Crushing and Energy Absorption of Graded Honeycomb Materials
Introduction
Honeycomb structures are natural or humanmade materials with the same geometry as bee honeycombs to allow a minimum amount of material used to reach minimal weight and material cost. The salient feature of all honeycomb materials is the array of hollow cells forming between the thin vertical walls. The empty cells are usually hexagonal, but can also be triangular, square, or rhombic in shape. The resulting honeycomb structure presents the material with minimum density and relatively high out-of-plane compression properties and out-of-plane shear properties. Honeycomb materials existing as humanmade polymers, metals, and ceramic materials are available as standard products used for numerous applications such as in doors or aerospace components, for energy-absorbing uses, and in high-temperature processing. These humanmade products are usually made by laying a honeycomb material between two thin layers, which provide strength in tension, forming a plate-like assembly. Also, natural materials such as wood can be idealized as honeycomb materials (Gibson & Ashby, 1997).
Graded honeycomb materials have one unique feature in that by altering their geometrical parameters in terms of height, thickness, cell size, and inner angles, and they result in different mechanical properties. The most significant purpose of the resulting structure is to reduce the effect of impact load by distributing it within a period. Honeycomb materials have been studied over the years for their suitability as impact energy absorbers. They undergo plastic deformation under compression and have a long stroke, which enables the designer to limit the decelerating force. This project aims to numerically investigate the crushing and energy absorption capacity of honeycomb material with graded densities under quasi-static and dynamic loading. To undertake this analysis, structural loads, geometrical properties, support conditions, and material properties will be determined empirically. The results to be obtained will include deformation, stress levels, and displacements, and these will be used compared to a criterion that indicates the conditions of failure. Don't use plagiarised sources.Get your custom essay just from $11/page
Literature review
What are Honeycomb materials?
Honeycomb materials can be natural or humanmade and take the geometry of the bee honeycomb. The geometry of honeycomb materials is such that it minimizes the quantity of material used to reduce the weight and cost of the material. The shape of cells in a honeycomb material is usually hexagonal or columnar. Honeycomb structures exhibit high stiffness and strength to weight ratio. Materials used to make honeycomb structures should provide excellent mechanical properties, low dielectric properties, low thermal conductivity coefficients, fluid control, good acoustic properties, excellent crushing properties, small cross-sectional areas, and the large exposed area within the cells.
Honeycomb materials for structural and thermal applications
Honeycomb materials are essential elements in the design of more eco-friendly products. The use of honeycomb panels, for instance, leads to the production of structures that fulfill intended properties such as minimum density, high stiffness, rigidity, and strength. Sandwich panels with honeycomb materials have many applications as efficient and lightweight structures. Honeycomb sandwich panels comprise two thin and hard surface sheets bonded to a thick and lightweight honeycomb structured core. The two parallel layers provide flexural stiffness and strength, whereas the honeycomb core gives support to the panel and contributes to the shear stress exerted to the panel. The center also offers flexural strength and out-of-plane shear and compressive strength of the panel. Materials for honeycombs are aluminum, polymers, composites, and natural fibers.
Honeycomb structures provide high flexural stiffness, reduced weights, and low cost, and they are widely used in many applications, including in the building and construction industry, manufacture of packaging material, transportation, aviation industry, space, and automotive production. Other benefits of the honeycomb structures include low cost, lightweight, practical mounting, eco-friendly, recyclable, and excellent acoustic insulation properties.
Gibson and Ashby, (1997), classify humanmade honeycomb materials as cellular solids. These materials are used in sandwich panels due to their high stiffness-to-weight ratio and high transverse shear strength. In addition, they are used as energy absorption foe instance in the vehicle-making industry due to the large energy dissipated during the progressive localized collapse. The progressive localized failure takes place over an almost constant condition of load called plateau load. Honeycomb materials come in various shapes and materials and for multiple applications. Chung and Waas (1999) have conducted studies on the static in-plane crush response of circular cell polycarbonate honeycombs, and in addition, they have also carried out research on the dynamic regime.
Some honeycomb structures are made of natural fibers, such as wood. These have advantages over humanmade honeycomb materials in terms of cost and weight. However, natural honeycomb structures possess inferior mechanical properties. Honeycomb structures contain open and large cell sizes. These provide spaces that can be filled by other materials for specific uses such as sound insulation, vibration, damping, thermal management, and structural integration.
Manufacture of honeycombs
Humanmade honeycomb structures are made using three methods; expansion, corrugation, and molding. The process involves the expansion and corrugation processes in which composite materials such as fiberglass, aluminium, and carbon fiber reinforced plastic are used. Extrusion is used to manufacture thermoplastic honeycomb cores using polypropylene. Aside from metal honeycomb structures, there exist paperboard honeycomb materials used in making paper pallets and package blocking, cushioning, and bracing.
Benefits and applications of honeycomb composites
Honeycomb materials have gained wide applications owing to their numerous benefits. They are preferred due to their exceptionally high strength to weight ratio, resistance to corrosion, resistant to fires and fungi, high-temperature performance, resistance to moisture, they are easily machinable and formable, low cost among others.
Honeycomb materials are widely used in automobile structures, rocket substructures and jet aircraft, wind turbine blades, heating, ventilation, and air conditioning appliances, energy absorption protective structures, in the marine industry, in the rail industry to make train doors, snowboards, etc.
Crushing of graded honeycomb materials
Previous studies indicate that all honeycomb materials have comparatively reasonable plastic energy absorption. However, at low crushing rates, the usual dissipated plastic energy rises slightly by increasing the relative density of the structure. I contrast, at high crush rates, the typical plastic energy dissipation of these structures is highly dependent on its relative density and is much higher for a honeycomb structure with low relative density. This is attributable to the dynamic effects and the nonlinearity as a result of cell wall contact.
Functionally graded honeycomb materials in which there are variations in cell sizes, shapes and thickness of the cell walls result in a functional change in the relative density and organization of the structures. Previous studies reveal the potential of functionally graded honeycomb materials to cushion materials by creating impact resist structures upon crushing forces.
Gibson and Ashby (1997) report that honeycomb materials have excellent energy-absorbing capabilities when exposed to compressional forces. They conclude that to be able to obtain excellent energy-absorbing characteristics of honeycomb structures, axial compressional tests are required.
In the past research on the experimental and numerical studies on the deformation mechanisms, damage revolution and macro-constitutive equations are performed under quasi-static loading. Wierzbicki developed an out-of-plane large deformation crushing model for metallic honeycombs, which gives an analytical forecast of the crushing pressure. For the in-plane crushing, Klintworth and Stronge formulated a large deformation model that takes account of localized deformation band effects. Mohr and Doyoyo have studied the out-of-plane crush behavior and have suggested criteria for plastic collapse initiation and propagation. Gibson and Ashby provided two smaller models for forecasting the elastic characteristics and yielding behavior of open and close foams analytically.
More studies have been undertaken on honeycomb materials under dynamic loading, and they indicate that these materials exhibit some extent of strength enhancement with an increase in loading rate. For instance, Goldsmith and Sackman have gathered some vital information on the out-of-plane crushing and the ballistic perforation of honeycombs. Their experiment fired a rigid projectile to a target made of honeycombs, and the result shows that mean crushing pressures at times increase up to fifty percent in relation to static results. Similar results have been found out by Zhang et al. in metallic honeycombs. It has been established in previous studies that the out-of-plane strength in honeycombs increases at the rate of forty percent when the loading rate rises from 5*10-4m/s to 30m/s, but the enhancement of in-plane strength is significant.
A theory of compressed air exists to explain the dynamic enhancement of cellular materials such as honeycombs. The theory postulates that dynamic tests on cellular materials are associated with the compressive forces of air that are trapped in the cells. So there is insufficient time for the air in the cells to escape when the loading rate is very high. Gibson and Ashby estimated the contributions of compressed air in the cells to the strength of the closed-cell foams. Zhou and Mayer also suggested that air trapped inside the honeycomb cells could be the main contributor to the increased crush strength. It is essential to establish the dynamic enhancement of honeycomb materials in order to gain an understanding of their behavior in the use of energy-absorbing designs. There is, however, no conclusive research that has been conducted to demystify this assertion. The results from experiments are insufficient, and some tests present results that are incompatible. The mechanisms of dynamic enhancement of honeycomb materials remain unclear, and the existing explanations are more or less dependent on assumptions rather than on experimental observations.
Honeycomb structures are increasingly being utilized in applications where efficiency with high strength ratio to weight is required. These structures comprise two thin face plates separated by core materials, and in most applications, the hexagonal shape is used. The application of sandwich structures consisting of honeycomb core and thin laminated composite face sheets has been prevailed in safety essential objects such as aircraft, transport means, vessels, and pipes of an important safety class due to their stiffness, stability, and weight savings and excellent energy-absorbing properties. In a study by ARL, the effect of the geometry on energy-absorbing material was investigated by applying blast load to the different geometries and pendulum material at a given standoff position. The result was that the flat shape of aluminum foam material transferred more energy to the structure.
The face sheets of honeycomb structures are resistant to almost all applied in-plane loads and bending forces and offer nearly all bending rigidity to the sandwich. To provide the highest strength levels, honeycomb structures are usually made, with the core being over three-quarters of the composite thickness. Various performance levels are attained when the core thickness, thickness, and material type of face sheet of the sandwich are varied according to desired outcomes.
Scientific tests do the characterization of honeycomb materials. The determination of the honeycomb material under crushing loads and the measurement of the plastic fracture limits is usually carried out by conducting compressional tests. The honeycomb is the weakest of the composite sandwich structure and often fails due to shear forces. The mechanical behavior of honeycomb structures depends on the loading rate. If static loading is carried out, the structure can have a tensile behavior, but in case of impact loading, the structure may behave in a brittle manner and fail catastrophically. It is, therefore, essential to forecast the impact behavior and collect data on the impact resistance of materials. Such structures should be designed to withstand static, and fatigue loads and as well be capable of maximum energy absorption in case of an impact. Energy absorption capabilities of honeycomb materials under impact are closely linked to core crushing. Crushing of the core is a complex mechanical phenomenon characterized by the appearance of numerous folds and failures in the hexagon structure.
In-pane deformation
Gibson and Ashby (1997), report that both elastomeric, elastic-plastic, and elastic-brittle honeycomb materials have similar shapes, but for different purposes. Under compressive forces, they all exhibit a linear elastic regime succeeded by somehow constant stress, which leads to a final regime of drastically increasing stress. Each of the above regimes is associated with a mechanism of deformation that can be identified by loading and photographing model honeycombs. The cell walls of the honeycombs upon first loading undergo bending resulting in linear elasticity provided that the cell wall material is linear-elastic. When a critical stress level is attained, the cells start to collapse. In elastomeric materials, however, failure is reached by elastic buckling of cell walls, which can be recovered. For materials that are elastic-plastic, failure is reached by the formation of plastic hinges at the point of the highest moment in the bent cells.
In contrast, for materials that are elastic brittle, collapse is attained by brittle fracture of the cell walls. Failure in the elastic-plastic and elastic-brittle materials is permanent and cannot be recovered. When the strain reaches its peak, the cells collapse sufficiently to the extent that the opposite sides of the cell walls come into contact, and any further compression breaks the cell walls themselves.
By increasing the relative density of the honeycombs, the relative thickness of the cell walls also increases. The ability of the cells to resist the cell wall rises, resulting in a higher modulus and plateau stress. Under tension force, the cell walls bend first, resulting in linear-elastic deformation as in compression. The difference is that in tension, the honeycomb does not buckle, but instead, the cell walls rotate towards the tensile axis, and the stiffness rises. Elastic-plastic honeycombs exhibit the same behavior as in compression while elastic-brittle fail abruptly under tension, at stress level below the crushing strength. Honeycombs made of metals and many other polymers are elastic-plastic and therefore collapse plastically when the pressure on the cell walls reaches its peak.
Until recently, there has been a growing interest in developing high-performance lighter materials to be used in energy-absorbing functions, such as structures subjected to localized impact, crash, and blast loading. A number of the studies have concentrated on using sandwich panels dependent on low-density core materials such as aluminum honeycombs, polymer foams, and fold core material. Airoldi et al. conducted a study on the crushing response of honeycomb cores based on a chiral design. The study revealed that chiral models present high-energy absorbing applications. However, the high cost of manufacturing these materials present a big challenge.
Honeycomb materials have high energy-absorbing properties, and therefore they are useful for the impact protection of structural members. Different configurations of honeycomb materials are developed for various purposes. Analytical models have been developed to establish the energy absorption properties of the regular hexagonal arrangement of honeycombs. There is a need, however, for a parameterized analytical model that can be used to determine the energy absorption properties of different honeycomb shapes. Honeycomb materials exhibit strain-rate effects at impact velocities. They can present high energy absorption under dynamic crush than under quasi-static crush.
Since honeycombs are an essential energy absorption material, many studies have been conducted to study their dynamic mechanical properties and energy absorption capabilities through theoretical analysis numerical simulation and experimental design (Ruan et al. 1999). Designing honeycomb materials based on the structure will greatly improve the uniformity of load and energy absorption efficiency (Gao & Ma,2015). Comparisons of the mechanical characteristics of homogenous and gradient honeycombs reveal that since the elastic wave does not attain equilibrium condition in high-velocity impact crushing, a gradient design where a high-density layer is placed at the impact end and a low-density layer is located at the distal end effectively enhances the energy absorption efficiency of honeycombs and lowers the impact force at the output end. As a result, there have been many new designs of honeycomb structures in which the structural components have been altered to achieve desired results. Comparisons of honeycombs with different composite materials have been conducted and reveal the distinctness of each material. These comparisons have indicated that the arrangement of the structure design of honeycomb materials has the effect of improving their load uniformly, and energy absorption efficiency also improves significantly (Zhang, 2015).
Mechanisms of energy absorption by honeycomb materials
Their characteristic stress-strain response illustrates the high level of energy absorption exhibited by honeycomb structures. Honeycomb materials comprising elastic-plastic materials show a linear elastic region where cell walls either bend or axially compress in response to in-plane compression. Beyond a critical stress level, the cell walls collapse through elastic buckling. A region of plateau stress is then observed as the cell walls fail row by row. Finally, when the void space is eliminated by cell wall collapse, the structure densities and stiffness increase rapidly to approach that of the material in the cell walls.
Energy absorption capacities of honeycomb materials are dependent on the relatively flat, extended region of plateau stress. When critical plateau stress is attained, honeycomb material absorbs enormous amounts of energy at the plateau stress level without exposing an underlying structure to additional compressive stress unless the energy imparted to the honeycomb is large enough to cause densification. The only disadvantage of using honeycomb materials for energy absorption is that energy absorption at the plateau regime requires plastic buckling, meaning the honeycombs must be replaced after a single-use.
Energy absorption of honeycomb material under blast loading
Recent research indicates that flat panels with different honeycomb materials dissipated more energy to a structure when put under blast loading as compared to a structure without energy absorbing material. Under normal circumstances, the honeycomb material should transfer less energy to the structure because it absorbs energy while it collapses plastically. Non-uniform deformation of the energy-absorbing material can increase pressure on the panel, causing kinetic energy to be transferred to the plate. There are scientific models used to simulate the non-uniform dynamic response of the honeycomb structure to blast loading, such as the LS-DYNA model.
Honeycomb structures can be used for energy absorption of blast loads for structural applications. The linear deformation pattern tends to increase the total energy applied to the structure, which in turn increases its final velocity. A considerable reduction in peak acceleration of the structure can be attained, however. This may have some advantages of the honeycomb structure, depending on the particular application of the material.
Deformation mechanisms in honeycomb materials
Numerous studies have been undertaken to establish the mode of deformation I regular honeycombs. The results suggest that the velocity of impact is an essential factor which affects the deformation mode of honeycombs. When the impact velocity increase, the deformation mode of regular honeycombs successively show X-shaped, V-shaped and I-shaped deformation modes. For composite honeycombs, the material is made of layers with different structures. Under low-velocity crushing, the effect of plastic collapse is predominant in the deformation mode, such that the honeycomb layer with low plastic collapse strength is the first one to deform. This is to imply that the in-plane crushing deformation modes of composite honeycombs are dependent on the plastic collapse strength of honeycomb layers, their arrangement, and the velocity of the impact.
Defects in honeycombs
Defects in honeycombs may be as a result of missing or broken cell walls. Gibson and Ashby, (1997), suggest that loss of five percent of the cell walls leads to the reduction in modulus or strength of over thirty percent. Percolation theory postulates that when thirty-five percent of the cell walls are lost from a hexagon network, there occurs a continuous path along the missing cell walls from one edge to the other. So the honeycomb is as good as broken into two parts.
When cell walls are lost, the pattern of failure of the honeycomb structure is also affected. In aluminium honeycombs, for example, the loss of one cell wall results in the failure to begin in the weakened cell and induces strain hardening as the intact cells collapse.
The effects of filling voids within the cells has been undertaken by filling some cells in an aluminum honeycomb with paraffin wax and it reveals that filed cells are stronger than empty cells since failure initiates away from the filled cells so that the initiation of the compressive stress plateau remains unaltered, but some strain hardening takes place at large strains.
Due to the limitations of existing honeycomb materials, new studies have come up with improved honeycomb materials and application in car bumpers, military and athletic helmets are taking shape. The University of Texas has developed a new honeycomb structure capable of withstanding even more impact. The new design is primarily meant to improve safety. The new honeycomb structures use a principle called negative stiffness, and the advantage is that they offer protection against repeated impacts and are thus more durable than other conventional honeycomb structures.
The limitation of the conventional honeycomb structure is the tendency of losing their protective characteristics after one impact. In most of them, collapse is irreversible and hence requires replacements after every other destructive impacts. Negative stiffness honeycomb structures have the ability to bounce back once an impact occurs. The design is such that the cell geometry is such that it is capable of elastic buckling, which offers the honeycomb structures the resilience to recover their energy-absorbing shape and properties after an impact.
Conclusion
Honeycomb materials are essential components of our everyday life, having applications in many sectors, including the automotive, packaging, aircraft, and rail industry, among others. Studying the crushing and energy absorption of graded honeycomb materials and their composite materials is essential for the design of honeycomb panels that would yield desired results in terms of strength and cost. Different honeycomb structures with various composite materials behave differently under similar conditions hence the need to study the unique properties of each material.
This research is based on analyzing the crushing and energy absorption of graded honeycomb materials. The research will use available numerical models to investigate the materials under both quasi-static and dynamic loading. Recognizing that numerous studies have been conducted before on the subject, many have failed to provide substantive explanations for the variations observed in honeycomb materials with graded densities. The research is, therefore, expected to fill the existing gap.
In this research, the influence of the different geometrical configurations of honeycomb graded honeycomb materials will be evaluated, and as such, the behavior of the different honeycomb material under different impact velocities will be analyzed. The paper will, therefore, present an evidence-based crushing and energy absorption of graded honeycomb material properties.
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