Week - 9 Material Modeling from Raw Data

Material Modeling from Raw Data

Aim:Material modeling using the diagram of the true stress-strain curve of graphite iron casting. Two curves are there for different material structures. We had taken the curve1 and used the data to create either a MAT_024 Piecewise Linear Plasticity model and then validate it with true stress vs Effective Plastic strain.

All units used here are in kg mm ms.

Steps followed:

• Use a data digitizer to create the data points from the curve of True Stress(Ksi) vs True Strain(%) image provided in .png format as shown in the image below:

• Now install the Data digitizer & Open the image under file option bys selecting appropriate downloaded image in .png format as shown below:

• Now set the scale for minimum & maximum X and Y values with the help of scale option, Xmin=0,Xmas=0.7%,Ymin=0 and Ymax=60 Ksi as shown in the image below:

• Now save the images with points in Notepad format by Export data option under Files & try opening it in notepad format in Notepad++ app:

• The material curve is opened in Notepad++ with True stress(Ksi) & True strain(%) as shown in the image below:

• Copy the True Stress & true strain in the Excel sheet from the notepad++ and change the unit of True stress from Ksi to GPa as 1 Gpa=1kg mm^-1 ms^-2, for conversion we multiply True stress at each of 93 points by 0.0068946 as shown in the excel file image below:

• Convert true strain from percentage to mm/mm by dividing it with 100 as shown in the image below:

• Convert the Young’s Modulus from 20.96 Psi given by multiplying with a conversion factor of 6.89476e-6 which results in 144.1 GPa.
• Calculate the Effective Plastic strain from formula=Total true strain-True Stress/E, where E=Young's Modulus=144.1GPa because Plastic Strain occurs after the Elastic strain, so Total True Strain is sum of Elastic Strain+Plastic Strain.

• Now after plotting the Effective plastic strain we can observe from the image above that it has both negative and positive values.The reason for the negative value is occurrence of only the Elastic part of strain without the Plastic one while the positive value indicates there is some plastic strain.
• Now we Plot the Graph of True stress in GPa vs Effective Plastic strain in excel with the help of Insert button at the Toolbar above and by selecting Chart with proper data as shown in the image below:

• Now we will open the LS Prepost and import the Dogbone file provided in the question in .k format as shown below by selecting import options under Files and selecting Keyword files after downloading the file.

• Now as this model is already provided with Geometry & shell type elements we have to define the section,materials,parts,boundary condition,types of solvers(Explicit or Implicit),Termination Time,Database outputs & curves.
• Now we check the type of element under Keyword option in Models in the left side Toolbar as shown in the image below with particular shell Id,part Id etc

• Section:

Now create section for Dogbone specimen with appropriate section id, which is in almost 2D geometry as we know for that we have to create a shell section of it with appropriate Element formulation of 2 which is Belytschko-Tsay membrane which is fully integrated & Ideal for fabrics with negligible bending stiffness and at the same time this formulation is economical. Shell thickness is taken as 1 mm as shown in the image below:

• Material selection:

Now select the MAT- 024 Piecewise linear Plasticity material for Dogbone specimen under Mat keyword by going into Toolbar at right containing Model and from there Keyword & from there to MAT- 024 Piecewise linear Plasticity material.This MAT- 024 Piecewise linear plasticity material is chosen with density of Graphite as 6.41E-07 kg/mm^3,Young’s Modulus as 144.1 kg mm^-1 ms^-2 & Poisson's ratio as 0.31 so that we can observe plastic deformation of Dogbone specimen upon tension test.

• Now we have to define the Load ID curve for LCSS which we are going to do by Define curve option & inserting 0,0 for True stress & Effective Plastic Strain.

• Now save the model you have edited & close it,go to excel sheet & select all the Positive Effective Plastic strain and their respective true stress in GPa and copy them.Negative Plastic strain is not taken because it indicates only True Elastic strain from which we can get Young’s modulus but as here Young’s Modulus is given we are interested in calculating the effect of true stress after Elastic part i.e Plastic part.
• Open the save .k file of model in Notepad++ and try pasting the Effective Plastic strain & True stress in LCSS by removing the 0,0 which have been provided above because here we are calculating behavior of curves in Plastic Zone as shown in the image below under same column for both Effective Plastic strain & True stress as shown in the image below:

• Parts creation:

Now the parts which are there after Geometry are assigned with section &, material Id under Part option keyword by going into Toolbar at right containing Model and from there Keyword & from there to Part by assigning section id,material id,part id & Part title as shown in the image below:

• Now define Boundary SPC for fixing the one side with the help of Create Entity Boundary SPC as shown below by selecting nodes properly as shown in the image below:

• Now define the Prescribed Rigid Motion in Boundary conditions with the help of Create Entity Boundary Conditions with help of Displacement by knowing the Strain at the last point i.e. 4.43E-03 X 145mm length of Dogbone Specimen which is 0.64 mm displacement with DOF=1 Translational along X axis.

We are applying this for displacement along X-axis.

• Now Define displacement curve by inserting Displacement vs Time graph for 0 ms to 0 mm then 1 ms 0.64 mm and 1.1 ms to 0.64 mm.

• Now go to Control-Termination and apply End time of 1 ms as shown in the image below for our simulation.

• Now apply Hourglass for shell elements so that we can calculate the deformations not captured in the form of hourglass energy.For IHQ=1 we have Hourglass control is viscosity or stiffness that is added to quadrilateral shell elements and hexahedral solid elements that use reduced integration. It also applies to formulation 1 tshells. Without hourglass control, these elements would have zero energy deformation modes which could grow large and destroy the solution. CONTROL_HOURGLASS can be used to redefine the default values of the hourglass control type and coefficient. If omitted or if IHQ = 0, the default hourglass control.

• Now we are taking Implicit solver for our simulation with Implicit general card as this tensile test of Dogbone is almost time independent or Quasi Static process.
• We are using Implicit general card with IMFLAG=1 for Implicit Analysis with Initial Time step size as 0.05 ms as shown in the image below:

• Now Implicit auto is used for Define parameters for automatic time step control during implicit analysis with IAUTO=0 for constant Time step size ,ITEWIN=11 & ITEOPT=5 as shown in the image below:

Output Requests:

• Now we are going to request for our outputs with DATABASE-ASCII-GLSAT for showing various energies while MATSUM for material internal energies as shown in the image below with Time interval between outputs(DT) as 0.1 ms:

• For Binary d3plot we even keep DT same as 0.1 ms as shown in the image below:

Results:

X stress d3plot:

Maximum X stress=0.3563 GPa.

Effective Plastic strain:

Maximum Effective Plastic strain=2.951E-03

Now we will go to Time History and we will select element we want and plot True Stress vs Time plot, Effective Plastic Strain vs Time plots as shown in the image below:

Save the True stress vs Time plot & Effective Plastic strain vs Time plot and go to the XY plot option for True stress vs Effective Plastic Strain plot:

Now save the plot of True Stress vs Effective Plastic strain graph and open it in the Notepad format as shown in the image below:

Copy the plots of true stress vs Effective Plastic strain in excel sheet and plot the graph again in excel as shown in the image below:

Comparison of effective plastic strain vs True stress graphs given and obtained:

Plot of input EFFECTIVE PLASTIC STRAIN VS tIME:

PLOT OBTAINED FROM TENSILE TEST:

So we can see from the images above that both the graph of effective plastic strain vs True stress is the best fit reason being both the curve as we can see maximum True stress & maximum effective strain as shown from the images above.Hence the graph obtained after tensile test is validated with Graph data plotted from the image.

Conclusions:

Mat_024_Linear Piecewise Plastic is taken and Effective plastic strain vs True stress obtained from the tensile test is best fit with Effective plastic strain vs True stress graph.

Hence the graph obtained after tensile test is validated with Graph data plotted from the image.