Question

The flow stress (in MPa) of a material is given by

$\sigma =500{ϵ}^{0.1},$

where $ϵ$ is true strain. The young's modulus of elasticity of the material is 200 GPa. A block of thickness 100 mm made of this material is compressed to 95 mm thickness and then the load is removed. The final dimension of the block (in mm) is

Answer 1

$\sigma =500{ϵ}^{0.1}$

Youngs modulus = 200GPa

$h_i=100;h_f=95forging$

After compression load is removed, what is final dimension

$ϵ=In\left(\frac{h_i}{h_f}\right)=0.0513$





${\sigma }_1=500(ϵ{)}^{0.1}=(0.0513{)}^{0.1}\times 500$

= 371.52 MPa

$ϵ=\frac{\sigma }{E}=\frac{371.52}{200\times {10}^3}$

= $1.8576\times {10}^{-3}$

${ϵ}_I=0.0018576$

$In\left(\frac{L_f}{95}\right)=0.0018576$

$L_f=95.1766mm$