Week - 9 Material Modeling from Raw Data

Aim:

• To perform the simulation and validate the curve as shown in the figure

Objective:

• Using the given video link, extract the data from the figure, and used it for validation
• Create a material model for the Dogbone specimen using the diagram of the true stress-strain curve (graphite iron)
• From the above condition simulate and validate the material model by performing a tensile test on a Dogbone specimen

Stress-Strain

For the material the engineering stress–strain curve plot the correlation between stress and strain. It is obtained by gradually applying a load to a test coupon and measuring the deformation, from which the stress and strain can be determined eg. tensile testing. These curves provide the material properties, such as young's modulus, yield strength, and ultimate tensile strength

• The term Engineering stress is the applied load divided by the original cross-sectional area.
• The term True stress is the applied load divided by the actual cross-sectional area (changing area with respect to time)

• The above image depicts the stress-strain curve from the graphite iron casting. The two curves with different material structures have been shown in the figure
• This acknowledgment should be occupied from either MAT_024(Piecewise linear plasticity) or MAT_018(Power law of plasticity) material model according to the problem statement

Procedure:

Data Extraction & Graph calculation

• Open the given image file plotting the true stress-strain graph of graphite iron using data digitizer software by extracting the data and export through an excel file
  Curve 2 is selected and the data points are chosen then, the data is extracted as an excel file
• For the Material card model, we are using the SI unit i.e Kg/mm/ms we noticed from the stress-strain graph units are given in KSI and percentage respectively
  So the unit of stress has to be changed from KSI to GPa and Strain has to change from percentage to actual value
• The stress-strain data file obtained from the data digitizer is opened in excel to plot a graph of true stress(GPa) vs true strain as shown in the below first graph
  Calculate the Effective Plastic Strain from the true stress and true strain values then, from the second graph shown below, the yield stress value is taken as 0.145 GPa as it is positive, cause the region beyond is a plastic region

The effective plastic strain can be calculated from the true stress and strain values to input the plastic region into the curve

• Elastic strain = True stress/Elastic modulus
• Effective plastic strain = (True strain - True stress)/Youngs modulus (E)

Material

• The material card chosen is MAT_24_PIECEWISE_LINEAR_PLASTICITY to define the behavior of an elastoplastic material with an arbitrary stress-strain curve
• The values of Density and Poisson's ratio are taken as generic values. The young’s modulus = 20.9E+06 psi `rArr` 144.1004 GPa, yield stress value from graph = 0.151 GPa
• The plastic behavior of the material is defined using the LCSS curve option. The curve is defined by inputting the values of effective plastic strain and effective stress (true stress)
  To define the LCSS curve the stress values beyond the yield stress values are considered

Section

• The section property of the dogbone specimen is assigned as a shell element with 1mm thickness along with ELFORM=2 (Belytschko-Tsay)

Part

• The material and section are assigned to their respective part ID

Boundary conditions- SPC & PSM

• The nodes at the fixed end are constrained in the X and Z direction, Y direction is not constrained because of lateral compression during the tensile test

• The nodes at the middle are constrained in the Y direction since the neutral axis passes through the middle of the specimen in the X-direction

• The nodes are pulling at one end are assigned with a boundary prescribed motion in X direction using VAD displacement with a load curve of 1.0 m/s

Control Cards

• To activate implicit analysis and define associated control parameters. The following keyword is required for all implicit analyses

• IMFLAG: Implicit/Explicit analysis type flag: 1- Implicit analysis
• DT0: Initial time step size for implicit analysis: 0.010000
• IMFORM: Element formulation flag for seamless spring back: 2 retain original element formulation (default)

IAUTO: set to 1 which automatically adjusts the timestep size
ITEOPT: optimizes the operation count step 11
ITEWIN: is the iteration window 5
DTMIN: Minimum allowable time step size 0
DTMAX: Maximum allowable time step size 0

Database

• BINARY_D3PLOT: It defines the frequency at which the animation file is to be created and is set to 0.01 ms

• DATABASE_ASCII_Option: The output request in ASCII format, The following keyword is activated
  1. ELOUT: Element Output Data and
  2. GLSTAT: Global Data

• DATABASE_EXTEND_BINARY: It plots the strain tensor to d3plot when STRFLG is set to 1

Results:
CONTOUR PLOTS OF VON MISES STRESS

CONTOUR PLOTS FOR EFFECTIVE PLASTIC STRAIN

Stress vs Strain

• The true stress vs true strain plot obtained from the simulation of tensile test on dogbone specimen is as shown in the image given below which resembles the given true stress vs true strain plot
  

Validation

• The Material-defined stress-strain data and simulated stress-strain data are distinguished by the elastic part as linear
  The linear elastic part is calculated directly through the given young’s modulus and the yielding portion starts at the defined point in the hardening curve

• There is an exact correlation between the experimental data and the given raw data
• Due to some non-linearities, there could be some deviation that is tolerable

Conclusion:

The stress-strain data is extracted and validated from the image using a Data digitizer by MAT_024(Piecewise linear plasticity) which captures the actual stress-strain behavior similarly.
Few variations in the simulation data lead to a lack of information data from Density and Poisson’s ratio for the raw data