Question

A sheet metal with a stock hardness of $250$ HRC has to be sheared using a punch and a die having a clearance of $1$ mm between them. If the stock hardness of the sheet metal increases to $400$ HRC, the clearance between the punch and the die should be (in mm)

Answer 1

Tensile strength $\alpha$ Hardness number
Shear strength = $0.5$ tensile strength (Tresca theory)
$=0.577$ tensile strength (Von-Mises theory

Shear strength $\alpha$ Hardness number and clearance,
$C=0.0032t\sqrt{\tau }$
$C\alpha \sqrt{Hardnessnumber}$
$\frac{C_2}{C_1}=\sqrt{\frac{(Hardnessnumber{)}_2}{(Hardnessnumber{)}_1}}$
or $C_2=1\times \sqrt{\frac{400}{250}}=1.265$ mm