Page 50 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)
P. 50
1656_C02.fm Page 30 Thursday, April 14, 2005 6:28 PM
30 Fracture Mechanics: Fundamentals and Applications
FIGURE 2.3 A through-thickness crack in an infinitely wide plate subjected to a remote tensile stress.
where Π is the potential energy of an uncracked plate and B is the plate thickness. Since the
o
formation of a crack requires the creation of two surfaces, W is given by
s
W s a = 4 B γ s (2.17)
where γ is the surface energy of the material. Thus
s
d ∏ πσ 2 a
− = (2.18a)
dA E
and
dW s = 2γ
dA s (2.18b)
Equating Equation (2.18a) and Equation (2.18b) and solving for fracture stress gives
/
2 E γ 12
σ = π a (2.19)
s
f
It is important to note the distinction between crack area and surface area. The crack area is
defined as the projected area of the crack (2aB in the present example), but since a crack includes
two matching surfaces, the surface area is 2A.
