THEORY The Theory used is quite simple and can be found on the references. For calculation on the R amberg-Osgood coeficient, the formulas are:
n
Ln( us / 0.2)
where
Ln( F tu / F ty )
us
F 100 100 r tu E
The material curve uses the equation :
0.002 E F ty
n
For calculation of the true stress-strain material curve, the equations are:
true
Ln(1 )
and
(1 )
true
NOTE: There are other formulas available for calculation of
n.
References:
1. Ramberg, 1. Ramberg, W. and Osgood W. R. - Description of stress-strain cur by three parametres - NACA TN 902 2. FAA 2. FAA FAR MMPDS-01 3. Hill, 3. Hill, H. N. - Determination of stress-strain relations from "offset" yield stregth values - NACA TN927
USE The stress-strain curves calculated here are useful for non linear calculations. Files CSV, that the spreadsheet creates, can be imported by Patran when using non linear isotropic material (SOL 106 for example). It is also possible to use the points generated for manual input of the TABLES1 on the bulk data fil Use of the Stress-strain curve or the true stress strain curve is a choice of the modeler. When calculating with the spreadsheet, fill up ONLY the fields marked marked in yelow. yelow. I make it useful for different applications, the calculation spreadsheet is NOT PRO If you are generating CVS files (using the butons), be sure to have Macros enabl and follow the instructions.
EXAMPLE One example is given, for Al Al 7050 T7351:
The data block to be filled:
material = Al 7050 T7351 E = 71018.5 N/mm Ftu= Fty= max =
2
(Young Modulus)
2
(Ultimate strength) (Yield strength) (strain at rupture)
468.8 N/mm 386.12 N/mm 2 10 %
The Ramberg-Osgood coeficient is calculated:
n=
19.81
A table with the stress-strain curve is created and also a plot of the curve: (MPa) 0.0 77.2 154.4 231.7 308.9 328.2 347.5 366.8 386.1 394.4 402.7 410.9 419.2 427.5 435.7 444.0 452.3 460.5 468.8
0.00000 0.00109 0.00217 0.00326 0.00437 0.00470 0.00514 0.00589 0.00744 0.00860 0.01026 0.01265 0.01609 0.02102 0.02806 0.03807 0.05222 0.07214 0.10000
Stress-Stra 500.0 450.0 400.0 350.0 ] 300.0 a P M250.0 [ s s e r 200.0 S
150.0 100.0 50.0 0.0 0.000
0.020
0.040
Ramberg-Osgood Stress-Strai
Also a table with the true stress -strain curve and plot is created: (MPa) 0.0 77.3 154.8 232.4 310.2 329.7 349.3 369.0
0.00000 0.00109 0.00217 0.00326 0.00436 0.00469 0.00513 0.00587
True Stress-S 600.0
500.0
400.0 ] a P 300.0 M [
. 397.8 406.8 416.1 425.9 436.4 448.0 460.9 475.9 493.8 515.7
. 0.00856 0.01021 0.01257 0.01596 0.02080 0.02767 0.03736 0.05091 0.06965 0.09531
s e r S
200.0
100.0
0.0 0.000
0.020
0.040
True Stress
A comparison of the two curves:
Engineering and True 600.0
500.0
400.0 ] a P M300.0 [ s s e r S
200.0
100.0
0.0 0.000
0.020
0.040
Ramberg-Osgood Stress-Strain Curve
Importing the CVS files created on Patran, the curves can be visualized (Fi
CONTACT EngineersToolkit can be conatcted at
DISCLAIMER
http://www.engineerstoolkit.
ves
.
n order to TECTED. d
in Curve
0.060
0.080
0.100
Strain Curve
Fty
rain Curve
Ftu
0.120
0.060
0.080
0.100
0.120
train -Strain Curve
Stress-Strain Curve
0.060
0.080
0.100
Strain Fty
Ftu
ields -> Show):
True stress-strain
0.120
com/contact-us/
1. ENTER DATA ON YELLOW CELLS HERE: ONLY T
material = Al 7050 T7351 E= Ftu= Fty= max =
2 71018.5 N/mm
(Young Modulus)
2
468.8 N/mm 386.12 N/mm2 10 %
ALL OT
(Ultimate strength) (Yield strength) (strain at rupture)
2. THE RAMBERG-OSGOOD COEFICIENT: The Ramberg-Osgood coeficient is calculated based on MMPDS-01: us =
uniform strain = plastic strain at end of uniform elongation (at max. tension load Ftu )
F 100 E tu
us
n
r
n=
Ln( us / 0.2) Ln( F tu / F ty )
19.81
3. THE MATERIAL STRESS-STRAIN CURVE (ENGINEERING STRESS-STR The material stress-strain curve is calculated based on MMPDS-01, equation 9.8.4.1.2(b):
0.002 F E ty
n
(MPa) 0.0 77.2 154.4 231.7 308.9 328.2 347.5 366.8 386.1 394.4 402.7 410.9 419.2 427.5 435.7 444.0 452.3
0.00000 0.00109 0.00217 0.00326 0.00437 0.00470 0.00514 0.00589 0.00744 0.00860 0.01026 0.01265 0.01609 0.02102 0.02806 0.03807 0.05222
Stress-Strain Curve 500.0 450.0 400.0 350.0 ] 300.0 a P M250.0 [ s s 200.0 e r S
150.0 100.0 50.0 0.0 0.000
0.020
0.040
0.060 Strain
0.080
460.5 468.8
0.07214 0.10000
Ramberg-Osgood Stress-Strain Curve
Fty
4. TRUE MATERIAL STRESS-STRAIN CURVE The engineering stress-strain curve can be corrected to the true curve that takes into account the reduction of area in tension: true
Ln(1 )
(1 )
true
(MPa) 0.0 77.3 154.8 232.4 310.2 329.7 349.3 369.0 389.0 397.8 406.8 416.1 425.9 436.4 448.0 460.9 475.9 493.8 515.7
0.00000 0.00109 0.00217 0.00326 0.00436 0.00469 0.00513 0.00587 0.00741 0.00856 0.01021 0.01257 0.01596 0.02080 0.02767 0.03736 0.05091 0.06965 0.09531
True Stress-Strain Curve 600.0 500.0 400.0 ] a P M300.0 [ s s e r S 200.0
100.0 0.0 0.000
0.020
0.040
0.060
0.080
Strain
True Stress-Strain Curve
5. COMPARISON OF MATERIAL CURVES
Engineering and True Stress-Strain Curve 600.0 500.0 400.0 ] a P M300.0 [ s s e r S 200.0
100.0 0.0 0.000
0.020
0.040
0.060
0.080
0.100
Ftu
True stres
Strain
Ramberg-Osgood Stress-Strain Curve
Fty
6. CREATION OF .cvs FILE FOR IMPORTING ON PATRAN You can create a .cvs file that can be imported on Patran (on Fields) for Material Property There are two options: engineering curve and true curve When creating the file/files, Excel may prompt you two windows like below. Click "YES" on (these windows may be different, depending on the Excel version, anyway click "YES")
CREATE CVS FILE (FOR PATRAN) - CLICK THE BUTON OF YOUR OPTION
NOTES:
1. The file or files will be created on the same directory of the Excel file. 2. Be sure that Macros are enabled. 3. The file(s) created are NOT updated if you change data. If you are working with more than one material, rename the files before creating new ones. 4. When importing the file(s) on Patran, be sure to select the option of CVS file and that th used on the file is selected in the options (CVS Import Options). You can check what sepa was used (it depends on computer settings), by openning the file(s) with a text editor (Wor 5. The spreadsheet is available "AS IS". Although checks were done, please contact if you have any correction, suggestion or comment. http://www.engineerstoolkit.com/contact-us/ 6. Read the disclaimer below:
E YELLOW CELLS HAVE TO BE FILLED !!! ER VALUES ARE CALCULATED
IN)
0.100
0.120
Ftu
0.100
0.120
0.120
s-strain
. Read the notes.
both:
(YOU CAN ALSO CREATE THE TWO FILES)
e separator rator dpad, Notepad, etc.)
