Marko Knezevic

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Viscoplastic crystal plasticity and application
to yield surfaces delineation of FCC polycrystals
April 21, 2008   

• Marko Knezevic

DEPARTMENT OF MATERIALS SCIENCE AND
ENGINEERING DREXEL UNIVERSITY
http//www.materials.drexel.edu/mmg
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Description of the Microstructure
Crystallographic texture has been selected as the
prime descriptor of interest in the
microstructure in predicting anisotropic yield
surfaces.
The distribution of the orientations in a
polycrystalline aggregate is referred to as
crystallographic texture.
Texture is developed as a consequence of
processing

• Solidification
• Metal Forming
• Heat Treatment

• Many properties demonstrate dependence on
  crystallographic orientation
• i.e. Elasticity, Plasticity, Magnetism, etc.
• Tools exist for identification of the
  crystallographic orientations (texture)
• i.e. EBSD, X-Ray, and polarized light.

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Outline

• Summary of Taylor type viscoplastic crystal
  plasticity
• Spectral crystal plasticity framework in terms
  of Discrete Fourier Transforms
• Efficient delineation of yield surfaces

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Viscoplastic Crystal Plasticity - FCC metals
Crystallographic slip

• Aluminum
• Copper

FCC Crystals
Potential Slip Systems
1 - 12
Applied Stretching Tensor
Shearing Rate
Rate sensitivity parameter
Resolved Shear Stress
Output
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General Deformation Path Description
Same deformation gradient in all of the
constituent crystals
Sample frame
Principal frame of D
Rotation
- Isochoric - Unit
Unique representations of all possible stretching
tensors q
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Database Approach to Crystal Plasticity
Spectral representations
r and q enumerate the grid points in the
orientation space and the strain space
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Retaining only the dominant transforms
Full Euler Space 360x360x360
Two orders of magnitude faster than conventional
calculations!
Restored using 500 of transforms
Taylor code values
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Efficient Computation of Yield surfaces
Principle Frame Space
Stretching Tensor Space
Polycrystalline yield surfaces based on a yield
surface of one single crystal e.g ( 0, 0, 0)
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Summary

• Viscoplastic crystal plasticity solutions have
  been successfully captured in spectral linkages
  cast using Discrete Fourier Transforms (DFT).
• Implemented database approaches provided a
  remarkable reduction in the computational time
  involved in the delineation of yield surfaces.

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• Questions