Answer to Question #180538 in Mechanical Engineering for Hari

Question #180538

 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)?


1
Expert's answer
2021-04-16T07:47:00-0400

We know that, for the composite material

"Y_cV_c= Y_1V_1+Y_2V_2\n\u200b"

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"

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