Abstract
The needs for materials science are to design components with desired performance, fabricated from materials with desired properties, and the processes to produce these components and materials via control of microstructure. Here the microstructure-property-performance relations are emphasized. In particular, microstructure is accessible experimentally, can be manipulated in processing, and determines properties and hence performance of materials.
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References
Baddeley, A, and Møller, J. (1989). Nearest-neighbor Markov point processes and random sets. International Stat. Rev. 57, 89–121.
Besag, J. (1986). On the statistical analysis of dirty pictures (with discussion). J. Roy. Stat. Soc. Ser. B 6, 259–302.
Besag, J., Milne, R. and Zachary, S. (1982). Point processes limits of lattice processes. Bul. International Stat. Inst. 19, 210–216.
Curtin, W.A. and Scher, H. (1990). Brittle fracture in disordered materials: A spring network model. J. Mater. Res. 5, 535–553.
Geman, D. (1991). Random fields and inverse problems in imaging. Lecture Notes in Math. 1427, 113–193. Springer, Berlin.
Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distribution, and Bayesian restoration of images. IEEE Trans. FAMI 6, 721–741.
Geyer, C. and Møller, J. (1994). Simulation procedures and likelihood inference for spatial point processes, Scand. J. Stat., 21, 359 373.
Grenander, U. (1993). General Pattern Theory. Oxford Univ. Press, Oxford.
Hall, P. (1988). Introduction to the Theory of Coverage Processes. Wiley, New York.
Jagota, A. and Bennison, S.J. (1994), Spring-network and finite-element models for elasticity and fracture. To appear in the proceedings of a workshop on Breakdown and Non-linearity in Soft Condensed Matter, K.K. Bardhan et al. (ed.) Springer, New York.
Karr, A. (1993). Statistics and materials science — report of a workshop. Tech. Report # 4, NISS.
Kira, E. (1994). Forthcoming Ph.D. thesis, Dept. of Stat., UNC-Chapel Hill.
Lawn, B. (1993). Fracture of Brittle Solids (2nd ed.). Cambridge Univ. Press, Cambridge.
Serra, J. (1982). Image Analysis and Mathematical Morphology, Vol.I. Academic Press, New York.
Sridhar, N., Yang, W., Srolovitz, D.J. and Fuller, E.R. (1994). Microstructural mechanics model of anisotropic thermal expansion induced microcracking, J. Amer. Ceramics Soc., 77, 1123–1138.
Stoyari, D., Kendall, W.S. and Mecke, J. (1987). Stochastic Geometry and Its Applications. Wiley, New York.
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Ji, C. (1996). Hierarchical Modelling for Microstructure of Certain Brittle Materials. In: Levinson, S.E., Shepp, L. (eds) Image Models (and their Speech Model Cousins). The IMA Volumes in Mathematics and its Applications, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4056-3_5
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DOI: https://doi.org/10.1007/978-1-4612-4056-3_5
Publisher Name: Springer, New York, NY
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