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As a basis for understanding the mechanism of crack propagation and fracture in ductile and brittle materials, we can examine the local stress near the tip of a crack (Figure 4.8). Theoretical analysis shows that the local stress σ_l ahead of a sharp crack of length c in an elastic solid due to an applied tensile stress σ in the Y direction is

(4.23)

where, x is the is the distance ahead of the crack tip in the X direction. The crack has the effect of amplifying the applied stress σ as the crack tip is approached. The closer the crack tip is approached, the higher the local stress σ_l. Depending on the values of σ and c, σ_l can become enormous near the crack tip, considerably larger than the yield stress of a ductile metal or the theoretical strength of a brittle solid.

Figure 4.8 Local stress σ_l as a function of distance x from the tip of a sharp crack of length c in (a) a ductile material and (b) a brittle material that is subjected to an applied stress σ . If the local stress is sufficiently high, plastic flow near the crack tip of the ductile material leads to crack blunting whereas cleavage of the atomic planes can occur in brittle materials. E, Young’s modulus.

In ductile metals, as the crack tip is approached, the local stress reaches the yield stress at some distance from the crack tip. Between this distance and the crack tip, plastic deformation occurs, turning the initially sharp crack into a blunt crack. As this process consumes a significant amount of energy, the energy available for the crack to propagate further is reduced considerably. This is equivalent to saying that the material has a high toughness (Section 4.2.6) or a high resistance to crack propagation through it. The stress at the blunted crack tip is, however, just sufficient to deform the material plastically and this, coupled with further linking up of microvoids within the metal, leads to crack growth and, eventually, to ductile failure.

In brittle materials such as ceramics, the stress at the crack tip can reach very high values because there is little or no plastic deformation to dissipate some of the energy available for crack propagation. When the local stress reaches the theoretical or ideal strength of the solid, equal to approximately E/3 to E/8, where E is the Young’s modulus, it is sufficient to break the interatomic bonds and the crack propagates rapidly between two atomic planes, a process described as cleavage. Ceramics, glasses and glass‐ceramics have low toughness or a low resistance to crack propagation when compared to ductile metals.

As ceramics almost invariably contain microstructural flaws, their measured strength in tensile or flexural loading is much lower than their theoretical strength, often by a factor of 10² to 10³ or more, due to the high amplification of the applied stress at the sharp tips of microcracks and pores. Another feature of ceramics is that their tensile or flexural strength is also much lower than their compressive strength, often by a factor of ~5–10 or more (Table 4.1). This is because cracks propagate more stably under compressive loads. Cracks have to twist out of their original orientation to propagate parallel to the direction of compression. Consequently, fracture does not occur by the rapid propagation of one crack (usually the largest crack) as in tensile loading. Instead, fracture in compression occurs by the slow extension of many cracks that eventually lead to crushing of the specimen.

Overall, because of the difference in crack propagation:

 Metals (and other ductile materials) have approximately the same measured strength in compression and in tension

 Ceramics (and other brittle materials) have a measured compressive strength that is much higher than their tensile (or flexural) strength

Consequently, proper design of structural ceramics is required to avoid their exposure to excessively high tensile stresses.

The fracture surface of ductile metals is often considerably rougher than that of ceramics or glasses due to the high degree of plastic deformation. Ceramics show a smoother fracture surface because crack propagation involves little or no plastic deformation but instead, involves cleavage of atomic planes. Another characteristic difference is that ductile fracture in metals occurs more slowly than brittle fracture of ceramics due to the energy absorbing process of plastic deformation during crack propagation.