Comparison study on different Materials and Failure Models

Comparison study on different Materials and Failure Models

Objective:

To study, analyse and compare the different material laws and the failure models associated with them.

Procedure:

Step 1: Import the solver deck (.rad) file and ensure all the recommended shell properties are assigned.

Step 2: Make a new directory/folder and run the simulation, so that the new files for each case are organised.

Step 3: Then create split window layout to accomodate HyperView and HyperGraph 2D, to open and read data .h3d and T01 files in respective layouts.

Step 4: Save the Report Template. And tweak and modify the appropriate necessary values for the next case and run the simulation in a new folder.

Step 5: Once the simulation is done, don't load the results or plot the graph rather continue with the simulations for the specified different cases.

Step 6: On completion of all simulation runs, open the result template and open the .h3d and T01 files to read and analyse the data, easily.

Step 7: The result data is then tabulated and compared to fetch the results.

Simulation Data:

The different cases studied in this assignment is tabulated below.

The simulations are run with following parameters, Tstop = 5.01 ms, Tfreq = 0.5 ms, Nprint = -1. The different cases of simulations are executed and the runtime and simulation data are compared. The energy and mass error values are well below the accepted limit of 15%. The mass error remained at zero as there was no mass added to or removed from the model.

The different energy values such as Internal, Kinetic, Total, Hourglass and Contact for each case is plotted using HyperGraph 2D. The internal, kinetic and total energy values of the simulated cases are charted out for comparison, however the contact and hourglass energies (cause of QEPH elements) remained at zero throughout the runtime across different simution cases.

The Von-Mises Stress and Displacement contours are created using HyperView and we can also animate the simulation to study the nature of the deformation or impact.

Observations:

The snapshots of the stress and displacement contours are captured at a timeframe of 3rd and 5rd ms respectively.

Case 1

The element failed at an E_f value determined by the D1,D2,D3,D4,D5 parameters and the element deletion occured as soon as one of the integration points in shell element reached the strain value of Eps_max=0.151, i.e., at 15.1% of equivalent total strain. The elements got deleted without crack formation. The Internal Energy is linear until the body was able to undergo strain and the curve flattens on the onset of element failure and deletion. And at removal of elements, the energy is dissipitated, the fall in Internal Energy plot at around 4th ms depicts that phenomenon.

Case 2

The element failed as in the previous case but the deletion of element involved crack formation in this case, by modifying the I_xfem and D_adv parameters in the failure card. So, the elements were not deleted completed rather cracked first and was able to take more strain which is stored as Internal energy (30.5 J (Case 2) compared to 27.2 J (Case 1)) and bear a little more stress before removal (294 MPa (Case 2) compared to 287 MPa (Case 1)), eventually. The delay in the kinetic energy spurt (after 4.5 ms (Case 2) compared to 4ms (Case 1)), is because of the crack formation, which inturn delayed the complete removal of elements.

Case 3

The element failure is abrupt in this case when compared to the previous 2 cases, since we have deleted the failure card. Now the element deletion occurs at the defined Eps_max value of 0.151. This case is very much comparable to Case 1 scenario but the only difference being the failure model being not defined in this case. The Internal and Kinetic energy values of Case 1 and 3 are almost comparable and the decrease in stress value (270 MPa (Case 3) compared to 287 MPa (Case 1)) can be attributed to the absence of a proper definitive failure model.

Case 4

Without a element failure model defined and for a zero value of Eps_max, it is explicit that the model is definitely not going to fail also no deletion/removal of elements. For a zero value value of Eps_max, it is essentially like infinite Eps_max. Because of this infinite Eps_max, the body undergone strain continously and corresponding strain energy being stored as the internal energy. Thus the internal energy increased throughout the simulation and no surge in Kinetic Energy is due to no failure and deletion. But the deformation or the loading bearing ability is constrained by the maximum SIG_0 value of 425 MPa. Hence, the Von-Mises stress peaked upto 424.68 MPa. This case behaved similar to an elastic material case.

Case 5

In this case, the Johnson-Cook material (Law 2) is replaced with Elastic (Law 1) material. As, there is no failure model or failure parameters associated with the Elastic Material, it is obvious that the model is going deform contiously without any failure or rupture, similar to the previous Case 4. Given the ability to deform contiously and bear high stress, it is already evident why the Case 5 resulted in the highest Stress and Energy values among all the cases.

Case 6

The model is assigned Elasto-Plastic Material with Brittle Failure (Law 27), this material law combines Johnson-Cook material with an orthotropic brittle failure model. So the material behaves like elastic material until yield limit and beyond that for higher stress values, the material exhibits plastic behavior. For the E_f strain value, the element gets removed from the simulation, while the failure is advocated by E_t, E_m and D_max parameters. For a strain value of E_t, the stress starts to decrease and accepting very small deformation eventually failing at E_m, where the stress becomes zero and D_max accelerates the strain change from E_t to E_m and inturn the element failure. The surge in Internal Energy levels compared to the previous cases (Case 1,2,3), is because of the brittle plasticity nature, where the strain withstanding is more but the failure is rapid and catastropic. The animation clearly showed this failure, where the elements at the periphery were removed.

Case 7

The Elastic-Plastic Piecewise Linear material (Law 36) is used in this case. The elastic behavior of the material is defined by the Elasticity Modulus, Density and Poisson's Ratio values and the post-yield is defined by the curve that is drawn using experimental lab data for different strain rates. The stress-strain curve defined below is used in this case study. The failure was decided on E_m and E_t parameters, while removal/deletion occured at the Eps_max. This case was able to bear more strain, as evident from the internal energy and increased stress values, among the previous where element failure was defined. The energy plot is also close to the lab stress-strain graph (with a dip near yielding and a surge after indicating strain hardening), implying the precision of this material to simulate crash.

Conclusion:

• The Case 4 and Case 5 are obviously out of considerations for the crash study simulations, because of the absence of the failure model and no plastic region, which is very essential.
• Among the case studies involving the failure model, the Law 36 (Case 7) is the best choice for the crash simulation analysis owing to its accuracy and its ability to withstand higher stresses and take more strain on deformation, before rupture or failure. Also,the provision to use the lab data curve for defining the plastic region, at different strain rates, adds more accuracy in capturing the crash behavior result.