Yield surface prediction of Aluminum on rolling

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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


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. 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.


Figure 1. (a)Initial texture; (b) rolled texture; (c)yield surfaces at various rolling strain levels.


The input data (fcc.sx) for Aluminum rolling simulation as follows:



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 


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