Page 303 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

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Fracture Mechanisms in Nonmetals 283

FIGURE 6.28 The process-zone mechanism for ceramic toughening. (a) Process zone formed by growing
crack (b) Schematic stress-strain behavior (c) Nonlinear deformation of second-phase particles

Evans [40] divides the toughening mechanisms for ceramics into two categories: process zone
formation and bridging. Both mechanisms involve energy dissipation at the crack tip. A third
mechanism, crack deflection, elevates toughness by increasing the area of the fracture surface
(Figure 2.6(c)).
The process zone mechanism for toughening is illustrated in Figure 6.28. Consider a material
that forms a process zone at the crack tip (Figure 6.28(a)). When this crack propagates, it leaves
a wake behind the crack tip. The critical energy release rate for propagation is equal to the work
required to propagate the crack from a to a + da, divided by da:

G = 2 ∫ h   ∫ ij ε i j d σ i j   dε y + 2 γ s (6.20)
R
0  0 
where h is the half width of the process zone and g is the surface energy. The integral in the square
s
brackets is the strain-energy density, which is simply the area under the stress-strain curve in the