Given the following material parameters for the Johnson-Cook model,
| A (MPa) | B (MPa) | C | n | m | rho | Tm (°C) | K (GPa) | G (GPa) | c (J/kg°C) |
|---|---|---|---|---|---|---|---|---|---|
| 1079.01 | 1119.69 | 0.007 | 0.25 | 0.6 | 18,600 | 1,200 | 92 | 58 | 117 |
a finite element model of Kalthoff problem was run for impact velocities of 10-60 and 100 m/s.
The following links allow graphical review of the time history of key elements.
| Impact Speed (m/s) | Maximum Principal Stress | von-Mises Stress |
|---|---|---|
| (criteria for brittle failure - 1.7 GPa) | (criteria for ductile failure - 90% max stress) | |
| 10 | 49 | 112 |
| 20 | 49 | 168 |
| 30 | 55 | 168 |
| 40 | 55 | 168 |
| 50 | 55 | 168 |
| 60 | 55 | 168 |
| 100 | ? | 168 |
The plot of failure times (generated with the Matlab script uranium_impact.m) shows that brittle failure always occurs before ductile failure for depleted uranium in the range of impact velocities 10-100 m/s. The significance of this can be understood by consideration of two things. One, yield stress of this material increases with plastic strain and increasing plastic strain-rate. Two, the yield stress decreases with increasing temperature. Both of these scenarios are taking place simultaneously. From numerical experiments, it has been shown that a shear band (ductile failure) initiates when the effective stress is 90% of the peak value. In the case of depleted uranium, this condition doesn't ever seem to take place before the brittle failure criteria (listed above in the chart) is satisfied, perhaps because of uranium's thermal conductivity.
