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I.

INTRODUCTION

The mechanism of creep deformation in metals at elevated temperatures is mainly classified into three types: dislocation creep, grain-boundary (GB) diffusion creep, and lattice diffusion creep.[1] Corresponding to these mechanisms, the mechanism of creep fracture is thought to be different, and is classified into the following three types: wedge cracking or void formation due to dislocation creep, cavity growth due to GB diffusion, and cavity growth due to lattice diffusion. With regard to diffusional cavitation, which is a dominant fracture in metals when they are subjected to high temperatures and low stresses, a number of analytical investigations have been devoted to this topic[2] since the pioneering work by Hull and Rimmer.[3] These investigations, however, were concerned with cavity growth in GB diffusion creep, and none of them examined cavity growth in lattice diffusion creep. This is because of the importance in engineering of the moderate-temperature range, where GB diffusion dominates over lattice diffusion in most metals. In this study, it is supposed that the atoms can be transported from the cavity surface to the grain boundary near the cavity by lattice diffusion due to the difference in chemical potential. A model and a method of numerical analysis of GB cavitation due to lattice diffusion are proposed. Also shown is an analysis of cavitation due to the effect of interaction between GB diffusion and lattice diffusion on cavity growth. II.

CAVITY GROWTH BY GB DIFFUSION

First, the analytical concept of GB cavity growth due to GB diffusion will be briefly reviewed, to provide a reference for the analysis on growth due to lattice diffusion. In this article, the cavity is assumed to be cylindrical with a unit depth, as per the treatment used many researchers to date.[2,3,4]

TADAHIRO SHIBUTANI, Graduate Student, TAKAYUKI KITAMURA, Associate Professor, and RYUICHI OHTANI, Professor, are with the Department of Engineering Physics and Mechanics, Kyoto University, Kyoto 606-8501, Japan. Manuscript submitted August 12, 1997.

METALLURGICAL AND MATERIALS TRANSACTIONS A

A. Governing Equations When stress is applied to a polycrystalline material at an elevated temperature, atoms are transported along the GBs. The flux, which is the volume of atoms crossing a unit depth per unit of time (Jb) is formulated as Jb 5

Db ]m kT ]x

[1]

where Db is the GB diffusivity, k is the Boltzmann’s constant, T is the absolute temperature, m is the chemical potential, and x is the local coordinate along the GB (Figure 1(a)). The chemical potential in the GB is evaluated by

m 5 m0 2 s V

[2]

where m0 is the potential for bulk, s is the normal stress to the GB, and V is the atomic volume. The conservation of matter requires that

db

]Jb z 1db 5 0 ]x

[3]

z Here, db is the thickness of the GB and db is the rate of accumulation or erosion of atoms in the GB. The positive z and negative signs of db represent the accumulation and the erosion, respectively. B. Periodic Allay of GB Cavities Hull and Rimmer[3] p