Simulation of subgrain growth by subgrain rotation: A one-dimensional model
- PDF / 527,751 Bytes
- 7 Pages / 630 x 792 pts Page_size
- 54 Downloads / 192 Views
I.
INTRODUCTION
N O R M A L grain growth has been studied extensively for a number of years and is still a subject of great interest, t1-13] During normal grain growth, the specific grain boundary energy, y(gb), is roughly the same for all grain boundaries and independent of annealing time. Grain growth results in a reduction of the total grain boundary area, and hence, the total energy of the material is reduced: N
6E = y(~b) Z t~Ai
[1]
i=1
The reduction in energy is obtained by the migration of the grain boundaries. It is generally accepted that larger grains grow by reducing the size of the smaller grains. Hence, there will always be small grains in the system which, in the end, disappear. A reduction in the number of grains leads to a larger average grain size and, consequently, a reduction in the total grain boundary area. Contrary to the case of normal grains, the specific subgrain boundary energy, y~,b), can vary substantially from boundary to boundary and for one particular boundary with time. Energy reduction can thus be obtained either by a decrease in the total subgrain boundary area, by a decrease in y~sb), or by a combination of both. The energy equation for subgrains can thus be written in the following way: N
N
6E = Z ( Tlsb)t~ai) d- Z (ait~T~sb)) i=1
[2]
i=1
The theoretical treatment of subgrain growth is thus much more complicated than normal grain growth, and only a few and rather incomplete investigations have been published. The two possible mechanisms have only been studied separately. If subgrain rotation is excluded from the treatment (6y ~sb) = 0), subgrain growth takes place by subgrain boundary migration. The problem is further simplified by assuming that y~sb) has the same value for all subgrain T.O. SAETRE, Head of Roiling Technology, is with the Research and Development Centre, Hydro Aluminum a.s, N-4265 Havik, Norway. N. RYUM, University Professor of Physical Metallurgy, is with the Department of Metallurgy, The University of Trondheim, N-7034 Trondheim, Norway. E. EVANGELISTA, University Professor of Materials Science, is with the Department of Mechanical Engineering, University of Ancona, 60131 Ancona, Italy. Manuscript submitted September 5, 1990. METALLURGICAL TRANSACTIONS A
boundaries. The only formal difference between normal grain growth and subgrain growth then is the mobility of the boundaries. Sandstr6m E14]has investigated this case and formulated a theory for it. However, he did not take into account the geometrical problems arising when y~sb) is constant. This aspect has recently been taken up by 0rsund and Nes. t15] How subgrain growth by subgrain migration should be treated when y(sb) and the boundary structure vary from boundary to boundary is far from clear. The second mechanism by which a reduction in energy of the material can take place is by subgrain rotation. This process is frequently referred to as subgrain c o a l e s c e n c e . Hu H61 found evidence of subgrain rotation by electron microscopic observations of subgrain growth. This led to the first
Data Loading...
