GATE 2020 BM – Question 50
During femoral arthroplasty, bone cement warms from 37°C to 87°C and has thickness 20 mm. Bone, cement and implant are concentric cylinders; bone–cement adhesion is absent and temperature is uniform. Cement expansion coefficient is 90×10⁻⁶/°C and Young’s modulus 3.5 GPa. Find thermal stress and corresponding thickness shrinkage magnitude.
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Correct answer: (A) 15.75 MPa,90 μm
Explanation
The temperature change is fifty Celsius degrees, giving thermal strain αΔT=90×10⁻⁶×50=.0045. The source’s constrained-strain stress magnitude is EαΔT=3.5 GPa×.0045=15.75 MPa. Corresponding thickness contraction magnitude on cooling is .0045×20 mm=.09 mm=90 μm. Thus A; the detailed stress field would depend on actual constraints beyond this simplified estimate.