Metal Forming: Rolling, Forging, Extrusion & Drawing — revision notes (GATE ME)
Bulk metal forming is a core GATE ME topic (~2 marks). Hot-vs-cold working, the four main processes, and flow-stress concepts are the reliably tested items.
Hot vs cold working
- Hot working (above recrystallization temperature): low forces, large deformation, no strain hardening, refined grain, poorer finish/tolerance.
- Cold working (below recrystallization): strain hardening (stronger, harder), better finish/tolerance, higher forces, residual stress; limited ductility.
Flow stress σ = K·εⁿ (n = strain-hardening exponent) governs the load.
The four processes
- Rolling: thickness reduced between rolls. Draft = h₀ − h_f; roll force depends on contact area and flow stress. Maximum draft limited by friction (bite condition).
- Forging: compressive shaping (open-die = free deformation; closed/impression-die = flash forms in a cavity). Barreling from friction.
- Extrusion: metal pushed through a die to form a constant cross-section. Direct (billet moves toward die, high friction) vs indirect/backward (die moves, lower force).
- Wire/rod drawing: metal pulled through a die (tensile) to reduce cross-section; reduction per pass is limited (drawing stress < material strength).
Exam Tricks & Tips
- 🎯 Hot working: no strain hardening, low force, poor finish; cold working: strain hardening, better finish, higher force — the master comparison.
- 🎯 Flow stress σ = Kεⁿ — the strain-hardening exponent n sets how much the metal strengthens as it deforms.
- 🎯 Extrusion: indirect (backward) needs LESS force than direct because there is no billet-container friction.
- 🎯 Rolling draft (h₀ − h_f) is friction-limited — the bite condition caps how much reduction one pass can achieve.
- 🎯 Drawing is a tensile (pull) process, extrusion is compressive (push) — a common conceptual mix-up.
- ❌ Common mistake: calling extrusion and drawing the same — extrusion pushes metal through a die (compression), drawing pulls it through (tension); their force limits differ fundamentally.
Expected exam pattern
A 1-mark hot/cold-working or process-classification MCQ, and a 2-mark rolling-draft, extrusion-ratio, or flow-stress problem. Direct-vs-indirect extrusion and drawing-vs-extrusion distinctions are frequent.
Quick recap
Hot working (> recrystallization: low force, no strain hardening, coarse finish) vs cold working (strain hardening, fine finish, high force). Flow stress σ = Kεⁿ. Rolling (draft h₀−h_f, friction-limited), forging (open/closed die), extrusion (direct vs indirect/lower force), drawing (pull, tensile). Extrusion pushes, drawing pulls.
Metal Forming — Flashcards
Cover the answer, recall, then check. 11 cards on bulk metal forming for GATE ME.
Q1. Difference between hot and cold working?
A1. Hot (above recrystallization): low force, no strain hardening, grain refinement, poor finish. Cold (below): strain hardening, better finish/tolerance, higher force.
Q2. What is the recrystallization temperature's role?
A2. It is the boundary between hot and cold working: above it, new strain-free grains form, so no strain hardening accumulates.
Q3. Write the flow-stress (strain-hardening) equation.
A3. σ = K·εⁿ, where K = strength coefficient and n = strain-hardening exponent.
Q4. Define draft in rolling.
A4. Draft = h₀ − h_f (initial minus final thickness); the reduction per pass, limited by friction (bite condition).
Q5. Open-die vs closed-die forging?
A5. Open-die: metal deforms freely between flat dies (barreling). Closed/impression-die: metal fills a cavity, excess forming flash.
Q6. Direct vs indirect extrusion — which needs less force?
A6. Indirect (backward) extrusion needs less force, since the billet does not slide against the container (no container friction).
Q7. Is wire drawing a compressive or tensile process?
A7. Tensile — the metal is pulled through the die, reducing its cross-section.
Q8. Is extrusion compressive or tensile?
A8. Compressive — the billet is pushed through the die.
Q9. Why is reduction per drawing pass limited?
A9. The drawing (pull) stress must stay below the material's strength; too large a reduction snaps the wire.
Q10. What causes barreling in forging?
A10. Friction at the die-workpiece interface restrains the ends, so the middle bulges outward.
Q11. Advantage of cold working?
A11. Higher strength/hardness (strain hardening), better surface finish, and closer dimensional tolerances.
Metal Forming: Rolling, Forging, Extrusion & Drawing
Metal forming shapes solid metal by plastic deformation — no chips, good strength (grain flow). GATE tests the force/load estimates, the geometry of each process, and the concept of flow stress. This is applied plasticity with process-specific formulas.
Core concept: forming deforms metal beyond its yield point so it takes a new shape permanently; the force needed depends on the material's flow stress and the deformation geometry.
Deep explanation
Beginner — flow stress and work of deformation
Above yield, metals strain-harden: flow stress σ_f = K εⁿ (K = strength coefficient, n = strain-hardening exponent). Hot working (above recrystallisation temperature) needs low force and gives no strain hardening; cold working needs more force but strengthens and improves surface finish.
- True strain ε = ln(L/L₀) = ln(A₀/A) — used in forming because deformations are large.
Intermediate — rolling and forging
- Rolling: reduces thickness between rolls. Draft Δh = h₀ − h_f; maximum draft Δh_max = μ²R (R = roll radius, μ = friction) — friction must "bite" the strip. Roll force ≈ contact length × width × average flow stress. Neutral point divides where the strip moves slower/faster than the roll.
- Forging: compressing between dies. Open-die upsetting: friction causes barrelling and raises force toward the centre. Forging force F = σ_f × A × (friction multiplier). Closed-die forging fills a die impression with flash.
Advanced — extrusion and wire drawing
- Extrusion: push billet through a die (forward/direct or backward/indirect). Extrusion ratio R = A₀/A_f; ideal work ∝ ln R. Ram pressure p = σ_f · ln(A₀/A_f) plus friction/redundant terms.
- Wire/rod drawing: pull metal through a die (tensile). Drawing stress σ_d = σ_f · ln(A₀/A_f); the reduction per pass is limited because the drawing stress must stay below the exit material's yield (else the wire snaps). Multiple passes achieve large reductions.
Worked example
A rod is drawn from 10 mm to 8 mm diameter through a die. If the average flow stress is 300 MPa, estimate the ideal drawing stress (frictionless).
Area ratio A₀/A_f = (10/8)² = 1.5625.
True strain ε = ln(A₀/A_f) = ln(1.5625) = 0.446.
σ_draw = σ_f × ε = 300 × 0.446 = 133.8 MPa. (Below the exit yield, so the pass is feasible; real drawing stress is higher due to friction and redundant work.)
GATE relevance
Rolling draft/force, forging load with friction, extrusion ratio and pressure (σ_f ln R), and drawing stress are standard Manufacturing numericals. Flow stress σ_f = Kεⁿ, true strain, and the hot-vs-cold-working distinction are frequently tested.
Exam tricks & shortcuts
- Ideal deformation work per volume = σ_f · ln(A₀/A_f) — the same ln(area ratio) drives extrusion and drawing.
- Rolling maximum draft = μ²R — friction and roll radius set the bite.
- Hot working: low force, no strain hardening; cold working: high force, strengthens.
- Mnemonic: "Extrude and draw both live on ln of the area ratio."
Using engineering strain instead of true strain in forming. Because deformations are large, forming uses true strain ε = ln(A₀/A_f); engineering strain badly underestimates the work. Also, wire drawing is limited by the exit yield — over-reducing in one pass snaps the wire.
- ✓- Flow stress σ_f = K εⁿ; true strain ε = ln(A₀/A).
- ✓- Hot working: low force, no hardening; cold: high force, strengthens.
- ✓- Rolling max draft Δh_max = μ²R.
- ✓- Extrusion/drawing work ∝ σ_f · ln(A₀/A_f).
- ✓- Drawing reduction limited by exit yield strength.
- ✓Forming force scales with flow stress and the ln of the area ratio, whether extruding or drawing. Use true strain for large deformations, remember rolling's μ²R draft limit, and note that hot working lowers force while cold working strengthens the part.
Metal Forming: Rolling, Forging, Extrusion & Drawing — Formula Sheet
Key formulas
- True strain: ε = ln(L_f/L₀) = ln(A₀/A_f).
- Rolling: max draft Δh = μ²R; contact length L = √(RΔh).
- Extrusion: extrusion ratio R = A₀/A_f; force F = A₀·σ_flow·ln(A₀/A_f).
- Wire drawing: stress σ_d = σ_flow·ln(A₀/A_f); % reduction = (A₀−A_f)/A₀.
- Flow stress: σ = Kεⁿ (n = strain-hardening exponent).
- ✓- True strain ε = ln(A₀/A_f).
- ✓- Rolling max draft = μ²R.
- ✓- Flow stress σ = Kεⁿ.
Forming forces depend on flow stress (σ = Kεⁿ) and area reduction; rolling draft is limited by friction.
Metal Forming: Rolling, Forging, Extrusion & Drawing — Worked Example
Worked Example
Problem: In a flat rolling operation a strip 20 mm thick is to be reduced to 15 mm in a single pass. The roll radius is 250 mm and the friction coefficient between roll and strip is µ = 0.1. Determine the maximum possible draft and state whether this reduction is feasible in one pass.
Solution:
The maximum draft (thickness reduction) that the rolls can "bite" and pull through is limited by friction:
d_max = µ²·R,
where R is the roll radius.
Substitute µ = 0.1 and R = 250 mm:
d_max = (0.1)² × 250 = 0.01 × 250 = 2.5 mm.
Compare with the required draft:
d_required = 20 − 15 = 5 mm.
Since d_required (5 mm) > d_max (2.5 mm), the strip cannot be drawn in by the rolls — the pass is NOT feasible.
To make it work: increase friction (rougher rolls), use larger-radius rolls, or split the reduction into multiple passes.
Answer: Maximum draft = 2.5 mm; the required 5 mm reduction is not feasible in a single pass.
- ✓- The maximum draft in rolling is d_max = µ²R — friction and roll radius set how much the rolls can bite.
- ✓- If the required reduction exceeds d_max, the strip slips and won't enter; use multiple passes or larger/rougher rolls.
- ✓- Bigger rolls or higher friction increase the achievable reduction per pass but raise roll separating force and power.