We are often concerned with how we can store and recover energy, for example using a spring. There are many different types of spring, for example coil or helical springs, leaf springs (shown in Figure 2.17) and cantilever springs.While they can work in
compression or tension and some springs are more efficient than others, the principle of energy storage is the same and is governed by the spring material’s ability to store elastic energy.
The elastic energy stored in a unit volume of material, Wv, is described mathematically in equation (2.15):
Wv12 (2.15)
where yis the yield stress for ductile materials, or the fracture strength for a brittle material, and E is the stiffness.
To select a spring that stores the largest amount of energy for a given volume (or size), or the smallest spring to store a given amount of energy, a material with the largest value of
E
y2
should be chosen. This equation can be further developed, to give equation (2.16), expressing the energy stored per unit mass (Wm in J kg1) by dividing the energy stored per unit volume (in J m3) by the density of the spring material (in kg m3):
Wm12 (2.16)
Materials with high values of
E
y2
will produce lightweight springs.Values for both these terms are presented in Table 2.10, which reveals a number of interesting points. It shows that by changing the strength of the steel used (through its composition and through processing) the maximum stored energy increases (since the yield stress increases and the stiffness remains unchanged). High-strength (spring) steels are a good and common choice for small springs (surpassed only by rubber for energy storage per unit volume, but the use of rubber can be limited by the magnitude of the load that can be applied before it fails). Titanium springs are good and corrosion resistant but are expensive. For light springs, steel is no longer so attractive and titanium (used as fasteners in F1 cars), GFRP and CFRP (used in truck and high-performance car leaf springs) and polymers (used in cheap toys) become better choices. Ceramics could be used as springs; in fact, glass springs are widely used in scientific instruments, but they can only be used safely in compression owing to their tendency to fail at low stresses in tension if they contain defects or if they are damaged in use.
2y
E 2y
E
Figure 2.17Images showing (left) helical or coil springs and (right) a leaf spring
The examples presented give an overview of the approach taken to select a material for a given application where constraints such as cost and weight may be a concern. The methodology is, however, applicable to any number of different design problems.
More generally, we need to analyse the problem by obtaining expressions that describe the response we wish to achieve from our design (the bending or stretching) under a given environment (load, temperature). In most cases we then need to obtain a second expression for our constraint, for example the mass, as a function of the geometry and density of the material chosen. Using this simple analysis method (where we do not have the complete freedom to change the shape of our design) we must decide which one of the dimensions can be varied, so that we might achieve the desired response for any material selected.
To enable a comparison of materials without having to make hundreds of individual calculations, we need to substitute and rearrange our expressions to make the constraint the subject of the equation, eliminating the free variable in the process. By separating terms that are fixed by the design and hence will not vary with the material selected (geometry, force, temperature, magnitude of deflection, extension) and terms that will vary with the material chosen (strength, stiffness, density, cost) we can substitute data for different materials and rank them accordingly.
This method is a useful means of narrowing the field of candidate materials, considering the most important property required to achieve functionality. The final choice of material may require consideration of other important materials properties (and hence repetition of this process), the material’s performance in its environment (its susceptibility to corrosion, for example), and how easily it can be manufactured to the desired shape.
Material Yield strength Young’s Density y2/ E
(MPa) modulus (GPa) (kg m3) y2/E
( 1000)
Mild steel 220 210 7850 230 0.03
Low alloy steel 690 210 7850 2267 0.29
Spring steel 1300 210 7850 8047 1.03
CFRP 650* 200 1500 2113 1.41
GFRP 300* 40 2000 2250 1.13
Titanium alloy 830 110 4500 6263 1.39
Aluminium alloy 400 70 2700 2286 0.85
Rubber 30* 0.05 850 18,000 21.18
High-density
polyethylene 30 0.7 970 1286 1.33
Nylon 45 3 1100 675 0.61
Wood (parallel
to grain) 55* 11 600 275 0.46
Table 2.10 Comparison of materials for small and light springs
* failure strength.
By the end of this section you will have learnt:
✔ The material selection process for an engineering design requires a mathematical analysis of the problem, in combination with the use of relevant material property data;
✔ The generic method for this material selection process;
✔ That the method used is ideal for narrowing the field of candidate materials and that the final choice may require consideration of other factors such as cost and ease of manufacture.
Learning summary
2.5 Materials processing
Materials are selected for a particular application in a component as a result of an attribute (or combination of their attributes) of the type that has been discussed previously, such as strength, density, thermal conductivity or cost.
There is a very wide range of processes that take a material and convert it into a component of the required shape. The selection of a suitable manufacturing process depends to some degree upon the attributes of the material. However, we must also be aware that certain properties of materials can be changed (sometimes quite markedly) by the processing of the material itself.
Sometimes, this change in properties is a byproduct of the process; for example, in bending a metal sheet to form a shape, the properties of the metal in the region of deformation will be markedly changed. In other cases, the process is conducted primarily to change the material properties; this is the basis of many processes where materials are heat treated.
Many of these changes in material properties are often controlled by changes in the material at the scale of the microstructure or at the atomic scale. It is thus very important for the engineer to understand the basic mechanisms that control these changes, since these will directly influence the attributes of the material.
When a component is being designed, the material and the processing route need to be considered at the same time. The properties of the component will be governed by the design and the material properties; however, the design and the choice of materials will constrain the choice of manufacturing route for the component. As such, the design, material and
manufacture need to be considered concurrently as part of the design process; designs where material and manufacture are considered following the main mechanical design will tend to require more design iterations and will tend to be suboptimal designs. Thus, for optimal designs, we need to understand the capabilities of various manufacturing processes before we can opt to use a given material–manufacturing route solution.
Casting
Casting is a process where a material is melted to form a liquid, poured into a mould and then solidified such that the material takes the shape of the mould. Casting almost always refers to the production of metallic components, which may range in size from a few millimetres (e.g.
electrical connectors) to tens of metres (e.g. a propeller for a ship). The solidified component needs to be removed from the mould; with expendable moulds, this is achieved by breaking the mould away from the component, and with reusable moulds, this is achieved by pulling apart a multipart mould and ejecting the component. Casting is generally used for making parts of complex shape that would be difficult or uneconomical to make by other methods, such as cutting from solid material. In its most advanced form, it is employed to make single-crystal turbine blades from nickel-based alloys for use in aeroengine turbines.
To achieve solidification, heat needs to be removed from the material, and this heat will be extracted through the walls of the mould; the rate of heat extraction will depend upon the thermal conductivity and heat capacity of the mould material, the size of the mould and how easily heat is transferred across the interface between the material and the mould. On
solidification of metals, there is volume change, normally a contraction (see Underpinning Principles 2); this volume change needs to be taken account of when designing a casting so that the mould remains full during solidification and no cavities are formed in the structure.When a metal alloy is melted and then resolidified, the resolidification may be a complex process, leading to a non-uniform structure in the metal. For details, see Underpinning Principles 4.