Variational approach to subgrain formation

Abstract A variational formulation of the incrementally-linear rigidplastic approximation to crystal plasticity is set up. A crystal deformed in plane strain by symmetric double slip is considered as an example. It is shown under which conditions an inhomogeneous deformation leading to subgrain formation is energetically more favorable than the homogeneous one.

[1]  Michael Ortiz,et al.  Nonconvex energy minimization and dislocation structures in ductile single crystals , 1999 .

[2]  E. Kröner,et al.  Kontinuumstheorie der Versetzungen und Eigenspannungen , 1958 .

[3]  Klaus Hackl,et al.  On the Calculation of Microstructures for Inelastic Materials using Relaxed Energies , 2003 .

[4]  Carsten Carstensen,et al.  Non–convex potentials and microstructures in finite–strain plasticity , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[5]  W. Blum,et al.  Creep of Pure Materials and Alloys , 1993 .

[6]  J. Parker Creep and fracture of engineering materials and structures , 2001 .

[7]  H. Mughrabi,et al.  Dislocation wall and cell structures and long-range internal stresses in deformed metal crystals , 1983 .

[8]  J. Z. Zhu,et al.  The finite element method , 1977 .

[9]  W. Blum,et al.  Two mechanisms of dislocation motion during creep , 1989 .

[10]  K. Thermann,et al.  Post-critical deformation pattern in plane strain plastic flow with yield-surface vertex effect , 2000 .

[11]  J. Kratochvíl,et al.  Deformation Induced Misorientations: Initial Stage of Subgrain Formation as a Plastic Instability , 2001 .

[12]  R. Asaro,et al.  Geometrical effects in the inhomogeneous deformation of ductile single crystals , 1979 .

[13]  The energy criteria of instability in time-dependent inelastic solids , 1991 .

[14]  D. C. Drucker,et al.  Mechanics of Incremental Deformation , 1965 .

[15]  J. Kratochvíl,et al.  Energetic approach to subgrain formation , 2004 .

[16]  Laurent Stainier,et al.  A theory of subgrain dislocation structures , 2000 .

[17]  Robert W. Cahn,et al.  Plastic deformation and fracture of materials , 1993 .

[18]  John W. Hutchinson,et al.  Bifurcation phenomena in the plane tension test , 1975 .

[19]  D. Kuhlmann-wilsdorf,et al.  Overview no. 96: Evolution of F.C.C. deformation structures in polyslip , 1992 .

[20]  J. Kratochvíl,et al.  Instability origin of dislocation substructure , 1990 .