Sheet-Metal Bend Springback

by the Machinery's Handbook relation Ks = Ri/Rf = 4 x^3 - 3 x + 1 with x = Ri x yield / (E x thickness). Elastic recovery makes the released radius Rf = Ri/Ks LARGER than the die radius, and the angle opens too, so the operator must OVERBEND. A 1 in tool radius in 0.1 in, 50 ksi steel gives Ks 0.948 -> the radius springs from 1.0 to 1.05 in (~5%); a high-yield or aluminum part (higher yield/E) springs more, a thicker part less. The exact overbend depends on the tooling (air bend vs bottoming vs coining -- coining nearly eliminates it), grain direction, and press, so the first article is confirmed with a protractor and radius gauge. A screen; the material cert, tooling method, and a test bend govern.

x = tool_radius x yield_strength / (modulus x thickness); springback factor Ks = Ri/Rf = 4 x^3 - 3 x + 1; released (final) radius Rf = tool_radius / Ks. E ~ 29-30e6 psi steel, ~10e6 aluminum.

Sheet-metal bend-springback relation (Machinery's Handbook / ASM Metals Handbook forming), by name; the material certificate, the tooling method, and a test bend govern the actual overbend.

The springback cubic is a published forming relation; the tool radius, thickness, yield strength, and modulus come from the setup and the material certificate.

Estimate. AHJ and licensed professional govern.

Field names used by the API: tool_radius_in, thickness_in, yield_strength_psi, modulus_psi, springback_factor_ks, final_radius_in

• Springback cubic Ks = Ri/Rf = 4 x^3 - 3 x + 1, x = Ri x yield / (E x thickness); released radius Rf = Ri/Ks > Ri (overbend needed)Machinery's Handbook / ASM Metals Handbook
• Tooling-dependent air bend springs most, bottoming less, coining nearly none; grain direction and press also matter; a test bend sets the final overbendpress-brake practice