homogeneous deformations

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Crystallography. H. K. D. H. Bhadeshia. Homogeneous deformations. austenite. body-centred tetragonal cell of austenite. body-centred cubic ferrite. contraction expansion. pure strain matrix symmetrical referred to principal axes principal axes are unrotated - PowerPoint PPT Presentation

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  • Homogeneous deformations

  • austenite

  • contraction

    expansion

  • pure strainmatrix symmetricalreferred to principal axesprincipal axes are unrotatedvolume change = determinant of (A S A) =

  • Similarity transformation

  • homogeneous deformation leaves points originally in a line, colinear, and lines originally in a plane, coplanar

  • similarity transformation

  • AssignmentFind and expression for the magnitude of a vector u in terms of the lattice parameters and angle in a monoclinic lattice

  • stretch and rotation

  • three simultaneous equations solved three times by substituting each eigenvalue in turn

  • stretch and rotation

  • Refinement of austenite grain sizerepeated recrystallisationpancakingRefinement of ferrite grain sizenucleation and growth

  • Smallest size possible in steel ?

  • Yokota & Bhadeshia, 2004

  • Pancaking

  • Singh & Bhadeshia, 1998courtesy Rongshan Qin, GIFT, POSTECH

  • uvv = Su

  • Cross Rollingxxyyfirst passsecond passrotate 90

  • courtesy of Rongshan Qin

  • Chae, Qin, ISIJ International 49 (2009) 115

  • *******************************************

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