Due Date: After Session $7($Midnight$)$

A gas turbine engine works at constant speed at service temperature of $760C.$ and the

blades initially have a $=1\mathrm{.}5mm$ clearance as shown in figure $1.$ The blades are

proportioned such that along a main section $150$ mm in length the centrifugal stress is

constant at $40$ MPa $.$ Tests have shown that at the steady state, the power$-$law creep rate at

$800C$ is $7\mathrm{.}3\frac{{10}^{-8}}{sec}$ and $950C$ it is $1\mathrm{.}5\frac{{10}^{-5}}{sec}.$ Estimate the time required for

the tip clearance to be reduced to $0\mathrm{.}5$ mm $.$

A steam turbine operates at a temperature of $550C$ under constant stress conditions. The

turbine blade is subjected to high$-$temperature and high$-$stress conditions, leading to

concerns about creep deformation. As an engineer, you are tasked with selecting an

appropriate material for the blade from the following options:

I. Material A: Nickel$-$based superalloy $($High melting point, good creep resistance,

moderate cost$)$

II$.$ Material B: Titanium alloy $($Low density, moderate creep resistance, lower cost$)$

III. Material C: Stainless steel $($Good oxidation resistance, low creep resistance, low

$cost$

Given that the turbine is expected to operate continuously for $50,000$ hours, and creep

deformation is a critical factor, which material would you recommend? Justify your choice by

considering the relevant properties of each material.