Material modeling from raw data using LS-Dyna

OBJECTIVE:

To model a material using the given true stress-strain curve of graphite casting and validate it using the given dogbone specimen. The following objectives has to be satisfied.

1. Extraction of data from the diagram.

2. Cleaning the data and matching it with the original data

3. Selecting a proper unit system as kg-mm-ms

4. To create a material card using the given data points

5. Validating the created material card using the dogbone specimen.

PROCEDURE:

1. The data points from the given material curve are extracted using data digitizer. The curve number 2 is selected for extracting the data.

2. These values are exported to excel using the export option in the software.

3. Now, there are two materials are given. They are *MAT_018 and *MAT_024. The description about the materials are given below.

*MAT_018: *MAT_POWER_LAW_PLASTICITY

Elastoplastic behavior with isotropic hardening is provided by this model. The yield stress, `sigma_y`, is a function of plastic strain and obeys the equation:

`sigma_y=kepsilon^n`

where `sigma_y`= Yield stress

k = Strength cofficient

`epsilon`= Total strain

n = Hardening Exponent

*MAT_024: *MAT_POWER_LAW_PLASTICITY

This is an elasto plastic material model which has an arbitary stress vs strain curve and arbitary strain rate dependency can be defined. Here, failure based on a plastic strain or a minimum time step can be defined. The stress strain behavior may be treated by a bilinear stress strain curve by defining the tangent modulus, ETAN.

So, in this challenge *MAT_024 is chosen for material modelling.

4. The extracted values gives true stress vs strain. So, these values are converted to effective plastic strain vs true stress. Using this values, the graph is plotted. The formulas used and graph obtained is shown in the figure below.

Effective Plastic Strain = True strain - (True Stress/E)

Here, value of E is given as 20.9E+06 psi which is 144.1 GPa. 

From the above true stress vs strain plot, it can be inferred that the curve is smooth. Hence, the values can be converted to effective plastic strain without any need of curve fitting.

From the true stress vs effective plastic strain plot it can be seen that the non-linearity begins at a stress of 0.15 GPa. Hence, this value can be taken as yield stress and also the values after this can be inputted for the LCSS curve definition.

5. The given dogbone model is impored using LS-Dyna manager in LS-PrePost.

6. For the boundary conditions are explained from the figures shown below.

For the above highlighted nodes, all the degrees of freedom is arrested except for translation along y-axis.

For the above highlighted nodes, the translation along y-axis is only arrested. This is done to achieve realistic deformation on the model.

7. For the other end of nodes, a boundary prescribed motion set is defined to apply the displacement. As the material steel is defined here, the displacement is given as 1.1 mm. This is shown in the figure below.

The displacement curve ID is shown in the figure below.

The value of displacement is arrived using the following method.

The maximum value of true strain given in the problem statement = 0.007 mm/mm

True strain = Displacement/Initial Dimension

Therefore, displacement = True Strain * Initial Dimension

Displacement = 0.007*145 = 1.015 mm

Therefore, the scaling factor is given as 1.1 mm in the boundary prescribed motion card.

8. The material card defined is shown in the figure below with the curve definition. The curve ID values are inputted using notepad++

9. The SECTION_SHELL card is defined with a thickness of 1.5 mm. The section and material cards are assigned to the part card.

10. The *CONTROL_IMPLICIT cards are defined since this analysis can be considered as static structural problem. The termination time is given as 1 ms. The cards are shown in the image below.

11. The necessary output requests are placed which includes *DATABASE_EXTENT_BINARY and *DATABASE_ASCII and BINARY_D3PLOT.

12. The model is saved with a suitable name with .k extension. The simulation is done using LS-Dyna Manager.

RESULTS AND DISCUSSIONS:

1. The Von-Mises stress contour is shown below.

The maximum stress observed is 0.2739 GPa which is higher than the yield stress defined which is 0.1511 GPa. Therefore, it can be inferred that plastic deformation is observed. Also, necking is not observed which signifies there is strain hardening taking place and the necking value is not achieved till the end of simulation. So, the stress value increases within the time step. The maximum stress is obtained in the middle region of the specimen.

2. The plastic strain contour is shown below.

As per the defined displacment, the maximum value of effective plastic strain obtained is 0.007932. The strain propagation is starting the reduction in cross section region and propagating further towards the centre.

3. The effective stress and plastic strain plots are shown in the figure below.

From the two plots, it can be inferred that the same behaviour is obtained as given by the contour. The element number 330 is in the middle portion of the specimen.

4. To validate the stress-strain data, we have to plot stress-strain using the data obtained above. This can be done in LS-Dyna using cross option.

The lower Ipt X-strain is chosen because the strain is maximum along x-axis since the displacement is applied along the x-axis.

5. The experimental values and simulated values are compared in the excel as shown in the figure below. The simulated values are saved as .csv file in the LS-Dyna prepost.

6. The results are validated by comparing the values in experimental data.

The curve we have obtained exactly fits the experimental data. Thus, the given values are validated using the MAT_024 material card. In the simulated data, the strain is higher than the experimental data. This is because the displacement defined is higher which caused the strain value to increase further beyond 0.007.

PROCESS AND FAILURE:

1. When the *CONTROL_IMPLICIT_SOLUTION card is defined, there is error in convergence of the solution. This happens because the card adds complexity while solving. For initial and simple probelm solving, this card can be neglected.

2. LS-Dyna always gives true stress vs strain as an output. But they were again converted to true stress vs strain and the values were compared which should be avoided.

3. Once the material card values are given in the notepad ++, they have to be verified in LS-PrePost. The following was the graph otained when the values were pasted in notepad ++. 

This has occured because there was an additional value entered in the tabulated values as shown below

This has caused non-convergence of solution. After deletion of 26th point, the simulation ran smoothly.

4. The displacement must be given within a certain limit. If it is too much it would lead to non-convergence of solution. For example, the displacement of 5mm lead to error in termination.

5. While extracting points in the first step, care must be taken that the points are spaced out sufficiently. The following points lead to error in termination.

This is because the points are so close and also the stress values should be continously increasing as the strain increases. But due to less spacing there is possibility that the stress value might become less than the previous point in certain areas. This would lead to numerical instability. Even fitting of data might not be accurate in this case. Hence, this must be avoided.

6. The Poisson's ratio must be in a proper range. Else, smooth curve for stress and strain cannot be obtained. Also, more reduction in Poisson ratio leads to non-convergence of solution. The strain curve obtained for Poisson ratio of 0.28 is shown below.

CONCLUSION:

The given experimental values are modelled using material card in LS-Dyna and validated using the dogbone specimen. All the objectives in the challenge are satsified.

Drive Link: https://drive.google.com/file/d/1y7ePefkOpMnEgCG0mkko9enrLUo8nTEQ/view?usp=sharing