Week - 9 Material Modeling from Raw Data

The given curve is shown below:

The given true stress strain curve data is digitized for curve 1 and confirming it matches with the given curve

Since this given stress is in ksi we convert it to kg mm ms by multiplying it by 0.0668947573 and strain % is coverted to strain by dividing it by 100.

From this curve we get yield stress at 0.14277 `(kg)/(mm*ms^2)`

SInce we need effective stress and effective strain data to create the material curve in LS PrePost, we convert this true stress and true strain

Effective stress = True Stress

Effective Strain = True Strain - (True Stress/Young's Modulus)

Given Young's modulus is 20.9E+06 psi and converting it to given units we get E = 144.1 `(kg)/(mm*ms^2)`

Strain %	Stress ksi	True Strain (mm/mm)	True Stress `(kg)/(mm*ms^2)`	Effective Strain (mm/mm)	Effective Stress `(kg)/(mm*ms^2)`
0.0000134	0.166	0.000000134	0.00114453	-7.81407E-06	0.00114453
0.00982	2.24	0.0000982	0.01544426	-9.05104E-06	0.015444256
0.0245	5.23	0.000245	0.03605958	-5.41202E-06	0.036059581
0.0402	8.55	0.000402	0.05895017	-7.37337E-06	0.058950175
0.0471	10.2	0.000471	0.07032652	-1.73753E-05	0.070326524
0.052	11	0.00052	0.07584233	-6.67919E-06	0.07584233
0.0569	12.4	0.000569	0.08549499	-2.47111E-05	0.08549499
0.0618	13.2	0.000618	0.0910108	-1.40150E-05	0.091010796
0.0667	14.4	0.000667	0.09928451	-2.24709E-05	0.099284505
0.0745	15.8	0.000745	0.10893717	-1.15028E-05	0.108937165
0.0805	17.3	0.000805	0.1192793	-2.33227E-05	0.119279301
0.0883	18.6	0.000883	0.12824249	-7.56663E-06	0.128242486
0.0951	20.1	0.000951	0.13858462	-1.13865E-05	0.138584622
0.105	21.6	0.00105	0.14892676	1.57936E-05	0.148926758
0.115	23	0.00115	0.15857942	4.87617E-05	0.158579418
0.122	24.4	0.00122	0.16823208	5.17298E-05	0.168232078
0.127	25.2	0.00127	0.17374788	6.34259E-05	0.173747884
0.135	26.3	0.00135	0.18133212	9.07579E-05	0.181332117
0.14	27	0.0014	0.18615845	1.07242E-04	0.186158447
0.145	27.7	0.00145	0.19098478	1.23726E-04	0.190984777
0.157	29.3	0.00157	0.20201639	1.67118E-04	0.202016389
0.163	30.2	0.00163	0.20822167	1.84026E-04	0.20822167
0.168	30.9	0.00168	0.213048	2.00510E-04	0.213048
0.173	31.5	0.00173	0.21718485	2.21782E-04	0.217184855
0.179	32.2	0.00179	0.22201118	2.48266E-04	0.222011185
0.183	32.8	0.00183	0.22614804	2.59538E-04	0.226148039
0.191	33.5	0.00191	0.23097437	3.06022E-04	0.230974369
0.201	34.8	0.00201	0.23993755	3.43779E-04	0.239937554
0.212	35.8	0.00212	0.24683231	4.05899E-04	0.246832311
0.221	36.8	0.00221	0.25372707	4.48019E-04	0.253727068
0.231	37.8	0.00231	0.26062183	5.00139E-04	0.260621826
0.244	38.9	0.00244	0.26820606	5.77471E-04	0.268206059
0.259	40.1	0.00259	0.27647977	6.70015E-04	0.276479767
0.269	40.9	0.00269	0.28199557	7.31711E-04	0.281995573
0.278	41.5	0.00278	0.28613243	7.92983E-04	0.286132428
0.296	42.6	0.00296	0.29371666	9.20315E-04	0.293716661
0.302	42.9	0.00302	0.29578509	9.65951E-04	0.295785088
0.309	43.3	0.00309	0.29854299	1.01680E-03	0.298542991
0.317	43.7	0.00317	0.30130089	1.07765E-03	0.301300894
0.346	45	0.00346	0.31026408	1.30540E-03	0.310264078
0.368	45.9	0.00368	0.31646936	1.48231E-03	0.31646936
0.391	46.7	0.00391	0.32198517	1.67401E-03	0.321985166
0.404	47.1	0.00404	0.32474307	1.78486E-03	0.324743069
0.434	48	0.00434	0.33094835	2.04176E-03	0.33094835
0.46	48.8	0.0046	0.33646416	2.26346E-03	0.336464156
0.476	49.2	0.00476	0.33922206	2.40431E-03	0.339222059
0.496	49.7	0.00496	0.34266944	2.58037E-03	0.342669437
0.515	50.1	0.00515	0.34542734	2.75122E-03	0.34542734
0.554	50.9	0.00554	0.35094315	3.10291E-03	0.350943146
0.581	51.4	0.00581	0.35439052	3.34897E-03	0.354390525
0.604	51.8	0.00604	0.35714843	3.55982E-03	0.357148428
0.627	52.2	0.00627	0.35990633	3.77067E-03	0.359906331
0.646	52.6	0.00646	0.36266423	3.94152E-03	0.362664234
0.67	52.9	0.0067	0.36473266	4.16715E-03	0.364732661
0.689	53.3	0.00689	0.36749056	4.33800E-03	0.367490564
0.7	53.4	0.007	0.36818004	4.44321E-03	0.368180039

This effective stress and effective strain are plotted in excel with positive values of strain and using curve fit the noise in data can be taken care.

The best curve fit from Trend line which suits the data is the power law and the curve we get

`y = 1.0062x^0.1806` which fits 99.13%

Using proper sequential data starting with the yield stress we get Effective strain as 0.00002 and adding with 0.0000876 we get 50 data points and using this above curve effective stress is calculated

Effective Strain	Effective Stress
0.00002	0.142577282
0.0001076	0.193210004
0.0001952	0.215151792
0.0002828	0.230049606
0.0003704	0.241538459
0.000458	0.250978557
0.0005456	0.259038205
0.0006332	0.266098607
0.0007208	0.272399096
0.0008084	0.278100406
0.000896	0.283316025
0.0009836	0.288129243
0.0010712	0.292603109
0.0011588	0.296786571
0.0012464	0.300718431
0.001334	0.304430006
0.0014216	0.307946955
0.0015092	0.311290584
0.0015968	0.314478788
0.0016844	0.317526753
0.001772	0.32044748
0.0018596	0.323252194
0.0019472	0.325950657
0.0020348	0.328551411
0.0021224	0.331061983
0.00221	0.333489034
0.0022976	0.335838494
0.0023852	0.338115665
0.0024728	0.340325307
0.0025604	0.342471712
0.002648	0.344558764
0.0027356	0.346589987
0.0028232	0.348568594
0.0029108	0.350497518
0.0029984	0.352379447
0.003086	0.35421685
0.0031736	0.356012001
0.0032612	0.357766999
0.0033488	0.359483784
0.0034364	0.361164157
0.003524	0.362809789
0.0036116	0.364422236
0.0036992	0.366002948
0.0037868	0.36755328
0.0038744	0.369074498
0.003962	0.370567789
0.0040496	0.372034267
0.0041372	0.373474978
0.0042248	0.374890905
0.0043124	0.376282977
0.0044	0.377652067

LS Dyna:

This above Effective stress ans strain data is using in simulating the given Dogbone specimen.

This is opened in LS PrePost

Necessary cards are generated for simulation

SECTION

Material CURVE

This effective stress vs effective strain saved in csv format is loaded with LoadXY data

Plotting it we get,

MAT 024

Boundary Conditions

Fixing the nodes

Displacement curve:

Giving displacement of max 1 mm gives close to the highest value strain in the curve

For displacement of nodes

Since this quasistatic process IMPLICIT is activated

Termination time is given 1 ms

Output data:

For strain data EXTENT_BINARY is activated with strflg = 1

In ASCII

ELOUT and GLSTAT is activated

Results:

The contour of vonmises stress

Uniaxial X Strain is plotted for center elements form History

Similarly X strain for the same element

Using cross plot we get True Stress vs True Strain

This curve is validated with the given true stress strain curve

Conclusion:

The given Stress strain curve is converted to material data and is validated with given Dogbone specimen.