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Throughout history the concept of the bicycle has been used and manipulated with materials from all over the spectrum exercised. In recent years, machining methods have become advanced enough to manipulate all different grades of metals, from the most popular being steel, to alloying titanium based alloys, however not only metal materials are being used. Carbon fibre, a generic term of the composition of carbon fibre weave and epoxy resin, is the world’s most recent popular material to be used on practically everything in the automotive industry, from gear knobs to the complete chassis on the Porsche Carrera GT for example, which is slowly expanding into the bicycle market and beyond. Nowadays bicycle manufacturers have an apparent unlimited array of materials, joining processes and finishing techniques, which should theoretically be able to produce the “best” bicycle frame on the market. Taking modern day complications into account, the “best” bicycle frame material(s) are perhaps inappropriate in terms of manufacturing price and market sale value. Despite this, using Cambridge Engineering Selector (CES Software), by setting up engineering constraints, looking at material selection indices and loading patterns on components; a single “best” material is to be determined.
As not all bicycles are aimed at the same user market, with the intention to design a bike for different purposes such as; mountain bikes, city bikes, leisure bikes, road bikes, race bikes, etc. the constraints and objectives of how the bicycle frame should react under pressure during use are different. It is because of this, the “best” material can differ from bicycle type, and therefore a category of bike must be specified.
The bicycle category to be specified is a small sub-category of road bikes called fixed gear bikes or “fixies”. This category of bike has recently sprung up all over the world, with its major uprising leading back to Brooklyn, New York; however a cult following has arisen in major cities around the globe. This type of bike and cycling style lends its origins back to track racing, where the same style of bike is used in the Olympics and other bike sporting events. The fixie style has become popular on the road for its agility and acceleration around town for commuting as well as its fitness affiliation for of course only having one gear. This sub category of bike is often used for part recreation, part fitness use, yet mainly as a means of transport in and around town.
This recent uprising has uncovered many different materials of bike frame, from old 1980’s track bikes made from steel to recently manufactured aluminium and carbon fibre composite frames which are used on this type of bike and style of riding.
Materials Selection Possible Constraints
The frame components will be subject to different forces, of which several will experience the same force depending on different loading conditions. The seat tube will experience constant compression forces from the weight of the rider as well reactions from road pushing back up towards the rider, whereas the down tube will experience tensional forces holding the crank area together with the fork assembly; however braking will give rise to compression. Other features such as the seat stays will experience constant compression and lateral stress from the braking mechanisms, of which stiffness is a vital property of the material. Young’s modulus or stiffness is also very important in the design of the forks due to instantaneous braking encouraging the forks to bend.
The density of the material will affect highly the efficiency and feel of the bike when ridden. More energy is required to brake or accelerate the bike that has a high density frame, consequently making the bike hard to control and manoeuvre. A lightweight material is vital to create the ideal bicycle frame to improve manoeuvrability, braking and acceleration performance. This is why a constraint of density is to be limited at 5000 KG/M^3. This encompasses common frame materials such as aluminium and titanium alloys. 
The stiffness of the frame is vital to prevent plastic deformation of the frame when ridden over obstacles, however if the frame is too stiff there will too much vibration from road surfaces. A constraint of materials above 30GPa are acceptable for the intended use, however materials above 400GPa are considered too stiff and will result in a harsh incontrollable bicycle. 
Tensile and Compressive Stress
Tensile stress occurs on many of the components of the bicycle frame and is a common failing property by overloading the frame which consequently makes it a high priority factor. Materials above of tensile stress value 300MPa and above are acceptable. Compression is also a major stress force abundant in the bicycle frame, in places such as the rear seat stays and seat tube from gravity pulling the weight of the rider toward the ground. Poor compressive forces will translate into a mess of buckled piping. 
The yield strength determines the amount of force required to plastically deform the material of which the material is permanently deformed after yielding. This can be applied to sudden impacts or over loading of the frame which can lead to failure of the frame, perhaps resulting in injury when ridden. The higher the yield strength, the higher force the frame will be able to withstand which is favourable in frame design. 
Elongation relates to brittle and ductile properties of a material, where high percentage elongation leads to ductile properties and low percentage elongation leads to brittle properties. If a material is too brittle, it theoretically could fracture into small parts which are to be avoided when cycling. It would be preferable for the material to plastically deform to a large extent before failure as this will prevent injury if a sudden stop is experienced. A material with a very high percentage elongation is also to be avoided as the frame will not keep its shape and deform with the weight of the rider. Materials below 40% elongation will provide favourable elongation properties. 
The maximum cyclical stresses can be examined and applied to a bicycle frame directly, mimicking the repetitive stresses when ridden. This can therefore extrapolate the life of the bicycle frame given the amount of repetitive load applied when ridden. 
Torsion loading occurs upon acceleration of the bicycle where the frame is moved from side to side under the lateral forces applied by the rider from the torque applied. The usual lateral loading on the frame is transferred to slight longitudinal loading. The torsion capabilities of the material must be taken into account which also highly affects the joining processes of the bicycle frame. 
Material Objectives Set-up and Index Selection
To find the “best” material for a fixed gear bike frame, the main objective is to prioritise engineering performance; reducing weight, increasing stiffness. The agility of the frame is the main characteristic of which turning reactions, acceleration and deceleration performance are vital to a successful fixed gear bike to be used in and around town as well as for training purposes.
The indices used to input into CES will define stiffness-limited design at minimum mass.
The frame features that are tensile loaded, creating a tie between two other frame beams will use the index Young’s Modulus / Density, E/ Ï. Increasing this index will locate suitable materials that exert stiffness, combined with low density, however also giving the best tensile properties.
The compression index, for components loaded in compression, is (Young’s Modulus ^ Â½)/Density, E1/2 / Ï will also locate the best materials for that type of loading. For components loaded in bending the index (Young’s Modulus ^ Â½)/Density, E1/2 / Ï, will also be used.
For strength limited design, locating the best material for tensile strength before yielding and plastic deformation of the frame occurs, the index yield strength/density, Ïƒf / Ï, is to be used. Locating the best material for compression strength will also use this index. For the seatstays and fork components, loaded in bending, the index Ïƒf2/3 / Ï will be used.
Maximising these indices will locate the best materials for each specified type of loading. 
Outcomes using CES
Function: Bicycle frame
Constraints: Must not fail under rider weight and road reactions.
Objective: Overall mass of bicycle frame is to be reduced, without sacrificing stiffness and strength.
Variables: Material choice, material section shape, finishing techniques.
Before inputting constraints, the graphs of Young’s Modulus over density and yield strength over density appear as follows using education level 2:
Figure 5. Young’s modulus over density CES.
Figure 6. Yield strength over density. CES.
Inputting the constraints, CES outlines groups of materials that meet the constraints:
Figure 7. Young’s modulus over density using constraints. CES.
Figure 8. Yield strength over density using constraints. CES.
CES software has outlined different materials from the groups: composites, metals and alloys, and technical ceramics. These materials are:
Carbon fibre composites
Silicon based technical ceramics
Aluminium alloys are extremely light and shows signs of high elongation, these factors direct aluminium toward being a good candidate for a bicycle frame, however aluminium has a low young’s modulus value and certain alloys exhibit low tensile strength values. These properties may give the bicycle frame flexibility, however current aluminium bicycle frames are certainly not flexible as they tend to have a larger diameter top tube and general radii over the frame components to counter act this. The fatigue values for aluminium alloys are very low, which indicates that after a while the frame will crack and fail, which is definitely something to avoid. Current bicycle frame manufacturers use butting technology in aluminium frames to combat this, by increasing the thickness of the tube at where the material is needed most. 
Titanium alloys are around double the weight of aluminium alloys, yet around half that density of steel alloys, making up for this are the high tensile strength and Young’s modulus values which enable to frame to be manufactured from thinner tube sections than aluminium which reduce overall weight. The fatigue values are also high which means that the frame will last for a long time. 
Magnesium alloys are even lighter than aluminium alloys and have a slightly better fatigue value. Magnesium alloys also have a low Young’s modulus value, lower than aluminium which indicates flexible frame properties which will have to be yet again solved using tube section thickness design. Magnesium alloys look promising and have good properties that can be applied to a bicycle frame, however they have low corrsosion resistance which has to be overcome by surface treatments. On the current market, few frames have been made from the material as they tend to be very expensive. 
CFRP, Carbon Fibre Re-enforced Plastic
CFRP, a composite material, is lighter than all the metals previously mentioned as well as having high a Young’s modulus, tensile value, and relatively high fatigue strength values. This material is currently being used all over the bicycle market, from strictly track bikes to road racers, complete frames or part CFRP frames, and components used in mountain bike off road frames. The modulus of the epoxy resin is extremely low, resulting in a brittle material; which consequently affects the method of which the CFRP layers are applied. CFRP has good tensile properties, however not very high compression or torsion properties, so the angle at which the carbon fibre layers are applied must be taken into consideration, otherwise turning bends could turn the frame into a fractured mess. This is also evident in the extremely low elongation value, 0.032% – 035% 
Technical Ceramics, Silicon Carbide
Silicon carbide, unlike ceramics in general has a good tensile value similar to that of titanium, aluminium and CFRP, and a young’s modulus value four times that of titanium. This implies that silicon carbide has a positively good outlook on a perspective bicycle frame, displaying high fatigue values and having a slightly lower density than titanium. Silicon carbide does however have a low percentage elongation at 0%  which boasts the potential for producing a hybrid material to increase this value.  
Beryllium is often used as an alloying material to increase hardness properties, however it also has a very high young’s modulus value and is lightweight. Beryllium could not be used to solely manufacture a bicycle frame as it is poisonous, especially with inhalation. 
It is visible to see the groups of materials commonly used on bicycle frames from the graphs produced; however there are not any specific materials shown. Enabling education level 3, the database of materials becomes more specific and materials that do not meet the constraints are ignored. By maximising the indices, individual materials can be identified.
CES software has located Cyanate ester/HM carbon fibre UD composite 0Â° lamina by maximising the indices as the best material for a bicycle frame. The unidirectional lamina allows the tensile and young’s modulus values to be uniform within the material, rather than have a directional flow providing room for failure by torsion. The composition of 30-40% polymer and 60-70% carbon fibre maintains a high level of stiffness and fatigue strength from the carbon fibre and reduces the brittle properties of the polymer resin.
The CES outcome may have located the “best” material for a fixed gear bike frame, with the objective minimise the weight of the overall frame, without sacrificing stiffness and strength, however joining processes, surface treatments/coatings and shapes need to be considered.
Current CFRP frames are either manufactured by using tubular lugs of aluminium or titanium, and then pre-made CFRP tubes aligned and stuck into place with further layered CFRP and epoxy adhesives. The joining between the two different types of materials has led to corrosion and failing, which has directed manufacturers to create frames solely using CFRP. Continuous laminating can be used to cover a mandrel of which the removal of the mandrel gives rise to a shaped tube or hollow section necessary for the specified component. One method used to create low batch numbers of CFRP frames is autoclave moulding, which builds up the CFRP layers by hand, this technique creates a monocoque CFRP shell which has superior stiffness, strength and is extremely lightweight; frames lower than one kilogram have been produced. 
Cyanate ester/HM carbon fibre UD composite 0Â° lamina has a maximum shape factor value for elastic bending (Max Ï•eB) of 12.3. By using this value, the shape efficiency can be compared against other materials determining if other materials exhibit better stiffness and resistance to bending properties.
Using CES a graph can be drawn of Young’s modulus over density with the index Ï /E1/ 2, which will show the maximum bending stiffness whilst reducing weight. As the shape of the material is not fixed, in general materials used for lightweight structural objectives require low Ï/(Ï†eBE)1/2 values. The materials will be selected as they provide the best properties. 
By comparing alloys used frequently in the manufacture of bicycle frames against the CFRP based material CES located, it is possible to see the benefits of firstly the shape factor attributed to aluminium, giving it good structural properties despite its low young’s modulus value. However the lower value of the determined CFRP material means that it has better shape efficiency and will have better in service properties at providing a lightweight stiff bicycle frame, resistant to bending forces.
The titanium, given its stiffness will be able to produce a lighter frame than one made of steel and aluminium, yet does not have a better bending shape factor shown by the aluminium alloy. Magnesium, despite having the lowest modulus has a maximum bending factor lower than the aluminium alloy, which is one of the reasons why it is becoming an increasingly popular base alloy for bicycle frames. 
Hybrid Bicycle Frame
The extreme stiffness of the Cyanate ester/HM carbon fibre UD composite 0Â° lamina bicycle frame will create a very stiff ride, of which the road surface will be felt through the frame to the rider. One way to prevent this is to use larger or thicker tyres, which will reduce vibration, however will significantly increase friction and reduce top speed and acceleration times. A method to reduce these problems would be to develop a frame that utilised a couple of materials and blended them together to give longitudinal damping properties yet maintain the transverse stiffness and lightweight properties. This could be achieved by using titanium on the main triangular frame due to its 5-10% elongation property, extremely high fatigue, tensile and lightweight properties; and using the CFRP on the chain stays, seat stays and fork components for its extremely high shape factor and bending stiffness value. This will also create a high fatigue resistance of the frame making it last for many miles of riding, however problems may occur with the joining of the two materials when using acrylic based or epoxy glues to bond the two sections together as this interferes with the structure and could lead to corrosion or failure from loading. 
A hybrid material could be answer to creating the perfect bike frame using silicon carbide, boron carbide and aluminium, also known as MMC duralcan alloys, or alumina B4C alloys. Alloys using these materials have already been created, making use of silicon and boron carbide’s mechanical properties and combining them with aluminium’s structural advantages.
The aluminium carbide composites exhibit good bending factor values as well as high Young’s modulus values, fatigue strength, tensile strength and very high compressive strength, which makes the material promising for use as a bicycle frame.
Surface treatments such as anodizing are common in today’s current bicycle market, for example on aluminium where the reactive surface is covered with an oxide layer and the thickness controlled using anodizing. This prolongs the life of the frame by reducing the risk of corrosion. Electroplating is also used for corrosion resistance or to improve hardness, this method is usually used on metals; however non-metals can be plated once painted with an electrically conductive material. This can give metals shiny mirror finishes, synthesizing the look of commonly expensive materials such as gold or silver. For metals and non-metals, organic solvent based paints are widely used to give the frame exciting colours and finishes. Organic solvent based paints are usually applied to carbon fibre; however it is sometimes preferred to show the craftsmanship of the carbon fibre in its natural form showing the weave pattern. 
The best materials for a fixed gear road bike come in the form of carbon fibre re-enforced plastics; this is because of the lightweight, high modulus frames they create. The shape factor contributes highly to the success of the material by creating stiff tubular sections that are resistant to bending and plastic deformation also improved by their high yield strength values. The tensile and compression properties shown by the material are very high and work well at absorbing shock, distributing the stress throughout the frame. The orientation of the carbon fibre is very important as this affects the tensile and compression values that the material can take before fracture in the longitudinal and transverse directions, vital to the frame staying in one piece when turning, decelerating or accelerating rapidly. A uni-directional laminate is preferable as the fibres provide optimum stress and strain abilities.
The metals mentioned provide lightweight solutions to the bicycle frame; however each has issues, whether it is low young’s modulus or fatigue limits that need to be addressed. These issues are usually solved by means of alloying or using shape factors to increase or decrease tube thicknesses or use of butting and other joining processes.
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