MATERIALS FOR SPRINGS

Springs come in many shapes (Figure 1 and Table 1) and have many purposes: think of axial springs (e.g. a rubber band), leaf springs, helical springs, spiral springs, torsion bars. Regardless of their shape or use, the best material for a spring of minimum volume is that with the greatest

Figure 1 Springs store energy. The best material for any spring, regardless of its shape or the way in which it is loaded, is that with the highest value of σf²/E, or, if weight is important, σf²/Eρ.

Table 1 Design requirements for springs

Function	Elastic spring
Constraints	No failure, meaning σ<σ­f throughout the spring
Objective	- Maximum stored elastic energy per unit volume, or - Maximum stored elastic energy per unit weight
Free variables	Choice of material

value of σf²/E, and for minimum weight it is that with the greatest value of σf²/ρE (derived below). We use them as a way of introducing two of the most useful of the charts: Young’s modulus E plotted against strength σf, and specific modulus E/ρ plotted against specific strength σf/ρ.

The model

The primary function of a spring is to store elastic energy and— when required—release it again. The elastic energy stored per unit volume in a block of material stressed uniformly to a stress σ is

where E is Young’s modulus. We wish to maximize Wv. The spring will be damaged if the stress σ exceeds the yield stress or failure stress σf; the constraint is σ<σf. Thus the maximum energy density is

Torsion bars and leaf springs are less efficient than axial springs because much of the material is not fully loaded: the material at the neutral axis, for instance, is not loaded at all. For leaf springs

and for torsion bars

But—as these results show—this has no influence on the choice of material. The best stuff for a spring regardless of its shape is that with the biggest value of

If weight, rather than volume, matters, we must divide this by the density ρ (giving energy stored per unit weight), and seek materials with high values of

The selection. The choice of materials for springs of minimum volume is shown in Figure 2(a). A family lines of slope 2 link materials with equal values of M1 = σf²/E; those with the highest values of M1 lie towards the bottom right. The heavy line is one of the family; it is positioned so that a subset of materials is left exposed. The best choices are a high-strength steel lying near the top end of the line. Other materials are suggested too: CFRP (now used for truck springs), titanium alloys (good but expensive), and nylon (children’s toys often have nylon springs), and, of course, elastomers. Note how the procedure has identified a candidate from almost every class of materials: metals, polymers, elastomers and composites. They are listed, with commentary, in Table 2(a). Materials selection for light springs is shown in Figure 2(b). A family of
lines of slope 2 link materials with equal values of

Figure 2(a) Materials for small springs. high strength (‘‘spring’’) steel is good. Glass, CFRP and GFRP all, under the right circumstances, make good springs. Elastomers are excellent. Ceramics are eliminated by their low tensile strength.

Figure 2(b) Materials for light springs. Metals are disadvantaged by their high densities. Composites are good; so is wood. Elastomers are excellent.

Table 2(a) Materials for efficient small springs

Material	M1=σf2/E (MJ/m3)	Comment
Ti alloys	4–12	Expensive, corrosion-resistant
CFRP	6–10	Comparable in performance with steel; expensive
Spring steel	3–7	The traditional choice: easily formed and heat treated
Nylon	1.5–2.5	Cheap and easily shaped, but high loss factor
Rubber	20–50	Better than spring steel; but high loss factor

Table 2(b) Materials for efficient light springs

Material	M1 = σf2/ρE (MJ/m3)	Comment
Ti alloys	0.9–2.6	Better than steel; corrosion-resistant; expensive
CFRP	3.9–6.5	Better than steel; expensive
GFRP	1.0–1.8	Better than spring steel; less expensive than CFRP
Spring steel	0.4 –0.9	Poor, because of high density
Wood	0.3–0.7	On a weight basis, wood makes good springs
Nylon	1.3–2.1	As good as steel, but with a high loss factor
Rubber	18–45	Outstanding; 20 times better than spring steel; but with high loss factor