A material is required for the blade of a rotary lawnmower. Cost is a consideration. For safety reasons, the designer specified a minimum fracture toughness for the blade: it is \(K_{1 c}>30 \mathrm{MPa} \mathrm{m}^{1 / 2}\). The other mechanical requirement is for high hardness, \(H\), to minimize blade wear. Hardness, in applications like this one, is related to strength:

\[H \approx 3 \sigma_{y}\]

where \(\sigma_{f}\) is the strength (Chapter 2, Engineering Materials and Their Properties gives a fuller definition). Use the \(K_{1 c}-\sigma_{f}\) chart of Fig. 3.8 to identify three materials that have \(K_{1 c}>30 \mathrm{MPa} \mathrm{m}^{1 / 2}\) and the highest possible strength. To do this, position a ' \(K_{1 c}\) ' selection line at \(30 \mathrm{MPa} \mathrm{m}{ }^{1 / 2}\) and then adjust a 'strength' selection line such that it just admits three candidates. Use the Cost chart of Fig. 3.19 to rank your selection by material cost, hence making a final selection.

Fig. 3.8

Fig. 3.19

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1000 100- Fracture toughness - strength Yield before fracture Design guidelines Fracture toughness, Kc (MPa.m1/2) Ktc Kild 10 Process zone 1000 100 10 size, dy, mm Low alloy steels Metals Stainless steels Ni alloys Cu alloys W alloys Carbon Al alloys 0.1 Ti alloys Zinc alloys, Cast frons 0.01 Mg alloys Lead alloys Leather Nontechnical Ionomers Kiela, ceramics- Brick Natural Stone Silicone 0.1 materials elastomers Concrete Buty rubber Flexible polymer foams Cork 0.01 0.1 1 10 Wood PP PE GFRP PTFE PA PC ABS PMMA Phenolic Silicon Silica glass Composites CERP Diamond Technical ceramics B.C Epoxies Soda glass Polyurethane Polymers and elastomers Lower limit for Kic Isoprene Neoprene Foams Rigid polymer foams Strength, + (MPa) 100 1000 Fracture before yield MFA 15