Page 55 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C02.fm Page 35 Thursday, April 14, 2005 6:28 PM

Linear Elastic Fracture Mechanics 35

The term rate, as it is used in this context, does not refer to a derivative with respect to time; G is
the rate of change in potential energy with the crack area. Since G is obtained from the derivative
of a potential, it is also called the crack extension force or the crack driving force. According to
Equation (2.18a), the energy release rate for a wide plate in plane stress with a crack of length 2a
(Figure 2.3) is given by

πσ a
2
G = (2.24)
E
Referring to the previous section, crack extension occurs when G reaches a critical value, i.e.,

dW
G = c dA S = 2 w f (2.25)

where G is a measure of the fracture toughness of the material.
c
The potential energy of an elastic body, Π, is defined as follows:
∏= U − F (2.26)

where U is the strain energy stored in the body and F is the work done by external forces.
Consider a cracked plate that is dead loaded, as illustrated in Figure 2.7. Since the load is fixed
at P, the structure is said to be load controlled. For this case

F P =∆
and

U ∫ ∆ P = d ∆ = P∆
0 2

FIGURE 2.7 Cracked plate at a fixed load P.