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This approach takes into account the severe deformation that occurs during each pass and also the possible reheating between passes. In predicting the grain size at the end of the rolling process, microstructural events such as dynamic recrystallization (DRX), metadynamic recrystallization (MDRX), and static grain growth are captured at every deformation step for superalloys. Empirical relationships between the average grain size from various microstructural processes and the macroscopic variables such as temperature (<jats:italic>T<\/jats:italic>) and effective strain (<jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mover><mml:mrow><mml:mi>\u03b5<\/mml:mi><\/mml:mrow><mml:mo>\u0304<\/mml:mo><\/mml:mover><\/mml:math><\/jats:inline-formula>) and strain rate (<jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mover><mml:mrow><mml:mover><mml:mrow><mml:mi>\u03b5<\/mml:mi><\/mml:mrow><mml:mo>\u0304<\/mml:mo><\/mml:mover><\/mml:mrow><mml:mo>\u0307<\/mml:mo><\/mml:mover><\/mml:math><\/jats:inline-formula>) form the basis for the current work. These empirical relationships are based on Avrami equations. The macroscopic variables are calculated using a finite element analysis package wherein the material being rolled is modeled as a non-Newtonian fluid with viscosity that depends on the effective strain rate, strain, and temperature. A two-dimensional transient thermal analysis is carried out between passes that can capture the MDRX and\/or static grain growth during the microstructural evolution. The presented microstructure prediction algorithm continuously updates two families of grains, namely, the recrystallized family and strained family at the start of deformation in any given pass. In addition, the algorithm calculates various subgroups within these two families at every deformation step within a pass. As the material undergoes deformation between the rolls, recrystallization equations are invoked depending on critical strain and strain rate conditions that are characteristics of superalloys. This approach predicts the microstructural evolution based on recrystallization kinetics and static grain growth only. The methodology was successfully applied to predict the microstructure evolution during the multi-pass rolling of nickel-base superalloys. The predicted results for Alloy 718 for a 4-stand rolling followed by air cooling and for a 16-stand rolling followed by a combination of air and water cooling are also compared with experimental observations.<\/jats:p>","DOI":"10.1186\/s40192-014-0027-3","type":"journal-article","created":{"date-parts":[[2014,11,24]],"date-time":"2014-11-24T18:02:57Z","timestamp":1416852177000},"page":"385-408","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Prediction of microstructure evolution during multi-stand shape rolling of nickel-base superalloys"],"prefix":"10.1186","volume":"3","author":[{"given":"Kannan","family":"Subramanian","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Harish P","family":"Cherukuri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,11,25]]},"reference":[{"key":"27_CR1","unstructured":"Minisandram RS, Thompson EG, Forbes Jones RM, Stedje-Larsen R (2001) Numerical simulation of a multi-stand rolling mill. 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