Page 399 - Mechanical Behavior of Materials

400 Chapter 8 Fracture of Cracked Members

Values of K Ic for a given material generally decrease along with ductility if the material is
processed to achieve higher strength. For a given material and processing, K Ic generally increases
with temperature, sometimes exhibiting a rather abrupt change over a narrow range of temperatures,
and also having relatively constant lower shelf and upper shelf values on opposite sides of the
temperature transition. Increased loading rate causes K Ic to decrease, having the effect of shifting
the transition to a higher temperature. The microstructure of the material may affect K Ic ,asinthe
detrimental effect of sulfur in some steels, the effect of crystal grain orientation from rolling of
aluminum alloys, and radiation embrittlement of pressure vessel steels.
If the plastic zone is too large, LEFM is no longer valid. Modest amounts of yielding can be
handled by using adjusted values K e calculated by adding half of the plastic zone size to the crack
length. However, above about 80% of the fully plastic force or moment, P o or M o , more general
methods such as the J-integral or the crack-tip opening displacement (CTOD, δ) are needed. The
flowchart of Fig. 8.53 also provides a guide for determining which of the various approaches is
required in a given situation.

NEW TERMS AND SYMBOLS

(a) Terms
bend specimen plane strain constraint
blunting line plastic zone
cleavage pop-in
compact specimen precrack
crack-tip opening displacement (CTOD): δ, δ c R-curve
dimpled rupture slow-stable crack growth
fracture modes I, II, and III strain energy release rate, G
fracture toughness: K c , K Ic stress intensity factor, K
fully plastic force, moment: P o , M o stress redistribution
internally flawed material superposition
J-integral: J, J Ic temperature transition
K-field transition crack length, a t
linear-elastic fracture mechanics (LEFM) unloading compliance
mixed-mode fracture

(b) Nomenclature
a Crack length
a c Critical (at fracture) crack length
a e Plastic-zone-adjusted crack length
b Maximum possible crack length; member width or half-width
c Major axis of elliptical crack; notch dimension analogous to a
√
F Dimensionless function F(a/b) for K = FS πa
√
F P Dimensionless function F P (a/b) for K = F P P/(t b)
h Member half-height
J Value of the J-integral
J Ic Plane strain fracture toughness in terms of J