Creep Strain Modeling of 9 to 12 Pct Cr Steels Based on Microstructure Evolution
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I.
INTRODUCTION
IN order to increase the thermal efficiency in steam power plants, thereby decreasing the fuel consumption, environmental impact, and cost, the operating temperature should be raised. This requires that the material properties are improved.[1] The most critical property that determines the mechanical strength of the material at high temperatures is creep. Creep proceeds mainly by glide and climb of dislocations in the lattice. The principle for developing new creep-resistant materials is to obstruct the dislocation movement. Careful selection of alloying elements to obtain fine precipitates improves the creep strength. In modern 9 to 12 pct Cr steels, the dislocation and particle structures must be stable in order to ensure high long-term creep strength. The development of the particle structure is analyzed in a parallel article.[2] In the classical approaches of creep modelling, a single dislocation density has been assumed. For example, primary creep was modeled by taking into account the back stress from a dislocation density that was initially quite low but gradually increased due to dislocation generation. Such a simple approach cannot describe the behavior of 9 to 12 pct Cr steels. In fact, the initial dislocation density in subgrain interiors after tempering is still high and it decreases during creep due to recovery. To describe this situation, a distinction must be made between immobile and free mobile dislocations that contribute to the plastic deformation. Furthermore, a substructure is already formed during tempering and is then further developed during creep. Because the dislocation processes are quite different in the subgrain boundaries and interiors, these two types must be HANS MAGNUSSON, Graduate Student, and ROLF SANDSTRO¨M, Professor, are with the Materials Science and Engineering and Brinell Centre, Royal Institute of Technology, 100 44, Stockholm, Sweden. Contact e-mail: [email protected] Manuscript submitted March 7, 2007. Article published online July 31, 2007. METALLURGICAL AND MATERIALS TRANSACTIONS A
distinguished. This also applies to the interaction with particles, which are different in the subgrain boundaries and interiors. At least three types of dislocation densities are needed to model this situation. These densities refer to free and immobile dislocations in the subgrain interiors and immobile dislocation in the subgrain boundaries. The aim of the present work is to develop kinetic equations for these three types of dislocation densities. The existence of subgrains is taken into account with the help of the composite model, which has been used previously to model creep.[3–6] The composite model divides the structure in mechanically soft subgrain interiors and hard subgrain boundaries. The total strength can then be summarized similar to traditional composite materials. The composite model is further developed and combined with the approach by Roters et al.[7] for free and immobile dislocations. Characterization of single dislocations and their arrangement into subgrain
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