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Dynamic and Time-Dependent Fracture 185

FIGURE 4.11 Schematic K ID -crack speed curves: (a) effect of crack speed on K ID and (b) effect of material
toughness.

Figure 4.11 illustrates the typical variation of K with crack speed. At low speeds, K is
ID
ID
relatively insensitive to V, but K increases asymptotically as V approaches a limiting value.
ID
Figure 4.12 shows K data for 4340 steel published by Rosakis and Freund [39].
ID
In the limit of V = 0, K = K , the arrest toughness of the material. In general, K < K , the
IA
Ic
IA
ID
quasistatic initiation toughness. When a stationary crack in an elastic-plastic material is loaded
monotonically, the crack-tip blunts and a plastic zone forms. A propagating crack, however, tends
to be sharper and has a smaller plastic zone than a stationary crack. Consequently, more energy is
required to initiate fracture from a stationary crack than is required to maintain the propagation of
a sharp crack.
The crack-speed dependence of K can be represented by an empirical equation of the form
ID
K
K = IA m (4.24)
ID
V  
1 −  V l 

FIGURE 4.12 Experimental K ID vs. crack speed data
for 4340 steel. Taken from Rosakis, A.J. and Freund,
L.B., “Optical Measurement of the Plane Strain Con-
centration at a Crack Tip in a Ductile Steel Plate.” Jour-
nal of Engineering Materials Technology, Vol. 104,
1982, pp. 115–120.