City Guilds Model Questions Vol1 2025 Engineering Question 50

A cylindrical steel billet of diameter \(100\) mm and length \(200\) mm is to be forged into a shape whose final cross‑sectional area is \(6000\;\text{mm}^2\). The material flow stress follows \( \sigma = K \epsilon^{n} \) with \( K = 800\;\text{MPa} \) and \( n = 0.15 \), where the true strain is \( \epsilon = \ln\!\left(\dfrac{A_0}{A_f}\right) \) ( \(A_0\) and \(A_f\) are the initial and final areas). A friction factor of \( m = 0.1 \) is assumed, and the average area during deformation is taken as \( A_{\text{avg}} = \dfrac{A_0 + A_f}{2} \). The required forging force is \( F = \sigma \; A_{\text{avg}} (1+m) \). Calculate the required forging force in kilonewtons and state whether a press rated at 400 kN can perform the operation.