Microstructure Mechanics Crystal Mechanics

Transcription

1 Microstructure Mechanics Crystal Mechanics Dierk Raabe Düsseldorf, Germany RWTH Class on Microstructure Mechanics 2013

2 Roters, Eisenlohr, Bieler, Raabe: Crystal Plasticity Finite Element Methods in Materials Science and Engineering, Wiley-VCH 1

3 Overview Roters et al. Acta Materi.58 (2010) 2

4 Plastic deformation of a single crystal by dislocation slip Gottstein, Physical Foundations of Materials Science; Springer 3

5 Plastic deformation of a single crystal by dislocation slip d dt dx n X b Z 1 dt bv m Gottstein, Physical Foundations of Materials Science; Springer 4

6 Boundary condition: determines lab frame constraints Constraints lead to specific crystal rotations Non-symmetric dislocation shear leads to rotation Symmetric-shear can lead to shape change without rotation Change in local constraints leads to heterogeneity Roters et al. Acta Mater.58 (2010) 5

7 Single crystal plasticity 6

8 Single crystal plasticity: constructing the yield surface /t mit /t mit 7

9 Single crystal plasticity: constructing the yield surface /t krit FCC, BCC 12 systems section /t krit BCC 24 systems section /t krit /t krit BCC 48 systems section /t krit /t krit 8

10 Overview Roters et al. Acta Mater. 58 (2010) 9

11 Iso-stress and iso-strain 10

12 Iso-stress and iso-strain 11

13 Iso-stress and iso-strain Roters et al. Acta Mater. 58 (2010) 12

14 Iso-stress and iso-strain for polycrystals Sachs Model (previous lecture on single crystal): All grains with aggregate or polycrystal experience the same state of stress; Equilibrium condition across the grain boundaries satisfied; Compatibility conditions between the grains violated, thus, finite strains will lead to gaps and overlaps between grains; Generally most successful for single crystal deformation with stress boundary conditions on each grain. Taylor Model (this lecture): All single-crystal grains within the aggregate experience the same state of deformation (strain); Equilibrium condition across the grain boundaries violated, because the vertex stress states required to activate multiple slip in each grain vary from grain to grain; Compatibility conditions between the grains satisfied; Generally most successful for polycrystals with strain boundary conditions on each grain. 13

15 Polycrystal model Roters et al. Acta Mater. 58 (2010) 14

16 The Taylor Model 15

17 The Taylor Model 16

18 Overview Roters et al. Acta Materi.58 (2010) 17

19 Multiscale crystal plasticity FEM Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002)

20 Homogeneity and boundary conditions at grain scale 3% 8% 15% Raabe et al. Acta Mater. 49 (2001) 3433 Sachtleber, Zhao, Raabe: Mater. Sc. Engin. A 336 (2002) 81 19

21 Crystal Mechanics FEM, grain scale mechanics (2D) Experiment (DIC, EBSD) v Mises strain Simulation (CP-FEM) v Mises strain Sachtleber, Zhao, Raabe: Mater. Sc. Engin. A 336 (2002) 81 20

22 Crystal plasticity FEM, grain scale mechanics (3D Al) 5mm exp., grain orientation, side A 5mm exp., grain orientation, side B 8mm equivalent strain 1mm FE mesh equivalent strain Zhao, Rameshwaran, Radovitzky, Cuitino, Roters, Raabe : Intern. J. Plast. 24 (2008) 21

23 Crystal plasticity FEM for large scale forming predictions too many grains D. Raabe: Advanced Materials 14 No. 9 (2002) p

24 Texture component crystal plasticity FEM for large scale forming Zhao, Mao, Roters, Raabe: Acta Mater. 52 (2004)

25 Texture component crystal plasticity FEM for large scale forming relative ear hight [1] 1,05 1,04 1,03 1,02 1,01 1,00 0,99 0,98 0,97 0,96 0,95 Experiment Simulation angle to rolling direction [ ] D. Raabe and F. Roters: Intern. J. Plast. 20 (2004)

26 Simulation result: Taylor model Color map: Equivalent total strain Roters et al. Acta Mater.58 (2010)

27 Simulation result: RGC scheme Color map: Equivalent total strain Roters et al. Acta Mater.58 (2010)

28 Multiscale crystal plasticity FEM for large scale forming Numerical Laboratory: From CPFEM to yield surface (engineering) DC04 study with Mercedes, Volkswagen, Audi, Inpro Kraska, Doig, Tikhomirov, Raabe, Roters, Comp. Mater. Sc. 46 (2009)