Phase Mixture Models for Metallic Materials with Submicrometer Grain Size
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Phase Mixture Models for Metallic Materials with Submicrometer Grain Size Yuri Estrin1, Hyoung Seop Kim2 and Mark Bush3 1 Department of Materials Science and Technology, Clausthal University of Technology, Agricolastr. 6, D-38678 Clausthal-Zellerfeld, GERMANY 2 Department of Metallurgical Engineering, Chungnam National University, Daejeon, 305-764, KOREA 3 School of Mechanical and Materials Engineering, The University of Western Australia 35 Stirling Hwy, Crawley, WA 6009, AUSTRALIA ABSTRACT Phase mixture models describing the mechanical properties of submicrometer grained metals are presented. In this approach, grain boundaries or cell walls are treated as a separate phase. Two cases are considered: the mechanical response of an ultrafine grained material and the process of grain refinement by equal channel angular pressing. Model predictions with regard to the evolution of the microstructure, strength and texture are verified for Cu. INTRODUCTION Structural applications of nanocrystalline (nc) materials hinge on reliable knowledge of their mechanical properties. While recent reviews [1-3] have provided insights into the mechanical behavior of nanocrystalline materials, the roles of the different deformation mechanisms, such as dislocation glide and grain boundary processes, are still not fully understood. A recent suggestion [4] that mechanical twinning is an important deformation mechanism in nc materials adds to the richness of the emerging picture. In this paper we present our current view on how strength, strain hardening and ductility of metallic materials with submicrometer scale grain size, particularly nc materials, can be modelled using a phase mixture approach [3,5-7]. It is based on the idea that grain boundaries can be treated as a separate phase that deforms by a diffusion mechanism. The other ‘phase’, viz. the grain interior, is considered to deform by a superposition of dislocation glide and diffusion controlled mechanisms, see Fig. 1. An outline of the model will be given and some results relating to strength and ductility will be discussed.
Figure 1. Schematic diagrams of the phase mixture model and the deformation mechanisms.
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Of significant interest to the materials community is the possibility to produce an ultrafine grain structure by severe plastic deformation, particularly equal channel angular pressing (ECAP) [8,9]. Modeling of the mechanical behaviour during ECAP, along with the evolution of its microstructure toward the submicrometer grain size scale, is a challenging exercise. Again, a model based on a phase mixture approach [10] proves to be successful. However, this time it is the dislocation cell walls and the cell interiors that are treated as two separate phases [11]. A selection of results obtained with this model will be presented. MECHANICAL PROPERTIES OF ULTRAFINE GRAINED MATERIALS Following [5-7], the grain boundary phase is considered to deform by a vacancy diffusion mechanism. The corresponding plastic strain rate is given by
ε&GB = A
Ωσ GB DGB . kT d 2
(
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