Grain growth behavior of tungsten heavy alloys based on the master sintering curve concept
- PDF / 315,384 Bytes
- 10 Pages / 612 x 792 pts (letter) Page_size
- 100 Downloads / 236 Views
E grain growth of tungsten heavy alloys (WHAs) is generally treated by variants of Ostwald ripening theory, which may or may not consider concurrent grain growth by coalescence. Ostwald ripening occurs when small grains dissolve in the matrix, which becomes saturated and reprecipitates solute atoms on large grains.[1] Coalescence can occur by grain boundary migration, liquid film migration, solution-reprecipitation through the matrix, and grain rotation.[2] Grain boundary migration and grain rotation do not require solubility of the grains in the matrix. Most grain growth studies consider only isothermal coarsening, but significant grain growth can occur during heating, even in the solid state. The concept of a master sintering curve, originally developed by Su and Johnson,[3] lends itself to analysis of nonisothermal sintering cycles. Although originally developed for densification, the master curve concept is generally applicable to any process in which the microstructural geometry is independent of the thermal processing path. Additionally, it can be modified to consider changes in the dominant process mechanism, as demonstrated recently for densification during heating of three WHAs[4] with W contents ranging from 83 to 93 wt pct. In this work, the master sintering curve concept is used to analyze grain growth of these WHAs during both solidstate and liquid-phase sintering. II.
MASTER SINTERING CURVE FOR GRAIN GROWTH
Greenwood[5] proposed the following equation for the growth rate of an individual grain by Ostwald ripening:
S.J. PARK, Associate Research Professor, is with the Center for Advanced Vehicular Systems, Mississippi State University, Mississippi State, MS 39762. Contact e-mail: [email protected] J.M. MARTIN, Staff Researcher, is with the Centro de Estudios e Investigaciones Te´cnicas de Guipu´zcoa (CEIT) and TECNUN, 20018 San Sebastia´n, Spain. J.F. GUO, Graduate Student, is with the Center for Innovative Sintered Products, The Pennsylvania State University, University Park, PA 16802. JOHN L. JOHNSON, Staff Engineer, is with Breakthrough Technology, Kennametal Inc., Latrobe, PA 15650. RANDALL M. GERMAN, Director and CAVS Chair Professor of Mechanical Engineering, is with the Center for Advanced Vehicular Systems, Mississippi State University. Manuscript submitted December 22, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A
dGi 2DCVg 1 1 5 dt RTG G Gi
[1]
where Gi is the size of one specific grain, G is the mean grain size, t is the time, D is the diffusivity of the grain atoms in the matrix, C is the grain atoms’ solubility in the matrix, V is the grain atoms’ molar volume, g is the grain-matrix surface energy, R is the gas constant, and T is the absolute temperature. Equation [1] was originally derived assuming a diffusion-controlled process, spherical grains, and a grain volume fraction close to zero. Under these circumstances, a mean concentration of solute in the matrix with only local gradients near the surface of the grains can be assumed, i.e., the mean field assumption is valid. The
Data Loading...
