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Toughness refers to the ability of a material to withstand rapid propagation of a crack through it. The toughness G_c of a material is defined as the energy absorbed per unit area of crack (units J/m²). A high G_c means that it is difficult for a crack to propagate through a material, as in pure ductile metals such as aluminum and copper, for example, which have G_c values in the range 100–1000 kJ/m². In comparison, brittle materials such as ceramics have low G_c values, in the range 0.01–0.1 kJ/m², and, thus, it is easy for cracks to propagate through them.

The toughness of a material is difficult to measure and, consequently, more easily measured parameters are used to provide a measure of toughness. One such parameter is the area under the stress–strain curve in a given loading mode such as tension or flexure (Figure 4.10). This area can be used to compare the relative toughness of specimens with a similar geometry but it is not equal to the toughness G_c of the material. As Figure 4.10 indicates, there is often no correlation between strength and toughness. The area under the elastic region of the stress–strain curve is often referred to as the resilience because it gives a measure of the energy recovered upon unloading a specimen.

Figure 4.10 Area under the stress–strain curve used as measure of the relative toughness between materials of the same geometry.

A more widely used parameter of toughness is the fracture toughness K_c. It is determined experimentally using standard techniques by inserting a crack of length c into a specimen and loading it until fracture occurs. K_c (units MN/m^3/2or MPa m^1/2) is related to G_c by Eq. (4.27).

Pure metals have K_c values in the range ~100–350 MN/m^3/2 (Table 4.1). The K_c values of the majority of ceramics and glasses are in the range ~0.5–5 MN/m^3/2. On the other hand, a few ceramics such as YSZ and silicon nitride (Si₃N₄) can have K_c values equal to ~10 MN/m^3/2. The higher fracture toughness of YSZ is due to the occurrence of a phase transformation in the region of the crack tip, which dissipates some of the energy available for crack propagation. This process is described as transformation toughening (Chapter 7). On the other hand, a unique fibrous structure of elongated grains coupled with an appropriate thin glass phase at the grain boundaries is responsible for the higher fracture toughness of Si₃N₄. A crack propagates along the weaker glass phase at the grain boundaries, making the crack path more tortuous when compared to a straighter path directly across the grains. This tortuous path consumes more energy than a straighter path. Polymers have G_c values between those for metals and ceramics but low K_c values because their Young’s modulus is low.