Yield surface prediction of Aluminum on rolling

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== Abstract ==
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{{template:Research_Paper
  
Rolling of polycrystalline aggregates of Aluminum was investigated by employing the Visco-plastic self-consistent polycrystal (VPSC) model. The starting texture is a series crystals represented by five hundred random orientations. Rolled texture and yield surfaces at rolling strain levels of -0.5, -1.0, -1.5, -2.0 and -2.5 were captured by VPSC modeling. The predicted texture showed a typical rolled texture components and the yield surfaces showed anisotropic shape and a saturation tendency.
+
|abstract=Rolling of polycrystalline aggregates of Aluminum was investigated by employing the Visco-plastic self-consistent polycrystal (VPSC) model. The starting texture is a series crystals represented by five hundred random orientations. Rolled texture and yield surfaces at rolling strain levels of -0.5, -1.0, -1.5, -2.0 and -2.5 were captured by VPSC modeling. The predicted texture showed a typical rolled texture components and the yield surfaces showed anisotropic shape and a saturation tendency.
  
Author(s): Q. Ma, E.B. Marin, M.F. Horstemeyer
+
|authors=Q. Ma, E.B. Marin, M.F. Horstemeyer
  
 +
|animation=
  
== Methodology ==
+
|images=
 +
{{paper_figure|image=rolling_texture_pcys.jpg|image caption=Figure 1. Rolling simulation of polycrystal Aluminum. (a)Initial texture; (b) rolled texture; (c)yield surfaces at various rolling strain levels}}
  
 +
|methodology=Aluminum conducts rolling through only {111}<011> slips at room temperature. A starting texture represented by 500 random orientations was shown in Figure 1a. Single crystal parameters were listed in FCC.SX file as follow. The self-hardening and latent hardening were set equal to one in this example. The rolling boundary conditions were set as: restricted 2 direction (transverse direction), 1 direction (rolling direction) was free and 3 direction (normal direction) conducted rolling strain. The final rolled texture is displayed in Figure 1b. The yield surfaces at each strain levels were captured by VPSC modeling as shown in Figure 1c.
 +
 
 +
|material model= [[Code:_VPSC|VPSC]]: ViscoPlastic Self-Consistent
  
 +
|input deck=
 +
See [[VPSC Input Deck for Yield_surface_prediction_of_Aluminum_on_rolling]]
  
Aluminum conducts rolling through only {111}<011> slips at room temperature. A starting texture represented by 500 random orientations was shown in Figure 1a. Single crystal parameters were listed in FCC.SX file. self-hardening and latent hardening were set equal to one in this example. The rolling boundary conditions were set as: restricted 2 direction (transverse direction), 1 direction (rolling direction) was free and 3 direction (normal direction) conducted rolling strain. The final rolled texture is displayed in Figure 1b. The yield surfaces at each strain levels were captured by VPSC modeling as shown in Figure 1c.
+
|results=Rolling process of polycrystal Aluminum was simulated by VPSC model. The typical rolled texture components and the yield surfaces at various strain levels can by captured by the VPSC model. VPSC can also capture both the crystal scale parameters (single crystal hardening parameters) and macroscale property (yield surfaces, stress-strain responses) of the polycrystalline aggregrate.
 +
|acknowledgement=The authors are grateful to the financial support from the Department of Energy, Contract No. DE-FC-26-06NT42755, and the Center for Advanced Vehicular Systems (CAVS) at Mississippi State University.
 +
|references=none
 +
}}
  
 
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[[Category: Research Paper]]
 
+
[[Category: mesoscale]]
[[image:rolling_texture_pcys.jpg|thumb|350px|Figure 1. (a)Initial texture; (b) rolled texture; (c)yield surfaces at various rolling strain levels.]]
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[[Category: aluminum]]
 
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[[Category: VPSC]]
 
+
 
+
The input data (fcc.sx) for Aluminum rolling simulation as follows:
+
 
+
 
+
{|border  ="0"
+
|<pre>
+
 
+
2                                      / elastID (1: iso, 2: ani) /
+
59.52d3 25.6d3 21.4d3 61.74d3 16.47d3  /c11(c1),c12(c2),c13(c3),c33(c4),c44(c5)/
+
0.0e0  0.0e0  0.0e0  0.0e0  0.0e0  0.0e0  /thermal expansion coeff/   
+
1.624        = c/a ratio (used when computing slip vectors)
+
5                  = nmodesx (total # of modes listed in the file)
+
3                  = nmodes  (# of modes to be used in the SCYS)
+
1  2  5  3  4    = mode(i) (label of the modes to be used)
+
121                = nvtx (number of vertices of scys)
+
vert_hcp.121.05    = filename for file with vertices of scys
+
*BASAL <A> SYSTEMS
+
  1    3    1  = modex,nsmx,isensex : <a>  basal (0001)<11-20>
+
  0.05 1.0e-3                                / xm, gam0 /
+
  5.0e-4                                  / bdrag /
+
  19.6d0  18.0d0  20.0d0  0.0d0  5.0d10 / h0, tausi, taus0, xms, gamss0 /
+
  18.0d0                                / initial slip system hardness (kappa0) /
+
  0.0  0    0.  0.                  twshx,isectw,thres1,thres2
+
  1.0  1.0  1.0  1.0                hlatx(1,im),im=1,nmodes
+
  0.  0.  0.  1.    1. -2.  1.  0.
+
  0.  0.  0.  1.    2. -1. -1.  0.
+
  0.  0.  0.  1.    1.  1. -2.  0.
+
*PRISMATIC <A> SYSTEMS
+
  2    3    1  = modex,nsmx,isensex : <a>  prism {-1100}<11-20>
+
  0.05 1.0e-3                                / xm, gam0 /
+
  5.0e-4                                  / bdrag /
+
  37.5d0  30.0d0  34.0d0  0.0d0  5.0d10 / h0, tausi, taus0, xms, gamss0 /
+
  30.0d0                                / initial slip system hardness (kappa0) /
+
  0.0  0    0.  0.                  twshx,isectw,thres1,thres2
+
  1.0  1.0  1.0  1.0                hlatx(1,im),im=1,nmodes
+
  1.  0. -1.  0.    1. -2.  1.  0.
+
  0.  1. -1.  0.    2. -1. -1.  0.
+
-1.  1.  0.  0.    1.  1. -2.  0.
+
*PYRAMIDAL <A> SYSTEMS
+
  3  6    1  = modex,nsmx,isensex : <a>  pyram {10-11}<11-20>
+
  0.05 1.0                                / xm, gam0 /
+
  5.0e-4                                  / bdrag /
+
  400.0d0  200.0d0  1000.0d0  0.005d0  5.0d10 / h0, tausi, taus0, xms, gamss0 /
+
  200.00d0                                / initial slip system hardness (kappa0) /
+
  0.0  0    0.  0.                  twshx,isectw,thres1,thres2
+
  1.0  1.0  1.0  10.0                hlatx(1,im),im=1,nmodes
+
  1.  0. -1.  1.    1. -2.  1.  0.   
+
  0.  1. -1.  1.    2. -1. -1.  0. 
+
-1.  1.  0.  1.    1.  1. -2.  0.
+
-1.  0.  1.  1.    -1.  2. -1.  0.   
+
  0. -1.  1.  1.    -2.  1.  1.  0. 
+
  1. -1.  0.  1.    -1. -1.  2.  0.   
+
*PYRAMIDAL <C+A> SYSTEMS
+
  4  12    1  = modex,nsmx,isensex : <c+a> pyram {10-11}<11-23>
+
  0.05 1.0                                / xm, gam0 /
+
  5.0e-4                                  / bdrag /
+
  400.0d0  200.0d0  1000.0d0  0.005d0  5.0d10 / h0, tausi, taus0, xms, gamss0 /
+
  200.00d0                                / initial slip system hardness (kappa0) /
+
  0.0  0    0.  0.                  twshx,isectw,thres1,thres2
+
  1.0  1.0  1.0  10.0                hlatx(1,im),im=1,nmodes
+
  1.  0. -1.  1.    -2.  1.  1.  3.   
+
  1.  0. -1.  1.    -1. -1.  2.  3. 
+
  0.  1. -1.  1.    -1. -1.  2.  3. 
+
  0.  1. -1.  1.    1. -2.  1.  3.
+
-1.  1.  0.  1.    1. -2.  1.  3.
+
-1.  1.  0.  1.    2. -1. -1.  3. 
+
-1.  0.  1.  1.    2. -1. -1.  3. 
+
-1.  0.  1.  1.    1.  1. -2.  3.
+
  0. -1.  1.  1.    1.  1. -2.  3.
+
  0. -1.  1.  1.    -1.  2. -1.  3. 
+
  1. -1.  0.  1.    -1.  2. -1.  3. 
+
  1. -1.  0.  1.    -2.  1.  1.  3.
+
*PYRAMIDAL <C+A> 2nd ORDER SYSTEMS
+
  5  6    1  = modex,nsmx,isensex : <c+a> pyram {11-22}<-1-123>
+
  0.05 1.0e-3                                / xm, gam0 /
+
  5.0e-4                                  / bdrag /
+
  18.8d0  44.0d0  46.0d0  0.0d0  5.0d10 / h0, tausi, taus0, xms, gamss0 /
+
  44.0d0                                / initial slip system hardness (kappa0) /
+
  0.0  0    0.  0.                  twshx,isectw,thres1,thres2
+
  1.0  1.0  1.0  1.0                hlatx(1,im),im=1,nmodes
+
-2.  1.  1.  2.    2. -1. -1.  3.
+
  1. -2.  1.  2.    -1.  2. -1.  3.
+
  1.  1. -2.  2.    -1. -1.  2.  3.
+
  2. -1. -1.  2.    -2.  1.  1.  3.
+
-1.  2. -1.  2.    1. -2.  1.  3.
+
-1. -1.  2.  2.    1.  1. -2.  3.
+
*TENSILE TWINNING (TT1) SYSTEMS
+
  6    6    0                    modex,nsmx,isensex
+
  0.05 1.0                                / xm, gam0 /
+
  5.0e-4                                  / bdrag /
+
  400.0d0  200.0d0  1000.0d0  0.005d0  5.0d10 / h0, tausi, taus0, xms, gamss0 /
+
  200.00d0                                / initial slip system hardness (kappa0) /
+
  0.13  1    0.25  0.85            twshx,isectw,thres1,thres2
+
  1.0  1.0  1.0  10.0              hlatx(1,im),im=1,nmodes
+
  1.  0. -1.  2.    -1.  0.  1.  1.
+
  0.  1. -1.  2.    0. -1.  1.  1.
+
-1.  1.  0.  2.    1. -1.  0.  1.
+
-1.  0.  1.  2.    1.  0. -1.  1.
+
  0. -1.  1.  2.    0.  1. -1.  1.
+
  1. -1.  0.  2.    -1.  1.  0.  1.
+
*COMPRESSIVE TWINNING (CT1) SYSTEMS
+
  7    6  0                    modex,nsmx,isensex
+
  0.05 1.0                                / xm, gam0 /
+
  5.0e-4                                  / bdrag /
+
  400.0d0  200.0d0  1000.0d0  0.005d0  5.0d10 / h0, tausi, taus0, xms, gamss0 /
+
  200.00d0                                / initial slip system hardness (kappa0) /
+
  0.225  1    0.00  0.50            twshx,isectw,thres1,thres2
+
  1.0  1.0  10.  5.  5.0          hlatx(1,im),im=1,nmodes
+
  1.  0. -1.  1.    1.  0. -1. -2.
+
  0.  1. -1.  1.    0.  1. -1. -2.
+
-1.  1.  0.  1.  -1.  1.  0. -2.
+
-1.  0.  1.  1.  -1.  0.  1. -2.
+
  0. -1.  1.  1.    0. -1.  1. -2.
+
  1. -1.  0.  1.    1. -1.  0. -2.
+
 
+
------------------------------------------------------------
+
elastID (1: iso, 2: ani)
+
  Iso:
+
    eMod, eNu
+
  Ani:
+
    c1, c2, c3        (FCC,BCC)
+
    c1, c2, c3, c4, c5 (HCP)
+
 
+
xm, gam0
+
h0, tausi, taus0, xms, gamss0
+
kappa0
+
 
+
For reference:
+
BASAL <A> + PRISMATIC <A> :
+
        nvtx = 18
+
        1:1      vert_hcp.018.00
+
BASAL <A> + PYRAMIDAL <A> :
+
        nvtx = 21
+
        1:1      vert_hcp.021.00
+
PRISMATIC <A> + PYRAMIDAL <A> :
+
        nvtx = 36
+
        1:1      vert_hcp.036.00
+
BASAL <A> + PRISMATIC <A> + PYRAMIDAL <A> :
+
        nvtx = 54
+
        1:1:1    vert_hcp.054.00
+
BASAL <A> + PRISMATIC <A> + PYRAMIDAL <A+C> :
+
        nvtx = 121
+
        1:1:1    vert_hcp.121.01
+
        1:1:3    vert_hcp.121.03
+
        1:1:5    vert_hcp.121.05
+
        1:1:10  vert_hcp.121.10
+
BASAL <A> + PRISMATIC <A> + PYRAMIDAL <A> + PYRAMIDAL <A+C> :
+
        nvtx = 241
+
        1:1:1:1  vert_hcp.241.01
+
        1:1:1:3  vert_hcp.241.03
+
        1:1:1:5  vert_hcp.241.05
+
        1:1:1:10 vert_hcp.241.10
+
 
+
NOTE: Recall
+
(1) if2d=-2 for basal<a>+prismatic<a> only (decoupled solution) NOT USED
+
    if2d=-1 otherwise NOT USED
+
(2) Rerun Tome's program if c/a ratio is changed to obtain new
+
    single crystal yield surface vertices (only if pyramidal slip
+
    systems are considered).
+
(3) The files vert_hcp for vtx = 18, 21, 36, 54 list (4 comp's):
+
    (11-22)/sqr2, 21*sqr2, 31*sqr2, 32*sqr2
+
(4) The files vert_hcp for vtx = 121, 241 list (5 comp's):
+
    (11-22)/sqr2, 33*sqr32, 21*sqr2, 31*sqr2, 32*sqr2
+
 
+
 
+
</pre>
+
|}
+
 
+
== Results ==
+

Latest revision as of 10:03, 29 May 2014

AbstractMethodologyMaterial ModelInput DataResultsAcknowledgmentsReferences

Abstract

Rolling of polycrystalline aggregates of Aluminum was investigated by employing the Visco-plastic self-consistent polycrystal (VPSC) model. The starting texture is a series crystals represented by five hundred random orientations. Rolled texture and yield surfaces at rolling strain levels of -0.5, -1.0, -1.5, -2.0 and -2.5 were captured by VPSC modeling. The predicted texture showed a typical rolled texture components and the yield surfaces showed anisotropic shape and a saturation tendency.

Author(s): Q. Ma, E.B. Marin, M.F. Horstemeyer


Figure 1. Rolling simulation of polycrystal Aluminum. (a)Initial texture; (b) rolled texture; (c)yield surfaces at various rolling strain levels (click on the image to enlarge).

Methodology

Aluminum conducts rolling through only {111}<011> slips at room temperature. A starting texture represented by 500 random orientations was shown in Figure 1a. Single crystal parameters were listed in FCC.SX file as follow. The self-hardening and latent hardening were set equal to one in this example. The rolling boundary conditions were set as: restricted 2 direction (transverse direction), 1 direction (rolling direction) was free and 3 direction (normal direction) conducted rolling strain. The final rolled texture is displayed in Figure 1b. The yield surfaces at each strain levels were captured by VPSC modeling as shown in Figure 1c.

Material Model

VPSC: ViscoPlastic Self-Consistent

Input Data

See VPSC Input Deck for Yield_surface_prediction_of_Aluminum_on_rolling

Results

Rolling process of polycrystal Aluminum was simulated by VPSC model. The typical rolled texture components and the yield surfaces at various strain levels can by captured by the VPSC model. VPSC can also capture both the crystal scale parameters (single crystal hardening parameters) and macroscale property (yield surfaces, stress-strain responses) of the polycrystalline aggregrate.

Acknowledgments

The authors are grateful to the financial support from the Department of Energy, Contract No. DE-FC-26-06NT42755, and the Center for Advanced Vehicular Systems (CAVS) at Mississippi State University.

References

none

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