International Journal of Fracture 38:241-273 (1988)
© Kluwer Academic Publishers, Dordrecht - Printed in the Netherlands 241
Creep crack growth by grain boundary cavitation: crack tip
fields and crack growth rates under transient conditions
F.Z. LI, A. NEEDLEMAN and C.F. SHIH
Division of Engineering, Brown University, Providence, Rhode Island 02912, USA
Received 25 February 1988; accepted in revised form 21 June 1988
Abstract. Transient creep crack growth due to grain boundary cavitation, and under plane strain and small scale
creep conditions, is investigated. Full account is taken of the finite geometry changes accompanying crack tip
blunting and the material is characterized as an elastic-power law creeping solid with an additional contribution
to the creep rate arising from a given density of cavitating grain boundary facets. All voids are assumed present
from the outset, distributed on a given density of cavitating grain boundary facets. Our analyses show the
competing effects of stress relaxation due to creep, diffusion and crack tip blunting, and the stress increase due
to crack growth. Another outcome of our analyses is the crack growth rate under various conditions of loading
and for various values of material properties and for various characterizations of the failure process. Prior to crack
growth, Hutchinson-Rice-Rosengren type singular fields dominate over the crack tip region, outside of a finite
strain zone that has dimensions of the order of the crack opening displacement. These singular fields scale with
the path integral C(t), which to a good approximation decays as K~/t, with t being the elapsed time since load
application and KI the imposed stress intensity factor. When the crack growth rate is faster than the growth rate
of the creep zone, our finite element results show that Hui-Riedel singular fields dominate over the crack tip region
and the magnitude of the Hui-Riedel fields scales with the crack growth rate. For a crack that grows more slowly
than the creep zone, Hutchinson-Rice-Rosengren type fields dominate over the crack tip region. In these
circumstances, the crack growth rate is found to scale as C(t) to a power. Regardless of which of the two singular
fields dominates for the growing crack, finite strain effects are found to be significant over a size scale of the order
of the crack opening displacement at crack growth initiation. The effect of increased mesh refinement is also
considered and very little mesh dependence is found.
1. Introduction
It is helpful to distinguish various stages of creep deformation in a cracked body. One stage
is a short time regime that is also referred to as small scale creep. Another stage is a long
time regime or extensive/steady state regime. In small scale creep, the creep zone is small
compared to the flaw in the body (or a relevant length of the body). Extensive creep is said
to be taking place when the creep zone is comparable to the largest dimension of the body.
The regime between small scale and extensive creep is referred to as transition creep. Since
the near-tip stresses and strain rates have a strong dependence on time during small scale and
transition creep, the term transient creep is frequently used to include both small scale and
transition creep. For a range of conditions, continuum stress analysis has clarified questions
concerning which parameter, e.g. the stress intensity factor Kt, or a path integral such as C*
or J, is appropriate for correlating creep crack growth rates. For example, under extensive
creep conditions C* is the appropriate parameter and this theoretical result is supported by
substantial experimental data on relatively ductile materials, e.g. Landes and Begley [1],
Nikbin et al. [2], Ohji et al. [3], Sadananda and Shahinian [4], Koterazawa and Mori [5],
Taira et al. [6], Ohji et al. [7], Saxena [8] and Riedel and Wagner [9]. Recently, Riedel and