The Selection

The selection of materials for springs of minimum volume is shown in Figure 9.2. Here the modulus of rupture, σ_MOR, has been used as the measure of the failure strength σ_f. The chart shows σ_MOR plotted against modulus, E. A family of lines of slope 1/2 link materials with equal values of M₁ = σ_f²/E. Those with the highest values of M₁ lie towards the top left. The heavy line is one of the family. It is positioned at 10 MJ/m³ such that a small subset of materials is left exposed. They include high-strength steel (spring steel, in fact) lying near the top end of the line, and, at the other end, rubber. But certain other materials are suggested too: GFRP (now used for truck leaf springs), titanium alloys (good but expensive), glass fibers (used in galvanometers) and — among polymers — nylon (children's toys often have nylon springs). The procedure identifies a candidate from almost every material class: metals, glasses, polymers, elastomers and composites. A protective stage, limiting the values of the toughness G_c (G_c = K_IC² / E) and the cost C_m to the those listed in the design requirements, has been added (Figure 9.3). The selection results are shown in Table 9.2.

Figure 9.2 A chart of the modulus of rupture, σ_MOR, against Young's modulus, E. The diagonal line shows M₁.

Figure 9.3 A 'protective' chart of the toughness, G_c, against cost per unit weight, C_m. The box restricts the selection to materials with G_c > 1 kJ/m² and C_m < 100 GBP/kg.

MATERIAL		COMMENT
Spring Steel	15 – 25	The traditional choice: easily formed and heat treated.
Ti Alloys	15 – 20	Expensive, corrosion-resistant.
CFRP	15 – 20	Comparable in performance with steel; expensive.
GFRP	10 – 12	Almost as good as CFRP and much cheaper.
Glass fibers	30 – 60	Brittle in tension, but excellent if protected against damage; very low loss factor.
Nylon	1.5 – 2.5	The least good; cheap and easily shaped, but high loss factor.
Rubber	20 – 60	Better than spring steel; but high loss factor.

Table 9.2 Materials for efficient springs of low volume

Materials selection for light springs is shown in Figure 9.3. It is a chart of σ_MOR/ρ against E/ρ, where ρ is the density. Lines of slope 1/2 now link materials with equal values of

One is shown at the value M₂ = 2 kJ/kg. The new selection is listed in Table 9.3. Composites, because of their lower densities, are better than metals. Elastomers are better still (you can store almost 8 times more elastic energy per unit weight in a rubber band than in the best spring steel). Elastomeric springs are now widely used in aerospace because of their low weight and high reliability. Wood — the traditional material for archery bows, now appears in the list.

Figure 9.4 A chart of σ_MOR/ρ against E/ρ. The diagonal line is a contour of M₂.