Real World Experience. Mechanics of Materials. Thermal Strain. Real World Experience. Real World Experience
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1 Mechanics of Materials Every day is a good day. Yun-Men Have you even put a soft drink or other beverage that comes in a can into the freezer, forgot about it, and then come back later to find the can ruptured and the freezer a mess? If you have, you have experienced thermal strain first hand Saturday, September 21, 2002 Meeting 11-2 Most materials when heated, tend to expand As energy is added, the atoms in the material absorb some of the energy and actually vibrate at a higher frequency and tend to want to move apart (simple simple science explanation) Also, when the same material is cooled, it will contract Unfortunately for you and your beverage, water doesn t behave like that It expands when it cools to a point close to freezing hat is very good for life on earth Saturday, September 21, 2002 Meeting 11-3 Saturday, September 21, 2002 Meeting 11-4
2 But back to mechanics of materials When typical engineering materials are heated, they tend to expand he amount that they expand with respect to their original length is known as thermal strain Within limits, the amount of thermal strain is linearly proportional to change in temperature of the material he thermal strain can then be calculated as = α Saturday, September 21, 2002 Meeting 11-5 Saturday, September 21, 2002 Meeting 11-6 is the amount of thermal strain α is the coefficient of thermal expansion is the change in temperature ake care that your units match = α Saturday, September 21, 2002 Meeting 11-7 able B-3 gives the α for some common engineering materials Notice that the units are inverse temperature his is because strain is dimensionless (length/length) = α Saturday, September 21, 2002 Meeting 11-8
3 If the material is constrained when the temperature is changed, the thermal strain will not be able to be expressed and so a strain in the opposite direction will have to be developed Either that or the material buckles = α Saturday, September 21, 2002 Meeting 11-9 his strain which offsets the thermal strain will have to be developed from some other stress in the material his responsive stress will generate a strain that is equal in magnitude and opposite in direction to the thermal strain = α Saturday, September 21, 2002 Meeting If we heat a constrained material with an axial length L, the amount of extension that it would have if unconstrained would be δ δ = α = L = α L Saturday, September 21, 2002 Meeting Since the material was constrained, the same amount of strain would have to be developed in the opposite direction δ = α = L δ = α L Saturday, September 21, 2002 Meeting 11-12
4 his would mean that the elongation would have to sum to 0 δ δ = α L δ = 0 Saturday, September 21, 2002 Meeting he axial stress offsetting the thermal stress is generated by some force, P, so we would have δ = α L PL δ = EA δ δ = 0 PL α L = 0 EA Saturday, September 21, 2002 Meeting Rearranging and dividing by L we have P α = 0 EA herefore the amount of force that the thermal stress will generate within a constrained object can be calculated as P = EAα Saturday, September 21, 2002 Meeting Saturday, September 21, 2002 Meeting 11-16
5 his is what breaks sidewalks apart when water enters pore spaces and expands and contracts Problem P = EAα Saturday, September 21, 2002 Meeting Saturday, September 21, 2002 Meeting Homework Saturday, September 21, 2002 Meeting 11-19
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