Methods (3D EBSD, CP-FEM) Characterization

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Presentation transcript:

Analysis of GNDs beneath indents of different depth using EBSD tomography E. Demir, S. Zaefferer, F. Roters, D. Raabe Department of Microstructure Physics and Metal Forming Düsseldorf, Germany d.raabe@mpie.de 27. October 2009, MS&T, Pittsburgh

Methods (3D EBSD, CP-FEM) Characterization Overview Methods (3D EBSD, CP-FEM) Characterization Orientation gradients and dislocation analysis Discussion Dierk Raabe, MS&T, Pittsburgh, 27. Oct. 2009, MPIE

Indents of different depths, Cu single crystal Motivation and approach: specific Relationship between ISE and GND: hardness and GND in the same experiment Indents of different depths, Cu single crystal 3D EBSD: plastic volume, orientation gradients, GNDs

Multiscale crystal plasticity FEM Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421

Nanoindentation [111] [-110] [11-2] 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads of 4000μN, 6000μN, 8000μN and 10000μN [-110] [11-2] [111] Wang, Raabe, Klüber, Roters: Acta Mater. 52 (2004) 2229

3D electron microscopy, 3D EBSD, tomography J. Konrad, S. Zaefferer, D. Raabe, Acta Mater. 54 (2006) 1369 Zaefferer,. Wright, Raabe, Metall. Mater. Trans. A 39A (2008) 374

Crystal orientation distribution around nanoindents Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN Misorientation angle 0° 20° [-110] [111] [11-2] Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31

scan 7 scan 8 scan 9 Comparison, crystal rotations about [11-2] axis viscoplastic CPFEM experiment 3D EBSD dislocation-based CPFEM experiment simulation scan 7 scan 8 scan 9 [-110] [111] [11-2] Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707 Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31

Simplify Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31

From local misorientations to GNDs misorientation angle 0° 20° misorientation orientation difference orientation gradient (spacing d from EBSD scan) Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

From local misorientations to GNDs distortion (sym, a-sym) dislocation tensor (GND) J. F. Nye. Some geometrical relations in dislocated crystals. Acta Metall. 1:153, 1953. E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559–569 E. Kröner. Kontinuumstheorie der Versetzungen und Eigenspannungen (in German). Springer, Berlin, 1958. E. Kröner. Physics of defects, chapter Continuum theory of defects, p.217. North-Holland Publishing, Amsterdam, Netherlands, 1981. Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

From local misorientations to GNDs Frank loop through area r DDT in terms of 18 b,t combinations DDT in terms of 9 b,t combinations Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

Distribution of GNDs for different gradient resolutions 50 nm 100 nm 200 nm center section, 2D analysis, color code: GND density (decadic log. (1/m2) ) Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

Identification of the plastic volume depth [mm] Reference volumes (red color) indicates the plastic volume using lower threshold of GNDs of 1014/m2 center section, 2D analysis, color code: GND density (decadic log. (1/m2) ) Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

Extract geometrically necessary dislocations Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

Conclusions GNDs have inhomogeneous distribution below indents with very high local density values. Total GND density below indents drops with decreasing indentation depths. Observation contradicts strain gradient theory.