ABSTRACT
Fig. 1 Variation of radial strain in creep test with 87% of axial compressive strength after Kranz(1979)
Fig. 2 Subcritical crack growth after Atkinson and Meredith (1987)
Continuum theory of localization phenomena 393
i
i
Creep behaviors can be reproduced by the following micromechanical model; see Yoshida and Horii (1992). Crack growth under compression is simply modeled as shown in Fig. 3 following Horii and Nemat-Nasser (1986). F = F(cl> σ2) represents the effect of an initial defect which drives the crack growth. Then the stress intensity factor at the crack tip is given explicitly. For static (or short term) behaviors or brittle crack growth, the Griffith criterion is assumed and for time-dependent behaviors Eqn. (1) is satisfied. That is,
(i)Kf=Kc dP
for short term behaviors
for time dependent behaviors
(2)
By Eqns. (2) the crack growth behavior is reproduced. The additional strain due to the crack growth is calculated by integrating crack opening displacement as,
,CR 1 Γ 1 V L 2 ^ ^ + ^ ^ d S = g ' J ( *' ° m n ) (3)
Results for crack growth under triaxial compression are shown in Fig. 4 together with experimental results by Kranz (1980). Time for the crack to grow up to the indicated crack length is plotted as solid curves for different values of axial stresses. At higher confining pressure, the crack growth is slower. The points in the figures indicate final failure time in experiments. It is seen that the failure occurs with the same crack length at
394 Horii and Okui
the same confining pressure. But the critical crack length at failure is different with different confining pressure.
