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Using LApp Los Alamos polycrystal plasticity

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Title: Using LApp Los Alamos polycrystal plasticity


1
Using LApp- Los Alamos polycrystal plasticity
  • 27-750, Advanced Characterization and
    Microstructural Analysis
  • A.D. Rollett
  • Spring 2005

2
Objective
  • The objective of this lecture is to demonstrate
    how to run LApp and obtain useful results in
    terms of texture prediction and anisotropic
    plastic properties.
  • LApp calculates the result (in terms of stress
    state) of applying a given strain (increment) to
    a set of orientations (grains). The number of
    grains can be varied from 1 to many thousands.
    The code can be used iteratively to find a
    macroscopic strain state that satisfies a certain
    applied stress state.

3
Principles of LApp
  • The principles governing the calculations in LApp
    are described in more detail in subsequent
    lectures.
  • This code is based on the Taylor assumption each
    grain/orientation experiences the same strain as
    the macroscopic body being deformed. A relaxation
    of this boundary condition is allowed for
    (relaxed constraints).
  • Since the strain (rate) is known for each grain,
    the objective of the calculation is therefore to
    obtain the stress state in each grain that
    permits the given strain to occur. This leads to
    an implicit equation relating strain rate to
    stress state.

4
Input Files
  • sxin lists of slip systems (for cubic crystals,
    also lists vertices on the single crystal yield
    surface).
  • texin list of orientations Euler angles with a
    weight (sometimes also state parameters).
  • bcin boundary conditions (strain and stress).
  • propin stress-strain constitutive relations
    (hardening).

5
LApp Flow Chart
outputfiles
rate-sensitivesolution
sxinbcintexinpropin
inputfiles
histlapp.dattexoutanal
sss
newton
preparation
updateorientationof eachgrain
grain, slipgeometry
stop
orient
maxwork
updatehardeningon eachslip system
harden
Bishop-Hill solution
6
sxin slip geometry
  • cubic lattices (this is fcc for bcc, LApp gives
    you option to transpose)
  • 1 28 nmodes,nvertex. mode nsys ktwin twsh -corr
    (all numbers must appear)
  • 1 12 0 0.0 0.0
  • 1 1 -1 0 1 1 pk
    -pk
  • 1 1 -1 1 0 1 pq
    -pq
  • 1 1 -1 1 -1 0 pu
    -pu
  • 1 -1 -1 0 1 -1 qu
    -qu
  • 1 -1 -1 1 0 1 qp
    -qp
  • 1 -1 -1 1 1 0 qk
    -qk
  • 1 -1 1 0 1 1 kp
    -kp
  • 1 -1 1 1 0 -1 ku
    -ku
  • 1 -1 1 1 1 0 kq
    -kq
  • 1 1 1 0 1 -1 uq
    -uq
  • 1 1 1 1 0 -1 uk
    -uk
  • 1 1 1 1 -1 0 up
    -up

fcc slipdirections
fcc slip planes
SlipSystems
7
sxin, contd.
number of active systems
  • 28 nvertex
  • 8 1
  • 2 0 0 0 0
  • 2 3 5 6 9 8 11
    12
  • 8 33
  • 0 2 0 0 0
  • 1 15 16 18 19 21 10
    24
  • 8 65
  • -2 -2 0 0 0
  • 13 14 4 17 7 20 22
    23
  • 6 97
  • 0 0 1 1 1
  • 1 2 17 18 7 9 25
    25
  • 6 103
  • 0 0 1 -1 1
  • 1 15 7 20 11 12 25
    25

stress vector
8-fold vertex
IDs of activeslip systems
8
propin strain hardening properties
  • Al for Stout's 1100 Al, kond2 for later batch
    (ten,com,chd)
  • c 1 lattice, nmodes. MODEs
  • 1 - no latent hardening
  • mode rs tau tau- h(m,1) h(m,2)
    h(m,3)........
  • 1 0.01 1.0 1.0 1.0 1.0 1.0 1.0
    1.0
  • STRESS LEVEL AND HARDENING LAWS
  • kond RATEref Tref muMPa tau0MPa th0/mu
    tauvMPa th4/th0 kurve
  • 1 1.0e-03 300. 25300. 20. 0.005
    30. 0.04 1
  • kurve ntaun DISCRETE HARDENING of TAUref, ntaun
    value pairs
  • 1 30 taun harn (taun(TAUref-TAU0)/tauv,
    harnth/th0)
  • .02 1.00
  • .04 .96
  • .08 .92
  • 1.40 .06
  • 1.60 .05

9
texin initial orientations, grain shape
  • texran use any portion (only file when less
    than tetr.cry.sym.)
  • Evm F11 F12 F13 F21 F22 F23
    F31 F32 F33
  • 0.000 1.000 0.000 0.000 0.000 1.000 0.000
    0.000 0.000 1.000
  • KocksPsi Theta phi weight (up to 6 state
    params, f8.2) XYZ 1 2 3
  • 158.61 44.96 -161.52 1.0 1. 1.
  • 176.88 77.35 -171.43 1.0 1. 1.
  • 30.33 72.20 158.06 1.0 1. 1.
  • -145.33 59.09 -143.55 1.0 1. 1.
  • 130.84 35.92 150.44 1.0 1. 1.
  • 99.57 79.29 10.73 1.0 1. 1.
  • 105.42 22.61 6.19 1.0 1. 1.

Euler angles
Weight
State Parameters
10
bcin boundary conditions
Test type
  • lttencomroltorgt,iplane,iline,evmstep,updt(g.a.),
    RCacc
  • 3 3 1 0.02500 0.0
    0.0
  • av.strain dir.lt33 (22-11) 223 231
    212gt epstol
  • 1.000 1.000 0.000 0.000
    0.000 0.5
  • exp'd stress dir.lt33-(1122)/2(22-11)/2233112gt
    ,99 if ?sigtol
  • 99.0 99.0 99. 99.0 99.0
    0.05

Stress components
Strain components
s33-(s22s11)/2, (s22-s11)/2, s23, s31, s12
e33, e22-e11, 2e23, 2e31, 2e12
Strain increment
99 means component can take any value
11
LApp dialog
User responses in red
  • KRYPTON.MEMS.CMU.EDUgt lapp68
  • (C)opyright 1988, The Regents of the University
    of California.
  • This software was produced under U. S.
    Government contract by
  • Los Alamos National Laboratory, which is
    operated by the
  • University of California for the U. S.
    Department of Energy.
  • Permission is granted to the public to copy and
    use this
  • software without charge, provided that this
    Notice and the
  • above statement of authorship are reproduced on
    all copies.
  • Neither the Government nor the University makes
    any warranty,
  • express or implied, or assumes any liability or
    responsibility
  • for the use of this software.


  • LA-CC-88-6
  • Los Alamos Polycrystal Plasticity
    simulation code
  • U.F. Kocks, G.R. Canova, C.N. Tome, A.D.
    Rollett, S.I. Wright
  • Center for Materials Science
  • Los Alamos National Laboratory
  • Los Alamos, New Mexico 87545, USA

ltRETURNgt
12
LApp 2
  • LApp Version 6.8, 22 Sep 1995
  • Needs single crystal deformation modes in
    SXIN,
  • kinetics and hardening data in PROPIN,
  • grain state data in TEXIN 3
    anglesgrwtstate pars.
  • (all must be in prescribed format)
  • TEXIN file
  • texlat.wts from texlat.write viii
    00
  • Enter title (8 chars.)

Enter a (short!) title
13
ksys Deformation System
  • Enter KSYS
  • 1 for FCC 111lt110gt slip (perhaps w/LH)
  • 2 for BCC restricted glide on 110
  • 3 for BCC pencil glide
  • 4 for FCC card glide
  • Enter a number for the lattice type (fcc vs. bcc)
    and the restriction on slip plane (bcc)/
    direction (fcc).
  • Typical use 1 for fcc, and 3 for bcc at
    ambient conditions, fcc metals deform in
    restricted glide, whereas bcc metals typically
    deform in pencil glide.

14
ksol Solution procedure
  • Enter KSOL
  • 0 for Bishop-Hill yield stress only, no
    evolutions
  • 1 for BH guess, then rate-sensitive Newton
    solution
  • 2 for BH guess on first step only, then
    recursive
  • 3 for Sachs guess on first step only, then
    recursive
  • 4 for Sachs guess on every step
  • (recommended 1)
  • (need 3 or 4 for Latent Hardening)
  • 1
  • 0 is the classical Taylor model in the
    rate-insensitive limit.
  • 2 and 3 allow for more efficient calculation,
    based on the (reasonable) assumption that the
    previous solution is close to the solution sought
    in the current step.

15
exponent Rate Sensitivity
  • PROPIN
  • propfe for Salsgiver's Fe-Si,exper.StoutLovat
    o 8/89
  • mode rs tau tau- h(m,1) h(m,2)
    h(m,3)........
  • Value for max. rate sensitivity exponent
    ltdefault 33gt?
  • 33
  • kond RATEref Tref muMPa tau0MPa th0/mu
    tauvMPa th4/th0 kurve(or LH)
  • 1 1.0e-03 300. 70000. 150. 0.0045
    120. 0.04 1
  • The exponent controls the rate sensitivity of the
    single crystal yield surface the lower the
    exponent, the more rounded the SXYS. In general,
    the results are not sensitive to the value of the
    exponent, unless you use a value less than 10.

16
kpath type of test
  • Reenter TTY input lt1gt, or same as in preceding
    test lt0gt ?
  • (Get to choose nsteps and YS-space anyway)
  • 1 (0 jumps to last question)
  • Enter strain path (KPATH)
  • 1 many steps in one straining direction (need
    BCIN)
  • 2 2-D yield surface probe
  • 3 3-D yield surface probe
  • 4 Lankford Coefficients R(angle) in the
    3-plane
  • 1 (i.e. texture evolution)

17
hardening law
  • REFERENCE STRESS AND ITS HARDENING LAW
  • Enter 0 for no hardening,
  • 1 " " " but stress scale
    (tau0),
  • 2 for linear hardening (stage II th0),
  • 3 for Voce law (stage III tauv),
  • 4 for Voce law plus stage IV (th4),
  • 5 for digital hardening according to
    KURVE
  • 1 (answer does not affect texture development,
    only hardening)

18
krc, ngrains
  • Relaxed Constraints when applicable ltKRC1gt or
    Full Constraints lt0gt?
  • 0 (boundary conditions on grain)
  • ngrains ltdefault whole file,.le.1152gt
    ?
  • 999 (defaults to max. number of orientations in
    texin)

On modern computers, the maximum number of grains
can be easily extended to gt100,000.
19
anal
  • Complete file ANAL on the first how many
    lt0,9,ngrainsgt?
  • 0 (use for debugging, checks)
  • mode,systems 1 12
  • n , b , nrs 0.577 0.577 -0.577 0.000
    0.707 0.707 33
  • n , b , nrs 0.577 0.577 -0.577 0.707
    0.000 0.707 33
  • n , b , nrs 0.577 0.577 -0.577 0.707
    -0.707 0.000 33
  • n , b , nrs 0.577 -0.577 -0.577 0.000
    0.707 -0.707 33
  • n , b , nrs 0.577 -0.577 -0.577 0.707
    0.000 0.707 33
  • n , b , nrs 0.577 -0.577 -0.577 0.707
    0.707 0.000 33
  • n , b , nrs 0.577 -0.577 0.577 0.000
    0.707 0.707 33
  • n , b , nrs 0.577 -0.577 0.577 0.707
    0.000 -0.707 33
  • n , b , nrs 0.577 -0.577 0.577 0.707
    0.707 0.000 33
  • n , b , nrs 0.577 0.577 0.577 0.000
    0.707 -0.707 33
  • n , b , nrs 0.577 0.577 0.577 0.707
    0.000 -0.707 33
  • n , b , nrs 0.577 0.577 0.577 0.707
    -0.707 0.000 33

20
bcin - echo input
  • input boundary conditions BCIN
  • c lttencomroltorgt,iplane,iline,evmstep,updt(g.a.
    ),RCacc
  • c 3 3 1 0.0250 0
    0.000
  • c av.strain dir.lt33 (22-11) 223 231
    212gt epstol
  • c -1.000 -1.000 0.000 0.000 0.000
    0.50
  • c exp'd stress dir.lt33-(1122)/2(22-11)/223311
    2gt,99 if ? sigtol
  • c 99.000 99.000 99.000 99.000 99.000
    0.05

21
nsteps
  • How many steps? -- Write every ? steps
  • 40,40
  • Thank you, now relax that I take care
  • For a step size of 2.5, 40 steps required per
    unit strain if the print interval is less,
    texout will have multiple sets of grains.

22
subroutines
  • subroutine graxes(mupt,vfrc,irc1,irc2,rcacc)
  • subroutine maxwork(icase,tayfac,ng,sirc1,sirc2)
  • subroutine sss(nsys,ksys,smax,niter,evmstep)
  • subroutine newton(niter,ksys,nsys)
  • subroutine simq(aa,bb,n,ks)
  • subroutine sigbc(sdirav,sigtol,itsbc)
  • subroutine harden(rlhm,khar,iref,ntaun,klh,namode
    s,emu)

23
subroutines, contd.
  • subroutine latent2(h,hq)
  • subroutine update(eps,iline,iplane)
  • subroutine twinor(ktw,ng,nomen,dbca)
  • subroutine orient(iline,iplane)
  • subroutine vecpro(k)
  • subroutine euler(iopt,nomen,d1,d2,d3,ior,kerr)
  • subroutine vectra(q,d)
  • subroutine vec5ten

24
output kpath1
  • test LApp68 14-Apr-01
  • c texlat.wts from texlat.write viii
    00
  • Evm F11 F12 F13 F21 F22 F23
    F31 F32 F33 nstate
  • 0.000 50.000 0.000 0.000 0.000 1.000 0.000
    0.000 0.000 0.020 2
  • c krc, ksys, klh, ksol,nrslim, khar,ngrains,
    iper,lsym, vfRC
  • c 0 1 0 1 33 1 999 1 2
    3 0 0.00

  • Evm 0.000 M 2.55 Svm 394. vfRC0.00 itSbc 0
    Niter 9 0.41 1.02max(devbimod
  • Evm 0.025 M 2.54 Svm 392. vfRC0.00 itSbc 0
    Niter 9 0.43 1.02max(devbimod
  • Evm 0.050 M 2.53 Svm 391. vfRC0.00 itSbc 0
    Niter 8 0.44 1.02max(devbimod

Strain, Taylor factor, von Mises equivalent
stress, vol frac in RC iterations in sigbc,
ltiters.in sssgt, standard deviation in stress
25
output files
  • texout similar to texin contains list of
    orientations corresponding to texin, rotated by
    accumulated slip.
  • anal details on a few grains
  • hist history of stress and strain
    used/calculated in each step

26
hist history
  • c Result of SSS( 9 newton iters.avg.)
  • c av strain dir -0.866 -0.500 0.000 0.000
    0.000
  • c av strain dev 0.002 0.000 0.000 0.000
    0.000
  • c av stress dir -0.821 -0.522 -0.226 0.053
    -0.016
  • c av stress dev 0.281 0.412 0.293 0.415
    0.230 avg 0.326
  • c 4th momentnor 0.966 1.024 0.876 0.914
    0.949
  • c av CA deviatoric stress -0.297 0.039
    -0.314 -0.171 -0.884
  • c av CA stress(ii) (SSSmean) 0.094 0.149
    -0.243
  • c F 50.000 0.000 0.000 0.000 1.000 0.000
    0.000 0.000 0.020
  • c Evm SIGvm TAYav TAYrs GAMav Savdev vfRC asas
    pl LHRlt
  • 0.000 393.6 2.55 2.40 0.00 0.33 0.00 4.59
    3.05 1.00
  • c Evm nreor atwfr etwfr mode-repartition n( -)
  • 0.000 0 0.00 0.00 0.43 0.57

27
texout final orientations
  • test texout LApp68 14-Apr-01
  • c texlat.wts from texlat.write viii
    00
  • c lttencomroltorgt,iplane,iline,evmstep,updt(g.a.
    ),RCacc
  • c 3 3 1 0.0250 0
    0.000
  • c av.strain dir.lt33 (22-11) 223 231
    212gt epstol
  • c -1.000 -1.000 0.000 0.000
    0.000 0.50
  • c exp'd stress dir.lt33-(1122)/2(22-11)/223311
    2gt,99 if ? sigtol
  • c 99.000 99.000 99.000 99.000
    99.000 0.05
  • c propfe for Salsgiver's Fe-Si,exper.StoutLova
    to 8/89
  • c mode rs tau tau- h(m,1) h(m,2)
    h(m,3)........
  • c 1 0.02 1.00 1.00 1.00
  • c kond RATEref Tref muMPa tau0MPa th0/mu
    tauvMPa th4/th0 kurve(or LH)
  • c 1 0.1E-02 300. 70000. 150.
  • c krc, ksys, klh, ksol,nrslim, khar,ngrains,
    iper,lsym, vfRC
  • c 0 1 0 1 33 1 999 1 2
    3 0 0.00
  • Evm F11 F12 F13 F21 F22 F23
    F31 F32 F33 nstate
  • 1.000117.778 0.000 0.000 0.000 1.000 0.000
    0.000 0.000 0.008 2
  • Bungephi1 PHI phi2 ,,gr.wt., tau,
    taustaumodes/tau XYZ1 2 3
  • 0.00 70.00 0.00 1.00 150.00 0.00

Re-statement of the input in bcin
28
r-value calculation
  • The next sequence gives an example of how to use
    LApp to calculate r-values based on a given
    texture (no evolution).

29
kpath 4 (r-values)
  • Angle increment (degrees lt15gt)
    ?
  • 15 (controls direction resolution)
  • to what frac.accuracy of stress should I
    iterate?lt0.01gt
  • .02 (0.01 minimum practical value)
  • What value of RCACC? (use 0 if in doubt)
  • 0 (trick for exaggerating relaxed constraints
    effect)

30
kpath 4, contd.
  • Enforce sample symmetry for property
    calculations?
  • 0 no
  • 1, 2, or 3 diad on that axis (use 2 or 3 with
    TEXREG)
  • 4 orthotropy
    LSYM
  • 0 (can add sample symmetry)

31
output (kpath 4)
  • ang.fr.X1 r q shears(tension coords)
    tayfavmax(sdevbimod) itsbc
  • 0.000 0.727 0.421 0.395 -0.037 0.044
    2.280 0.372 0.962 7
  • 15.000 0.480 0.324 0.268 -0.129 0.111
    2.440 0.362 1.002 10
  • 30.000 0.299 0.230 0.045 -0.106 0.127
    2.638 0.319 1.058 5
  • 45.000 0.233 0.189 -0.250 -0.085 0.050
    2.658 0.312 0.953 13
  • 60.000 0.861 0.463 -0.322 -0.004 -0.068
    2.712 0.332 0.973 5
  • 75.000 2.109 0.678 -0.183 0.082 -0.045
    2.693 0.385 1.003 6
  • 90.000 2.811 0.738 0.094 0.102 0.003
    2.664 0.372 1.017 4

  • r-bar, as calculated from an average of all
    q-D22/D11 is 0.696

q r/(1r) this output is also recorded in
lapp.dat
32
R-value,q plotted (kpath 4)
Input texture contained high fraction of Goss,
giving rise to maximum in r-value at 90 to the
rolling direction
33
Yield Surface calculation
  • The next sequence of slides shows how to
    calculate the locus of points on a yield surface.

34
kpath 2 (2D yield surface)
  • Enter strain path (KPATH)
  • 1 many steps in one straining direction (need
    BCIN)
  • 2 2-D yield surface probe
  • 3 3-D yield surface probe
  • 4 Lankford Coefficients R(angle) in the
    3-plane
  • 2

35
kpath 2, contd.
  • Relaxed Constraints when applicable ltKRC1gt or
    Full Constraints lt0gt?
  • 0
  • ngrains ltdefault whole file,.le.1152gt
    ?
  • 999
  • Complete file ANAL on the first how many
    lt0,9,ngrainsgt?
  • 0

36
kpath 2, contd.
  • YS projection (0) or YS section (enter SIGTOL)
    ?
  • 0 (typical to assume proj.)
  • you want tayfac lt0gt or stress MPa lt1gt
    ?
  • 0 (stress proportional to ltMgt)
  • Rate dep.on stresses only (0) or also on facets
    (1) ?
  • 0 (allows contrast of Bishop-Hill soln. with RS
    solution)

37
kpath 2, contd.
  • Angle increment in strain-rate space (gt2
    degreeslt5gt)?
  • Enter negative values if you want to scan /-
    range
  • 15
  • Select one of the indices
  • 0 for Cauchy(22) vs (11), with (33)0
  • 1 for pi plane -- 2 for S22-S11 vs Sij
  • 3 for S11-S33 vs Sij -- 4 for S22-S33 vs Sij
  • 5 for S11 vs Sij -- 6 for S22 vs Sij
  • 7 for Sij vs S33 -- 8 for Sij vs Skl
    0 (as in most texts)

38
kpath 2, contd.
  • Enforce sample symmetry for property
    calculations?
  • 0 no
  • 1, 2, or 3 diad on that axis (use 2 or 3 with
    TEXREG)
  • 4 orthotropy
    LSYM
  • 0 (again, can compensate for a texture lacking
    symmetry)

39
lapp.dat
  • KRYPTON.MEMS.CMU.EDUgt more lapp.dat
  • xs ys -xs -ys active_sys 2 3 4 5 6 7 8 9
  • 0.93894 -4.58022 -0.93894 4.58022 1
    2 3 4 5 6 7 8 9 10 11 12
  • 0.68739 -2.21556 -0.68739 2.21556 1
    2 3 4 5 6 7 8 9 10 11 12
  • 1.12168 -2.00816 -1.12168 2.00816 1
    2 3 4 5 6 7 8 9 10 11 12
  • 1.62587 -1.66510 -1.62587 1.66510 1
    2 3 4 5 6 7 8 9 10 11 12
  • 1.80145 -1.44043 -1.80145 1.44043 1
    2 3 4 5 6 7 8 9 10 11 12

stress components, - active slip systems
40
hist (kpath 2)
Output contains pairs of lines
  • KRYPTON.MEMS.CMU.EDUgt more hist
  • nosort
  • c ys HIST LApp68 14-Apr-01
  • c dirs.,perp. sub-space RC comps.grainsvfRC
    ksollsym
  • c 12 0 1 1 2 0 0 999 0.00
    2 0
  • -1.00000 0.00000 0.00000 0.00000
    0.00000 2.83891
  • -4.58022 0.93894 -0.21041 0.01443
    -0.19175 4.04711
  • -0.96593 0.25882 0.00000 0.00000
    0.00000 2.92495
  • -2.21556 0.68739 -0.05986 -0.03260
    -0.08404 0.51476
  • -0.86603 0.50000 0.00000 0.00000
    0.00000 2.90462
  • -2.00816 1.12168 -0.05832 -0.06920
    -0.06329 0.60977

(5) strain components Taylor factor
(5) stress components standard deviation
41
Yield Surface example (kpath2)
42
Summary
  • The interface to the LApp code has been described
    with examples of problems that can be computed.
  • LApp is essentially a polycrystal plasticity code
    for solving the Taylor/Bishop-Hill model.
  • LApp can be used to compute the anisotropic
    (plastic) properties of textured polycrystals,
    e.g. yield surfaces, r-values.
  • Other codes are required for different approaches
    to plastic deformation, e.g. self-consistent
    models, finite element models (incorporating
    crystal plasticity as a constitutive model).
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