Study of annealing twins in fcc metals and alloys
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p --
Do -
Po
--
D log
D
DO
where Po and Do are constants independent of temperature. An analysis of published results in other fcc metals and alloys shows an excellent agreement with the proposed formulation. The temperature dependence observed in the present study is in agreement with other available experimental results and in conflict with a model of the formation of annealing twins proposed by Gleiter.
I.
INTRODUCTION
ANNEALING twins have been investigated for over 50 years. They occur in a variety of materials from simple alloys like brass to technological materials such as nickel-base superalloys. In this paper, our aim is to obtain definitive experimental results that could help in understanding the growth of these twins and act as a rigorous test for the various twinning models proposed. Finally, we propose a simple model that accounts for our results. An atomistic model explaining in detail our experimental results, such as twin densities as a function of material parameters (such as grain size, stacking fault energy, and twin boundary energy), is in preparation and will be published separately. As mentioned before, several models for the formation of annealing twins in many fcc metals and their alloys have been proposed. These models can be classified under three groups: (1)growth accident models, tl-61 (2) grain encounter models, t7,8'91 and (3) models involving nucleation of twins by stacking faults or fault packets. t~~ These models have been recently reviewed by Meyers and McCowan. 02] Briefly, in the growth accident model, it is suggested that a coherent twin boundary forms at a migrating grain boundary due to a stacking error during growth under energetically favorable conditions. In a grain encounter model, different grains initially separated "encounter" each other during grain growth. If these grains happen to be in twin orientation to each other, the boundary between them becomes a coherent twin boundary by reorienting itself. Finally, the third model suggests that a grain boundary during its migration nucleates a twin such that its incoherent segment remains at the grain boundary. The twin then is supposed to grow by the migration of the other noncoherent boundary. It is not clear what is the driving force for its migration.
In an attempt to elaborate upon the growth accident model, Gleiter t41 has given an atomistic mechanism for the formation of twins. Whereas the original growth accident model of Fullman and Fisher t31 essentially dealt with the development of a comer twin under an energetically favorable situation, Gleiter's analysis is more detailed in predicting a twin density, p (proportional to the number of twin boundaries intersected by a straight line of unit length), as a function of grain size, D, and temperature, T, by the following equation: p=exp~
{-Q/kT + lnAG/kT~ -~e~2- ~ ) \
Qo"
METALLURGICAL TRANSACTIONS A
/
where Q is the activation enthalpy of grain boundary migration, AG is the driving energy per atom for recrystaUization, which is supposed to be related t
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