Title: Using LApp Los Alamos polycrystal plasticity
1Using LApp- Los Alamos polycrystal plasticity
- 27-750, Advanced Characterization and
Microstructural Analysis - A.D. Rollett
- Spring 2005
2Objective
- 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.
3Principles 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.
4Input 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).
5LApp 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
6sxin 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
7sxin, 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
8propin 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
9texin 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
10bcin 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
11LApp 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
12LApp 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
13ksys 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.
14ksol 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.
15exponent 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.
16kpath 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)
17hardening 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)
18krc, 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.
19anal
- 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
20bcin - 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
21nsteps
- 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.
22subroutines
- 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)
23subroutines, 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
24output 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
25output 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
26hist 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
27texout 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
28r-value calculation
- The next sequence gives an example of how to use
LApp to calculate r-values based on a given
texture (no evolution).
29kpath 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)
30kpath 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)
31output (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
32R-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
33Yield Surface calculation
- The next sequence of slides shows how to
calculate the locus of points on a yield surface.
34kpath 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
35kpath 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
36kpath 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)
37kpath 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)
38kpath 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)
39lapp.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
40hist (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
41Yield Surface example (kpath2)
42Summary
- 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).