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ASPECTS OF DESIGN

When reviewing initial component feasibility or undertaking a scoping exercise on a design it is often the case that considerations can be limited to the major elements of the system - typically beams, plates or shells of various forms and sizes. Applied loadings and environmental conditions are also commonly considered differently in the stages of design. Initially the major loads such as tension, torque and pressure are employed to assess an overall laminate construction. Global estimates of weight, stiffness and strength can usually be made of sufficient accuracy to allow judgements to be made as to whether or not to proceed to the next phase of the product development programme. In the next design step an altogether different level of detail must be accommodated. For example, individual elements must be joined together not only to achieve physical connection, but also to ensure efficient load transfer from one part to another, perturbations in applied stress fields due to the effects of free edges and discontinuities need to be minimised and account must be taken of fabrication-induced influences. At this point more rigour is also applied to evaluation of the operating environment. Interactions between mechanical loads, cyclic stresses and transients such as impact events or temperature excursions may all feature in the assessment. Additionally, permutations in materials of construction, e.g. hybrid combinations and sandwich structures, may need to be considered to achieve a higher level of structural optimisation. Inevitably the boundaries between the different levels of design will not be well defined and certainly the conclusions made in the early stages will need to be revisited in the context of the results of the more detailed study. This is especially the case with composites as the most efficient engineering solutions are usually those where all requirements are fully integrated within the design. Of course, the ideal situation would be one where all of these issues are addressed at the outset, but the economics of component development usually dictate a staged approach. It falls on the experience of the engineer, therefore, to attempt to ensure that the initial design basis is sufficiently robust to take into account aspects of performance which will arise should the programme continue to proceed. If you wish to learn more about how to design your structure using composite materials then visit the VIRCON site. 

• Jointing
• Adhesive bonding
• Mechanical fastening
• Welding
• Impact
• Free edge effects
• Hybrid composites
• Sandwich Panels
• Environmental effects

Jointing

Ideally, load-bearing structures would be designed without joints or connections, eliminating a source of added weight, complexity and weakness. In reality this is seldom possible for a number of technical, commercial or practical reasons such as size restrictions during moulding, requirements for disassembly for transportation, inspection or repair, and the inclusion of structural fittings or bearings, all of which may be called for in the component design. The main purpose of a structural jointing configuration is to transfer load from one component to another. As consequence there is likely to be a complex stress distribution in the joint region as well as in the joining feature itself and an objective of a given design will be to minimise stress concentrations arising in order to enhance structural efficiency. This is especially true with composites as they are often associated with a weight-saving concept, and also rapid variations in stress tend to cause significant through-thickness tensile stresses which can cause failure due to low strengths in these directions. Primary methods of attachment for composite materials are mechanical fastening, adhesive bonding or some combination of these.

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Adhesive bonding

Adhesive bonding offers potential advantages over other fastening methods such as riveting or bolting as it does not reduce the adherend strength and is efficient in terms of low weight and increased stiffness. This is particularly true in the case of thin structural systems. However, the need for careful design and surface preparation, and the effects of low composite transverse strength and moisture degradation of the substrate/adhesive interface can limit their use in specific areas. Typical advantages of bonding include:

• Ability to join thin sheets and dissimilar materials.
• Improved structural efficiency, often with fewer pieces.
• Superior fatigue performance compared with bolted construction.
• Smooth external appearance.
• Sealant behaviour between dissimilar adherends thus reducing electrochemical corrosion and moisture ingress.
• Good damping characteristics.
• Avoidance of bolt holes which act as severe stress concentrators.

The figure below shows a number of basic joint configurations.

Basic joint configurations

The purpose of an adhesive is to join surfaces together, using a mixture of chemical and physical bonds, and to transmit structural loads without separation. Modern structural adhesives are generally composed of mixtures of several different polymers, each of which are added to satisfy certain fabrication conditions or to improve properties required in the final joint. Toughness is one property where the design of the adhesive system, often on the molecular scale, can be effective in achieving enhanced behaviour. The base resin is commonly an epoxide, an acrylic or a polyurethane, but they can be blended with a variety of constituents to improve processing or in-service performance. Generally, the stronger adhesives solidify by chemical reaction whereas weaker adhesives rely on some physical change or natural surface tackiness. New formulations and applications are constantly in demand, and since there is not yet a universal adhesive, it is difficult to be fully acquainted with new developments and the detailed aspects of adhesive selection and joint design. Recently, information on adhesives and selection procedures has been compiled either in a desktop database or as a computer-based expert system.

Most surfaces need to be cleaned before adhesive application, structural bonds and metals usually require chemical pretreatments. Metals, for example, require surface preparation to ensure that the metal oxide is firmly attached and its morphology is suitable for bonding. Joint durability in the long term is critically dependent on surface condition even though initial joint strengths with untreated surfaces may be satisfactory. This is due to the damaging effects of moisture attacking the interface and is exacerbated by combinations of high stress levels and elevated temperature. The uncured adhesive should be capable of spreading freely over the surface to ensure good wetting and to displace entrapped air and any residual traces of contaminants. Pretreatments for composite materials usually involve manual abrasion or dry alumina grit blasting to remove traces of release agent.

The distribution of stresses within an adhesive bond subjected to tensile or shear loads is uneven along the bond length and has a marked stress concentration at the ends of the joint overlap. The figure below shows the deformations and stress distributions for a single lap joint subjected to a simple tensile load. (Note that calculated stress distributions are approximate and are derived from a simple analysis - for example, shear stresses at the free edge must be zero, but this is not indicated by the calculation method.)

Deformations and simplified stress distributions for a single lap joint

Both the shear and peel stresses are important in the context of design. As the joint length reduces, so does the length of bond area in the centre which is at zero stress. For very short joints the stress distribution can be considered to be effectively constant along the length. The effect of stress peaks at joint edges can be made more severe for dissimilar adherends where the stiffness change can influence the distribution of load. The figure below shows a typical design case, in this case the shear strain distribution in a coaxial CFRP/ steel joint subjected to a torsional load.

Strain distribution for a CFRP/ steel joint in torsion

Calculations of these stresses - either by finite element analysis or by classical analysis based on continuum mechanics - is essential in design to ensure that all of the key stress values are identified. Generally, analysis by either of these techniques should be capable of taking into account factors such as non-linearity of the adhesive, orthotropic adherends, shear deflection in the composite, thermal stresses and changing geometrical parameters. In order to modify the nature of the stress or strain distribution to suit design criteria, a number of simple guidelines can be applied. For example, increasing the adhesive thickness reduces the peak strains and flattens the strain distribution for a CFRP/steel joint subject to a torsional load. profile of the strain distribution. Conversely, decreasing the adhesive thickness increases maximum strains. Increasing the length of the joint will reduce the strains due to mechanical loads; however, this reduction will only occur until the strains in the centre of the joint reach a minimum, after which there is little worthwhile reduction. In some cases strains due to thermal mismatch between the adherends can be an important factor and these tend to become more significant with longer-bond lengths. To reduce the very high stress concentrations at the edges of the joint a more compliant adhesive can be used. If the adherend properties, applied loads and joint geometry remain constant then peak stresses or strains within the joint can be controlled to a certain extent through careful selection of adhesive modulus.

Validation of predictive models can be performed by experimental stress analysis. Laser Moiré Interferometry (LMI) is a powerful technique which can be applied to joints as a means of producing a full field strain map of the adhesive layer and adherends. The figure below shows Moiré displacement fringes for a thick lap shear test joint under increasing loads.

Average peel strains across the adhesive thickness and along the bond length can be readily calculated from fringe displacement. The peel strains are compressive in the central region and become tensile near the ends of the overlap. At 3,000 N the fringes are continuous over the whole bonded region. The peel strain concentration at the cut-out can be clearly seen. At loads greater than 4,000 N small interfacial cracks are observed growing from the cut-outs and extend with increasing load. Plastic deformation is also observed in the steel adherend adjacent to the cut-out. The geometry of the adherends can have a dramatic effect on joint performance, not only affecting the stresses within the parent substrates but also the method of load transfer. The figures below show different types of joint, together with the corresponding stress distributions.

Adhesive shear stress distribution - profiled joint

Adhesive shear stress distribution - stepped joint

Adhesive shear stress distribution - double joint

These joints are of tubular form with different geometries of end fitting. Each type of joint has its own characteristics and the selection of one configuration in preference to another depends on the requirements of each particular design case.

With the wide number of options available it is important to specify what type of joint would represent an optimum design. The aim of an optimisation procedure is to arrive at a design which is most effective in terms of weight, material utilisation, ease of manufacture and cost, whilst fully satisfying operating requirements. It is governed by the load case under consideration and the way in which the stress distribution varies with design variables. In an adhesive joint, different criteria may apply, depending oil whether the loading is static, short term, creep or fatigue.

Possible design criteria for a short-term static load could be:

• The maximum adhesive strain must not exceed the strain to failure for the adhesive.
• The overlap length should be as small as possible for structural efficiency.
• The strain should ideally be constant across the whole joint length so as to make best use of the adhesive area.
• The maximum strain in the joint should not be sensitive to small changes in joint length.

In the application of such criteria the starting point would be to assume the adhesive layer thickness is initially set to the maximum allowable value to obtain a constant strain distribution. A minimum value of joint length to support the applied load would then be calculated by assuming that the average stress in the joint is at the elastic limit for the adhesive.

For a fatigue load a different approach should be adopted. Here a region of low stress within the joint would be desirable to allow some scope for redistribution of peak stresses during cyclic loading. At the joint edges the maximum adhesive strain must not exceed the allowable strain for the adhesive. What constitutes a maximum adhesive strain would need to be derived by experience but, for example, an exponential law based upon the failure strain, elastic strain limit and the number of cycles could be used. Again, quantification of the extent of the desired low stress area would need to be the subject of some consideration, but a basis along the lines that more than 50% of the joint length should be stressed below 10% of the elastic limit for the adhesive could be established. In the calculation the first step would be to set the thickness of the adhesive to a minimum value so as to maximise the unstressed region in the joint. A minimum value of joint length to support the applied load would then be calculated by assuming that the average stress in the joint was at the elastic limit for the adhesive. An initial stress analysis would be carried out with a joint length several times the minimum value. If the resultant maximum shear strain was greater than the allowable strain, then the adhesive thickness would be increased progressively until the maximum strain falls below the allowable strain, or until the maximum adhesive thickness is reached. If the strain falls below the allowable value, then the adhesive thickness is fixed and the length of the joint is altered to ensure that the required unstressed length of joint is obtained. The figure below compares the strain distributions for the static and fatigue criteria.

Possible criteria for design optimisation

The procedures described provide a means of determining optimum values for bond line thickness and overlap length. Clearly, to define the engineering details of the joint completely there are many more aspects of the arrangement that need to be considered. The figure below shows a joint between a composite (glass fibre/carbon fibre hybrid) driveshaft and a metal end fitting.

Profiled end fitting design for hybrid composite/ aluminium shaft

The figure below shows the associated strain distribution compared with a reference design that consists of a simple plain ended plug fitting.

Calculated strain distribution for hybrid shaft

Profiling the end fitting reduces strain concentrations significantly. In this case the analysis is nonlinear, and this reduction in strain at working load would not proportionally result in the same increase in maximum strength. In fact, an increase in strength of approximately 50% would be predicted for these designs. However, reduction in strain levels at working load would give a significant improvement on fatigue life. The effect of increasing bondline thickness locally at the edge is beneficial, but it is interesting to note that an optimum amount of thickening can be observed from the analysis. The figure below shows the effect of an increase in bondline thickness.

Effect of variation of bondline opening on peak shear strain

Attention to details of the design such as adherend geometry can pay dividends in terms of component performance in both the short and long term.

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Mechanical fastening

Mechanically fastened joints have the advantages of ease of assembly and disassembly, and of little or no preparation of surfaces; they also often exhibit good properties in thermal cycling or high humidity conditions. Their main disadvantages - increased weight, stress concentrations and low joint stiffness often render them unfavourable for highly stressed, thin composite skins where bonding tends to be preferred. This is usually more effective at joining relatively thick sections of materials as loads can be transferred through the laminate thickness. Failure of mechanically fastened joints can occur in a number of ways, including tensile, shear-out or bearing modes, and in varying degrees of magnitude from resin cracking to complete failure. Bolted connections are most commonly used, although in some designs which are comparatively lightly loaded, other types of fasteners, such as screws, rivets and bolts can be used. Because of high stress concentrations associated with thread fortes, etc., this type of connection can significantly weaken the surrounding composite. The figure below shows the stress distributions around a pin-loaded hole.

Typical in-plane stress distribution around a pin-loaded hole

The maximum bearing stresses for pin-loaded holes vary around the circumference, reaching a maximum value in the direction of load transfer. This maximum stress tends to become larger as the clearance in the pin fit is increased and therefore a good fit can improve the bearing strength considerably. Drilled and reamed holes perform better than moulded holes, probably because in the latter case the fibres are not evenly distributed and leave resin-rich regions adjacent to the opening. The maximum bearing stress for a pin-loaded hole is reduced if the diameter to thickness ratio is greater than I. but this does not appear to be true when clamping pressure is present. as is the case with bolted connections. Generally, mechanical fastening is efficient in joining relatively thick composites as the load can be distributed through the laminate thickness. This can be dependent on the laminate construction, for example, the inclusion of [± 45°] plies has been shown to be beneficial. Interference fit fasteners give the best results and where multi-bolt arrays are employed accurate alignment is paramount to ensure load transfer within the bolt configuration is as per expectations. For joints between adherends of uniform thickness there is little advantage in having more than two fasteners in a line as those at the end of a sequence would carry most of the load. The load can be made more uniform if laminate thickness is varied between rows of fasteners. The optimum geometry in terms of pitch number and diameter depends primarily on the properties of the material as the interactions between stress systems around adjacent holes can have adverse effects. In terms of joint performance there are three major stress components around a pin-loaded hole; bearing on the loaded side of the pin, tensile on the net cross-section at the pin position and shear.

Simplistically, average values for these stresses are given by :

                       s_t = P / ( w - d ) t

                       s_b = P / d t

                       s_s = P / 2 e t

where s_t, s_b and s_s are tensile, bearing and shear stresses respectively, w and t are the width and thickness of the plate, e is the length from the bolt hole to the end of the plate, and P is the applied load. From the distributions shown above and these equations it can be seen that joint performance is strongly dependent on geometry. Relatively wide joints will fail in bearing and as width is reduced, the failure mode changes to that of tension. Variations in the value of plate edge/hole distance, e, has an analogous effect. To achieve adequate bearing strength the joint must have sufficient end distance. The figures below show the effect of geometry on calculated bearing stress.

Effect of width on bearing failure stress of single hole joints in CFRP

Effect of width on bearing failure stress of single hole joints in GRP and aramid composites

The plateau regions correspond to those configurations where failure is dominated by bearing. The effect of laminate configuration can also be seen. For very simple laminate orientations the probable failure mode can be deduced intuitively. For example, a unidirectional material loaded parallel to the fibres would be expected to fail in shear whereas for the converse case, where fibres are perpendicular to the load, failure would be in tension. Complex laminates, on the other hand, vary considerably. The figure below shows the influence of fibre orientation on the failure mode of bolted joints in [0/ ± 45°] type laminates.

Influence of fibre orientation on failure mode of bolted joints in [0/ ±45°] CFRP

As the percentage content of the [±45°] plies is increased, the shear strength of the laminate increases and bearing becomes the observed failure mode. An additional increase will cause further change to a tensile mode because of the low laminate strength in tension.

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Welding

Welding processes are not normally associated with the joining of composite materials and it is only with the advent of thermoplastics that the methods have become of interest. Welding has attractions as it is potentially faster and more easily automated than adhesive bonding, while mechanical fasteners do not provide a continuous joint and drilling can be difficult and costly. The welding processes which are potentially available can be divided into two groups:

• Processes involving mechanical, movement -- these include ultrasonic welding, friction welding (spin, angular and orbital) and vibration (linear friction) welding.

• Processes involving external heating- these include hot plate welding, hot gas welding and resistive and inductive implant welding.

Studies on welded structures indicate that for short fibre reinforced systems the techniques produce satisfactory results, but for continuous systems there are significant difficulties. Discontinuity of load transfer and disruption of the fibre arrangement close to the weld are key issues that must be considered.

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Impact

Damage of composite structures through impact events is perhaps one of the most important aspects of behaviour inhibiting widespread application. For ductile systems the materials are able to dissipate the incident kinetic energy through elastic and plastic deformation. Although this may result in some cases to permanent deformation, its effect is often localised. In composites, however, the scope for plastic deformation is limited and the consequences of an impact event can lead to a substantial amount of damage, the influence of which on residual properties is difficult to predict. The variables controlling the events during an impact include material properties, boundary conditions, deformation/ failure mechanisms, environmental factors, imposed constraints and the parameters defining the impact event itself.

During an impact, a stress field is established on contact. A series of stress waves is then propagated through the thickness of the material which may or may not cause damage. In order to provide an understanding of the phenomena concerned, consider an elementary one-dimensional model. For an incident compressive wave of magnitude s_m with pulse length l (see figure below), the wave will be reflected from the free surface with a net tensile stress s_t, defined by:

s_t = s_m - s_i

where s_i, is the compression incident stress at the same point as the leading edge of the reflected wave. If s_m. > s_f where s_f is the tensile failure stress there will be some position where failure occurs.

At this instant:

s_f = s_m = s_i

Net stress for reflection of load pulse at various times

It can be shown from geometry that the position of failure, t₁ measured from the free surface is given by:

Therefore, if s_m = s_f  failure occurs at l/2 from the free surface and s_m < s_f  no fracture will occur and if s_m > s_f   multiple fractures may occur. In this latter case with the aftermath of each failure there will be a new wave and a new free surface. Further analysis shows:

where l_n =  l_n-1 -  2 t _n-1 and s_m,n = s_i at the instant of the (n-1)^th failure and n denotes the number of failures which for a given wave will be :

n = s_m / s_f

Such an analysis can only be considered as qualitative but it does allow an appreciation of the phenomena involved during impact. For example, it can readily be seen how the result of an impact can manifest itself. With the application of load the dynamic stress system which is established which may result in damage propagation at a number of sites within the thickness of the material. Composites with their low transverse tensile strength can be prone to this type of effect. In the case of carbon composites which are opaque the damage may not be apparent without the application of a sophisticated inspection method. Such barely visible damage is a major design issue. The first stage in an attempt to provide a quantitative assessment is to derive relationships for the contacting force and resulting stress distribution for an impact event. Proceeding, using a simple analysis which ignores system vibrations, to consider the contact between a stationary semi-infinite target and an impactor gives expressions for the rates of change of velocity during impact :

where m₁ and v₁ are the mass and velocity of the target and m₂ and v₂ those for the projectile (see figure below).

Pressure distribution due to impact

The assumption regarding system vibrations must only be regarded as approximate, but it provides a useful starting point which can be justified if the contact times are long in comparison with vibration periods.

The internal stresses for a solid subjected to a surface pressure caused by impact is shown below :

The position of maximum stress during impact is :

The figure below gives distributions of stresses for quasi-isotropic lay-ups. The values shown are normal and radial compressive stresses which arise as a result of an impact-induced surface pressure.

Stress distributions for quasi-isotropic GRP plate subjected to impact

Shear failure is one of the dominant modes of failure, followed by compression. In the latter case damage would take the form of local crushing. A point to note is the relative superiority of glass reinforced systems over carbon reinforced materials. The extent of the damage zone can also be assessed as a function of surface pressure. The figure below shows damage area for a CFRP material with increasing surface pressure.

Propagation of damage zone in CFRP with increasing surface pressure

Failure is initiated as the point of contact and thereafter grows with increasing pressure. A somewhat different response occurs if the composite target is relatively flexible. In addition to contact forces the material will undergo bending deformation, the significance of which will be related to structural parameters such as stiffness and edge boundary conditions. The effect of the bending stress will be additive to the stress due to surface pressure and this could change both the position of damage initiation and its subsequent progression. The figure below shows an example of a relatively thin plate where the bending is sufficiently great to cause tensile failure on the opposite surface to where pressure is applied.

Damage zone for an impacted plate structure

Further damage develops from this area and eventually propagates through the full thickness. Conventional failure criteria for composites do not address all of the aspects of behaviour encountered in an impact. Both the different types of mode of failure and the dynamics of the situation need to be accommodated in the analysis.

Computer codes which can accommodate the complexities of the calculations are becoming available and these need to be linked to the type of failure criterion which is appropriate to impact. The figure below shows the results of such a dynamic calculation where the interactions of the projectile and plate are simulated explicitly, together with the dynamic response of the specimen.

Comparison of measured and calculated delamination areas for [0/90] CFRP

In this case penetration of the plate is predicted.

During an impact event there are a large number of possible damage mechanisms. Each has a range of characteristics and affects the properties of the composite in different ways. Damage modes include :

• delamination

• multiple matrix microcracking

• compression damage/ crushing

• transverse splitting

• debonding

• fibre pull-out

• fibre breakage

Energy absorption is a parameter which is often used to describe impact-type events. As a rule those modes that involve matrix or interphase failure absorb much less energy than those concerned with fibre fracture or pull-out. Fibres are the dominant constituent when considering most property characteristics and the same is true when assessing impact performance. For low velocity impact the stored energy capability of the fibre is of key importance. As a result materials such as aramids, and to a lesser extent glass, which have large areas under their stress/strain curves, offer relatively good performance. Composites made from these materials tend to fail in a progressive manner through delamination. Carbon fibre systems, on the other hand, can be brittle and fail catastrophically at the maximum load.

Of interest to designers of composite structures is the concept of residual strength, the load-carrying capability after an impact event. Such a value is often used as a means of quantifying material behaviour. Care must be taken in using this criterion in isolation. as, although impact resistance of certain materials may be good and therefore relative reductions in strength low, this may not be too helpful in design as high extensibility fibres tend to have low mechanical properties in the first instance. This can be overcome by the use of hybrid materials where the attributes of each constituent are used. A further consequence of impact can be the initiation of modes of failure which would not occur in an undamaged laminate. The effects of compressive load, for example, can be particularly damaging as any delamination could seriously affect elastic stability.

Matrix properties are, of course, a key consideration for impact performance. Not only do they provide the mechanism of load transfer into the fibres, but if damaged during the impact the resulting cracks could allow ingress of moisture, etc., which could then cause degradation. The figure below shows the relationship between the impact resistance of a composite, measured as residual compression strength, as a function of resin strain to failure.

Variation of residual compression strength with resin failure strain

It is possible to derive a rule of thumb as to the effect of constituent properties. Because of the importance of impact there have been a number of attempts to improve the energy-absorbing characteristics of matrix materials. These have included the use of plasticisers, the addition of rubber or thermoplastic particles, control of cross-link density (the lower the density of cross-links, the more flexible the resin), the use of thermoplastic matrices and the use of interlayers within plies. Although improvements can be achieved (see figure below), in most cases the enhanced resin toughness is not wholly transferred to the composite.

Effect of resin toughness on residual compressive strength

The properties of the interface are also important, but perhaps more difficult to control given a preselected matrix/ fibre combination. For weak interfaces failure is generally through large areas of delamination. This can be used to advantage if containment of projectiles or debris is important. If residual strength is the more important criterion, an interface region of greater strength would be preferred where damage is more localised in nature. Laminate construction and orientation can be an important factor in the design for impact performance. Simple unidirectional materials do not perform particularly well, primarily because of the high stresses generated transverse to the fibre direction. Also the tendency for delamination is increased where the disposition of individual plies leads to large discontinuities in stiffness. Adopting woven materials or three-dimensional stitched fabrics, which tend to promote increased through-thickness tensile strength, can be used to good effect (see figure below).

Effect of woven material on impact performance

For a number of applications, particularly in the transport industry, the control of energy absorption under impact conditions is an important design feature. In metal structures this is often done by making use of the work done during plastic deformation. The simplest structural form where use is made of this effect is the inverted cylinder. Here a thin walled tube is punched on to a radiused die to achieve either internal or external inversion (see below), and an approximately linear energy absorption characteristic is obtained.

External inversion of a metal tube

Load-shortening curve for external inversion of aluminium tube

Such devices are used for collapsible steering wheels, seat anchors and landing dampers. In composites there is little or no scope for gross plastic deformation of this nature, although there are considerable opportunities for energy absorption. This arises through the promotion of fibre/matrix debonding over the large surface area of interface. The key to achieving a high level of impact absorption is to design the component such that as great a volume of material as possible becomes involved in the failure process. For example, in a simple composite tubular structure under compression failure by simple fracture in the central region of the cylinder is likely. The figure below shows the force displacement plot for such an event and, as can be seen, although the initial peak force is high, the overall area absorbed is small.

Force displacement curves for composite cylinders

By providing a chamfer to the edges of the cylinder, however, a different mode of failure can be initiated. The high stress levels in the chamfered regions result in local crushing and this can then propagate through the tube as a crush zone. The force displacement curve for this mechanism is also shown above. Although the initial failure load is lower than that for the plane tube, energy-absorbing characteristics are much more attractive. The figure below shows a schematic representation of the types of crush mechanism which can be obtained.

Schematic representation of possible crush mechanisms

The details of these vary according to material properties and geometrical arrangements. Expressing energy absorption in a specific sense, i.e. area under the force displacement curve divided by material density, is a useful means of ranking materials especially if weight is an important feature of the design. The Table below shows specific energy absorption for tubular structures for a number of materials.

On this basis, the composite options compare well; however, it should be noted that these values are only realised if crushing mechanisms such as those shown above can be achieved.

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