~ Pergamon
lnt. J. Solids Structures Vol.34, No. 6, pp. 703-726, 1997
Copyright © 1997 Elsevier Science Ltd
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PII: S0020-7683(96)00051-0
INFLUENCE OF MICROSTRUCTURAL
VARIATIONS ON STEADY STATE CREEP AND
FACET STRESSES IN 2-D FREELY SLIDING
POLYCRYSTALS
PATRICK ONCK and ERIK VAN DER GIESSEN
Delft University of Technology, Laboratory for Engineering Mechanics, P.O. Box 5033,
2600 GA Delft, The Netherlands
(Received 31 October 1995; in revised form 13 March 1996)
Abstract--At elevated temperatures, creep in polycrystalline aggregates is often accompanied by
free grain boundary sliding, which tends to enhance the macroscopic creep rate and the transverse
facet stresses. This paper deals with the influence on these phenomena of variations in the micro-
structure, in terms of variations in the size and shape of grains in an aggregate. Numerical results
for two-dimensional cell analyses involving many grains are presented which demonstrate that
random rnicrostructural variations relative to an array of regular hexagonal grains invariably lead
to an increase of the creep rate enhancement due to sliding. For power-law creeping grains and for
the variations considered here, the effects amount to up to a 60% increase. Moreover, it is shown
that microstructural variations lead to a wider distribution of transverse facet stress levels with a
considerably higher average than for regular hexagonal grains. Both effects are of significance for
creep rupture life time estimates. Copyright © 1997 Elsevier Science Ltd.
1. INTRODUCTION
At elevated temperatures and typical creep loading conditions, creep in polycrystalline
engineering metals is often accompanied by grain boundary sliding. This is due to the fact
that the resistance of grain boundaries against sliding of the adjacent grains relative to each
other is low compared to the creep resistance of the grains themselves. Even though
irregularities of the grain boundaries, such as ledges, and second-phase particles act as
barriers for grain boundary sliding, the sliding resistance in many materials is frequently
considered to be negligible all together (see, e.g., Ashby, 1972).
In such cases of completely free grain boundary sliding, the overall creep rate of the
polycrystalline material is increased appreciably compared to that in the absence of grain
boundary sliding. There has been substantial interest in linking the overall (macroscopic)
creep response to that of the (microscopic) response of the constituting grains for over two
decades. Assuming simple isotropic creep models for the behavior of the grain material,
various simple theoretical models were considered initially, such as the slip line approach
of Brunner and Grant (1959), while shortly after, the phenomenon was studied more
accurately by using numerical methods, first by Crossman and Ashby (1975) and cul-
minating in Ghahremani's (1980) paper. The cited studies were all concerned with 2-D
arrays of hexagonal grains. They have been complemented more recently by the 3-D works
of Anderson and Rice (1985) and Dib and Rodin (1993).
In addition to creep rate enhancement, free sliding leads to an enhancement of the
average normal stress transmitted by grain boundaries that are normal to the macroscopic
maximum principal tensile stress direction. This has been discussed in a 2-D context by,
e.g., Rice (1981) and for 3-D by Anderson and Rice (1985) and by Dib and Rodin (1993).
As this so-called principal facet stress is an important driving force for the development of
grain boundary cavitation, there is an obvious interest in adequate descriptions of this
phenomena because of the implications for creep fracture (see, e.g., Nix et al., 1989).
All 2-D studies mentioned above have used periodic arrangements of completely
regular hexagonal grains. Similarly, the cited 3-D studies used regular truncated octa-
hedrons as space-filling model grains. It is clear that grains in real materials vary in size
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