Page 184 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C003.fm Page 164 Monday, May 23, 2005 5:42 PM

164 Fracture Mechanics: Fundamentals and Applications

FIGURE A3.6 The RDS crack growth criterion. The
crack is assumed to extend with a constant opening
displacement δ c at distance r m behind the crack tip. This
criterion corresponds approximately to crack extension
at a constant crack-tip-opening angle (CTOA).

Rice et al. proposed a failure criterion that corresponds approximately to crack extension at a
constant crack-tip-opening angle (CTOA). Since dd/dr = ∞ at the crack tip, CTOA is undefined,
but an approximate CTOA can be inferred a finite distance from the tip. Figure A3.6 illustrates the
RDS crack-growth criterion. They postulated that crack growth occurs at a critical crack-opening
displacement d at a distance r behind the crack tip. That is
c
m
δ c = α dJ + β σ o  eR 
r m σ da E ln   r m   = constant (A3.43)
o
Rice et al. found that it was possible to define the micromechanical failure parameters δ and r m
c
in terms of global parameters that are easy to obtain experimentally. Setting J = J and combining
Ic
Equation (A3.39), Equation (A3.42), and Equation (A3.43) gives

eEJ 
Eδ β  λ
T = o ασ om − α ln  r σ o 2 Ic   (A3.44)
c
r
m 
where T is the initial tearing modulus. Thus for J > J , the tearing modulus is given by
o
Ic
β  J 
T T = o − α ln   J   (A3.45)
Ic

Rice et al. computed normalized R curves (J/J vs. ∆a/R) for a range of T values and found that
o
Ic
T = T in the early stages of crack growth, but the R curve slope decreases until the steady-state
o
plateau is reached. The steady-state J can easily be inferred from Equation (A3.45) by setting T = 0:
α T 
J ss J = IC exp   β o   (A3.46)

Large-Scale Yielding
Although the RDS analysis was derived for small-scale yielding conditions, Rice et al. speculated
that the form of Equation (A3.38) might also be valid for fully plastic conditions. The numerical
values of some of the constants, however, probably differ for the large-scale yielding case.
The most important difference between small-scale yielding and fully plastic conditions is the
value of R. Rice et al. argued that R would no longer scale with the plastic zone size, but should