CURVATURAS: MEDIDAS E COMPARAÇÃO COM MODELOS GEOMÉTRICOS
CURVATURES: MEASURES AND COMPARISON WITH GEOMETRIC MODELS
Fonseca, Glaucio Soares da
http://dx.doi.org/10.4322/tmm.00503007
Tecnol. Metal. Mater., vol.5, n3, p.162-166, 2009
Resumo
A curvatura média do contorno de grão, a curvatura média das arestas do grão e a curvatura média do grão foram medidas em amostras de estrutura cúbica de face centrada (liga Al-1% massa Mn) e em amostras de estrutura cúbica de corpo centrado (aço elétrico de grãos não orientados, aço microligado ao nióbio, aço livre de intersticiais e ferro puro). Modelos geométricos simples em função do comprimento médio das intersecções dos grãos foram usados como parâmetro de comparação, apresentando boa concordância com os dados experimentais.
Palavras-chave
Curvatura, Contorno de gão, Regras de Plateau
Abstract
The average grain boundary curvature, average edge curvature and average grain curvature were measured in face centered cubic structure samples (Al-1mass% Mn alloy) and in body centered cubic structure samples (electric steel of non-oriented grains, Niobium-low alloyed steel, steel interstitial free and pure iron specimen). The resulting experimental data is compared with existing geometric models relating these three curvatures to the mean intercept length of the grains. The models showed good agreement with experimental data.
Keywords
Curvature, Average grain, Plateau Rules
Referências
1 AUGUSTO, F.P.M. Medida das curvaturas do grão em metais. 2006. 111 p. Dissertação (Mestrado em Engenharia Metalúrgica) – Universidade Federal Fluminense, Volta Redonda, 2006.
2 HAROUN, N.A.; BUDWORTH, D.W. Modifications to the Zener formula for limitation of grain size. Journal of Materials Science, v. 3, n. 3, p. 326-8, May 1968.
3 PATTERSON, B.R.; LIU, Y. Relationship between grain boundary curvature and grain size. Metallurgical Transactions, v. 23A, n. 9, p. 2481-2, Sept. 1992.
4 RIOS, P.R.; FONSECA, G.S. Grain boundary curvature and particle pinning in an Al-1mass%Mn alloy. Scripta Materialia, v. 50, n. 11, p. 1373-7, June 2004.
5 DEHOFF, R.T.; LIU, G.Q. On the relation between grain size and grain topology. Metallurgical Transactions, v. 16A, n. 11, p. 2007-11, Nov. 1985.
6 CANH, J.W. The Significance of Average mean curvature and its determination by quantitative metallography. Transactions of the Metallurgical Society of American Institute of Mining and Engineers, v. 239, n. 5, p. 610-6, May 1967.
7 DEHOFF, R.T. The Quantitative estimation of mean surface curvature. Transactions of the Metallurgical Society of American Institute of Mining and Engineers, v. 239, n. 5, p. 617-21, May 1967.
8 TAYLOR, J.E. II – Mean curvature and weighted mean curvature. Acta Metallurgica et Materialia, v. 40, n. 7, p. 1475-85, July 1992.
9 RIOS, P.R.; FONSECA, G.S. Geometrical models for grain, grain boundary and grain edge average curvature in an Al-1 mass%Mn alloy. Scripta Materialia, v. 52, n. 9, p.893 -7, May 2005.
10 RIOS, P.R.; FONSECA, G.S. Grain boundary pinning by Al6Mn precipitates in an Al-1wt%Mn alloy. Scripta Materialia, v. 50, n. 1, p. 71-5, Jan. 2004.
11 FONSECA, G.S.; RIOS, P.R. Estudo geral das curvaturas dos grãos e apresentação de modelos geométricos. In: CONGRESSO ANUAL DA ABM - INTERNACIONAL, 60., 2005, Belo Horizonte. Anais... São Paulo: ABM, 2005. 1 CD
12 RUSS, J.C.; DEHOFF, R.T. Practical stereology. 2. ed. New York: Kluwer Academic, 2000.
13 DEHOFF, R.T. The spherical image concept applied to grain structures. Acta Metallurgica et Materialia, v. 42, n. 8, p. 2633-43, Aug 1994
14 GLICKSMAN, M.E. Analysis of 3-D network structures. Philosophical Magazine, v. 85, n. 1, p. 3-31, Jan. 2005.
2 HAROUN, N.A.; BUDWORTH, D.W. Modifications to the Zener formula for limitation of grain size. Journal of Materials Science, v. 3, n. 3, p. 326-8, May 1968.
3 PATTERSON, B.R.; LIU, Y. Relationship between grain boundary curvature and grain size. Metallurgical Transactions, v. 23A, n. 9, p. 2481-2, Sept. 1992.
4 RIOS, P.R.; FONSECA, G.S. Grain boundary curvature and particle pinning in an Al-1mass%Mn alloy. Scripta Materialia, v. 50, n. 11, p. 1373-7, June 2004.
5 DEHOFF, R.T.; LIU, G.Q. On the relation between grain size and grain topology. Metallurgical Transactions, v. 16A, n. 11, p. 2007-11, Nov. 1985.
6 CANH, J.W. The Significance of Average mean curvature and its determination by quantitative metallography. Transactions of the Metallurgical Society of American Institute of Mining and Engineers, v. 239, n. 5, p. 610-6, May 1967.
7 DEHOFF, R.T. The Quantitative estimation of mean surface curvature. Transactions of the Metallurgical Society of American Institute of Mining and Engineers, v. 239, n. 5, p. 617-21, May 1967.
8 TAYLOR, J.E. II – Mean curvature and weighted mean curvature. Acta Metallurgica et Materialia, v. 40, n. 7, p. 1475-85, July 1992.
9 RIOS, P.R.; FONSECA, G.S. Geometrical models for grain, grain boundary and grain edge average curvature in an Al-1 mass%Mn alloy. Scripta Materialia, v. 52, n. 9, p.893 -7, May 2005.
10 RIOS, P.R.; FONSECA, G.S. Grain boundary pinning by Al6Mn precipitates in an Al-1wt%Mn alloy. Scripta Materialia, v. 50, n. 1, p. 71-5, Jan. 2004.
11 FONSECA, G.S.; RIOS, P.R. Estudo geral das curvaturas dos grãos e apresentação de modelos geométricos. In: CONGRESSO ANUAL DA ABM - INTERNACIONAL, 60., 2005, Belo Horizonte. Anais... São Paulo: ABM, 2005. 1 CD
12 RUSS, J.C.; DEHOFF, R.T. Practical stereology. 2. ed. New York: Kluwer Academic, 2000.
13 DEHOFF, R.T. The spherical image concept applied to grain structures. Acta Metallurgica et Materialia, v. 42, n. 8, p. 2633-43, Aug 1994
14 GLICKSMAN, M.E. Analysis of 3-D network structures. Philosophical Magazine, v. 85, n. 1, p. 3-31, Jan. 2005.
Facebook
Google+
Twitter
LinkedIn
Mendeley
StumbleUpon
CiteULike
Reddit
Email