An analytical assessment of the influence of skin imperfections on the indentation collapse mechanism in composite sandwich beams

The influence of skin imperfections, in the form of delamination damage or thickness variations, on the indentation collapse mechanism in composite sandwich beams with compressive yielding cores is studied using the models of non-prismatic beam and beam-column resting on a nonlinear Winkler foundation. Upper and lower threshold solutions are derived for the indentation response and collapse load and the transition between the two limits is defined as a function of size, magnitude and position of the imperfections. In beams where global bending effects are not negligible, the collapse load is limited from above by the indentation collapse load of beams with rigid-plastic cores and the face wrinkling collapse load of beams with elastic cores; the transition between the two limits is controlled by material/structure properties and the magnitude of the imperfections. Characteristic lengths, which depend on material and geometrical properties, define the minimum size of the imperfections with the strongest effect on the solution and the minimum distance between load and imperfections with no effect on the solution.     

Prediction of the dynamic response of composite sandwich beams under shock loading

Finite element calculations are reported for the dynamic shock response of fully clamped monolithic and sandwich beams, with elastic face sheets and a compressible elastic–plastic core. Predictions of the peak mid-span deflections and deflected shapes of the beams are compared with the previously reported measured response of end-clamped sandwich beams, made from face sheets of glass fibre reinforced vinyl ester and a core of PVC foam or balsa wood [1]. Good agreement is observed, and the maximum sustainable impulse is also predicted adequately upon assuming a tensile failure criterion for the face sheets. The finite element calculations can also be used to bound the response by considering the extremes of a fully intact core and a fully damaged core. It is concluded that the shock resistance of a composite sandwich beam is maximised by selecting a composite with fibres of high failure strain.     

Flexural behaviour of structural fibre composite sandwich beams in flatwise and edgewise positions

The flexural behaviour of a new generation composite sandwich beams made up of glass fibre-reinforced polymer skins and modified phenolic core material was investigated. The composite sandwich beams were subjected to 4-point static bending test to determine their strength and failure mechanisms in the flatwise and the edgewise positions. The results of the experimental investigation showed that the composite sandwich beams tested in the edgewise position failed at a higher load with less deflection compared to specimens tested in the flatwise position. Under flexural loading, the composite sandwich beams in the edgewise position failed due to progressive failure of the skin while failure in the flatwise position is in a brittle manner due to either shear failure of the core or compressive failure of the skin followed by debonding between the skin and the core. The results of the analytical predictions and numerical simulations are in good agreement with the experimental results.     

Stability of the face layer of sandwich beams with sub-interface damage in the foam core

This paper addresses the effect of local indentation/impact damage on the bearing capacity of foam core sandwich beams subjected to edgewise compression. The considered damage is in a form of through-width zone of crushed core accompanied by a residual dent in the face sheet. It is shown that such damage causes a significant reduction of compressive strength and stiffness of sandwich beams. Analytical solutions estimating the Euler’s local buckling load are obtained for two typical modes of damage. These solutions are validated through experimental investigation of three sandwich configurations. The results of the analytical analysis are in agreement with the experimental data.     

An assessment of several displacement-based theories for the vibration and stability analysis of laminated composite and sandwich beams

Several displacement-based theories are assessed by analyzing the free vibration and the buckling behaviors of laminated beams with arbitrary layouts as well as soft-core sandwich beams. The equations governing the dynamic response of laminated structures are derived by using Hamilton’s principle. However, equations of equilibrium for buckling problems are given by employing the principle of virtual displacements. Moreover, using Navier’s technique and solving the eigenvalue equations, analytical solutions based on the global–local higher-order theory used in this paper are first presented in present study. At the same time, the effect of the order number of higher-order shear deformation as well as interlaminar continuity of transverse shear stress on the global response of both laminated beams and soft-core sandwiches has been also studied. Numerical results show that by increasing the order number of in-plane and transverse displacement components, the global higher-order theories can reasonably predict the natural frequencies and the critical loads of laminated beams with arbitrary layouts and soft-core sandwich beams whereas these global higher-order theories are still less accurate compared to the global–local higher-order theory and the zig-zag theory used herein.     

Comments on the paper “Modification of composite hardness models to incorporate indentation size effects in thin films”, D. Beegan, S. Chowdhury and M.T. Laugier, Thin Solid Films 516 (2008), 3813-3817

Since the original work of Bückle concerning the substrate influence on the hardness measurement of thin film, more than 20 models were proposed to separate the contribution of the substrate. Subsequently to the development of these numerous models, a question arises: Which is the most relevant models among them? Indeed, the authors usually consider that their proposed model leads to the best prediction of the film hardness which is probably correct for a given experimental condition applied to a particular material. In addition, the authors also assume that the other models are not so relevant. But to have a sound discussion about the existing models, it is necessary to correctly apply them according to the author statement. In this paper, we better specified the application of the Jönsson and Hogmark model and that of Chicot and Lesage applied to the results obtained on copper films by Beegan et al. Contrarily to these authors, we show that the above-mentioned models lead to a good representation of the experimental data and a good predicted value of the film hardness.     

粘弹性复合材料夹芯板的稳态响应分析

芯材采用Kelvin粘弹性本构模型,推导了复合材料夹芯板的动力学方程,运用模态正交原理,以Navier完备解形式求解了四边简支正交对称铺层层合板的稳态响应,并给出了固有频率和结构损耗因子的解析解。通过固有频率的有限元解对比验证了数值计算的可靠性。分析了芯材剪切模量和芯材厚度对结构固有频率和损耗因子的影响。探讨了稳态响应的收敛性,并得到结构稳态响应振幅与频率的关系,分析了芯材损耗因子对结构稳态响应的影响。结果表明：芯材剪切模量存在最佳设计值;结构首阶模态特性主导结构的稳态动态响应。     

An analytical study of the effect of slamming pressures on the interlaminar behaviour of composite panels

This paper discusses the effect of material properties on the interlaminar behaviour of ship panels made of composite materials under stress waves caused by slamming loads. First, a brief reference to the analytical model developed to simulate the propagation of stress waves caused by slamming impact on composite materials which has been recently published in Composite Structures is made. Then, some parametric studies are done, discussing the influence of material Young’s modulus on the interlaminar peak stresses. The influence of strain rates is also discussed.     

Numerical investigation on the failure phenomena of stiffened composite panels in post-buckling regime with discrete damages

The aim of this work is to investigate the final failure response of damaged composite stiffened panels in post buckling regime under compressive load, by using progressive failure analysis (PFA) methodology. The selected panel is characterized by T shaped stringers and it is representative of the upper skin panel, toward the wing tip, of the wing box of a typical regional aircraft. PFA methodology has been applied in order to predict in addition to the initiation of the local failure also its propagation up to the final collapse of the panel, in presence of local damage (barely visible impact damage, BVID) and in post-buckling regime. For this purpose, discrete damages have been considered in the skin of the panel. According to the indications contained in many guidelines finalized to the preliminary design of composite structures, a simplified design model of BVID has been considered in this work, in particular a hole 1/4 in. in diameter has been used to simulate this damage. The collapse load of the panel has been evaluated considering different locations of a single damage and also considering multi-damage maps (the latter are more representative of a real damage scenario). The results of PFA presented in this work illustrate the combined effect of the reduction of the panel stiffness and of the damage propagation, and the sensitivity of the buckling onset and of the residual strength of the panel with respect to different damage locations and damage density.     

Higher order composite beam theory built on Saint-Venant’s solution. Part-II: Built-in effects influence on the behavior of end-loaded cantilever beams

The higher order composite beam theory (HOCBT), established in Part-I, is a refinement of the one-dimensional beam-like theory related to 3D Saint-Venant’s solution. HOCBT is based on a displacement model including in/out-of plane warpings and is devoted to symmetric and orthotropic composite beams.