POLYCRYSTAL MODELING (1 day)
Dr. Carlos Tomé, tome@lanl.gov
and
Dr. Ricardo Lebensohn, lebenso@lanl.gov
MST Division
Los Alamos National Laboratory
Los Alamos, NM 87545 USA
Polycrystal models represent the material as an aggregate of grains with different orientations, and predict the material's response as an average over the constituent grains. As a consequence, they capture the mechanical anisotropy associated with the texture. In addition, they are based on the physical mechanisms acting at the grain level (i.e.: dislocation slip systems).
In these lectures we review and compare available polycrystal models. We discuss the basic elements, assumptions and range of applicability of the models. We discuss hardening and texture evolution associated with several strain paths (rolling, torsion, compression) and provide hands-on training on how to simulate polycrystal plastic forming using the Visco-Plastic Self-Consistent (VPSC) Polycrystal Code.
Outline
1. The Basics (1.5 hours)
1.1 What is a polycrystal model? Upper Bound, Lower Bound and Self-Consistent models.
1.2 Effective Medium formulation. Visco-Plastic Self-Consistent (VPSC) polycrystal model. Interaction equation. Taylor and Sachs as limit cases of inclusion-medium interaction.
1.3 Compression, tension and rolling of FCC aggregate. Texture development, slip system activity, comparison of Taylor and self-consistent results.
1.4 Case of an HCP aggregate with initial rolling texture, deforming in compression by ‘soft’ prismatic and ‘hard’ pyramidal slip. Anisotropy, texture development and system activity. Comparison of Taylor and self-consistent results.
2. Practical cases (1.5 hours)
2.1 Concept of Polycrystal Yield Surface and normality rule. Lankford coefficient. Relevance to prediction of forming response.
2.2 Case of rolled FCC plate. Yield surface (?-plane projection) and Lankford coefficient.
2.3 Case of rolled FCC plate with superimposed shear component. Texture gradient across sheet. Associated Yield Surface and Lankford coefficient.
2.4 Torsion of FCC aggregate. Free-end and fix-end modes. Evolution of shear stress vs. shear strain (geometric hardening). Evolution of axial stress (axial strain) vs. shear strain. Interpretation using the polycrystal yield surface of the deformed aggregate.
Lecture 3: Hands-on Session (3 hours)
The students will run the simulations discussed in Lecture 2 using the Polycrystal Plasticity Code VPSC (Visco Plastic Self Consistent). Students will have access to the source and to an executable version of the code, a Manual, and example Input/Output files. Students will plot pole figures of deformation textures using popLA or POLE. Students will plot stress-strain curves, system activity, and sections of the Polycrystal Yield Surface using standard graphic software.
References:
"Texture and Anisotropy”, U.F. Kocks, C.N. Tomé and R.H. Wenk, Cambridge University Press (2nd Edition) (2000).
Manual of VPSC7 code.
Pre-requisites
Participants should be familiar with:
- Tensor algebra.
- Crystallographic slip systems in FCC and HCP materials
- Plastic mechanisms at the single crystal level.
- Pole figure representation.
- Basic manipulation of ASCI data files and data plotting.
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