Materials for Bicycle Helmets
IntroductionThe case study in this section illustrates how CES can be used for selecting materials. The underlying methodology for selection, used here, is described in more detail in references [1, 2].
Even in a small country such as England, cycling fatalities exceed 200 per year. An increasing number of cyclists wear helmets, giving a significant level of head-protection in an accident. The major impact-absorbing element of the helmet is a foamed polymer liner, commonly made of expanded polystyrene (EPS). Polymer foams are chosen because they are easily fabricated and because, unlike honeycombs, their ability to absorb energy is omni-directional. The helmet designer empirically selects the density and thickness to meet standard impact-tests which are at constant velocity (5 m/s) onto rigid anvils . Could some of this empiricism be replaced by a more rational selection procedure? Figure 1 is a schematic of a helmet. The liner thickness is limited by practicalities and, to some extent, styling. All helmets have almost the same liner-thickness: 20mm. The best choice of liner material is that which absorbs the most energy/unit volume, while limiting the load on the head to a less-than-damaging level.
Figure 1 A cycle helmet designed to maximise energy absorption while keeping the deceleration of the skull below 300g
|FUNCTION||Protective cycle helmet|
|OBJECTIVE||Maximise energy absorption / unit volume|
|CONSTRAINTS||Load on skull < damage load|
The ModelThe helmet liner performs two impact-mitigating functions. First, it redistributes a localised external force over a larger area, reducing the local stress on the skull. Second, it sets an upper limit to the magnitude of this distributed force, as determined by the plateau-stress of the foam. The key step in selecting a material for the liner is that of establishing the acceptable maximum value for this distributed force. The arguments can become very sophisticated, but the underlying reasoning is as follows.
The maximum tolerable deceleration, a, of the human head is approximately 300 g, provided it is applied for a few milliseconds only. Longer impacts at this deceleration level cause irreversible injury. The mass m of a head is approximately 3 kg, so the maximum allowable force, from Newton's Law, is
F = m a = 9 kN.
As the foam crushes between the obstacle (on the outside) and the skull (on the inside) it beds-down, distributing the load over a projected area A of order 10-2m2. To prevent F rising above 9 kN, the foam must crush with a plateau stress of approximately:
sc(0.25) = F/A = 0.9 MPa.
Impact mitigation depends on the ability to absorb energy.
The SelectionFigure 2 is a materials selection chart generated by CES, which enables selection of foams for energy absorption. It shows the maximum compressive strain (the 'densification strain'), eD, plotted against another measure of the compressive strength: it is sc(0.25), the 'plateau stress' at 25% strain level. The ability of a foam to absorb energy is measured by the product eD. sc(0.25). Materials above the selection line absorb the most energy per unit volume.
Figure 2 Densification strain plotted against plateau stress (which we take as the compressive strength at 25% strain) for commercially-available foams. Output from CES Materials. Foams above the selection line have high values of energy absorption per unit volume (MJ/m3). The contour lines show values of equal energy absorption per unit volume.
A second stage, figure 3, shows a chart with the same axes as figure 2, but this time selects foams which absorb energy below the plateau stress of 0.9 MPa (the constraint determined by the load on the skull).
Figure 3 Densification strain plotted against plateau stress (which we take as the compressive strength at 25% strain) for commercially-available foams. The selection line delineates the constraint of a plateau stress of 0.9 MPa. Output from CES Materials.
Figure 4 shows those materials that pass both stages and are therefore viable candidates. They are Expanded Polystyrene with a density of 0.05 Mg/m3 —EPS (0.05), Cork and ultra low density Balsa wood (see the selection results below).
Figure 4 Densification strain plotted against plateau stress (which we take as the compressive strength at 25% strain) for commercially-available foams, showing the candidates that pass the selection. Output from CES Materials
EPS (0.05) can absorb about 0.8 MJ/m3, which is more than the other candidate materials that lie wholly below a plateau stress of 0.9 MPa. The liners of most current cycle helmets are made of EPS, but they vary considerably in density and thus weight. There is a tendency to select a low-density foam because it makes the helmet lighter. Figure 3 shows that alternative selections with the same plateau stress absorb much less energy: Polyurethane of density 0.53 Mg/m3, PU(0.53), for instance, absorbs only 0.4 MJ/m3.
The value of figure 3 is the ease with which a first selection can
be made, giving a short-list of viable candidates. Had the maximum permissible
stress been 0.04 MPa, then the best choice among commercially available
foams would be the low-density polyethylenes; had it been 10 MPa,
then Al-Si metal foams or end-grain balsa would become the best choices,
absorbing almost 10 MJ/m3.
|Materials Passing All Stages|
|Balsa, ultra low density, perpendicular to grain|
|Polystyrene foam closed cell (0.050)|
Table 2 Selection Results: Materials for bicycle helmets
- Ashby, M.F. 'Materials Selection in Mechanical Design', Pergamon Press, Oxford, UK, 1992.
- 'Cambridge Materials Selector User's Manual', Granta Design Limited, Cambridge, UK, 1994.
- Mills, N.J. and Gilchrist, A. 'The Effectiveness of Foams in Bicycle and Motorcycle Helmets', Accid. Anal. and Preview, 23, pp153-163, 1991.
- Gibson, L.J. and Ashby, M.F. 'Cellular Solids, Structure and Properties', 2nd edition, Cambridge University Press (1996).