An external panel of a satellite is made of the Grade 9 titanium alloy Ti\(3 \mathrm{Al}-2 \mathrm{~V}\), with a yield strength \({ }_{\gamma}\) of \(550 \mathrm{MPa}\) and Poisson's ratio \(u\) of 0.36 . The panel heats up when the face of the satellite is directly exposed to the sun and cools when the sun is obscured by Earth. The panel is rigidly constrained around its edges by attachment to the frame of the satellite, which is maintained at a constant temperature in order to stabilize the electrics it contains. If the temperature of the panel can vary from \(-80^{\circ} \mathrm{C}\) to \(+120^{\circ} \mathrm{C}\), is there any risk that the resulting thermal stress might cause the panel to yield? Read the value of the thermal stress parameter \(\alpha E\) for titanium alloys from Fig. 3.13 and use it to find out. (Here \(\alpha\) is the thermal expansion coefficient and \(E\) is Young's modulus.)

Fig. 3.13

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(ustrain/K) Thermal expansion, a 1000 Isoprene 100 10 0.01 0.1 E=1 MPa/K 10 Silicones Elastomers Polyurethane Ionomers T-expansion modulus Polymers PTFE PE PP ABS PC EVA Cork PEEK Phenolic PET Acetal Leather Metals PMMA Flexible polymer foams PS Mg alloys Lead GERP Epoxies alloys Concrete Zinc alloys Al alloys Cu alloys Foams Rigid polymer foams Natural materials Wood Nontechnical ceramics MFA 15 0.01 0.1 Cast irons Steels Talloys AN WC SiC 10 W alloys SNBC Silicon Stone Soda Brick glass Composites CFRP Diamond- Technical ceramics Silica aE 0.01 MPa/K glass 0.1 10 Young's modulus, E (GPa) 100 1000