Effect of Temperature on Materials. June 20, Kamran M. Nemati. Phase Diagram

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1 Effect of Temperature on Materials June 20, 2008 Kamran M. Nemati Phase Diagram Objective Phase diagrams are graphical representations of what phases are present in a material-system at various temperatures, pressures and compositions. Understanding phase diagram is important because there is a strong correlation between microstructure of an alloy and mechanical properties. 2 1

2 What is a Phase? A phase has the following characteristics: 1. A phase has the same structure or atomic arrangement throughout, 2. A phase has roughly the same composition and properties throughout, 3. There is a definite interface between the phase and surrounding phases. Example: If we enclose a block of ice in a vacuum chamber, the ice begins to melt and some of the water vaporizes. Three phases existing: solid, liquid and gaseous H 2 O... Water vapor..... ICE Water 3 Phase Rule (Gibbs Rule) Gibbs rule describes the state of a material and has the general form of: F = C P + 2 C= Number of components (compounds) or elements in a B Liquid system. 1.0 atm A F=Number of variables such as temperature, pressure and composition, and Solid Vapor P=Number of phases present C Temperature (C) Constant 2 in the equation implies that both temperature and Unary phase diagram pressure are allowed to change. for pure Magnesium Pressure 4 2

3 Solubility Limit For many alloying systems, there is a maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution. This is called a Solubility limit. The addition of solute in excess of this solubility limit results in the formation of another phase. Example: If we add small quantity of salt to a glass of water, and stir, the salt dissolves completely in the water (one phase of salt water is formed). If we add too much salt to the water, the excess salt sinks to the bottom of the glass (two phases of saturated brine and solid salt are formed). 5 Phase Equilibrium Concepts A system is at Equilibrium if its free energy is minimum under specific temperature, pressure and composition conditions. Free Energy is a function of the internal energy of a system and also the randomness or disorder of the atoms or molecules (Entropy). Binary Phase Diagram is constructed when only two elements are present in the alloy. Example: Cu-Ni system. 6 3

4 Binary Phase Diagram Ni (in Ni-Cu) Liquidus=1280C (begins to solidify) Solidus=1240C (below this temp. solidification is completed) Freezing range= =40C Temperature (C) Cu α L L+α 1240 Liquidus Solidus Weight percent Nickel (wt%) Ni Cu-40% Ni alloy (Isomorphous binary phase diagram) Binary Phase Diagram only liquid (L) is present containing 40% 1270C: Two phases L and α are present. End point at liquidus which is in contact with liquid is at 37% Ni. End point at solidus which is in contact with the α region is at 50% Ni. Therefore, the liquid contains 37% Ni and solid contains 50% Again two phases are present (L+ α). Liquid contains 32% Ni and Solid contains 45% Only solid α is present, so the solid must contain 40% Ni Temperature (C) Cu Alloy α L L+α Weight percent Nickel (wt%) 1455 Ni 8 4

5 Equilibrium Solidification of Cu-40% Ni L Alloy 1455 L 28 α 40 L 40 α 52 L 32 α Temperature (C) L (First Solid) (last Liquid) L+α α α Cu Weight percent Nickel (wt%) Ni 9 Microstructure of Pb-Sn VS Temperature (Alloy 2) Liquid=76% (Proeutectic α =24%) (c) (Proeutectic α =51%) Liquid=49% Eutectic β (d) 100% Liquid (a) Temp (C) α Eutectic β Eutectic α Alloy 2 a Alloy 1 b L 232 α+l c 183C d β+l 18.3 e β (Eutectic Point) α+β 100% Eutectic Composition (Alloy 1) Eutectic α Proeutectic α (e) 0 Pb wt% Sn Sn 10 5

6 Plain-Carbon Steel Steel can be defined as an Iron alloy which transforms to Austenite on heating. A plain-carbon steels has no other major alloying element beside carbon. When a plain-carbon steel is slowly cooled from the Austenitic range it undergoes the eutectoid transformation. Construction steel alloys used for concrete reinforcing bars and structural shapes have been traditionally been % C plaincarbon steels with only minor additional elements, (this is now changing as the steel industry becomes more sophisticated). In general these alloys are called Low-alloy Steel and for most purposes they can be considered plain-carbon steel. 6

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9 Introduction to Thermal Sciences Thermal-fluid sciences: The physical sciences that deal with energy and the transfer, transport, and conversion of energy. Thermal-fluid sciences are studied under the subcategories of thermodynamics heat transfer fluid mechanics The design of many engineering systems, such as this solar hot water system, involves thermal-fluid sciences. 17 THERMODYNAMICS Thermodynamics: The science of energy. Energy: The ability to cause changes. The name thermodynamics stems from the Greek words therme (heat) and dynamis (power). Conservation of energy principle: During an interaction, energy can change from one form to another but the total amount of energy remains constant. Energy cannot be created or destroyed. The first law of thermodynamics: An expression of the conservation of energy principle. The first law asserts that energy is a thermodynamic property. Energy cannot be created or destroyed; it can only change forms (the first law). 18 9

10 The second law of thermodynamics: It asserts that energy has quality as well as quantity, and actual processes occur in the direction of decreasing quality of energy. Classical thermodynamics: A macroscopic approach to the study of thermodynamics that does not require a knowledge of the behavior of individual particles. It provides a direct and easy way to the solution of engineering problems and it is used in this text. Statistical thermodynamics: A microscopic approach, based on the average behavior of large groups of individual particles. It is used in this text only in the supporting role. Conservation of energy principle for the human body. Heat flows in the direction of decreasing temperature. 19 Heat Transfer Heat: The form of energy that can be transferred from one system to another as a result of temperature difference. Heat Transfer: The science that deals with the determination of the rates of such energy transfers and variation of temperature. Thermodynamics is concerned with the amount of heat transfer as a system undergoes a process from one equilibrium state to another, and it gives no indication about how long the process will take. But in engineering, we are often interested in the rate of heat transfer, which is the topic of the science of heat transfer. We are normally interested in how long it takes for the hot coffee in a thermos to cool to a certain temperature, which cannot be determined from a thermodynamic analysis alone

11 What is temperature? Temperature (T) is a measure of how hot or cold something is Temperature is not energy nor is it heat Temperature is a measure of the motion (vibration or translation) of the atoms/molecules that make-up an object The greater the motion/vibration the greater the T The smaller the motion/vibration the lower the T Temperature is measured in 3 common scales: Fahrenheit (US), o F Celsius or Centigrade (Metric), o C Kelvin (SI), K {note: units of Kelvin are not degrees K (or o K), just K} 21 The Common Temperature Scales Fahrenheit & Celsius Celsius & Fahrenheit 22 11

12 Heat and Internal Energy Heat is energy that flows from a high temperature object to a lower temperature object When something absorbs heat its internal energy (or the energy of its atoms/molecules) increases When something releases heat its internal energy decreases The SI units of heat are joules (J) Two things occur when an object absorbs or releases heat energy (Q): The temperature will change (which is why they expand/contract, due to changes in molecular motion) The object (or part of it) will change phase (solid, liquid, gas) 23 Heat and Temperature Change When an solid (or liquid) of mass, m, absorbs and no phase change occurs: Q = c. m. ΔT {Black s Heat Equation} Q is heat absorbed/lost, ΔT is the temperature change, and c is called the specific heat capacity Specific Heat Capacity: A physical property that relates how energy absorbed reflects changes in temperature for a given substance In SI terms:the amount of energy required to change the temperature of 1 kg of a substance by 1 o C (or 1 K) SI units for specific heat capacity are J/(kg. K) Metals tend to have low specific heat capacities (which is one reason they make great cooking vessels) Non-metal substances tend to have higher specific heat capacities Water has an unusually high specific heat capacity 24 12

13 The Mechanical Equivalent of Heat Before it was established that heat was indeed energy, heat was traditionally measured in units of calories (cal): 1 calorie = amount of heat required to raise the temperature of 1 g of water by 1 o C James Prescott Joule established that heat energy is the equivalent of mechanical energy: 1 cal = J In nutrition we often invoke the kilocalorie (or nutritional calorie): 1 kcal = 1 Cal = 1000 cal = 4186 J The typical person needs to eat ~2000 Cal daily (or 2x10 6 cal of food energy) 25 Heat and Phase Change When a substance absorbs/loses heat energy its temperature will change until: the substance reaches its critical temperature it will no longer change temperature gain/loss of additional heat energy will also result in the phase transformation of the matter from one phase to another: Solid liquid gas The relationship that describes heat energy (Q) gained/lost to mass of substance (m) that undergoes a phase change is: Q = m. L L is called the latent heat (the SI units are J/kg) Latent heat is a physical property that describes how much energy is required to transform the mass of a substance from one phase to another (e.g. latent heat of fusion or vaporization, etc.) 26 13

14 Fourier s Law for Heat Conduction Q (heat flow) Hot T h L Cold T c Q = T ka T L h c = dt ka dx Thermal conductivity 27 Heat Diffusion Equation 1 st law (energy conservation) Heat conduction = Rate of change of energy storage k 2 2 T x T = C t Specific heat Conditions: t >> τ scattering mean free time of energy carriers L >> l scattering mean free path of energy carriers 28 14

15 Linear Thermal Expansion Most solid materials expand or contract depending on their temperature: As T increases object expands As T decreases object contracts This is referred to as linear thermal expansion 29 Linear Thermal Expansion (cont.) The extent to which something expands/contracts with temperature (ΔL) depends on: the physical properties of the material (a property called the coefficient of linear expansion, or α) the original length of the object (L o ) The increase/decrease in temperature (ΔT) in o Cor K units ΔL = αl o ΔT {α is measured in units of o C -1 or K -1, since ΔT is the same for both scales} 30 15

16 Volume Thermal Expansion Objects will expand in volume as well as in length Volume thermal expansion is analogous to linear thermal expansion: ΔV = βv o ΔT The coefficient, β, is called the coefficient of volume thermal expansion and is related the coefficient of linear thermal expansion (α) β = 3α 31 Thermal Expansion Thermal Expansion is the tendency of matter to change in volume in response to a change in temperature. When a substance is heated, its constituent particles move around more vigorously and by doing so generally maintain a greater average separation. Materials that contract with an increase in temperature are very uncommon; this effect is limited in size, and only occurs within limited temperature ranges. The degree of expansion divided by the change in temperature is called the material's coefficient of thermal expansion and generally varies with temperature

17 Thermal Expansion Common engineering solids usually have thermal expansion coefficients that do not vary significantly over the range of temperatures where they are designed to be used, so where extremely high accuracy is not required, calculations can be based on a constant, average, value of the coefficient of expansion. Materials with anisotropic structures, such as crystals and composites, will generally have different expansion coefficients in different orientations. 33 Building Materials Thermal Behavior Phase Phase A B Rise in Temperature Difference in coefficient of expansion results in residual stress 34 17

18 Thermal Stresses σ = Eε Hook s Law ε = αδt σ = REαΔT Where: σ = Thermal stresses R = Restraint (0 < R < 1) E = Modulus of elasticity α = Coefficient of thermal expansion ΔT = Temperature drop 35 Heat Loss from Solid Bodies θ 0 = Initial temperature difference θ m = Final temperature difference h 2 = Thermal diffusivity 2 h = k cρ k = Conductivity c = Specific heat ρ = density 36 18

19 Sample Problem At a certain elevation, an arch concrete dam is 70 ft. thick and has a mean temperature of 100 F. If exposed to air at 65 F, how long will it take to cool to 70 F? Assume thermal diffusivity of concrete, h 2 =1.20 ft 2 /day. 37 Sample Problem Solution

20 Sample Problem Solution θ 0 = Initial temperature difference = 100 F - 65 F = 35 F θ m = Final temperature difference = 70 F - 65 F = 5 F θm 5 = = Slab θ 35 0 From the Heat loss for solid bodies chart: 2 ht = D 0.18D t = 2 h 2 ( 70) 0.18 = = 735 days 39 Useful Unit Conversion Formulas Temperature: (where F is Fahrenheit / C is Celsius / K is Kelvin) F to C = (F-32) x 5/9 F to K = (F-32) x 5/9 = K to F = (K ) x 9/ C to F = (C x 9/5) + 32 C to K = C = K to C = K Measure: (Feet) x (30.48) = Centimeters (Feet) x (0.3048) = Meters (Meters) x (3.2808) = Feet (Meters) x (1.0936) = Yards (Inches) x (2.540) = Centimeters (Centimeters) x (0.3937) = Inches 40 20