A8 Thermal properties of materials

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1 A8 Thermal properties of materials

2 Thermal properties the melting temperature, T m, and the glass temperature (temperatura de transição vítrea), T g, relate directly to the strength of the bonds in the solid crystalline solids have a sharp melting point, T m for non-crystalline solids, T g characterizes the transition from true solid to very viscous liquid in engineering design, it is helpful to define the maximum and minimum service temperatures, T max e T min T max tells us the highest temperature at which the material can be used continuously without oxidation, chemical change or excessive distortion becoming a problem T min is the temperature below which the material becomes brittle or otherwise unsafe to use

3 Thermal properties - heat capacity It costs energy to heat a material up A measured quantity of energy (here, electrical energy) is pumped into a sample of material of known mass. The temperature rise is measured, allowing the energy/kg.k to be calculated.

4 Thermal properties - thermal expansion Most materials expand when they are heated linear thermal expansion coefficient, α

5 Thermal properties - thermal conductivity The rate at which heat is conducted through a solid at steady-state (meaning that the temperature profile does not change with time) is measured by the thermal conductivity, λ (W/m.K) the heat flux q (W/m 2 ) flowing through the material from a surface at higher temperature T 1 to a lower one at T 2 separated by a distance x is recorded The thermal diffusivity, a (m 2 /s) governs the transient heat flow the thermal diffusivity can be measured directly by measuring the time it takes for a temperature pulse to traverse a specimen of known thickness when a heat source is applied to the one side

6 Thermal expansion, α, and thermal conductivity, λ linear thermal expansion coefficient themal conductivity, λ Metals and technical ceramics have high thermal conductivities and modest expansion coefficients. Polymers and elastomers have thermal conductivities ~100 times less and their expansion coefficients ~10 times higher than those of metals.

7 Thermal conductivity, λ, and thermal diffusivity, a λ = 3x10 6 a thermal diffusivity the heat capacity per unit volume, ρc p 3x10 6 J/m 3.K is almos constant for all solids. Foams have low conductivities (and are widely used for insulation because of this), but their thermal diffusivities are not necessarily low. This means that they don t transmit much heat, but they do change temperature quickly.

8 Thermal conductivity, λ, and mechanical strength, σ y Metals, particularly the alloys of copper, aluminum and nickel, are both strong and good conductors, a combination of properties we seek for applications as heat exchangers.

9 The physics of thermal properties: heat capacity Atoms in solids vibrate about their mean positions with an amplitude that increases with temperature Atoms in solids can t vibrate independently of each other because they are coupled by their inter-atomic bonds; the vibrations are like standing elastic waves longitudinal transversal Some of these waves have short wavelengths and high energy, others long wavelength and lower energy In a solid with N atoms there are N discrete wavelengths, and each has a longitudinal mode and two transverse modes, 3N modes in all. Their amplitudes are shuch that, on average each has energy k B T. If the volume occupied by an atome is Ω, the number of atoms per unit volume is N=1/ Ω and the total thermal energy per unit volume is 3k B T/ Ω. Ω 2x10-29 m 3

10 The physics of thermal properties: Thermal expansion If a solid expands when heated (and almost all do) it must be because the atoms are moving further apart. Thermal expansion is a nonlinear effect; if the bonds between atoms were linear springs, there would be no expansion. Materials with high modulus (stiff springs) have low expansion coefficients, those with low modulus (soft springs) have high expansion: α= 1.6x10-3 / E (E em GPa, α em K -1 ) It is an empirical fact that all crystalline solids expand by about the same amount on heating from absolute zero to their melting point: it is about 2%: α 0.02 / T m

11 The physics of thermal properties: thermal conductivity Heat is transmitted through solids in three ways: by thermal vibrations; by the movement of free electrons in metals; and, if they are transparent, by radiation When a solid is heated the heat enters as elastic wave packets or phonons. The phonons travel through the material and, like any elastic wave, they move with the speed of sound (c 0 = E/ρ). Phonons travel only a short distance before they are scattered by the slightests irregularity in the lattice of atoms through which they travel, even by other phonons. On average they travel a distance called the mean free pass, l m, before bouncing off something, and this pass is short: typically less than 0.01 µm Note: in metals, the electrons transport the thermal energy, and get the same equation applied to electrons.

12 Managing thermal stress Most structures, small or large, are made of two or more materials that are clamped, welded or otherwise bonded together. When temperatures chagen, differential thermal expansion generates thermal stress. Thermal stresses in thin films arise on cooling or heating when their expansion coefficients differ These mechanical tensions may cause fracture of the film

13 Thermal sensing and actuation Upward displacement of the bi-material strip (assumed to be thin) is δ (a large aspect ratio L 0 /t produces a large displacement, and one that is linear in temperature

14 Thermal gradients Even though a material has just one expansion coefficient, the presence of a temperature gradient will cause different strains in different places. a= ρ λ C p characteristic distance x that heat diffuses in a time t Want to minimize the thermal expansion coefficient α and maximize the thermal conductivity λ we want high values of the λ/α ratio

15 Insulation: thermal walls Forno choose materials that minimize λ foams are the best materials (polymer, metal or ceramic, depending on the maximum service temperature )

16 Creep At room temperature, most metals and ceramics deform in a way that depends on stress but not on time. ( low-temperature response) As the temperature is raised, loads that are too small to give permanent deformation at room temperature cause materials to creep: to undergo slow, continuous deformation in time, ending in fracture. ( high-temperature response) Depending on the application, we need to know how the strain rate dε/dt depends on the stress σ, temperature T and time t Creep curve (curva de fluência) T constante Metals, ceramics and polymers have creep curves with this general shape

17 Creep The initial elastic and the primary creep strains occur quickly and can be treated in much the way that elastic deflection is allowed for in a structure. Secondary creep (s -1 ) 4 constants characterize the steady-state creep of a material

18 Melting point The temperature at which materials start to creep depends on their melting points. Creep starts for metals when T 0.35 T m and for ceramicst 0.45 T m. Crystalline polymers, most with melting points in the range ºC, creep slowly if loaded at room temperature; glassy polymers, with T g of typically ºC, do the same.

19 Maximum service temperature and strength

20 Creep in polymers Polymers start to creep as the temperature approaches T g and that, for most, is between ºC. This means that the temperature range in which most polymers are used is that near T g when they are neither simple elastic solids nor viscous liquids; they are visco-elastic solids (spring-dashpot model at the simplest). Applying a load causes creep, but at an ever-decreasing rate because the spring takes up the tension. Releasing the load allows slow reverse creep, caused by the extended spring.

21 Summary and conclusions Thermal energy is atomic-level vibration Increasing the a amplitude of this vibration causes expansion The vibrations propagate as phonons, giving conduction In metals the free electrons the ones responsible for electrical conduction also transport heat, and they do so mor effectively than phonons, giving metals their high thermal conductivities Thermal properties are manipulated by interfering with these processes: alloying to scatter phonons and electrons; foaming to dilute the solid with lowconductivity, low-specific-heat gases. The thermal response can be a problem in design thermal stress, for example, causes cracking. Thermal response can also be useful thermal distorsion can be used for actuation and sensing. It is the specific heat that makes an oven take 15 minutes to warm up, but it also stores heat in a way that can be recovered on demand. Good thermal conduction is not what you want in a coffee cup, but when it cools the engine of your car or the chip in your computer it is a big help.

22 Next classes HW3 due on Sunday, March 15 A9 Degradation of materials A10 Microstructure and materials processing

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