The Effect of Load and Geometry on the Failure Modes of Sandwich Beams

Facing compressive failure, facing wrinkling and core shear failure are the most commonly encountered failure modes in sandwich beams with facings made of composite materials. The occurrence and sequence of these failure modes depends on the geometrical dimensions, the form of loading and type of support of the beam. In this paper the above three failure modes in sandwich beams with facings made of carbon/epoxy composites and cores made of aluminum honeycomb and two types of foam have been investigated. Two types of beams, the simply supported and the cantilever have been considered. Loading included concentrated, uniform and triangular. It was found that in beams with foam core facing wrinkling and core shear failure occur, whereas in beams with honeycomb core facing compressive failure and core shear crimping take place. Results were obtained for the dependence of failure mode on the geometry of the beam and the type of loading. The critical beam spans for failure mode transition from core shear to wrinkling failure were established. It was found that initiation of a particular failure mode depends on the properties of the facing and core materials, the geometrical configuration, the type of support and loading of sandwich beams.     

Elastic structural response of anisotropic sandwich plates with a first-order compressible core impacted by a Friedlander-type shock loading

The foundation of the non-linear theory of asymmetric anisotropic sandwich plates with a first order compressible weak orthotropic core under a Friedlander-type explosive blast is presented. The equations of motion are developed by means of Hamilton’s Principle. Within the theory, the face sheets are asymmetric while adopting the Love-Kirchoff model. In addition, the core layer is assumed to be compressible (extensible) in the transverse direction thereby capturing any wrinkling or global instabilities. The theory is then simplified and applied for the case of sandwich plates with symmetric unidirectional fiber reinforced laminated composite facings with the axes of orthotropy not necessarily coincident with the geometrical axes. The governing solution is developed using the Extended-Galerkin method resulting in two coupled non-linear second order ordinary differential equations which are then solved using the 4th-order Runge–Kutta method for a system of differential equations.     

Dynamic analysis of an axially moving sandwich beam with viscoelastic core

A development of the beam model of the axially moving sandwich continua with elastic faces and the core characterized by viscoelastic properties is presented in this paper. Two-parameter Kelvin–Voigt rheological model is used to describe material properties of the core. The Galerkin method is used to solve the governing partial differential equation. Dynamic analysis of the composite with two aluminum facings and a polyurethane core is carried out. The effect of the transport speed, the core thickness and the internal damping of the core material on the dynamic behavior of the system is investigated in undercrtitical and supercritical range of transport speed.     

Structural performance of composite sandwich bridge decks with hybrid GFRP–steel core

This paper presents the static and fatigue performance of composite sandwich bridge decks with hybrid GFRP–steel core. The composite sandwich bridge deck system is comprised of wrapped hybrid core of GFRP grid and multiple steel box cells with upper and lower GFRP facings. Its structural performance under static loading and fatigue loading with a nominal frequency of 5 Hz was evaluated. The responses from laboratory testing were compared with the ANSYS finite element predictions. The failure mode of the proposed composite sandwich bridge deck was more favourable because of the yielding of the steel tube when compared with that of all-GFRP decks. The ultimate failure of the composite sandwich deck panels occurs by shear of the bonded joints between GFRP facings and steel box cells. Results from fatigue load test indicated no loss in stiffness, no signs of de-bonding and no visible signs of deterioration up to 2 million load cycles. The thickness of the composite sandwich deck retaining the similar stiffness may be decreased to some extent when compared with the all-GFRP deck. This paper also presents design of a connection between composite sandwich deck and steel girder.     

Fundamental frequency and design of the CFCF composite sandwich plate

The design efficiency of sandwich panels is often associated with the value of fundamental frequency. This paper investigates the free vibrations of rectangular sandwich plates having two adjacent edges fully clamped and the remaining two edges free (CFCF). The vibration analysis is performed by applying Hamilton’s principle in conjunction with the first-order shear deformation theory. The analytical solution determining the fundamental frequency of the plate is obtained using the generalised Galerkin method and verified by comparison with the results of finite element modal analysis. The approach developed in the paper and equations obtained are applied to the design of sandwich plates having composite facings and orthotropic core. Design charts representing the effects of the thickness of the facings and core on the mass of composite sandwich panel for a given value of the fundamental frequency are obtained.     

PLLA/Flax Mat/Balsa Bio-Sandwich Manufacture and Mechanical Properties

This paper describes the manufacture and mechanical characterization of a sandwich material which is 100% bio-sourced. The flax mat/PLLA facings and balsa core can also be composted at end of service life. Manufacture is by vacuum bag moulding. The optimum moulding time and temperature are a compromise between ensuring good impregnation and avoiding degradation, and holding for 60 min at 180°C was found to be satisfactory. The mechanical properties of the bio-sandwich obtained are compared to those of a traditional glass reinforced polyester balsa sandwich. The flexural strength is 30% lower, as predicted based on the facing properties. Skin/core adhesion is also measured using debonding tests. Crack propagation occurs at the skin/core interface in the traditional sandwich but within the facing in the bio-sandwich. The impregnation of the core in the two materials is examined using X-ray micro-tomography.     

Wrinkling on irreversibly deforming foundations

Wrinkling is a mechanical instability occurring in multi-layer structures comprising a thin and stiff layer resting on a supporting underlying compliant layer. The present study is motivated by experimental observations of wrinkling leading to irreversible deformation and to the initiation of defects. An incremental Spectral Method is employed to solve the governing differential equations. This approach enables the analysis of wrinkling processes non-linear foundations and under cyclic loading. Numerical simulation results are compared to a set of analytical solutions describing wrinkling events on nonlinear foundations. Wrinkling is analyzed for cases of elastic, elastic damageable, and elastic plastic foundations. The behavior of homogeneous foundation properties is contrasted to situations where local defects are present.     

纸木复合蜂窝材料蠕变性能研究

主要是利用四元件Burger模型对纸木复合蜂窝材料蠕变性能进行研究,其中蠕变实验采用三点弯曲的加载方式.研究结果表明:四元件模型可以用来模拟纸木复合蜂窝材料的短期蠕变行为;瞬间弹性变形和延迟弹性变形均随着应力水平的加大而加大;参数A和B、 C和D关联度大小依次为B＞D＞C,该材料的瞬时弹性变形和延迟弹性变形之间联系紧密.建议可通过单板与纸板直接胶合来提高纸木复合蜂窝复合材料的胶接性能.     

Crushing energy absorption of GFRP sandwich panels and corresponding monolithic laminates

Steady quasi-static compression of GFRP monolithic laminates and sandwich panels made of a randomly oriented continuous filament mat/polyester were undertaken. The effects of facing/laminate thickness, trigger collapse system and aspect ratio on their failure mechanisms, hence their energy absorption capability were examined. A numerical model, using a non-linear finite element explicit code, LS-DYNA, was used for pre-analysis of the effect of aspect ratio. A collapse trigger configuration was also studied numerically. The experimental data showed that high values of energy absorbed per unit mass were a predominant feature of the thickest monolithic laminates and sandwich panels with the thickest facings. The monolithic laminates showed higher specific energy than their sandwich panel counterparts. It seems that this difference was due to instability of the sandwich specimens.     

On the Rigidity in Bending of a Sandwich with Thick CFRP Facings and Thin Soft Core

Flexure tests in three-point bending were performed in the elastic domain on sandwich specimens whose facings were made of T800H/3900-2 laminates, and the core by a soft rubbery layer. The contribution of the shear and flexural deformations to the overall deflection was varied by varying the slenderness ratio. The rigidities yielded by the load-displacement curve were corrected for the indentation occurring at the points of load introduction, using an experimentally determined calibration curve. Due to the thinness of the sandwich, indentation negligibly affected the precision of the results, with the apparent rigidities differing from the actual ones by less than 2%. By an analytical formula previously developed for sandwich structures, a prediction of the rigidities in flexure was attempted, adopting elastic constants available in the literature. The correlation with the data points was poor, with the theoretical results largely overestimating the actual rigidities. However, the reliability of the closed-form formula was supported by finite element analysis, carried out modelling the facings by 2D plate elements, and the core by 3D brick elements. Through the formula, the core shear modulus was individuated as responsible of the discrepancies observed. Assuming a suitable value for this parameter, both the analytic solution and the finite element models were able to match with accuracy the rigidities measured.     

木质蜂窝夹芯包装材料抗弯性能研究

根据夹层结构原理,就木质蜂窝夹芯材料抗弯性能进行研究,同时根据三点外伸梁和简支梁原理对夹芯结构的抗弯刚度进行了理论分析.结果表明:木质蜂窝夹芯材料的抗弯性能较原蜂窝纸板大大提高,给出的木质蜂窝夹芯材料抗弯刚度的近似公式可以预测夹芯结构的刚度.木质蜂窝夹芯材料作为一种具有良好性能的绿色包装材料,将会有很好的应用前景.     

Deformation and impact energy absorption of cellular sandwich panels

The response and energy absorption capacity of cellular sandwich panels that comprises of silk-cotton wood skins and aluminum honeycomb core are studied under quasi-static and low velocity impact loading. Two types of sandwich panels were constructed. The Type-I sandwich panel contains the silk-cotton wood plates (face plates) with their grains oriented to the direction of loading axis and in the case of Type-II sandwich panel, the wood grains were oriented transverse to the loading axis. In both of the above cases, aluminum honeycomb core had its cell axis parallel to the loading direction. The macro-deformation behavior of these panels is studied under quasi-static loading and their energy absorption capacity quantified. A series of low velocity impact tests were conducted and the dynamic data are discussed. The results are then compared with those of quasi-static experiments. It is observed that the energy absorption capacity of cellular sandwich panels increases under dynamic loading when compared with the quasi-static loading conditions. The Type-I sandwich panels tested in this study are found to be the better impact energy absorbers for low velocity impact applications.     

The effect of pin reinforcement upon the through-thickness compressive strength of foam-cored sandwich panels

Titanium and carbon fibre pins have been inserted into the polymethacrylimide foam core of a sandwich panel (with carbon fibre face sheets) in order to increase the through-thickness strength. The elevation in compressive strength has been measured both quasi-statically and dynamically using a direct Kolsky bar, and the sensitivity of strength to the relative density and thickness of foam have been determined. An X-ray CAT scan machine was used to examine the deformed shape of the pins during interrupted compression testing of the sandwich specimens. It was found that the foam core stabilises the pins against elastic buckling, and the pin-reinforced core has a strength and energy absorption capacity in excess of the individual contributions from the foam and unsupported pins. It is shown that the compressive strength is governed by elastic buckling of the pins, with the foam core behaving as an elastic Winkler foundation in supporting the pins. The peak strength of the pin-reinforced core is increased by a factor of about four when the speed of loading is increased from the quasi-static rate of about 10⁻⁶ ms⁻¹ to the dynamic value of 10 ms⁻¹; it is concluded that the micro-inertia of the pins stabilises them against elastic buckling and leads to the observed elevation in strength.     

Thermal buckling of bimodular sandwich beams

This paper presents a model that explores the thermal buckling of three-layer sandwich beams possessing thick facings and moderately stiff cores. Bimodular facings and core material are used. In contrast to conventional theory, the effects of transverse shear deformation in the facings as well as the effect of the stretching and bending action in the core on thermal buckling are considered. The governing equations are derived using the principle of minimum total potential energy and the fact that its second derivative is zero. The finite-element results are presented in order to investigate the effects of important parameters such as thickness, thermal expansion coefficients and moduli ratio on critical buckling temperatures.     

Instance of hidden instability traps in intermittent transition of moving masses along a flexible beam

The problem of an elastic beam under the periodic loading of successive moving masses is investigated as a pragmatic case for studying dynamic stability of linear time-varying systems. This model serves to highlight the odds of multi-solutions coexistence, a form of hidden instability which reveals dangerous as it may be precipitated by the slightest disturbance or variation in the model. Since no engineering model perfectly represents a physical system, such situations for which Floquet theory naively predicts stability are potentially inevitable. The harmonic balancing method is used in order to thoroughly explore the stability diagrams for detecting these instability gaps. Although this phenomenon has also been described in other physical systems, it has not been addressed for beam–moving mass systems. This result may find particular importance in applications involving self-induced vibrations of elastic structures and hence also appears of practical relevance.     

Optimum distribution of smart stiffeners in sandwich plates subjected to bending or forced vibrations

The problems of optimum distribution of active stiffeners manufactured from piezoelectric or shape memory alloy materials and bonded to or embedded within the facings of a sandwich plate are considered. The sandwich plate consists of thin composite or isotropic facings which are in the state of plane stress and a thick shear deformable core. The amplitude of forced vibrations of the plate is reduced using symmetric couples of piezoelectric stiffeners subjected to out-of-phase dynamic voltages. Shape memory alloy stiffeners are used to reduce bending deformations. In the latter case, a desirable effect is achieved by activating the stiffeners on one side of the middle surface. Optimum design is considered based on the requirement of minimal transverse static or dynamic deflections subject to a constraint on the volume of smart stiffeners. The variables employed in the process of optimization are the ratios of the cross-sectional areas of the stiffeners in each direction to their respective spacings. It is shown, that, dependent on the load, materials, and geometry, optimum design can significantly reduce deflections, i.e. enhance the strength, of sandwich plates.     

Effect of a Thin Soft Core on the Impact Behaviour of CFRP Laminates

Low-velocity impact tests were carried out on sandwich plates having CFRP facings and thin rubbery core. Two types of cores, differing in the material nature and thickness, were used. For comparison, similar tests were performed on the monolithic laminate. Various impact parameters, among which indentation, first failure energy, perforation energy, absorbed energy and maximum contact force, were analyzed, to highlight the effect of the core on the material response. The influence of the core on the macroscopic behaviour of the panels was quite limited, except in the elastic phase, where the lower stiffness of the sandwich configurations resulted in a higher energy at first failure. More relevant differences were found from the study of failure modes, carried out combining ultrasonic C-scan and a limited number of microscopic observations. In particular, in correspondence of the energy for barely visible impact damage, besides considerable facing-core debonding, both the facings of the sandwich structures exhibited fibre breakage at their back side.     

Improved impact performance of marine sandwich panels using through-thickness reinforcement: Experimental results

This paper presents results from a test developed to simulate the water impact (slamming) loading of sandwich boat structures. A weighted elastomer ball is dropped from increasing heights onto rigidly supported panels until damage is detected. Results from this test indicate that honeycomb core sandwich panels, the most widely used material for racing yacht hulls, start to damage due to core crushing at impact energies around 550 J. Sandwich panels of the same areal weight and with the same carbon/epoxy facings but using a novel foam core reinforced in the thickness direction with pultruded carbon fibre pins, do not show signs of damage until above 1200 J impact energy. This suggests that these will offer significantly improved resistance to wave impact. Quasi-static test results cannot be used to predict impact resistance here as the crush strength of the pinned foam is more sensitive to loading rate than that of the honeycomb core.     

Analysis of local bending effects in sandwich plates with orthotropic face layers subjected to localised loads

This paper presents a method for the approximate analysis of local bending effects in sandwich plates with specially orthotropic face layers subjected to localised external loads. The local bending analysis is based on the assumption that the relative deflection of the loaded face against the deflection of the face not loaded can be modelled by application of an elastic foundation model. This is achieved by introducing a two-parameter elastic foundation model which takes into account the shearing interaction effects between the loaded face and the core material. An approximate solution to the complete problem is achieved by superposition of the local solution and an overall solution derived by application of classical sandwich plate theory. The results obtained are compared with finite element analysis results, and a good match between the solutions is observed. Finally a brief parametric study shows that the local bending effects are strongly influenced by the modular ratio and the thickness of the loaded face.     

Linear stress relations for a metal matrix composite sandwich beam with any core material

In this paper, it is shown that shear stresses are developed in the interface between the facing material and the core of a sandwich beam. The sandwich beam is composed of a core of any suitable material sandwiched between an upper unreinforced metal facing and a bottom facing made from metal matrix composite (MMC) material. The shear stress is shown to be a consequence of the differences in the core and facing elastic moduli. The magnitude of the shear stress increases as the core stiffness is made to diminish. The shear stress can exceed the bond strength between facing and core, resulting in delamination. Consequently, structural materials using this type of construction and particularly flexural experiments should contain a relatively stiff core. The magnitude of the facing stresses is shown to be relatively insensitive to the assumption or neglect of these shear stresses. In the worst case considered, neglecting the interfacial shear stresses results in an overestimation of the compressive and tensile stresses by less than 5%.