Damage Fit Assignment
This assignment was divided into two parts. The first part was to use damage fit to calibrate the ISV model to the stress strain curve determined in homework 3 and plot for comparison. The second part was to run a one element finite element simulation in ABAQUS to verify the results from part 1 and plot all three stress-stain curves.
The stress-strain data from the 400 grain simulation from the crystal plasticity model used in homework 3 was collected and used in the DMG_FIT software provided by Mississippi State to determine material constants. The hardening parameters were set as follows: h0 = 29.56 MPa, k0 = 3.36 MPa, and ks = 47.75 MPa. The stress-strain curve is shown below.
The process which allowed for the quickest determining of the material constants was as follows:
Estimate the yield point of the material and input it as C3 Enter minimum values for C7 and C9 and optimize those values Enter minimum values for C13 and C15 and optimize C7, C9, C13, and C15 Optimize C1, C3, C7, C9, C13, and C15 Enter minimum values for Ccoef, cd1, cd2, bn, and Cacon and optimize only those values Optimize Ccoef, cd1, cd2, bn, Cacon, Ca and Cb Optimize C1, C3, C7, C9, C13, C15, Ccoef, cd1, cd2, bn, Cacon, Ca and Cb
Any parameter optimized to a value outside the boundary values were set to the nearest boundary and optimized again. Continued violation of the constraints resulted in the value being set as the minimum manually.
Since only one temperature and strain rate was available constants C2, C4, C5, C6, C8, C10, C11, C12, C14, C16 through C20, CTD, and NDT were inactive. C21 through C26 were also inactive do to the lack of cyclic loading data. There was also no data for grain size, porosity, or void volume so constants Z, beta, and wfr4 were also inactive. The loading condition (tension) resulted in an and cn also being inactive.
The optimized constants are shown in the image below.
The fitted stress strain curve is displayed over the original data points in the image below. Note that the average error of the model was 0.0, the max error was 0.1, and the percent error was 0.06%.
The goal for Part 2 was to verify the plasticity-damage ISV model determined in Part 1 through a one element finite element simulation in ABAQUS with UMAT. This was achieved by editing the ABAQUS input file and placing the material definition in the proper location. The ABAQUS input file used in this analysis was determined in Part 1 and is provided below.
The single 500-grain element simulation was performed using this data and the tensile stress-strain data was obtained. The stress-strain data from the ABAQUS simulation matches exactly with the DMG_FIT model from part 1, effectively verifying the model. The stress-strain data is shown below.