A process model for the microstructure evolution in ductile cast iron: Part I. the model
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. INTRODUCTION
DUCTILE cast irons possess a wide range of physical and mechanical properties, which make them excellent candidate materials for structural applications.[1,2] At the same time, they offer positive impact on economical, safety, and environmental aspects by allowing production of high quality, low priced products from recycled metal scrap. The main disadvantage is weight, but considerable weight savings can be obtained by the use of stronger irons and thinner sections. In practice, this is made possible through a more effective nucleation and growth of the graphite phase during solidification, often in combination with some additional heat treatment of the iron matrix (e.g., austempering).[2] Because of the increased emphasis on microstructure control, significant progress has been made in the understanding of the mechanisms of microstructure evolution in ductile cast iron over the past decade, both during solidification and in the solid state.[3] At the same time, the recent advances in computer technology and numerical methods have made it possible to analyze transport phenomena (e.g., heat, mass, and fluid flow in the mushy zone) to a high level of detail.[4] A synthesis of that knowledge has, in turn, been consolidated into various kinds of deterministic models to predict the cast structure.[5–13] Some of these also include a consideration of the subsequent solid-state transformations, based on approximate analytical solutions for the carbon diffusion field in the vicinity of the graphite nodules.[6,11] Although the ideal is a true physical model, the approach has shown to work well for certain alloy systems, provided that the models are tuned to experimental microstructure data. Alternatively, the problem can be handled by means of analytical modeling techniques to ensure a sufficient degree M.I. ONSØIEN and Ø. GUNDERSEN, Research Metallurgists, are with SINTEF Materials Technology, N-7034 Trondheim, Norway. Ø. GRONG, Professor, is with the Department of Metallurgy, Norwegian University of Science and Technology, N-7034 Trondheim, Norway. T. SKALAND, Research Metallurgist, is with Elkem a/s Research, N-4602 Kristiansand, Norway. Manuscript submitted March 5, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
of accuracy in all components of the model without employing complex numerical solutions.[14–18] Experience has shown that constitutive models describing nonisothermal transformation behavior are best derived by using the internal state variable approach, according to the formalism originally proposed by Richmond.[19] In this case, the microstructure evolution is captured mathematically in terms of differential variation of the primary state variables with time for each of the relevant mechanisms.[15,18] At the same time, appropriate heat flow calculations are required to predict the thermal history. Solution of the coupled differential equations is then carried out by stepwise integration in temperature-time space, using an appropriate numerical integration procedure. Moreover, by utilizing the
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