14.3 Casting Processes, Metal Forming & Welding Metallurgy

13.3 Casting Processes, Metal Forming & Welding Metallurgy

Manufacturing technology transforms raw engineering materials into functional components through solid-state casting, plastic deformation, and fusion joining. In mining engineering and plant construction, heavy cast gearboxes, forged turbine shafts, extruded pipeline sections, and welded structural frames must meet rigorous metallurgical and dimensional integrity standards.

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1. Sand Casting Engineering & Pattern Design

Casting involves pouring molten metal into a refractory mold cavity containing the negative geometry of the desired part.

                    [ Pouring Basin ]
                            │
                     [ Downsprue ] (Tapered to prevent air aspiration)
                            │
                    [ Sprue Well ]
                            │
                      [ Runner ] ─── [ Ingate ] ───> [ Mold Cavity ] ───> [ Riser ]

Pattern Allowances

Patterns are enlarged or modified representations of the final casting, incorporating five critical allowances:

1. Shrinkage Allowance: Metals undergo three distinct stages of volumetric contraction:
   • Liquid Contraction (Pouring temp $\to$ Freezing temp): Compensated by the riser.
   • Solidification Shrinkage (Liquid $\to$ Solid phase change): Compensated by the riser.
   • Solid Contraction (Solid freezing temp $\to$ Room temp): Compensated by enlarging pattern dimensions.
   • Typical solid shrinkage values: Steel ($2.0% = 20\text{ mm/m}$), Cast Iron ($1.0% = 10\text{ mm/m}$, gray iron can expand during graphite precipitation), Aluminum ($1.3\text{--}1.5% = 13\text{--}15\text{ mm/m}$), Brass ($1.5% = 15\text{ mm/m}$), Invar ($0%$).
2. Draft (Taper) Allowance: Vertical pattern surfaces are tapered by $1^{\circ}\text{ to }3^{\circ}$ ($15\text{--}25\text{ mm/m}$) to permit withdrawal without damaging sand cavity walls.
3. Machining (Finish) Allowance: Additional stock ($1.5\text{--}5.0\text{ mm}$) provided on mating surfaces to be cleaned up by machining.
4. Distortion (Camber) Allowance: Provided on U-shaped, V-shaped, or unequal-thickness castings that warp due to differential cooling stresses.
5. Rapping (Shake) Allowance: A negative allowance subtracted from pattern dimensions to compensate for cavity enlargement during mold rapping.

Gating System Dynamics

To prevent air aspiration in the vertical downsprue, the sprue must be parabolically or linearly tapered following the continuity and Bernoulli equations:

$A_1 \sqrt{h_1} = A_2 \sqrt{h_2} \implies \frac{A_1}{A_2} = \sqrt{\frac{h_2}{h_1}}$

• Gating Ratio: The ratio of cross-sectional areas: $\text{Sprue Area } (A_s) : \text{Runner Area } (A_r) : \text{Total Ingate Area } (A_g)$.
  • Pressurized Gating ($1 : 2 : 1$ or $1 : 0.75 : 0.5$): Choke area is at the ingate. High discharge velocity, full gating system, turbulent flow; suitable for ferrous alloys (cast iron, steel).
  • Unpressurized Gating ($1 : 2 : 2$ or $1 : 2 : 4$): Choke area is at the sprue base. Low exit velocity, laminar filling, minimal oxide/dross entrapment; essential for aluminum, magnesium, and copper alloys.

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2. Solidification Kinetics & Riser Design

Chvorinov's Rule of Solidification

The total solidification time $t_s$ of a casting is governed by its geometric modulus ($M = V/A$):

$t_s = B \left(\frac{V}{A}\right)^n = B \cdot M^2 \quad (\text{with } n = 2)$

where $V$ is casting volume, $A$ is heat dissipating surface area, and $B$ is the mold constant (depending on metal latent heat, density, pouring temperature, and mold thermal diffusivity).

Modulus Method of Riser Design

To ensure directional solidification and feed liquid shrinkage, the riser must solidify after the casting:

$t_{s, \text{riser}} \ge t_{s, \text{casting}} \implies M_{\text{riser}} \ge 1.2 \cdot M_{\text{casting}}$

$\text{Optimum Top Riser } (h = d/2): \quad M_{\text{riser}} = \frac{V}{A} = \frac{\frac{\pi}{4}d^2 h}{\frac{\pi}{4}d^2 + \pi d h} = \frac{d}{6}$

$\text{Optimum Side Riser } (h = d): \quad M_{\text{riser}} = \frac{V}{A} = \frac{\frac{\pi}{4}d^3}{2\left(\frac{\pi}{4}d^2\right) + \pi d^2} = \frac{d}{6}$

Worked Step-by-Step Numerical Example

Problem: Compare the solidification times of three castings of equal volume $V_0$: (a) a Sphere of diameter $D$, (b) a Cube of side $a$, and (c) a Cylinder with height equal to diameter ($h = d$).

1. Sphere: $V_0 = \frac{\pi}{6}D^3 \implies D = \left(\frac{6V_0}{\pi}\right)^{1/3}$. Surface area $A = \pi D^2 = (36\pi V_0^2)^{1/3} \approx 4.836 V_0^{2/3}$. Modulus $M_{\text{sphere}} = \frac{D}{6} = 0.2068 V_0^{1/3}$.
2. Cube: $V_0 = a^3 \implies a = V_0^{1/3}$. Surface area $A = 6a^2 = 6.000 V_0^{2/3}$. Modulus $M_{\text{cube}} = \frac{a}{6} = 0.1667 V_0^{1/3}$.
3. Cylinder ($h=d$): $V_0 = \frac{\pi}{4}d^3 \implies d = \left(\frac{4V_0}{\pi}\right)^{1/3}$. Surface area $A = \frac{3\pi}{2}d^2 \approx 5.536 V_0^{2/3}$. Modulus $M_{\text{cyl}} = \frac{d}{6} = 0.1806 V_0^{1/3}$.

$\text{Ratio of Solidification Times: } \quad t_{\text{sphere}} : t_{\text{cyl}} : t_{\text{cube}} = (0.2068)^2 : (0.1806)^2 : (0.1667)^2 = 1.54 : 1.17 : 1.00$

(Conclusion: The Sphere possesses the lowest surface area per unit volume, maximum modulus, and takes the longest time to solidify).

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3. Advanced & Special Casting Processes

• Investment Casting (Lost-Wax): Precision disposable wax pattern coated with refractory ceramic slurry, autoclave dewaxed, fired at $1000^{\circ}\text{C}$, poured, and broken. Unmatched surface finish ($1.6;\mu\text{m}$), intricate geometry, used for single-crystal gas turbine blades.
• Die Casting: Liquid metal injected into permanent tool steel dies under high pressure ($20\text{--}150\text{ MPa}$).
  • Hot Chamber: Injection plunger submerged in molten metal; rapid cycle; restricted to low-melting alloys (Zn, Pb, Mg) because molten Al erodes ferrous plungers.
  • Cold Chamber: Molten metal ladled into cold shot chamber; used for Al, Cu, and brass alloys.
• Centrifugal Casting: Molten metal poured into a mold rotating at high speed ($G\text{-factor} = \frac{\omega^2 R}{g} \approx 60\text{--}80$). True centrifugal casting produces hollow seamless pipes without internal cores; slag and low-density oxides float to the inner bore and are machined away.
• Continuous Casting: Molten metal feeds continuously through a water-cooled oscillating copper mold to produce endless billets, blooms, and slabs ($>95%$ of modern primary steel production).

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4. Metal Forming Mechanics

Plastic deformation occurs when applied mechanical stresses exceed the material's yield strength, governed by the flow curve (Hollomon power law):

$\sigma = K \varepsilon^n$

where $\sigma$ is true stress, $\varepsilon = \ln(A_0/A_f)$ is true strain, $K$ is strength coefficient, and $n$ is strain hardening exponent.

                 Flat Rolling Mechanics
                    Roll Radius (R)
                       ┌───────┐
        h0 (Initial)   │ (•) ->│ v_r           h1 (Final)
    ───────────────────┘       └───────────────────
     Entry (v0 < vr)     Neutral Point    Exit (vf > vr)
    ───────────────────┐       ┌───────────────────
                       │ (•) <-│ v_r
                       └───────┘

Rolling Mechanics & Limiting Parameters

• Draft ($\Delta h$): Reduction in plate thickness: $\Delta h = h_0 - h_1$.
• Maximum Angle of Bite without External Push: $\tan\alpha \le \mu \implies \alpha_{\max} = \arctan(\mu)$.
• Maximum Single-Pass Draft:

$\Delta h_{\max} = \mu^2 R$

• Neutral (No-Slip) Point: The specific point along the roll-strip contact arc where strip velocity equals the horizontal component of roll peripheral speed ($v = v_r \cos\theta$).
• Forward Slip ($S_f$): $S_f = \frac{v_f - v_r}{v_r} \times 100%$.

Extrusion & Wire Drawing Mechanics

• Direct (Forward) Extrusion: Billet slides against container walls; heavy friction causes high initial peak pressure, decaying as stroke progresses.
• Indirect (Backward) Extrusion: Die moves into stationary billet; zero relative motion between billet and container; constant extrusion pressure, $\sim 25\text{--}30%$ lower force requirement.
• Wire Drawing Maximum Theoretical Single-Pass Reduction: Under ideal plastic deformation without friction or redundant shear work:

$\sigma_d = \sigma_0 \ln\left(\frac{A_0}{A_f}\right) \le \sigma_0 \implies \ln\left(\frac{A_0}{A_f}\right) \le 1 \implies \frac{A_f}{A_0} = \frac{1}{e} \approx 0.3679$

$R_{\max} = 1 - \frac{A_f}{A_0} = 1 - \frac{1}{e} = 1 - 0.3679 = 0.6321 \implies 63.21\%$

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5. Welding Processes & Welding Metallurgy

                     Oxy-Acetylene Flame Types
  Neutral (1:1)       [Inner Cone 3200°C]=====[Outer Envelope]======>
  Oxidizing (1.5:1)   [Pointed Sharp Cone 3400°C]===[Short Envelope]=>
  Carburizing (0.9:1) [Inner Cone]==[Acetylene Feather 3000°C]==[Outer Envelope]=>

Welding Process Fundamentals

• Shielded Metal Arc Welding (SMAW): Consumable flux-coated stick electrode provides protective $\text{CO}_2$ gas shield, deoxidizers, and slag cover.
• Gas Tungsten Arc Welding (GTAW / TIG): Non-consumable tungsten electrode + inert Argon/Helium shield. Direct Current Electrode Negative (DCEN) provides $70%$ heat at workpiece (deep penetration). Direct Current Electrode Positive (DCEP) or AC provides cathodic cleaning to break refractory $\text{Al}_2\text{O}_3$ films on aluminum alloys.
• Gas Metal Arc Welding (GMAW / MIG): Continuous consumable wire electrode; modes of transfer include short-circuiting, globular, spray (requires high current + Ar shield), and pulsed spray.
• Submerged Arc Welding (SAW): Arc is fully buried beneath a blanket of granular fusible flux; zero spatter, ultra-high current ($>1000\text{ A}$) and deposition rates; restricted to $1\text{G}/1\text{F}$ flat positions.
• Resistance Spot Welding (RSW): Joule heating at contact interface:

$H = I^2 R t$

Because faying surface contact resistance $R_{\text{contact}}$ is highest, the molten weld nugget nucleates precisely at the sheet interface.

Heat-Affected Zone (HAZ) & Weld Defects

  [ Base Metal ] ───> [ Subcritical HAZ ] ───> [ Intercritical ] ───> [ Coarse Grain HAZ ] ───> [ Weld Fusion Zone ]
  (Unaltered)          (Stress Relieved)         (Fine Grain α+γ)      (>1100°C, Brittle Martensite) (Cast Dendrites)

1. Coarse Grain HAZ: Peak temperatures $>1100^{\circ}\text{C}$ induce severe austenite grain growth. Upon rapid cooling, this region transforms into coarse, low-toughness martensite, becoming the primary site for Hydrogen-Induced Cold Cracking (HICC).
2. Solidification (Hot) Cracking: Caused by low-melting $\text{FeS}$ liquid films at dendrite boundaries under shrinkage stress. Prevented by maintaining $\text{Mn}/\text{S} > 30$.
3. Hydrogen Cold Cracking Prevention: Requires preheating ($150\text{--}250^{\circ}\text{C}$), low-hydrogen electrodes (AWS E7018), and post-weld heat treatment (PWHT).