Widely used for fastener heads (nails, bolts).

Maximum length upset in single blow: three times initial wire stock diameter.

Reduces diameter of tube or rod to create a tapered section.
Rotating dies hammer workpiece radially inward.
Mandrel controls internal diameter for tubular parts.
Radial Forging: Similar to swaging, but dies don't rotate; workpiece rotates as it feeds into hammering dies.

Reduces cross-section of cylindrical/rectangular rod by passing it through opposing rolls with matching grooves.
Combines rolling and forging; classified as forging.
Roll-forged parts are stronger with desired grain structure compared to machined parts.

Cone-shaped upper die simultaneously rolls and presses workpiece. Work supported on lower die.
Small contact area due to inclined cone axis reduces press load requirement.

Hot-forging where workpiece and dies are maintained at elevated temperature.
Avoids chilling of work, metal flows more readily, reduced force.
Expensive, used for difficult-to-forge metals (Ti, superalloys) and complex shapes.
Done in vacuum/inert atmosphere to prevent die oxidation.

Bulk forming process: metal forced through a die hole to produce desired cross-section.
Advantages: Variety of shapes, enhanced grain structure/strength (cold/warm extrusion), close tolerances (cold extrusion).
Types: Direct (forward), Indirect (backward).

Metal billet loaded into container with die holes. Ram compresses material, forcing it through die holes.
Significant friction between billet surface and container walls, increasing ram force.
Hot direct extrusion: oxide layer on billet surface increases friction and can cause defects.
Dummy block used to leave oxide layer in container, producing oxide-free product.
Butt: extra portion of billet that cannot be extruded, separated from product.

Die mounted to ram, not container. Ram compresses metal, which flows through die hole in opposite direction to ram movement.
No relative motion between billet and container, so no friction at interface, lower ram force.
Limitations: Lower rigidity of hollow ram, difficulty supporting extruded product.

Made by preparing billet with hole parallel to axis. Material flows through gap between mandrel and die opening.

Extrusion Ratio ($r_e$): $r_e = A_0 / A_f$ (where $A_0$ is initial CSA, $A_f$ is extruded CSA).
True Strain (ideal deformation): $\varepsilon = \ln(r_e) = \ln(A_0 / A_f)$.
Ram Pressure (ideal deformation): $p = Y_f \ln(r_e) = Y_f \ln(A_0 / A_f)$, where $Y_f$ is average flow stress.
Actual Pressure: Greater than ideal due to friction between billet/die and billet/container wall.
Johnson Formula (actual true strain): $\varepsilon_x = a + b \ln r_e$. (Typical $a=0.8, b=1.2-1.5$).
Ram Pressure (with friction): $p = Y_f \varepsilon_x$.
Billet-Container Friction Force: Additional ram force to overcome friction.
- Sliding friction: $\mu p_e \pi D_0 L = \frac{p_f \pi D_0^2}{4}$ (where $p_e$ is pressure against container wall).
- Sticking fri