1. a) Derive the equation to calculate the energy required for i) elastic deformation and ii) plastic deformation. Note: Must use the Johnson Cook thermal plasticity material constitutive equation for the plastic deformation.
b) Draw the stress-strain curve and label the following terms i) Young's modulus, ii) Yield point,
iii) Ultimate strength, iv) Fracture point, v) Strain hardening, vi) Elastic region, vii) Plastic region, viii) Energy required for plastic deformation.
c) Describe one limitation of the Johnson Cook empirical model.
2. a) Draw and label the phase diagram of carbon steel with up to 2.11% of carbon.
b) Explain how to increase Martensite microstructure for hypo eutectoid steel.
c) Derive the equation which relates Young's modulus and geometry of the material with material stiffness
3. Table 1 below shows the Johnson-Cook constants for three different workpiece materials.
| Material |
A (Mpa) |
B (MPa) |
n (-) |
C (-) |
m (-) |
T melt (deg C) |
Fracture strain (-) |
| Usibor 1500 |
1040 |
4630 |
0.253 |
0 |
0.1245 |
1500 |
1 |
| DP 600 |
120 |
1020 |
0.196 |
0.125 |
1.287 |
1538 |
3 |
| TRIP 800 |
412 |
2153 |
0.66 |
0.014 |
0.76 |
1540 |
2 |
a) Use Microsoft EXCEL and plot the stress strain curves for the following conditions:-
|
Temperature (deg C) |
Strain rate (s^-1) |
| Condition 1 |
150 deg C |
1 |
| Condition 2 |
300 deg C |
100 |
| Condition 3 |
300 deg C |
10,000 |
Fixed the reference strain rate to 10 s^-1 and fixed reference temperature is 25 deg C. Note:
When drawing all the graphs, fixed the x-axis scale from 0 to 3 and the y-axis from 0 MPa to 5500 MPa.
b) Based on Condition 2, calculate the energy required to deform Usibor 1500 and TRIP 800 to fracture.
c) Explain why Usibor 1500 is most sensitive to thermal softening when compared to DP 600. Support your answer with plastic flow stress magnitude at different temperature magnitudes.