Question

 15 mm dia SS (Young’s modulus = 200 Gpa) rod is coated with HA (Young’s modulus = 300 Gpa). What should be the coating thickness (in mm) so that the Young’s modulus of the composite is 209 Gpa (use mixture rule)?

Answer 1

We know that, for the composite material

$Y_cV_c= Y_1V_1+Y_2V_2 ​$

Where, Y₁, Y₂ are the young modulus for composite material; and

V₁ and V₂ are the volume

Since, height will be same and only their cross sectional area is changing

$209(15+x)^2=(15^2\times 200) +(x^2\times300)$

$47025 +209 x^2+6270x=45000+300x^2$

$0 = 91x^2-6270x-2025$

$91x^2-6270x-2025= 0$

$x=0.32 mm$