Week - 9 Material Modeling from Raw Data

Aim-

By using the diagram of the true stress-strain curve of graphite iron casting. Two curves are there for different material structures. We need to pick any one of them and use the data to create either a MAT_024 or MAT_018 material model and then validate it.

Objective-

1. To extract the data from the diagram.
2. Clean the data and visually confirm that it matches the original data and the elastic modulus is 20.9E+06 psi.
3. Convert the data to (kg-mm-ms) unit system.
4. Process the data and create the material as demonstrated.
5. Use the material model with a dogbone specimen and validate the same.

Given Curve Model

Procedure-

• As mentioned above we have to download the GetData Graph Digitizer software and then have to install it.
• Then we have to save the above image from .png to .jpg format, as it is only acceptable file format in graph digitizer.
• Now we have to create the co-ordinate axes and then set the data as per graph then we have to start selecting the point accoringly.

• From above snap we can observe that, I have selected curve no.1 in graph.
• Now we will export this table date to .xls format to start getting the input values accordingly.
• Now we will open the excel file and do the calclulations.

Now from Curve plot data,

• Here polynomial pf order 3 is used as equation for graph and we are getting 99.97% of Matching.
• Stress values in ksi required our data in the kg-mm-ms unit. we are modeling the elastic-plastic material, so instead of engineering stress and strain values convert to the data in Effective stress and Effective plastic strain using the following formulas,

            1. True Strain = Ln(1+Engg.strain)

            2. True Stress = Engg.Stress(1+Engg.strain)

            3. Effective Stress = True Stress

            4. Effective Plastic Strain = True Strain -(True Stress/E), where E = 20.9e+06 psi 

             Where, 1 psi(pound-force per square inch) = 6.89476e-6 GPa and 

                        1 ksi(kilopound-force per square inch) = 0.00689476 GPa.

• By solving we will get the values of true stress, effective stress and effective plastic strain.

• As per this we will plot the graph for same to get exact calulation formula.

• After Solving this equation we will get the input value for material curve.

• We have to open the given LS-Dyna keyword (.k file) file in LS-PrePost, using option File>Open>LS-Dyna Keyword File as shown in below snap.

• 

• 
• Now we will go to the Define>>curve and input the value of curve data to get the curve.

• First we will start with section card, to create section card from keyword>>all>>section>>solid>>here we will input id, elform type as shown below.

• Now we will create the MAT card for it as MAT24_PIECEWISE_LINEAR_PLASTICITY.

• Finally we have to assign the section and material to the part.

•  Constrain all the nodes of one end of the dog bone specimen in all directions except translational Y direction.

• Constrain the mid nodes of both ends of the dog bone specimen in Y translation to restrict the slip during simulation.

• Assign Displacement for the specimen onset of nodes on another side with the curve defined.

• Now we have to create the control cards for finalisation of output.
• Now we will create the control_ternimation card.

• Now we will create Control Implicit General, Control Implicit Auto & Control Implicit Solver.

Note- As is a tensile type of test so we have used implicit analysis method here.

• Now we will create the database file.
• BINARY_D3PLOT -  It defines the frequency at which the animation file is to be created and is set to 0.1ms.
• Extent Bianry database card.

The output request in ASCII format, The following keyword are activated

1. ELOUT-Element Output Data
2. GLSTAT- Global Data
3. MATSUM- Material Energies and
4. RCFORC: Resultant Interface Forces

• Now we will check the model and then head for simulation.

• Since there is no error we can proceed further to save and run the keyword file.

• As simulation ended with Normal Termination. Therefore, the model is simulated successfully.
• Now we can open this files one by one using LS-post processor.

Results & Plots-

Effective Stress (V-M)-

Effective Plastic Strain-

Plots-

Effective Stress (V-M)-

Effective Plastic Strain-

Now Effective Stress Vs Effective Plastic Strain-

Validation-

From above data we can observe that the graph values, calculated values and simulated values are almost equal to we can say that our material model is correct.

Conclusion-

•  The stress-strain data extracted from the image is validated with the MAT_024(Piecewise linear plasticity) material model.
• The stress-strain behaviour after yielding is considered by a hardening curve which is given as an input through the MAT_024 card.
• The MAT_024 material model captures the actual stress-strain behaviour similarly and almost matched the defined stress-strain curve in the material model.
• Also we have seen little variation in the simulation data, which can due to the lack of information like density and Poisson’s ratio for the raw data, Mesh Size of the model or defining proper strain rate. These variations can be fine-tuned by trying different values of these properties and by selecting more data points to better capture the curve feature.

Animations-

Effective Stress (V-M)-

Effective Plastic Strain-