Week - 9 Material Modeling from Raw Data

OBJECTIVE :

1. Extracting the data from the given diagram of the true stress strain curve of the graphite iron casting.

2. Cleaning the data and making the sure that it matches the original data given in the diagram.

3. Processing the data and creating the material for the FEA analysis.

4. Using the material model for the dogbone specimen and carrying out the FEA analysis.

5. The data from the FEA analysis is used for validating the data extracted from the diagram.

Fig 1 Given stress vs strain Plot for the material

EXTRACTING THE DATA AND CREATING THE MATERIAL MODEL :

1. Extracting the data from the given stress strain plot using the digitizer plot

         The given plot is uploaded in the Getdata graph digitizer plot and the data is extracted through the following steps

i. Setting up the scale 

      The scale is set by entering the value for the x-max , x-min , Y-max & Y-min and picking the respective points on the diagram by using the set scale option available in the getdata graph digitizer tool.

Fig 2 Setting up the scale on the Getdata graph digitizer

  ii. Picking the points on the stress vs strain curve for extracting the data

          After setting the scale, the points are picked on the curve unidirectionally using the point capture mode option in the getdata graph digitizer so that the respective x & Y values for the points being picked on the curve are recorded and saved as the excel file.

Fig 3 Capturing the values on the curves in the given diagram

2. Converting the captured data units

        All the units of the stress are in Kilo pound square inch which is converted in terms of `kg//(ms)^2mm`.

3. Cleaning up the given data and making the Visual comparison of the captured data with the given plot

        The captured data is cleaned up for ensuring that there is no negative slope when the extracted data is plotted and a visual comparison of the curve plotted for the captured data is made with the given diagram. The cleaning up of the data involves creating the trendline for the curve plotted and modifying the values of the stresses by giving strain values as input values in the equation for the trendline.

Fig 4 Captured plot from the diagram of the stress vs strain plot

It can be seen visually that the extracted data from the plot is similar to the stress vs strain plot no 2 given in the diagram.

4. Identifying the yield Stress

        The Yield stress from the graph is identifies by plotting an offset line to the elastic line in the stress strain curve such that the offset line intersects the strain axis at 0.2% of the total strain i.e, the offset line crosses the strain axis at 0.1804% in our case . The offset line intersects the stress strain curve at the other end. The Corresponding stress at the point where the offset line intersects the stress strain curve is the Yield point stress for the given material curve.

      Although the Yield point with the 0.2% offset method was found to be 0.230 `strong>`kg//(ms)^2mm` , the material is given an Yield strength of 0.0875634 `kg//(ms)^2mm`, since the graph visually tends to change from that point onwards.

 5. Plotting the plastic stress vs strain values and shifting of the graph

           The plastic strain values are calculated for each effective strain points plotted in the plastic region by using the formula

`underset(e)(epsilon)=underset(t)(epsilon) - (underset(y)(sigma)/E)`

where , 

            `underset(p)(epsilon) =`True plastic strain

             `unsderset(t)(epsilon)=`Total strain

              `underset(y)(sigma)=` Yields strength

                E= Young's modulus

           The plastic strain values are plotted against the corresponding stress values and the plot is shifted such that the Strain values at the yield strength becomes zero.ie. the value of the strain at the time of the yield stress is subtracted from all the calculated plastic strain values and these plastic strains are plotted against the stress values in the plastic region.

Fig 6 Plotting the Effective Plastic Stress vs Effective Plastic Strain with Shifting

CASE SET UP :

1.Setting up the Boundary conditions:

        i. Creating the Single point constraint 

             The nodeset at the on the edge of the Specimen in the left hand side (in the x- direction) are constrained in all the degrees of freedom except for the traslational degree of freedom in y-direction.

Fig 7 Constraining one end of the Specimen in the all degrees of freedom

         The Node set on the neutral axis have to be constrained for all the degrees of freedom except for the translational in x-direction.

Fig 8 Constraining the Nodeset on the neutral axis in all degrees of freedom except for translational in x- direction

   ii. Creating the prescribed motion set card for applying the displacement

          The Prescribed motion of displacement is applied to all the nodeset of the edge of the specimen in the right end( in the x-direction). The Prescribed motion of the displacement is applied in the x-direction.The displacement vs time curve is plotted and is assigned for the displacement in the prescribed motion set card.

Fig 9 Creating the displacment vs Time curve for the Prescribed motion set

Fig 10 Applying the Displacement motion to the other edge of the specimen

2.Creating the material card

    i. Defining the curve for the material

            The data from the material model created is converted in to the comma seperated value (CSV)form. The CSV file is then uploaded while defining the curve for the material.

 Fig 11 Defining the Curve for the Material

    ii. Creating the 024_MAT_PIECEWISE_LINEAR_PLASTICITY Material card

       The material card chosen for this simulation is 024-MAT_PIECEWISE_LINEAR_PLASTICITY .The material card is created using the material model created earlier and the Plastic Stress vs Plastic Strain curve data is uploaded in the form of CSV. The other parameters such as the density, Young's Modulus, Yield Strength and Poisson's ratio are entered in the card.

Fig 12 Creating the _024-Piecewise linear Plasticity Material card

3. Creating the section for the Elements of the Specimen

        The section card is created using the Shell card in the keyword manager. The Thickness and the Elementform type are assigned in the Section card.

Fig 13 Creating the Section card for the Shell elements

4. Assigning the Section ID and the Material ID to the Part ID 

           The Section ID and the Material ID created are assigned to the Part ID of the Specimen. 

 Fig 14 Assigning the Section and the Material to the Part

5. Creating the Control cards for the Implicit analysis

        i. Adding the Implicit_Genral card

             In addition to the already existing cards, the Implicit_general control card is added in order to carry out the Implicit analysis. The IMFLAG value is kept at "1" in order for turning ON the flag for the Implcit analysis.

Fig 15 Creating the Implcit general card for turning the implicit flag ON

  ii.Creating the IMLICIT_AUTO card for automatic adjustment of timestep

                     The flag for the automatic adjustment of the timestep is turned ON by entering the value for AUTO in the IMPLICIT_AUTO card.

Fig 16 Creating the card Implicit_auto for automatic adjustment of the timestep

 iii. Creating the IMPLICIT_SOLUTION card for setting the limit for the no of iterations and the tolerance limit for the displacement relative convergence .

                                 The IMPLICIT_SOLUTION card is created for setting the limit for the no iterations at each timestep for convergance. In this card, the displacement realative convergance tolerance limit can also be set.

Fig 17 Creating the IMPLICIT_AUTO card for limiting the no of Iterations for each timestep and setting the tolerance limit for the displacement convergance

iv. Creating the IMPLICIT_SOLVER card 

                 This an optional card which  applies to implicit calculations. The linear equation solver performs the CPU-intensive stiffness matrix inversion.

Fig 18 Creating the IMPLICIT_SOLVER card

6.Creating the Control termination Card for the runtime

       The Simulation runtime is assigned by entering the ENDTIME in the Control Termination card that is created from the keyword manager.

Fig 15 Creating the control termination card for the Simulation runtime

7.Creating the Time History card for the Element Output

    The Keyword *DATABASE_HISTORY is created for the element whose stress and strain outputs are to be extracted with respect to time.

Fig 16 Creating the keyword DATABASE_HISTORY for the element whose stress and strain values are to be extracted

8.Creating the Keyword Dartabase for the Output

      i. Creating the ASCII card 

           The ASCII card is created in the keyword manager with the options for the GLSTAT, MATSUM & ELEOUT being checked on. The timesteps at which these results must be plotted are also entered in the box for the DT.

Fig 17 Creating the ASCII card for the DATABASE_OUTPUT

       ii. Creating the binary D3Plot card for the animation output

              The binary D3plot card with the timestep at which these outputs must be given out is mentioned in DT value.

Fig 18 Creating the D3plot card for the animation output

       iii. Creating the Binary_Extent card for the Strain output

                    The Extent_Binary card is created under the keyword *database in the keyword manager & the strainflag is made equal to one so that strain tensor data is written on the d3plot and the eleout.

Fig 19 Creating the extent_binary card for strain tensor data

RESULTS:

Comparison of the FEA results with the extracted data of the Material

INFERENCE:

     The data that we get from the FEA process are almost validates the Experimental Test data. The results can converge further if the size of the mesh can be smaller or the stiffness of the material can be more accurately entered in the material card.

CONCLUSION:

1. The material test data were extracted successfully from the diagram.

2. All the test data were succesfully used for creating the material model .

3. The Material model was successfully used for the dog bone specimen used for the validation in the FEA.

4.  The Implicit analysis of the dogbone specimen was carried out successfully.

5. The FEA results almost validates the Experimental test data given in the diagram.