Page 141 - Applied Petroleum Geomechanics

134 Applied Petroleum Geomechanics

in rock is characterized by the generation of microcracks around the crack tip, i.e., an
inelastic zone or the fracture process zone is formed. This zone is examined using
fracture mechanics theory. The mechanical properties and stress-deformation be-
haviors in fractured rock mass are also discussed.

Keywords: Fracture mechanics; Fracture process zone (FPZ); Fracture toughness;
Fracture width; Stress at fracture tip; Stress intensity factor.

4.1 Stress concentration at the crack tip

Inglis (1913) calculated stresses and strains in an elastic plate due to the
presence of cracks and sharp corners. Fig. 4.1 shows an elliptic hole or crack
in a thin plate subjected to a tensile stress (s L ), and the major and minor
axes of the crack are 2a and 2b, respectively. He found that the maximum
stress at the crack tip, s max , could be given by:

2a

s max ¼ 1 þ s L (4.1)
b
The ratio of the maximum stress to the applied stress is referred to as the
elastic stress concentration factor (F s ):
2a

F s ¼ 1 þ (4.2)
b

y
σ L

σ max

σ y
2b O A x
B
2a

σ L
Figure 4.1 An elliptic hole in a thin plate subjected to uniform tension, causing stress
concentration.