Page 56 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C02.fm Page 36 Thursday, April 14, 2005 6:28 PM

36 Fracture Mechanics: Fundamentals and Applications

Therefore

∏= −U

and

G = 1  dU  = P  d ∆  (2.27)
B  da  P 2B  da  P

When displacement is fixed (Figure 2.8), the plate is displacement controlled; F = 0 and Π = U. Thus

G =− 1  dU  =− ∆  dP  (2.28)
B  da  ∆ 2B  da  ∆

It is convenient at this point to introduce the compliance, which is the inverse of the plate stiffness:

∆
C = (2.29)
P

By substituting Equation (2.29) into Equation (2.27) and Equation (2.28) it can be shown that

P dC
2
G = (2.30)
2 B da

for both load control and displacement control. Therefore, the energy release rate, as defined in
Equation (2.23), is the same for load control and displacement control. Also

 dU  =−  dU 
 da  P  da  ∆ (2.31)

FIGURE 2.8 Cracked plate at a fixed displacement ∆.