View source for Channel Die Compression of Mg

== Abstract ==

Deformation of polycrystalline aggregates of HCP crystals was investigated by employing crystal plasticity and finite element simulations. Results were validated using channel die compression tests. The three dimensional polycrystal, represented by Voronoi techniques, was assigned an initial distribution of crystallographic orientations determined from X-Ray Diffraction. The mechanical properties from the channel die compression tests were used to correlate the material parameters of the crystal plasticity model. Simulations predicted grain-to-grain interactions and the resulting texture evolution under channel die compression. The inhomogeneous deformation among grains was mapped by a stress and a strain distribution and grain orientation spread. The simulation results were compared with experimental observations of an HCP polycrystal subjected to channel die compression.  

Author(s): Q. Ma, E.B. Marin, A. Antonyraj, Y. Hammi, H. El Kadiri, P.T. Wang and  M.F. Horstemeyer


== Methodology ==



Magnesium has a hexagonal close-packed (HCP) structure whose deformation modes are different from those of aluminum. Typical deformation modes in magnesium are basal <a>-{0002}<11-20> slip, prismatic <a>-{10-10}<11-20> slip, second pyramidal <c+a>-{11-22}<11-23> slip and extension twinning {10-12}<10-11>. In this study, a commercial extruded AM30 alloy (mass %, 2.54% Al, 0.40% Mn, Mg in balance) was selected as the HCP experimental material to conduct channel die compression at high temperature 200C and at strain rate of 0.001/S to strain 30%. At these loading conditions, twinning would not be profuse and, hence, only slip will be the predominant deformation mode. The hardening parameters of the three slips modes were obtained using material point simulations to fit the experimental stress-strain curve recorded from the channel die compression test as shown in Figure 1d.


The texture of AM30 was measured by X-ray diffraction method (XRD). The recalculated pole figures were calculated based on the orientation distribution functions (ODFs) which was obtained using the measured six incomplete pole figures {10-10}, {0002}, {10-11},{10-12}, {11-20} and {10-13}. The initial and the channel die compressed texture of AM30 plotted by the texture software MTEX [http://code.google.com/p/mtex/].

The commercial finite element software ABAQUS 6.9 and a user subroutine UMAT incorporating the crystal plasticity constitutive theory and the magnesium AM30 materials parameters were used to simulate texture evolution and mechanical response. The initial texture used in this CPFEM simulation was measured in the undeformed sample and was represented by 343 discrete orientations as shown in Figure 1a. The 3D polycrystal is represented by the 3D Voronoi grains created by the code Neper [http://neper.sourceforge.net/].  The undeformed polycrystal and the channel die compressed 3D polycrystal up to a strain of 30% are presented in Figures 1b and 1c.The simulated and measured channel die compression stress-strain curves are presented in Figure 1e.

[[image:AM30 channel die compression.jpg|thumb|350px|Figure 1. (a)Initial texture; (b) undeformation 3D Voronoi structure; (c)channel die compressed 3D Voronoi grains; (d) materials point simulated and measured stress-strain curves and (e) crystal plasticity and 3D structure predicted and measurd stress-strain curves .]]

The input data (hcp.sx) for AM30 channel die compression simulation as follows:


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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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== Results ==


Plane strain compression simulations of a three dimensional microstructure of HCP magnesium AM30 were performed using an elastic-plastic crystal plasticity model and the finite element method. The mechanical response, global texture evolution and the intergranular heterogeneous plasticity of discrete grain were captured by the 3D Voronoi microstructure channel die compression simulation. Simulation results showed that the effect of grain interaction could play an important role on global texture evolution, the orientation spread and the local heterogeneity deformation of one grain.


== 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.


[[Category:Research Paper]]
[[Category:Channel Die Decomposition]]
[[Category:Magnesium]]