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)_____.

• A. 1.265

Answer 1

The correct option is A 1.265
Tensile strength $\alpha$ Hardness number
Shear strength = $0.5$ tensile strength (Tresca theory)
$=0.577$ tensile strength (Von-Mises theory)

Shear strength $\propto$ Hardness number and clearance,

$\Rightarrow C=0.0032t\sqrt{\tau }$

$\Rightarrow C\propto \sqrt{\text{Hardness number}}$

$\Rightarrow \frac{C_2}{C_1}=\sqrt{\frac{(\text{Hardness number}{)}_2}{(\text{Hardness number}{)}_1}}$

$\text{or,}{C}_2=1\times \sqrt{\frac{400}{250}}=1.265\text{mm}$