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Dr Jim Quinn, Quinn Associates
The design process for composite materials is described and detailed in order to demonstrate the similarities and differences with other materials. Examples are drawn specifically for glass fibre composites but the principles apply equally to the other composite material options.
Introduction
Composites differ from common engineering materials in many ways but perhaps the most important are that they are not isotropic, they lack yield, they have low shear modulus, they have infinite variety and possibly the most profound difference is that the material doesn't exist until the component itself is made.
All of these differences present challenges to the engineer that may seem daunting. But the appropriate use of composite materials can bring profound benefits to an application and may mean the difference between failure and success.
Firstly we will look at the design process for composites and then consider some of the differences in detail and what codes of practice are available to aid the process.
The Design Process
Unlike metals, composite materials are only created at the component manufacturing stage. Thus there is an added dimension to the design process. The materials, the geometry to be produced and the manufacturing process to be used are entirely interrelated.
The design process consists of several iterative stages, which result, hopefully, in the designer reaching a satisfactory solution to his problem. The first stage is to determine the brief. This consists of for example:-
What general shape,
What size,
Quantity,
Performance,
Timescale etc
The creative stage considers the interaction of the materials, the processes and the geometry options. This uses ingenuity, intuition, experience, guesswork and even prejudices. This stage is highly iterative in itself. A particular material may not work with one process but will work with another. Several shapes may be candidates but they each use different materials. This is a melting pot of ideas and options from which candidate solutions appear.
The candidate solutions are then analysed and compared to determine if any are adequate to meet the design requirements.
The design process with composite materials has the advantage that there are a large number of options available to the designer. The reinforcement type and its form produce an infinite variety. Thus stiffness and strength properties can be selected from a range that is comparable with thermoplastic materials to those, which are greater than high performance steel.
Although in principle the design process remains the same, in practice different activities dominate depending whether the design process is primarily 'selective' or whether the intention is to produce an optimum such that the lowest possible cost or weight has been achieved. There are techniques available which allow this to be carried out efficiently.
Selective design requires the same activities but the design brief stipulates or implies a particular area of search. Once a solution has been found very little or no attempt is made to optimise it. This is the case when designing with standard structural elements; Pultruded 'I' beams for example. Particular sizes are available from which to select. This provides rapid economic solutions to common engineering problems. But there is no opportunity to refine or optimise the design.
Composite structural elements are available as standard pultrusion in the form of Box beams, Angles, Channels etc. The properties and performance are known thus allowing structural analysis to be carried out. Hence designs may be made on a selective basis from these 'off-the-shelf' composites.
On the other hand, composites in general and pultrusions in particular may be 'tailor made' for a particular design brief and allowing an optimised design to be achieved.
In the case of optimum design of composites not only is the geometry (shape) designed but also the material itself. Material design and geometry cannot be solved in isolation. Candidate solutions are analysed and compared. The process is iterated until the optimum solution is found.
Classical Analysis using isotropic equations can be used under appropriate circumstances but for complex constructions using multi-layers of differing materials laminate analysis is likely to be required.
Laminate analysis of composite materials is discussed in detail elsewhere. It is a powerful tool for the analysis of composite materials. It allows materials to be modelled consisting of multi-layers of differing fibre reinforcements at any angle. The elastic properties may be predicted and with the application of a failure criterion, the failure can be predicted.
Anisotropic nature
It is relatively straightforward to design with materials that are Isotropic (with same physical properties in all directions) such as steel and aluminium. However complications arise when the material to be designed is anisotropic such as a fibre composite.
For example a composite may consist of unidirectional fibres but with the fibre pointing off axis. If a tensile load is applied to the strip it will stretch as would be expected but it will also deform in shear.
Similarly in the case of a laminate strip reinforced with two layers of unidirectional fibre each offset from the axis by small but opposite angles. When a tensile load is applied to the axis the strip extends but will also twist. The resulting stresses and strains must be determined and this requires the use of laminate analysis methods.
These problems are significantly simplified if the laminate is balanced both in plane and about the neutral axis. Bi-directional reinforcements such as woven fabric can fall into this classification and are defined as orthotropic.
Laminates with random reinforcement such as chopped strand mat can be considered to be isotropic (in plane but not through the thickness).
Yield
Composites do not exhibit a yield zone in their stress/strain response. In practice this means that two components one say in aluminium and one in GRP each designed to do the same job will behave differently when subjected to a severe stress. Take for instance the wheel arch of a car, one made from GRP and the other from aluminium. If these were impacted with a hammer blow one would expect the aluminium to deform and stay deformed. The GRP on the other hand, due to its elasticity would spring back into shape. If it was hit hard enough it would show local damage, star crazing and or delamination, but it would still return to its original shape.
In the design of steel and aluminium elements 'local yielding' is often relied upon to solve certain design problems. For instance steelwork elements that are misalignment generate stress concentrations, this dissipates as the steel is allowed to yield. If the elements were composite, the material would not yield and the stress would remain in place and may result in premature failure. Similarly bolted connections in composites, due to the lack of a yield zone, often require the use of large washers to allow local stresses to be spread more evenly.
Young's Modulus
The design procedure for a steel or aluminium beam would generally consider the strength requirements first. Subsequently the deflection criterion would be checked and usually found to be appropriate. However some composites, notably glass fibre have a significantly lower Young's modulus than steel or aluminium. Consequently the design procedure is concerned initially to ensure that the deflection limits are not exceeded. Once an appropriate design is achieved for deflection requirements the strength requirements are dealt with. This is usually found to be suitable.
The relatively low modulus of glass fibre composites also requires that buckling characteristics be assessed a little more critically than would be the case with a steel component, which have an abundance of stiffness relative to their strength.
Shear
The shear stiffness of composite materials is relatively low. This can give rise to deflections due to shear in beams that are appreciable, and can be of similar magnitude to those due to bending. It is therefore essential to determine the values of these deflections to ensure they are insignificant or that they are taken into account. This is particularly important with deep sections, short spans and hollow sections.
Material Choice
The designer of composite systems has available an extraordinary degree of variety in choice of fibre, fibre geometry, matrix and amount of fibre present. This results in an enormous range of potential properties, which allows optimised, very efficient designs to be created. But that is an expensive operation that would not be cost effective in many mundane applications.
In order to achieve the most effective design the designer has the option to optimise not only the construction but also the shape of the component by, for instance, putting the fibres in the direction of the principal stresses. Thus every design can have a different construction depending on the stresses being applied. For those applications that are mundane the amount of work required would be prohibitive. Choosing between the two design approaches that are available alleviates this problem. It can be a selective process by the use of prescriptive design codes or it can be an analytical process and thus allow an optimum solution to be determined.
Design Codes
Design codes are of paramount importance to cost effective design. They provide a level playing field for the tendering process. Also the cost of producing the design is considerably reduced.
There is no widely accepted structural design standard for composites, but the Eurocomp Design Standard provides some useful information, albeit not all validated or calibrated.
Limit State Framework
The design of composites is best based on a Limit State framework:
where S is a destabilising load effect such as a stress, xLi are the load variables, g FLi are the associated partial safety factors, R is the structure resistance, xGi the geometric variables, xMithe material variables, and g mi the material partial safety factors.
Ultimate Limits States include fibre rupture, global delamination, and global buckling leading to loss of equilibrium of the structure and collapse. Serviceability limit states include deflection limits, vibration limits, strain limits to avoid initial damage, local buckling, and localised impact damage. Durability limit states include fatigue failure and creep rupture. Accidental load conditions include fire and impact.
The partial material factor g m should be built up from a factor to take into account the statistical variability of the material property, and factors to take into account hygrothermal conditions and creep/age:
In the above:
g V is the partial factor taking material variability and probability of failure into account. It is equivalent to g m in other structural codes and is determined by the variability of the constituent materials and of the manufacturing process.
g E is an environmental factor taking into account the influence of short-term hygrothermal conditions
g t is a time-dependent factor taking into account creep and age-dependent damage
The resulting partial material factor at ULS for e-glass composites will typically be in the range of 2.0 to 4.0.
Generally, loads and partial load factors gFL as specified in Limit State codes of practice for conventional construction materials would also be applicable to structures in composite materials. It must be borne in mind, however, that live loads represent a significantly greater proportion of the total design load due to the low self weight of FRP. Furthermore, the duration of the live load needs to be assessed in order to allow the time dependent behaviour of the structure to be predicted.
Methods of Modelling and Analysis
Composite components and structures may be analysed using standard methods of structural analysis but these need to be extended to take into account material anisotropy and through thickness lamination. The following points should be noted:
1) Laminates should be modelled as anisotropic or layered plates or shells.
2) Linear elastic material behaviour should generally be assumed
3) Shear deformations should be taken into account, particularly in the case of sandwich panels
4) Large deflection analysis may be necessary depending on the slenderness of the structure
5) Stress concentrations should be taken into account.
6) Time-dependent creep effects should be taken into account
7) Hygrothermal effects should be taken into account
Statically determinate structures may be analysed by the usual methods of structural analysis. Statically indeterminate structures should be analysed by finite element analysis.
Some finite element packages support modelling composites as layered shells in which the stacking sequence is specified as a section property. In most practical applications it is however sufficient to precalculate laminate properties by laminate analysis and assign the resulting rigidity matrix to the shell or plate elements.
In the calculation of sectional strength, plastic stress redistribution may not be assumed, therefore formulae taken from steel codes for compact sections in terms of plastic moduli etc. should not be used.
Design Guidelines
When predicting the buckling strength or deflection of an element, an appropriate gm value should be applied to the Young's modulus of the material, taking into account environmental factors, creep and age.
When checking laminates for strength, the multi-axial stress state should be taken into account, using a multiaxial failure criterion such as the Tsai-Hill criterion or the tensor polynomial criterion. It should be noted that the strength of composites varies according to direction and whether the stress is tensile or compressive. The Tsai Hill criterion is: 
The ratios of shear strength and compressive strength to principal tensile strength are considerably less for most orthotropic composite laminates than for steel or aluminium plate. The interlaminar shear strength of composites is likewise considerably less in relation to principal tensile strength. Therefore careful attention should be paid to Limit States involving these properties.
The buckling strength of laminates can be low and should be checked early in the design process. The buckling strength of an orthotropic laminate is a function of all the moduli. For example, for a rectangular plate of width b supported along its edges the critical buckling stress resultant may be estimated by: 
where Dij are the flexural rigidity coefficients of the plate, taking into account creep. These can be calculated using standard laminate analysis.
When checking the strength of structural details where stress concentrations are present, such as pinned connections, bonded connections, sections at ply drop-off, etc., material strength properties specific to the geometry of the detail may be necessary. For delamination and adhesion Limit States, a fracture energy release rate based failure criterion is frequently preferable to a limiting stress based criterion.
Conclusion
Thus a set of rules has been developed over the years to allow the designer to produce appropriate designs, which will be cost effective and appropriate to the circumstances.
The design process is not simple nor is it too expensive. Therefore design evaluations can be made that consider the use of composites as competitive materials against the common engineering materials. If it appears daunting bear in mind that designers happily work with timber, the most traditional engineering material and which is a natural composite.
Further reading
Clarke J L. "Structural design of Polymer Composites" Eurocomp Design Code and Handbook. Published E & F Spon 1996.
Quinn J A. Composites - Design Manual, 2nd Edition, James Quinn Associates Ltd, Liverpool, 1998.
R M Jones. Mechanics of Composite Materials, 2nd Edition, Taylor and Francis, 1998.
Eckold G. Design and Manufacture of Composite Structures. Woodhead Publishing Ltd, Cambridge, 1994.
Hollaway L and Head P R. Advanced Polymer composites and Polymers in Infrastructure, Elsevier, 2001. |