Strength and toughness

Strength and toughness

Strength and toughness? Why both? What’s the difference?

Strength, when speaking of a material, is its resistance to plastic flow. Think of a sample loaded in tension. Increase the stress until dislocations sweep right across the section, meaning the sample just yields, and you measure the initial yield strength. Strength generally increases with plastic strain because of work hardening, reaching a maximum at the tensile strength. The area under the whole stress–strain curve up to fracture is the work of fracture. Toughness is the resistance of a material to the propagation of a crack. Suppose that the sample of material contained a small, sharp crack, as in Figure A(a). The crack reduces the cross-section A and, since stress ? is F/A, it increases the stress. But suppose the crack is small, hardly reducing the section, and the sample is loaded as before. A tough material will yield, work harden and absorb energy as before—the crack makes no significant difference. But if the material is not tough (defined in a moment) then the unexpected happens; the crack suddenly propagates and the sample fractures at a stress that can be far below the yield strength. Design based on yield is common practice. The possibility of fracture at stresses below the yield strength is really bad news. And it has happened, on spectacular scales, causing boilers to burst, bridges to collapse, ships to break in half.

It could be argued, with some justification, that were it not for their brittleness, the use of ceramics for structural applications, especially at elevated temperatures, would be much more widespread since they possess other very attractive properties such as hardness, stiffness, and oxidation and creep resistance.

As should be familiar to most, the application of a stress to any solid will initially result in a reversible elastic strain that is followed by either fracture without much plastic deformation (Fig. B a) or fracture that is preceded by plastic deformation (Fig. B b). Ceramics and glasses fall in the former category and are thus considered brittle solids, whereas most metals and polymers above their glass transition temperature fall into the latter category.

The theoretical stress level at which a material is expected to fracture by bond rupture was discussed in Chap. 4 and estimated to be on the order of Y/10, where Y is Young s modulus. Given that Y for ceramics ranges between 100 and 500 GPa, the expected "ideal" fracture stress is quite high — on the order of 10 to 50 GPa. For reasons that will become apparent shortly, the presence of flaws, such as shown in Fig. C, in brittle solids will greatly reduce the stress at which they fail.