical simulations were performed with ABAQUS/Explicit to compare the numerical predictions with experiments. 3D numerical simulations were also performed for single plate of 1.0 mm thickness and two layered plate of 0.5 mm thickness impacted by blunt‐, ogive‐ and hemispherical‐nosed projectiles. Good agreement was found between the numerical simulations and experiments. 3D numerical simulations accurately predicted the failure mode of target plates.     

3D numerical simulations of sharp nosed projectile impact on ductile targets

Three-dimensional FE model is presented for perforation under normal and oblique impact of sharp nosed projectiles on single and layered ductile targets. Numerical simulations have been carried out to study the behavior of Weldox 460 E steel and 1100-H12 aluminum targets impacted by conical and ogive nosed steel projectiles respectively. Weldox 460 E steel targets of 12 mm thickness in single and double layered combination (2 × 6 mm) and 1100-H12 aluminum targets of 1 mm thickness in single and double layered combination (2 × 0.5 mm) impacted at 0°, 15° and 30° obliquity were considered for simulations. The results of monolithic and layered targets were compared for each angle of impact. Monolithic targets were found to have higher ballistic resistance than that of the layered in-contact targets of equivalent thickness. Failure of both the targets occurred through ductile hole enlargement. However, ogive nosed projectile failed 1 mm thick aluminum target through petal formation and conical nosed projectile failed 12 mm thick steel target through a circular or elliptical hole enclosed by a bulge at rear surface. The explicit algorithm of ABAQUS finite element code was used to carry out the numerical simulations. Various parameters which play critical role in numerical simulation such as element size and its aspect ratio have been studied.     

Nonlinear dynamic analysis of tapered sandwich plates with multi-layered faces subjected to air blast loading

The nonlinear dynamic behavior of simply supported tapered sandwich plates subjected to air blast loading is investigated theoretically and numerically. The plate is supposed to have both tapered core and tapered laminated face sheets and be subjected to uniform air blast load. The theory is based on a sandwich plate theory, which includes von Kármán large deformation effects, in-plane stiffnesses, inertias and shear deformations. The sandwich plate theory for plates with constant thickness which have one-layered face sheets found in the literature is developed to analyze the tapered sandwich plates with multi-layered face sheets. The equations of motion are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations. The Galerkin method is used to obtain the nonlinear differential equations in the time domain. The finite difference method is applied to solve the system of coupled nonlinear equations. The tapered sandwich plate subjected to air blast load is also modelled by using the finite element method. The displacement–time and strain–time histories are obtained. The theoretical results are compared with finite element results and are found to be in an agreement.     

Experimental study on mechanical properties and fracture toughness of structural thick plate and its butt weld along thickness and at low temperatures

The thick plate induces the variation of mechanical properties and fracture toughness, especially in cold regions. At the low temperature, the brittle behaviour of steel becomes worse. A series of tests (such as uniaxial tensile test and three‐point bending test) were carried out at low temperature to investigate the mechanical properties and fracture toughness of structural steel plates of Q345B with thickness of 60 to 150 mm, as well as the fracture toughness of 150 mm thick butt welded plate. The test specimens are all manufactured from plates along thickness with small size, and the tensile test specimens included through‐thickness specimens additionally. The ductility index (percentage reduction of area) and the fracture toughness index (critical CTOD values) all decrease with the temperature decreases and the distance from plate surface increases. The results obtained in this paper provide technical basis for preventing brittle fracture of thick plate steel structures in cold regions.     

The fracture stress of float glass

A fracture test [1] which uses concentrically loaded square plates supported near their corners has been used to measure the fracture stress of float glass. The plates were 102mm square and 5.98mm thick. The maximum displacement at fracture was less than 0.4mm. Under these circumstances it has been shown that use of a linear finite element solution for the stress distribution and the plate deflections is justified. The glass plates had greater edge damage than had the alumina plates tested in an earlier investigation. In order to secure an adequate proportion of failures in the central plate region, it was necessary to move the supports inwards towards the centre of the plate. This reduced the ratio of the maximum edge stress to the maximum stress in the plate. Batches of plates were tested with loading circle diameters of 7.5 and 25mm, to measure volume effects, with the side of the plate that had been in contact with the liquid tin in tension. Median ranking was used in the statistical analysis and edge failures were treated as suspensions, it being assumed that the minimum fracture stress of the central region of the edge-fractured plates was the plate centre stress at the fracture load. The Weibull modulus was determined by a linear regression in which extreme members of the population were given reduced weighting using the relationship of Faucher and Tyson [3]. The average fracture stresses were 147.2 and 107.3 N mm^–2 for the 7.5 and 25 mm loading circles, respectively, and the Weibull moduli were 4.49 and 5.44. These data are shown to agree well with Weibull statistics. Tests using a 7.5 mm diameter loading circle on plates with the non-tin side in tension gave a significantly higher average fracture stress of 242.1 N mm^–2, confirming the fact that the non-tin side has a higher strength.     

A layerwise finite element formulation for vibration and damping analysis of sandwich plate with moderately thick viscoelastic core

Abstract

Most previous studies of viscoelastic sandwich plates were based on the assumption that damping was only resulting from shear deformation in the viscoelastic core. However, extensive and compressive deformations in the viscoelastic core should also be considered especially for sandwich plates with moderately thick viscoelastic core. This paper presents a finite element formulation for vibration and damping analysis of sandwich plates with moderately thick viscoelastic core based on a mixed layerwise theory. The face layers satisfy the Kirchhoff theory while the viscoelastic core meets a general high-order deformation theory. The viscoelastic core is modeled as a quasi-three-dimensional solid where other types of deformation such as longitudinal extension and transverse compression are also considered. To better describe the distribution of the displacement fields, auxiliary points located across the depth of the sandwich plate are introduced. And based on the auxiliary points, the longitudinal and transverse displacements of the viscoelastic core are interpolated independently by Lagrange interpolation functions. Quadrilateral finite elements are developed and dynamic equations are derived by Hamilton’s principle in the variation form. Allowing for the frequency-dependent characteristics of the viscoelastic material, an iterative procedure is introduced to solve the nonlinear eigenvalue problem. The comparison with results in the open literature validates the remarkable accuracy of the present model for sandwich plates with moderately thick viscoelastic core, and demonstrates the importance of the higher-order variation of the transverse displacement along the thickness of the viscoelastic core for the improvement of the analysis accuracy. Moreover, the influence of the thickness and stiffness ratios of the viscoelastic core to the face layers on the damping characteristics of the viscoelastic sandwich plate is discussed.     

实体退化板单元及其在板的振动分析中的应用

经典板壳单元是由板壳理论构造出来的,而经典的板壳理论是在空间弹性理论的基础上考虑板壳的基本假定得来的。在空间等参数单元的基础上,直接引入板壳的基本假定,修改空间等参数单元的弹性矩阵,从而构造出适合于厚薄板壳分析的20结点实体退化板单元,并将其应用于开口圆柱薄壳的静力分析和厚薄板的固有振动分析。数值算例表明,该单元收敛快,稳定性好,具有较高的精度。此外,该单元还可以用于曲边变厚度板、壳体及层合板的振动分析。     

Three-dimensional elastodynamic solution for an arbitrary thick FGM rectangular plate resting on a two parameter viscoelastic foundation

A three-dimensional semi-analytic analysis based on the linear elasticity theory is offered to study the transient vibration characteristics of an arbitrarily thick, simply supported, functionally graded (FGM) rectangular plate, resting on a linear Winkler–Pasternak viscoelastic foundation, and subjected to general distributed driving forces of arbitrary temporal and spatial variations. The problem solution is obtained by adopting a laminate model in conjunction with the powerful state space solution technique involving a global transfer matrix and Durbin’s numerical Laplace inversion algorithm. Numerical calculations are carried out for the transient displacement and stress responses of aluminum-zirconia FGM square plates of selected thickness parameters and compositional gradients, resting on “soft” or “stiff” elastic foundations, under the action of moving transverse forces as well as uniformly distributed blast loads. Also, the response curves for the FGM plates are compared with those of equivalent bilaminate plates containing comparable total volume fractions of constituent materials. It is observed that the material gradient variation is substantially more influential on the dynamic stress concentrations induced across the plate thickness than on the displacement response of the inhomogeneous plates. In particular, the displacement response of the equivalent bilaminate plates can provide an accurate estimate for prediction of the dynamic response of the corresponding FGM plates, especially for thick plates resting on a stiff foundation. Limiting cases are considered and good agreements with the data available in the literature as well as with the computations made by using a commercial finite element package are obtained.     

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.     

High‐order layerwise finite element for the damped free‐vibration response of thick composite and sandwich composite plates

A high‐order layerwise finite element methodology is presented, which enables prediction of the damped dynamic characteristics of thick composite and sandwich composite plates. The through‐thickness displacement field in each discrete layer of the laminate includes quadratic and cubic polynomial distributions of the in‐plane displacements, in addition to the linear approximations assumed by linear layerwise theories. Stiffness, mass and damping matrices are formulated from ply to structural level. Interlaminar shear stress compatibility conditions are imposed on the discrete layer matrices, leading to both size reduction and prediction of interlaminar shear stresses at the laminate interfaces. The C¹ continuous finite element implemented yields an element damping matrix in addition to element stiffness and mass matrices. Application cases include thick [0/90/0], [±θ]_S and [±θ] composite plates with interlaminar damping layers and sandwich plates with composite faces and foam core. In the latter case, modal frequencies and damping were also experimentally determined and compared with the finite element predictions. Copyright © 2008 John Wiley & Sons, Ltd.     

陶瓷复合装甲优化设计及弹击后剩余弯曲强度

根据防护要求和防护机制,设计了一种C/C-SiC陶瓷/铝基复合泡沫复合装甲。在确保复合装甲面密度为44 kg/m²的前提下,以弹击后剩余弯曲强度为评价标准,以陶瓷板布置位置、各组成层厚度、泡沫金属中泡沫孔径尺寸为研究因素,设计了三因素三水平的正交模拟优化方案,利用有限元软件ABAQUS模拟了子弹侵彻陶瓷靶板的过程及弹击损伤后复合装甲的弯曲实验过程,预测了剩余弯曲强度,并进行了结构优化。根据数值模拟结果制备陶瓷复合装甲试样,进行实弹打靶和弯曲实验以验证复合装甲试样剩余弯曲强度。结果表明,以MIL-A-46103E Ⅲ类2A级为防护标准,剩余弯曲强度最高的陶瓷复合装甲最优化结构形式为：陶瓷板厚度12 mm、陶瓷板做防弹面板、Al基复合泡沫孔径为4 mm+10 mm的混合;对剩余弯曲强度的主次影响因素排序为：陶瓷板厚度>陶瓷板布置位置>Al基复合泡沫孔径。