A process model for the heat-affected zone microstructure evolution in duplex stainless steel weldments: Part I. the mod
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I. INTRODUCTION
DUPLEX stainless steels offer many attractive properties that are not easily achievable in austenitic or ferritic stainless steels. Their increased use in the last decades is due to excellent corrosion resistance and mechanical properties.[1] These favorable properties are strongly dependent on the austenite-ferrite phase ratio, which in the base material is designed to be approximately 1:1.[2] In addition, a number of secondary transformation products such as the s phase, the x phase, etc., may form within the grain interiors,[2] but such side reactions will not be dealt with here. In order to retain the favorable properties in a welded component, the phase balance must be maintained, in both the weld metal and the heat-affected zone (HAZ). The microstructure and the properties of the weld metal are generally controlled by adjusting the filler material composition. However, the microstructure in the HAZ is determined by the weld thermal cycle and is therefore very sensitive to variations in the welding conditions. Because of the increased emphasis on microstructure control, modeling of the HAZ transformation behavior in duplex stainless steel weldments has been the topic of a number of previous investigations.[3–15] These range from pure empirical models to more in-depth theoretical analyses based on thermodynamics and transformation kinetic theory. The latter studies have clearly demonstrated the advantage of using
H. HEMMER, Section Head, is with the Institute of Energy Technology, N-2027 Kjeller, Norway. Ø. GRONG, Professor, is with the Department of Materials Technology and Electrochemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway. Manuscript submitted January 29, 1999.
METALLURGICAL AND MATERIALS TRANSACTIONS A
analytical modeling techniques to describe the HAZ microstructure evolution instead of relying solely on experimental observations. Alternatively, the problem can be handled by process modeling techniques that ensure a sufficient degree of accuracy in all components of the model without employing complex numerical solutions.[16–20] Experience has shown that constitutive models describing nonisothermal transformation behavior are best derived using the internal-state variable approach according to the formalism originally proposed by Richmond.[21] In such cases the microstructure evolution is captured mathematically in terms of differential variation of the primary-state variables with time for each of the relevant mechanisms.[17,20] 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 concept of group variables, different kinds of process diagrams and mechanism maps can be constructed to illustrate the competition between different variables involved.[16–20] In the present investigation, the methodology is furthe
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