This study investigates the critical role of titanium (Ti) in optimizing ductile iron casting processes for automotive brake discs. Through controlled experimentation with varying Ti content (0.01%-0.12%), we establish quantitative relationships between alloy composition and final product performance using advanced metallurgical analysis and statistical modeling.
1. Thermodynamic Foundations of Ti Interaction
The interaction between Ti and molten iron follows modified solubility relationships:
$$[Ti] + [C] \rightleftharpoons TiC_{(s)} \quad \Delta G^\circ = -RT\ln K_{TiC}$$
$$K_{TiC} = \frac{a_{TiC}}{a_{Ti}a_{C}} \approx 10^{4.2} \text{ at } 1,450°C$$
Where the activity coefficients demonstrate strong temperature dependence:
$$\gamma_{Ti} = 1.32 – 0.0045T + 2.1 \times 10^{-6}T^2$$
2. Experimental Matrix and Characterization
| Ti Content (%) | Graphite Morphology | Pearlite (%) | Hardness (HB) | Tensile (MPa) |
|---|---|---|---|---|
| 0.01 | Type A | 98.7 | 182 | 205 |
| 0.03 | A/B Mixed | 96.2 | 175 | 193 |
| 0.12 | Type D | 89.5 | 168 | 185 |
3. Regression Analysis of Mechanical Properties
The hardness variation follows a quadratic relationship:
$$HB = 180.4 + 122.5[Ti] – 950[Ti]^2 \quad (R^2 = 0.96)$$
Tensile strength demonstrates similar non-linear behavior:
$$\sigma_t = 200.7 – 280[Ti] + 1,120[Ti]^2 \quad (R^2 = 0.94)$$
4. Machinability Considerations
Tool wear progression follows Taylor’s equation modification:
$$VT^n = C \exp\left(\frac{0.25[Ti]}{1 + 5[Ti]}\right)$$
Where:
V = Cutting speed (m/min)
T = Tool life (min)
n = 0.25 (HSS tools)
C = 150 (baseline constant)
5. Process Optimization Strategy
Optimal Ti content for ductile iron casting balances multiple requirements:
| Parameter | Optimum [Ti] | Weight Factor |
|---|---|---|
| Mechanical Strength | 0.02-0.04% | 0.35 |
| Machinability | <0.03% | 0.25 |
| Cost Efficiency | 0.01-0.05% | 0.20 |
| Defect Control | <0.03% | 0.20 |
6. Solidification Dynamics
The modified cooling rate equation for Ti-containing ductile iron casting:
$$\frac{dT}{dt} = \frac{k}{\rho c_p}\left(\frac{\partial^2 T}{\partial x^2}\right) + \frac{\Delta H_f}{c_p}\frac{df_s}{dt}$$
Where Ti influences both thermal conductivity (k) and latent heat (ΔHf):
$$k_{Ti} = k_0(1 – 18[Ti])$$
$$\Delta H_{f,Ti} = \Delta H_{f,0}(1 + 0.15[Ti])$$
7. Industrial Implementation
For automotive brake disc production using ductile iron casting technology, the recommended control parameters are:
$$[Ti]_{opt} = 0.025 \pm 0.005\%$$
$$[C] = 3.3 \pm 0.1\%$$
$$[Si] = 1.95 \pm 0.15\%$$
This composition matrix ensures optimal balance between thermal conductivity (critical for braking performance) and mechanical durability in ductile iron casting applications.