Etk Material Curves 20121018

THEORY

The Theory used is quite simple and can be found on the references.

For calculation on the Ramberg-Osgood coeficient, the formulas are:

where

The material curve uses the equation :

For calculation of the true stress-strain material curve, the equations are:

and

References:

by three parametres - NACA TN 902

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 file.

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 in yelow. In order to

make it useful for different applications, the calculation spreadsheet is NOT PROTECTED.

If you are generating CVS files (using the butons), be sure to have Macros enabled

and follow the instructions.

NOTE: There are other formulas available for calculation of n.

1. Ramberg, W. and Osgood W. R. - Description of stress-strain curves

2. FAA FAR MMPDS-01

3. Hill, H. N. - Determination of stress-strain relations from "offset"

n=Ln (εus /0 .2)Ln(F tu/F ty )

ε= σE

+0 .002⋅( σF ty )n

ε true=Ln(1+ε ) σ true=σ (1+ε )

ε us=100⋅(εr−F tuE )

EXAMPLE

One example is given, for Al Al 7050 T7351:

The data block to be filled:

The Ramberg-Osgood coeficient is calculated:

A table with the stress-strain curve is created and also a plot of the curve:

Also a table with the true stress-strain curve and plot is created:

material =

E = 71018.5 N/mm2 (Young Modulus)

Ftu= 468.8 N/mm2 (Ultimate strength)Fty= 386.12 N/mm2 (Yield strength)

e max = 10 % (strain at rupture)

Al 7050 T7351

n = 19.81

s (MPa) e0.0 0.0000077.2 0.00109154.4 0.00217231.7 0.00326308.9 0.00437328.2 0.00470347.5 0.00514366.8 0.00589386.1 0.00744394.4 0.00860402.7 0.01026410.9 0.01265419.2 0.01609427.5 0.02102435.7 0.02806444.0 0.03807452.3 0.05222460.5 0.07214468.8 0.10000

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

500.0

0.000 0.020 0.040 0.060 0.080 0.100 0.120

Sres

s [M

Pa]

Strain

Stress-Strain Curve

Ramberg-Osgood Stress-Strain Curve Fty Ftu

s (MPa) e0.0 0.0000077.3 0.00109154.8 0.00217232.4 0.00326310.2 0.00436329.7 0.00469349.3 0.00513369.0 0.00587389.0 0.00741397.8 0.00856406.8 0.01021416.1 0.01257425.9 0.01596436.4 0.02080448.0 0.02767460.9 0.03736475.9 0.05091493.8 0.06965515.7 0.09531

0.0

100.0

200.0

300.0

400.0

500.0

600.0

0.000 0.020 0.040 0.060 0.080 0.100 0.120

Sres

s [M

Pa]

Strain

True Stress-Strain Curve


A comparison of the two curves:

Importing the CVS files created on Patran, the curves can be visualized (Fields -> Show):

s (MPa) e0.0 0.0000077.3 0.00109154.8 0.00217232.4 0.00326310.2 0.00436329.7 0.00469349.3 0.00513369.0 0.00587389.0 0.00741397.8 0.00856406.8 0.01021416.1 0.01257425.9 0.01596436.4 0.02080448.0 0.02767460.9 0.03736475.9 0.05091493.8 0.06965515.7 0.09531

0.0

100.0

200.0

300.0

400.0

500.0

600.0

0.000 0.020 0.040 0.060 0.080 0.100 0.120

Sres

s [M

Pa]

Strain



0.0

100.0

200.0

300.0

400.0

500.0

600.0

0.000 0.020 0.040 0.060 0.080 0.100 0.120

Sres

s [M

Pa]

Strain

Engineering and True Stress-Strain Curve

Ramberg-Osgood Stress-Strain Curve Fty Ftu True stress-strain

CONTACT

EngineersToolkit can be conatcted at

DISCLAIMER

http://www.engineerstoolkit.com/contact-us/


s (MPa) e0.0 0.0000077.2 0.00109154.4 0.00217231.7 0.00326308.9 0.00437328.2 0.00470347.5 0.00514366.8 0.00589386.1 0.00744394.4 0.00860402.7 0.01026410.9 0.01265419.2 0.01609427.5 0.02102435.7 0.02806444.0 0.03807452.3 0.05222460.5 0.07214468.8 0.10000

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

500.0

0.000 0.020 0.040 0.060 0.080 0.100 0.120

Sres

s [M

Pa]

Strain

Stress-Strain Curve


s (MPa) e0.0 0.0000077.3 0.00109154.8 0.00217232.4 0.00326310.2 0.00436329.7 0.00469349.3 0.00513369.0 0.00587389.0 0.00741397.8 0.00856406.8 0.01021416.1 0.01257425.9 0.01596436.4 0.02080448.0 0.02767460.9 0.03736475.9 0.05091493.8 0.06965515.7 0.09531

0.0

100.0

200.0

300.0

400.0

500.0

600.0

0.000 0.020 0.040 0.060 0.080 0.100 0.120

Sres

s [M

Pa]

Strain



Importing the CVS files created on Patran, the curves can be visualized (Fields -> Show):

s (MPa) e0.0 0.0000077.3 0.00109154.8 0.00217232.4 0.00326310.2 0.00436329.7 0.00469349.3 0.00513369.0 0.00587389.0 0.00741397.8 0.00856406.8 0.01021416.1 0.01257425.9 0.01596436.4 0.02080448.0 0.02767460.9 0.03736475.9 0.05091493.8 0.06965515.7 0.09531

0.0

100.0

200.0

300.0

400.0

500.0

600.0

0.000 0.020 0.040 0.060 0.080 0.100 0.120

Sres

s [M

Pa]

Strain



0.0

100.0

200.0

300.0

400.0

500.0

600.0

0.000 0.020 0.040 0.060 0.080 0.100 0.120

Sres

s [M

Pa]

Strain





1. ENTER DATA ON YELLOW CELLS HERE:

material = Al 7050 T7351 ONLY THE YELLOW CELLS HAVE TO BE FILLED !!!E = 71018.5 (Young Modulus)

Ftu= 468.8 (Ultimate strength) ALL OTHER VALUES ARE CALCULATEDFty= 386.12 (Yield strength)

10 % (strain at rupture)

2. THE RAMBERG-OSGOOD COEFICIENT:

The Ramberg-Osgood coeficient is calculated based on MMPDS-01:

n = 19.81

3. THE MATERIAL STRESS-STRAIN CURVE (ENGINEERING STRESS-STRAIN)

The material stress-strain curve is calculated based on MMPDS-01, equation 9.8.4.1.2(b):

e0.0 0.00000

77.2 0.00109154.4 0.00217231.7 0.00326308.9 0.00437328.2 0.00470347.5 0.00514366.8 0.00589386.1 0.00744394.4 0.00860402.7 0.01026410.9 0.01265419.2 0.01609427.5 0.02102435.7 0.02806444.0 0.03807452.3 0.05222460.5 0.07214

N/mm2

N/mm2

N/mm2

e max =

eus = uniform strain = plastic strain at end of uniform elongation (at max. tension load Ftu )

s (MPa)

0.000 0.020 0.040 0.060 0.080 0.100 0.1200.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

500.0

Stress-Strain Curve


Strain

Sres

s [M

Pa]

ε us=100⋅(εr−F tuE ) n=Ln (εus /0 .2)Ln(F tu/F ty )

ε= σE

+0 .002⋅( σF ty )n

468.8 0.10000

4. TRUE MATERIAL STRESS-STRAIN CURVE

The engineering stress-strain curve can be corrected to the true curvethat takes into account the reduction of area in tension:

e0.0 0.00000

77.3 0.00109154.8 0.00217232.4 0.00326310.2 0.00436329.7 0.00469349.3 0.00513369.0 0.00587389.0 0.00741397.8 0.00856406.8 0.01021416.1 0.01257425.9 0.01596436.4 0.02080448.0 0.02767460.9 0.03736475.9 0.05091493.8 0.06965515.7 0.09531

5. COMPARISON OF MATERIAL CURVES

s (MPa)

0.000 0.020 0.040 0.060 0.080 0.100 0.1200.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

500.0

Stress-Strain Curve


Strain

Sres

s [M

Pa]

0.000 0.020 0.040 0.060 0.080 0.100 0.1200.0

100.0

200.0

300.0

400.0

500.0

600.0



Strain

Sres

s [M

Pa]

0.000 0.020 0.040 0.060 0.080 0.100 0.1200.0

100.0

200.0

300.0

400.0

500.0

600.0



Strain

Sres

s [M

Pa]

ε true=Ln(1+ε ) σ true=σ (1+ε )

6. CREATION OF .cvs FILE FOR IMPORTING ON PATRAN

When creating the file/files, Excel may prompt you two windows like below. Click "YES" on both:(these windows may be different, depending on the Excel version, anyway click "YES")

NOTES:

You can create a .cvs file that can be imported on Patran (on Fields) for Material Property. Read the notes.

There are two options: engineering curve and true curve

CREATE CVS FILE (FOR PATRAN) - CLICK THE BUTON OF YOUR OPTION (YOU CAN ALSO CREATE THE TWO FILES)

1. The file or files will be created on the same directory of the Excel file.

2. Be sure that Macros are enabled.

0.000 0.020 0.040 0.060 0.080 0.100 0.1200.0

100.0

200.0

300.0

400.0

500.0

600.0



Strain

Sres

s [M

Pa]

than one material, rename the files before creating new ones.

used on the file is selected in the options (CVS Import Options). You can check what separatorwas used (it depends on computer settings), by openning the file(s) with a text editor (Wordpad, Notepad, etc.)

if you have any correction, suggestion or comment.

3. The file(s) created are NOT updated if you change data. If you are working with more

4. When importing the file(s) on Patran, be sure to select the option of CVS file and that the separator

5. The spreadsheet is available "AS IS". Although checks were done, please contact


6. Read the disclaimer below:


ONLY THE YELLOW CELLS HAVE TO BE FILLED !!!

ALL OTHER VALUES ARE CALCULATED

3. THE MATERIAL STRESS-STRAIN CURVE (ENGINEERING STRESS-STRAIN)

The material stress-strain curve is calculated based on MMPDS-01, equation 9.8.4.1.2(b):

= uniform strain = plastic strain at end of uniform elongation (at max. tension load Ftu )

0.000 0.020 0.040 0.060 0.080 0.100 0.1200.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

500.0

Stress-Strain Curve


Strain

Sres

s [M

Pa]

0.000 0.020 0.040 0.060 0.080 0.100 0.1200.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

500.0

Stress-Strain Curve


Strain

Sres

s [M

Pa]

0.000 0.020 0.040 0.060 0.080 0.100 0.1200.0

100.0

200.0

300.0

400.0

500.0

600.0



Strain

Sres

s [M

Pa]

0.000 0.020 0.040 0.060 0.080 0.100 0.1200.0

100.0

200.0

300.0

400.0

500.0

600.0



Strain

Sres

s [M

Pa]

When creating the file/files, Excel may prompt you two windows like below. Click "YES" on both:

for Material Property. Read the notes.

- CLICK THE BUTON OF YOUR OPTION (YOU CAN ALSO CREATE THE TWO FILES)

0.000 0.020 0.040 0.060 0.080 0.100 0.1200.0

100.0

200.0

300.0

400.0

500.0

600.0



Strain

Sres

s [M

Pa]

used on the file is selected in the options (CVS Import Options). You can check what separatorwas used (it depends on computer settings), by openning the file(s) with a text editor (Wordpad, Notepad, etc.)

When importing the file(s) on Patran, be sure to select the option of CVS file and that the separator

Documents

Etk Material Curves 20121018