LAMMPS Fracture

From EVOCD
Revision as of 15:28, 28 April 2011 by Nrr43 (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Contents

Abstract

This example shows how to run an atomistic simulation of fracture of an iron symmetric tilt grain boundary. A parallel molecular dynamics code, LAMMPS[1], is used to calculate stresses at the grain boundary as the strain of the bicrystal is incrementally increased. A stress-strain curve is plotted as a result of the simulation.

Author(s): Mark A. Tschopp, Nathan R. Rhodes

Corresponding Author: Mark Tschopp

Input

Description of Simulation

This molecular dynamics simulation calculates the stress-strain relationship of an iron symmetric tilt grain boundary under fracture. The grain boundary structure used in this example is a <100> Σ5(210) symmetric tilt grain boundary. The potential used to generate the structure, the Hepburn and Ackland (2008) Fe-C interatomic potential[2], is also used in this script. The simulation cell is defined such that the bicrystal is pulled in the y-direction, or perpendicular to the boundary interface, to increase strain. The strain in increased for a specified number of times in a loop, and the stress is calculated at each point before the simulation loops. The stress and strain values are output to a separate file which can be imported in a graphing application for plotting.

Grain boundary structure file

This grain boundary structure was generated prior to this example. To use it, store the text in "Fe_100_sig5_210.txt."

# Minimum Energy GB Structure for LAMMPS   

380 atoms 
2 atom types 
0.000000 6.384670 xlo xhi   
-121.638000 121.638000 ylo yhi   
0.000000 2.855310 zlo zhi   

Atoms 

1 1 4.460670 -121.056000 1.427660   
2 1 0.121831 -121.349998 0.000000   
3 1 0.614806 -119.457001 1.427660   
4 1 2.536320 -120.134003 0.000000   
5 1 3.193350 -118.271004 1.427660   
6 1 5.056950 -118.997002 0.000000   
7 1 5.717690 -117.030998 1.427660   
8 1 1.272510 -117.596001 0.000000   
9 1 1.907410 -115.704002 1.427660   
10 1 3.820340 -116.360001 0.000000   
11 1 4.457650 -114.445999 1.427660   
12 1 6.366010 -115.097000 0.000000   
13 1 0.623987 -113.174004 1.427660   
14 1 2.543940 -113.799004 0.000000   
15 1 3.182210 -111.888000 1.427660   
16 1 5.096380 -112.530998 0.000000   
17 1 5.735870 -110.615997 1.427660   
18 1 1.265040 -111.255997 0.000000   
19 1 1.905550 -109.338997 1.427660   
20 1 3.821420 -109.974998 0.000000   
21 1 4.461220 -108.060997 1.427660   
22 1 6.375800 -108.699997 0.000000   
23 1 0.631379 -106.785004 1.427660   
24 1 2.545990 -107.422997 0.000000   
25 1 3.186490 -105.508003 1.427660   
26 1 5.101420 -106.146004 0.000000   
27 1 5.741860 -104.231003 1.427660   
28 1 1.271840 -104.870003 0.000000   
29 1 1.912420 -102.955002 1.427660   
30 1 3.827090 -103.593002 0.000000   
31 1 4.467730 -101.678001 1.427660   
32 1 6.382440 -102.316002 0.000000   
33 1 0.638419 -100.401001 1.427660   
34 1 2.553070 -101.039001 0.000000   
35 1 3.193740 -99.124397 1.427660   
36 1 5.108410 -99.762802 0.000000   
37 1 5.749090 -97.847702 1.427660   
38 1 1.279090 -98.486000 0.000000   
39 1 1.919780 -96.570999 1.427660   
40 1 3.834430 -97.209297 0.000000   
41 1 4.475120 -95.294296 1.427660   
42 1 0.005111 -95.932602 0.000000   
43 1 0.645805 -94.017502 1.427660   
44 1 2.560460 -94.655899 0.000000   
45 1 3.201160 -92.740799 1.427660   
46 1 5.115820 -93.379204 0.000000   
47 1 5.756520 -91.463997 1.427660   
48 1 1.286510 -92.102402 0.000000   
49 1 1.927220 -90.187202 1.427660   
50 1 3.841870 -90.825600 0.000000   
51 1 4.482580 -88.910500 1.427660   
52 1 0.012563 -89.548897 0.000000   
53 1 0.653283 -87.633698 1.427660   
54 1 2.567930 -88.272102 0.000000   
55 1 3.208660 -86.356796 1.427660   
56 1 5.123310 -86.995300 0.000000   
57 1 5.764040 -85.080002 1.427660   
58 1 1.294010 -85.718399 0.000000   
59 1 1.934750 -83.803200 1.427660   
60 1 3.849390 -84.441597 0.000000   
61 1 4.490130 -82.526299 1.427660   
62 1 0.020102 -83.164803 0.000000   
63 1 0.660844 -81.249496 1.427660   
64 1 2.575490 -81.887901 0.000000   
65 1 3.216230 -79.972603 1.427660   
66 1 5.130870 -80.611099 0.000000   
67 1 5.771630 -78.695801 1.427660   
68 1 1.301590 -79.334198 0.000000   
69 1 1.942350 -77.418900 1.427660   
70 1 3.856990 -78.057297 0.000000   
71 1 4.497740 -76.141998 1.427660   
72 1 0.027709 -76.780502 0.000000   
73 1 0.668470 -74.865196 1.427660   
74 1 2.583110 -75.503601 0.000000   
75 1 3.223870 -73.588303 1.427660   
76 1 5.138510 -74.226700 0.000000   
77 1 5.779270 -72.311401 1.427660   
78 1 1.309240 -72.949799 0.000000   
79 1 1.950010 -71.034500 1.427660   
80 1 3.864640 -71.672997 0.000000   
81 1 4.505410 -69.757698 1.427660   
82 1 0.035374 -70.396103 0.000000   
83 1 0.676151 -68.480797 1.427660   
84 1 2.590780 -69.119202 0.000000   
85 1 3.231560 -67.203903 1.427660   
86 1 5.146190 -67.842400 0.000000   
87 1 5.786980 -65.927002 1.427660   
88 1 1.316930 -66.565498 0.000000   
89 1 1.957720 -64.650200 1.427660   
90 1 3.872350 -65.288597 0.000000   
91 1 4.513140 -63.373299 1.427660   
92 1 0.043091 -64.011703 0.000000   
93 1 0.683885 -62.096401 1.427660   
94 1 2.598510 -62.734901 0.000000   
95 1 5.153930 -61.458000 0.000000   
96 1 3.239310 -60.819599 1.427660   
97 1 5.794730 -59.542702 1.427660   
98 1 1.324680 -60.181099 0.000000   
99 1 1.965490 -58.265800 1.427660   
100 1 3.880110 -58.904301 0.000000   
101 1 4.520920 -56.988899 1.427660   
102 1 0.050868 -57.627399 0.000000   
103 1 0.691679 -55.712101 1.427660   
104 1 2.606300 -56.350498 0.000000   
105 1 3.247110 -54.435200 1.427660   
106 1 5.161730 -55.073601 0.000000   
107 1 5.802550 -53.158298 1.427660   
108 1 1.332500 -53.796799 0.000000   
109 1 1.973320 -51.881500 1.427660   
110 1 3.887930 -52.519901 0.000000   
111 1 4.528760 -50.604599 1.427660   
112 1 0.058702 -51.243000 0.000000   
113 1 0.699532 -49.327702 1.427660   
114 1 2.614150 -49.966202 0.000000   
115 1 3.254980 -48.050900 1.427660   
116 1 5.169590 -48.689301 0.000000   
117 1 5.810430 -46.773998 1.427660   
118 1 1.340370 -47.412399 0.000000   
119 1 3.895820 -46.135601 0.000000   
120 1 1.981210 -45.497101 1.427660   
121 1 4.536660 -44.220299 1.427660   
122 1 0.066599 -44.858700 0.000000   
123 1 0.707446 -42.943401 1.427660   
124 1 2.622050 -43.581799 0.000000   
125 1 3.262900 -41.666599 1.427660   
126 1 5.177510 -42.305000 0.000000   
127 1 5.818360 -40.389702 1.427660   
128 1 1.348300 -41.028099 0.000000   
129 1 1.989150 -39.112900 1.427660   
130 1 3.903760 -39.751301 0.000000   
131 1 4.544610 -37.836102 1.427660   
132 1 0.074546 -38.474499 0.000000   
133 1 0.715404 -36.559200 1.427660   
134 1 2.630010 -37.197601 0.000000   
135 1 3.270870 -35.282398 1.427660   
136 1 5.185470 -35.920799 0.000000   
137 1 5.826330 -34.005600 1.427660   
138 1 1.356260 -34.644001 0.000000   
139 1 1.997120 -32.728901 1.427660   
140 1 3.911730 -33.367298 0.000000   
141 1 4.552590 -31.452101 1.427660   
142 1 0.082520 -32.090500 0.000000   
143 1 2.637990 -30.813700 0.000000   
144 1 0.723381 -30.175400 1.427660   
145 1 3.278850 -28.898600 1.427660   
146 1 5.193450 -29.537001 0.000000   
147 1 5.834320 -27.621901 1.427660   
148 1 1.364240 -28.260300 0.000000   
149 1 2.005110 -26.345200 1.427660   
150 1 3.919710 -26.983500 0.000000   
151 1 4.560580 -25.068501 1.427660   
152 1 0.090508 -25.706800 0.000000   
153 1 0.731376 -23.791800 1.427660   
154 1 2.645970 -24.430099 0.000000   
155 1 3.286830 -22.515100 1.427660   
156 1 5.201450 -23.153400 0.000000   
157 1 5.842320 -21.238300 1.427660   
158 1 1.372240 -21.876699 0.000000   
159 1 2.013090 -19.961599 1.427660   
160 1 3.927680 -20.600100 0.000000   
161 1 4.568500 -18.685101 1.427660   
162 1 0.098511 -19.323200 2.855310   
163 1 0.739356 -17.408100 1.427660   
164 1 2.653910 -18.046499 0.000000   
165 1 3.294660 -16.131399 1.427660   
166 1 5.209240 -16.770100 0.000000   
167 1 1.380180 -15.492800 0.000000   
168 1 5.849840 -14.855400 1.427660   
169 1 2.021010 -13.577200 1.427660   
170 1 3.935270 -14.216300 0.000000   
171 1 4.575630 -12.301200 1.427660   
172 1 0.105523 -12.941000 0.000000   
173 1 0.745482 -11.027400 1.427660   
174 1 2.661980 -11.660800 0.000000   
175 1 3.303420 -9.742730 1.427660   
176 1 5.215560 -10.386400 0.000000   
177 1 5.854650 -8.472240 1.427660   
178 1 1.384840 -9.115630 0.000000   
179 1 2.023040 -7.207600 1.427660   
180 1 3.946290 -7.820610 0.000000   
181 1 4.593240 -5.888760 1.427660   
182 1 0.107342 -6.560490 0.000000   
183 1 0.736295 -4.654560 1.427660   
184 1 2.661220 -5.308910 0.000000   
185 1 3.308560 -3.425320 1.427660   
186 1 5.251020 -3.931570 0.000000   
187 1 5.922660 -1.878590 1.427660   
188 1 1.382770 -2.796470 0.000000   
189 1 1.956110 -0.866116 1.427660   
190 1 3.884190 -1.577170 0.000000   
191 1 4.490600 0.288597 1.427660   
192 1 0.151759 0.582346 0.000000   
193 1 5.279410 4.607850 0.000000   
194 1 5.940150 2.641370 1.427660   
195 1 1.419070 3.367500 0.000000   
196 1 2.076100 1.503900 1.427660   
197 1 3.997620 2.181050 0.000000   
198 1 4.631090 6.541390 1.427660   
199 1 0.154781 7.192120 0.000000   
200 1 0.792089 5.277900 1.427660   
201 1 2.705010 5.934540 0.000000   
202 1 3.339920 4.042430 1.427660   
203 1 5.261230 11.022900 0.000000   
204 1 5.900710 9.107370 1.427660   
205 1 1.430210 9.750370 0.000000   
206 1 2.068490 7.839800 1.427660   
207 1 3.988440 8.464370 0.000000   
208 1 4.621300 12.938200 1.427660   
209 1 0.151208 13.577700 0.000000   
210 1 0.791010 11.663500 1.427660   
211 1 2.706870 12.299300 0.000000   
212 1 3.347390 10.382800 1.427660   
213 1 2.066440 14.215000 1.427660   
214 1 3.981050 14.853500 0.000000   
215 1 5.255240 17.407301 0.000000   
216 1 5.895680 15.492400 1.427660   
217 1 1.425940 16.130301 0.000000   
218 1 4.614660 19.322300 1.427660   
219 1 0.144696 19.960501 0.000000   
220 1 0.785341 18.045401 1.427660   
221 1 2.700010 18.683800 0.000000   
222 1 3.340590 16.768700 1.427660   
223 1 5.248010 23.790701 0.000000   
224 1 5.888690 21.875601 1.427660   
225 1 1.418680 22.514000 0.000000   
226 1 2.059360 20.598900 1.427660   
227 1 3.974010 21.237301 0.000000   
228 1 4.607320 25.705799 1.427660   
229 1 0.137305 26.344101 0.000000   
230 1 0.777994 24.429001 1.427660   
231 1 2.692650 25.067400 0.000000   
232 1 3.333340 23.152300 1.427660   
233 1 5.240580 30.174400 0.000000   
234 1 5.881280 28.259199 1.427660   
235 1 1.411260 28.897600 0.000000   
236 1 2.051960 26.982500 1.427660   
237 1 3.966620 27.620899 0.000000   
238 1 3.325920 29.535999 1.427660   
239 1 4.599860 32.089500 1.427660   
240 1 0.129844 32.727901 0.000000   
241 1 0.770558 30.812700 1.427660   
242 1 2.685210 31.451099 0.000000   
243 1 5.233060 36.558399 0.000000   
244 1 5.873790 34.643101 1.427660   
245 1 1.403770 35.281502 0.000000   
246 1 2.044490 33.366299 1.427660   
247 1 3.959140 34.004700 0.000000   
248 1 4.592330 38.473598 1.427660   
249 1 0.122297 39.112000 0.000000   
250 1 0.763037 37.196800 1.427660   
251 1 2.677680 37.835201 0.000000   
252 1 3.318420 35.919899 1.427660   
253 1 5.225470 42.942600 0.000000   
254 1 5.866220 41.027302 1.427660   
255 1 1.396190 41.665798 0.000000   
256 1 2.036940 39.750500 1.427660   
257 1 3.951580 40.388901 0.000000   
258 1 4.584720 44.857899 1.427660   
259 1 0.114684 45.496399 0.000000   
260 1 0.755441 43.581100 1.427660   
261 1 2.670080 44.219501 0.000000   
262 1 3.310830 42.304199 1.427660   
263 1 5.217830 49.327000 0.000000   
264 1 5.858590 47.411701 1.427660   
265 1 1.388560 48.050098 0.000000   
266 1 2.029320 46.134800 1.427660   
267 1 3.943960 46.773201 0.000000   
268 1 4.577050 51.242298 1.427660   
269 1 0.107013 51.880699 0.000000   
270 1 0.747787 49.965401 1.427660   
271 1 2.662420 50.603901 0.000000   
272 1 3.303190 48.688499 1.427660   
273 1 5.210120 55.711300 0.000000   
274 1 5.850910 53.796001 1.427660   
275 1 1.380860 54.434502 0.000000   
276 1 2.021640 52.519199 1.427660   
277 1 3.936280 53.157600 0.000000   
278 1 4.569340 57.626701 1.427660   
279 1 0.099290 58.265099 0.000000   
280 1 0.740080 56.349800 1.427660   
281 1 2.654710 56.988201 0.000000   
282 1 3.295490 55.072899 1.427660   
283 1 5.843170 60.180401 1.427660   
284 1 1.373120 60.818802 0.000000   
285 1 2.013920 58.903500 1.427660   
286 1 3.928540 59.542000 0.000000   
287 1 5.202370 62.095699 0.000000   
288 1 4.561560 64.011002 1.427660   
289 1 0.091508 64.649399 0.000000   
290 1 0.732316 62.734100 1.427660   
291 1 2.646940 63.372601 2.855310   
292 1 3.287740 61.457298 1.427660   
293 1 5.194550 68.480003 0.000000   
294 1 5.835370 66.564697 1.427660   
295 1 1.365310 67.203201 0.000000   
296 1 2.006130 65.287903 1.427660   
297 1 3.920750 65.926300 0.000000   
298 1 4.553720 70.395401 1.427660   
299 1 0.083667 71.033798 0.000000   
300 1 0.724493 69.118500 1.427660   
301 1 2.639110 69.756897 0.000000   
302 1 3.279930 67.841599 1.427660   
303 1 5.186670 74.864403 0.000000   
304 1 5.827510 72.949097 1.427660   
305 1 1.357450 73.587502 0.000000   
306 1 1.998280 71.672203 1.427660   
307 1 3.912890 72.310699 0.000000   
308 1 0.716608 75.502800 1.427660   
309 1 3.272060 74.225998 1.427660   
310 1 4.545830 76.779701 1.427660   
311 1 0.075764 77.418098 0.000000   
312 1 2.631220 76.141296 0.000000   
313 1 5.178740 81.248703 0.000000   
314 1 5.819590 79.333397 1.427660   
315 1 1.349520 79.971802 0.000000   
316 1 1.990370 78.056503 1.427660   
317 1 3.904980 78.695000 0.000000   
318 1 4.537880 83.163902 1.427660   
319 1 0.067814 83.802299 0.000000   
320 1 0.708670 81.887100 1.427660   
321 1 2.623280 82.525497 0.000000   
322 1 3.264130 80.610199 1.427660   
323 1 5.170770 87.632698 0.000000   
324 1 5.811630 85.717598 1.427660   
325 1 1.341560 86.356003 0.000000   
326 1 1.982420 84.440697 1.427660   
327 1 3.897020 85.079102 0.000000   
328 1 4.529910 89.547897 1.427660   
329 1 0.059838 90.186302 0.000000   
330 1 0.700700 88.271103 1.427660   
331 1 2.615300 88.909500 0.000000   
332 1 3.256160 86.994301 1.427660   
333 1 1.974440 90.824699 1.427660   
334 1 5.162780 94.016502 0.000000   
335 1 5.803650 92.101402 1.427660   
336 1 1.333580 92.739799 0.000000   
337 1 3.889050 91.462997 0.000000   
338 1 4.521920 95.931602 1.427660   
339 1 0.051848 96.569901 0.000000   
340 1 0.692713 94.654900 1.427660   
341 1 2.607320 95.293198 0.000000   
342 1 3.248180 93.378098 1.427660   
343 1 5.154780 100.400002 0.000000   
344 1 5.795650 98.485001 1.427660   
345 1 1.325590 99.123299 0.000000   
346 1 1.966450 97.208298 1.427660   
347 1 3.881050 97.846603 0.000000   
348 1 4.513920 102.315002 1.427660   
349 1 0.043927 102.953003 0.000000   
350 1 0.684743 101.038002 1.427660   
351 1 2.599330 101.677002 0.000000   
352 1 3.240190 99.761703 1.427660   
353 1 5.787860 104.867996 1.427660   
354 1 1.317770 105.507004 0.000000   
355 1 1.958510 103.592003 1.427660   
356 1 3.873070 104.230003 0.000000   
357 1 3.232240 106.146004 1.427660   
358 1 5.147260 106.782997 0.000000   
359 1 4.506900 108.696999 1.427660   
360 1 0.036794 109.336998 0.000000   
361 1 0.677159 107.421997 1.427660   
362 1 2.591410 108.060997 0.000000   
363 1 5.142450 113.166000 0.000000   
364 1 5.781540 111.251999 1.427660   
365 1 1.309010 111.896004 0.000000   
366 1 1.950450 109.977997 1.427660   
367 1 3.866940 110.611000 0.000000   
368 1 4.505080 115.078003 1.427660   
369 1 0.019188 115.750000 0.000000   
370 1 0.666139 113.818001 1.427660   
371 1 2.589390 114.431000 0.000000   
372 1 3.227590 112.523003 1.427660   
373 1 5.074440 119.760002 0.000000   
374 1 5.746080 117.707001 1.427660   
375 1 1.303870 118.212997 0.000000   
376 1 1.951210 116.329002 1.427660   
377 1 3.876130 116.984001 0.000000   
378 1 0.728234 120.060997 1.427660   
379 1 2.656320 120.772003 0.000000   
380 1 3.229660 118.842003 1.427660  

LAMMPS input script

This input script was run using the November 2010 version of LAMMPS. Changes in some commands in more recent versions may require revision of the input script. This script runs the simulation with a previously generated grain boundary file, which is fed to the variable "datfile." The variable "nloop" defines how many times the strain will be increased and the number of points at which the stress is calculated. To run this script, store it in "in.gb_fracture.txt" and use "lmp_exe < in.gb_fracture.txt" in a UNIX environment where "lmp_exe" refers to the LAMMPS executable.

############################################################################
# Interfacial fracture
# Mark Tschopp, 2010

# lmp_exe -var datfile Fe_100_sig52_10.txt -var strain 0.001 -var nloop 100 -var minlength 20 < in.gb_fracture.txt
############################################################################

variable datfile index Fe_100_sig5_210.txt
variable strain equal 0.001
variable nloop equal 100
#variable repl equal 1
variable strain2 equal "1+v_strain"

######################################
# INITIALIZATION
units 		metal
dimension		3
boundary		p	p	p
atom_style		atomic
atom_modify map array

######################################
# SIMULATION CELL VARIABLES (in Angstroms)

read_data ${datfile}

#variable minlength equal 100
variable xlen equal lx
variable ylen equal ly
variable zlen equal lz

print "lx: ${xlen}"
print "ly: ${ylen}"
print "lz: ${zlen}"

# Determine number of increments for displacement grid in the in-plane GB directions 
variable xrepl equal "ceil(v_minlength / v_xlen)" 
variable zrepl equal "ceil(v_minlength / v_zlen)" 

replicate ${xrepl} 1 ${zrepl}

######################################
# INTERATOMIC POTENTIAL
pair_style	eam/fs
pair_coeff	* * Fe-C_Hepburn_Ackland.eam.fs Fe C

##########################################
# Minimize first?
reset_timestep 0
thermo		10
thermo_style custom step lx ly lz press pxx pyy pzz pe
min_style cg
fix 1 all box/relax x 0.0 z 0.0 couple none vmax 0.001 
minimize 1.0e-25 1.0e-25 1000 10000
unfix 1

variable ly1 equal ly
variable ly0 equal ${ly1}
variable lydelta equal "v_strain*v_ly0/2"

# Setup file output (time in ps, pressure in GPa)
variable p1 equal "(ly-v_ly0)/v_ly0"
variable p2 equal "-pxx/10000"
variable p3 equal "-pyy/10000"
variable p4 equal "-pzz/10000"
variable p5 equal "-pxy/10000"
variable p6 equal "-pxz/10000"
variable p7 equal "-pyz/10000"
variable p8 equal "pe"

fix equil1 all print 1 "${p1} ${p2} ${p3} ${p4} ${p5} ${p6} ${p7} ${p8}" file data.${datfile}_${minlength}.txt screen no
fix 1 all nve
run 1
unfix 1
variable pressf1 equal pyy
variable pressf equal ${pressf1}

##########################################
# MS Deformation loop

variable a loop ${nloop}
label loop

# Increase box bound and minimize again
reset_timestep 0
#displace_box all y scale ${strain2}
#fix 1 all box/relax x 10000.0 z 10000.0 couple none vmax 0.001 
displace_box all y delta -${lydelta} ${lydelta} units box
minimize 1.0e-25 1.0e-25 1000 10000

run 1

print "Pressf: ${pressf}"
variable pdiff equal "pyy - v_pressf"
print "Pressf: ${pressf}"
print "Pdiff: ${pdiff}"
if ${pdiff} > 10000 then "exit"
variable pressf1 equal pyy
variable pressf equal ${pressf1}

next a
jump in.gb_fracture.txt loop 

unfix equil1

######################################
# SIMULATION DONE
print "All done"

Output

LAMMPS datafile

The following file, named "data.Fe_100_sig52_10.txt" should have been created in addition to the log.lammps file. This file stores strain information in the first column, stress tensor information in the second through seventh columns, and stores the total potential energy of the cell in the eight column. The simulation should have looped 100 times (as per the "nloop" variable), so there should be 100 entries (which end at a strain of 0.1) plus the initial entry of stress and strain at zero.

# Fix print output for fix equil1
0 -2.219884235e-05 -0.09436668009 5.407552011e-06 1.221556825e-05 1.110009611e-09 4.462377068e-12 -48716.72405
0.001 0.1468487572 0.1387359115 0.1431841846 -6.180770704e-09 -2.564170766e-12 -2.40791993e-12 -48716.76403
0.002 0.2598702618 0.4058469325 0.2847557426 -4.808171999e-12 9.566142713e-16 -3.41722654e-15 -48716.52319
0.003 0.3720478051 0.6731956939 0.4254156925 1.311052574e-10 3.449206559e-15 -2.636944941e-14 -48716.04581
0.004 0.483977058 0.9402201271 0.5652029445 -6.629325468e-12 1.129857588e-15 2.416966446e-14 -48715.3319
0.005 0.5948099239 1.207643528 0.7041151176 -9.516316287e-13 2.79361336e-15 7.471854238e-15 -48714.38144
...


Post-Processing

Stress-Strain Plot

The stress-strain curve in Figure 1 can be generated using the following MATLAB script. Note that the definitions of stress and strain are negative. This is done to counteract the negative values of compressive stress and strain so that positive axes and a familiar shape are retained. The "exportfig" command saves the plot to a tiff files, but the plot can also be saved as a Mathcad figure once it appears.

% Analyze def1.txt files and plot the responses

d = dir('*.def1.txt');
for i = 1:length(d)
    fname = d(i).name;
    A = importdata(fname);
    strain = -A.data(:,1);
    stress = -A.data(:,2:4);
    
    plot(strain,stress(:,1),'-or','LineWidth',2,'MarkerEdgeColor','r',...
        'MarkerFaceColor','r','MarkerSize',5),hold on
    plot(strain,stress(:,2),'-ob','LineWidth',2,'MarkerEdgeColor','b',...
        'MarkerFaceColor','b','MarkerSize',5),hold on
    plot(strain,stress(:,3),'-og','LineWidth',2,'MarkerEdgeColor','g',...
        'MarkerFacecolor','g','MarkerSize',5),hold on
    axis square
    ylim([0 7])
    xlim([0 0.2])
    set(gca,'LineWidth',2,'FontSize',24,'FontWeight','normal','FontName','Times')
    set(get(gca,'xlabel'),'String','Strain','FontSize',32,'FontWeight','bold','FontName','Times')
    set(get(gca,'ylabel'),'String','Stress (GPa)','FontSize',32','FontWeight','bold','FontName','Times')
    set(gcf,'Position',[1 1 round(1000) round(1000)])
    
    % Export the figure to a tif file
    exportfig(gcf,strrep(fname,'.def1.txt','.tif'),'Format','tiff',...
        'Color','rgb','Resolution',300)
end
Figure 1. Stress-strain curve for uniaxial compressive loading of single crystal aluminum in the <100> loading direction.

Deformation Movie

This assumes that you already have AtomEye and ImageJ downloaded.

  • Visualize the dumpfile in AtomEye by typing the following command, "/A dump.tensile_0.cfg" (UNIX).
  • Use the AtomEye options to select how you want to visualize deformation. In this example, the centrosymmetry parameter was used to show only atoms in a non-centrosymmetric environment (see Fig. 2).
    • Use Alt+0 to activate centrosymmetric (csym) view.
    • Adjust threshold, or set of atoms to view, by using Shift+T. This will allow creation of a set for the current parameter (in this case, csym).
    • Make atoms with values outside of the threshold invisible by using Ctrl+A.
  • Press 'y' within AtomEye to produce an animation script.
  • The folder "Jpg" now contains snapshots of all dumpfiles.
  • Open ImageJ
  • Drag the folder Jpg into ImageJ
    • Select "Convert to RGB" to keep the color from the AtomEye images.
    • Choose "yes" to load a stack.
  • Adjust the size as needed (Image/Adjust/Size)
  • Adjust frame rate as desired (Image/Stacks/Animation Options)
  • Save as Animated Gif file
Figure 2. Image of nucleated dislocation near peak stress.
Movie showing compressive deformation of single crystal aluminum loaded in the <100> direction at a strain rate of 1010 s-1 and a temperature of 300 K. Only atoms in non-centrosymmetric environment are shown.

Cell Size Comparison

In order to test the difference that the number of atoms can have on a simulation, the above script was run with 32,000 and 108,000 atoms in addition 4,000 atoms. Editing the values (currently "10") in the following line in the input script will change the size of the simulation cell and the number of atoms used in the simulation. Values of "20" will result in 32,000 atoms, and values of "30" will result in 108,000 atoms.

region whole block 0 10 0 10 0 10 


Shown below are movies of the 4,000, 32,000, and 108,000 atom simulations, which show only atoms in a non-centrosymmetric environment. As one might expect, more slip planes become visible as the atom count of the simulation increases.

Movie showing compressive deformation of a 4,000 atom single crystal of aluminum loaded in the <100> direction. Only atoms in non-centrosymmetric environment are shown.
File:Al comp 32k.gif
Movie showing compressive deformation of a 32,000 atom single crystal of aluminum loaded in the <100> direction. Only atoms in non- centrosymmetric environment are shown.
Movie showing compressive deformation of a 108,000 atom single crystal of aluminum loaded in the <100> direction. Only atoms in non-centrosymmetric environment are shown.

Temperature Comparison

The temperature of the simulations also makes a difference in the outputs. To show this difference, the above simulations (previously at 300 K) were run at 10 K. In order to change the temperature of the simulation, three lines in the input script must be edited. Two lie under the 'Equilibraion' section while the third lies under 'Deformation.'

The velocity and fix commands shown below contain temperature data. The velocity command specifies the thermal velocity of the system while the fix command specifies the desired temperatures at the beginning and end of the simulation. In order to run the simulation at 10 K instead of 300 K, change the three '300' values to '10' in the velocity and fix command lines.

# EQUILIBRATION
reset_timestep	0
timestep 0.001
velocity all create 300 12345 mom yes rot no
fix 1 all npt temp 300 300 1 iso 0 0 1 drag 1 

The temperature values in the fix command under 'Deformation' also needs to be changed to '10' instead of '300.' The values are being changed again because between 'Equilibration' and 'Deformation' the fix ID 1 was unfixed. Here fix 1 is being redefined.

# DEFORMATION
reset_timestep	0

fix		1 all npt temp 300 300 1 y 0 0 1 z 0 0 1 drag 1

All three simulation cell sizes were run at 10 K. Below are the movies from the simulations. Once again, only atoms in a non-centrosymmetric environment are viewable. The difference between the 300 K and 10 K simulations is that there is less non-centrosymmetry induced by thermal velocity. At 10 K, many fewer atoms are seen before slip occurs, and the slip planes are more cleary visible and absent of "noise" created by atoms that are non-centrosymmetric solely due to thermal activity.

Movie showing compressive deformation of a 4,000 atom single crystal of aluminum at 10 K loaded in the <100> direction. Only atoms in non-centrosymmetric environment are shown.
Movie showing compressive deformation of a 32,000 atom single crystal of aluminum at 10 K loaded in the <100> direction. Only atoms in non-centrosymmetric environment are shown.
Movie showing compressive deformation of a 108,000 atom single crystal of aluminum at 10 Kloaded in the <100> direction. Only atoms in non-centrosymmetric environment are shown.

Go Back

Acknowledgments

The authors would like to acknowledge funding for this work through the Department of Energy.

References

  1. S. Plimpton, "Fast Parallel Algorithms for Short-Range Molecular Dynamics," J. Comp. Phys., 117, 1-19 (1995).
  2. D.J. Hepburn and G.J. Ackland, "Metallic-covalent interatomic potential for carbon in iron," Phys. Rev. B 78, 165115 (2008).
Personal tools
Namespaces

Variants
Actions
home
Materials
Material Models
Design
Resources
Projects
Education
Toolbox