Polycrystalline strengthening
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I.
INTRODUCTION
POLYCRYSTALS consist of grains which, due to a mutual interaction, cannot deform freely during a deformation process. Higher stresses are therefore required to deform polycrystals than are needed for isolated single crystals, which can deform by glide on a single slip system. This polycrystalline strengthening relates to macroscopic deformation processes which normally are considered to be independent of the grain size. Beyond this an additional factor affecting .the strength of polycrystals is that of the size of the grains. This grain-size dependent contribution to the strength is demonstrated by the well-known experimental observation that the low temperature strength of polycrystalline specimens normally increases when the grain size is decreased. A major part of the theoretical and experimental work in the last 50 years has concentrated on the macroscopic deformation of polycrystalline specimens with the main aim of understanding the stress-strain relationship and the texture development during cold deformation. However, in the last 20 years increasing attention has been paid to the effect of grain size on the yield stress and the flow stress of polycrystalline specimens. An important part of this work has been to interpret empirical strength-grain size relationships on the basis of the microstructural observation of the surface and the bulk behavior. Similarly, the changes in the dislocation structures in or at the grain boundaries during deformation have been studied in detail. This paper deals primarily with the microstructural aspects of polycrystalline strengthening at low and medium strains andat temperatures where dislocation climb is not important. The strength-structure relationships under such NIELS HANSEN is Head of the Metallurgy Department, Rise National Laboratory, 4000 Roskilde, Denmark. This paper is based on a presentation made at the symposium "50th Anniversary of the Introduction of Dislocations" held at the fall meeting of the TMS-AIME in Detroit, Michigan in October 1984 under the TMSAIME Mechanical Metallurgy and Physical Metallurgy Committees. METALLURGICALTRANSACTIONS A
conditions have been described in a number of models based on various assumptions regarding the deformed microstructures. Such models are reviewed and their predictive capability discussed below, as well as the degree to which their basic assumptions accord with microstructural observations. In this presentation the first section is a review of polycrystalline deformation concentrating upon the aspects of macroscopic and microscopic strain accommodation during deformation. These subjects are recapitulated in the discussion and related to the observations of deformation microstructures in fcc and bcc polycrystalline specimens. II.
POLYCRYSTALLINE STRENGTHENING
The subject of deformation and strengthening of polycrystalline specimens has been reviewed extensively; see, e.g., References 1 through 13. The strengthening processes may be related in general to interaction phenomena taking place during defor
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