CME 260 Properties of Materials – Spring 2018
Professor McNallan, Michael J
Elastic deformation – represented by the linear area on the stress versus strain graph – it is always reversible and calculated using Hooke’s law.
Plastic deformation – occurs when the applied stress is greater than the yield strength – it is irreversible and is the curve portion of the graph with a peak (called ultimate or tensile strength) – the deformation is permanent.
Yield strength – is the end of the elastic deformation and the beginning of the plastic deformation – the limit after which any deformation is permanent.
Ultimate strength (also called tensile strength) – is the maximum strength after which necking occurs on the graph – maximum load a material can stand.
Resolved shear stress is the stress needed to initiate grain slip in the crystal or metal. It is also a stress applied to a slip plan other than parallel or perpendicular. This is calculated using Schmid equation:
τ = σ *cos(φ) cos(λ)
σ is the applied stress and φ+λ ≠ 90 degree
Hall-Petch relation: the smaller the grain size, the higher the yield strength – high impurity in alloy results in an increase of the yield strength and tensile stress. Thus, metals can be strengthened by making grains small.
σy = σ0 + (ky * d-1/2)
d is grain diameter
ky is a constant Don't forget about the age old question of What does extrapolate mean?
σ0 yield strength for large grain metal We also discuss several other topics like What is the definition of external fertilization?
σy yield strength
Strain hardening: metal hardening by plastic deformation that occurs at cold temperature – this deformation is expressed as percent cold work
% CW = ((A0 – A1) / A0) * 100
Cold work can be removed by a heat treatment without changing the dimensions of the sample; this process is called annealing
Hardness testing: a force is applied on material to make a dent (the smaller the dent, the harder the material) – this test is low cost, quick and non-destructive, used for quality control.
Failure by a mechanism other than exceeding yield strength – fracture (separation in multiple pieces) may occur at stress lower than that of the yield strength.
- Ductile fracture: fracture caused by formation of small cavities formed in the interior of the cross section We also discuss several other topics like What is the content of los ultimos de filipinas?
- Brittle fracture: fracture without any sign of plastic deformation, due to rapid propagation of any crack. We also discuss several other topics like What are the five components of cvp analysis?
Fatigue – failure due to many cycles of loading at stress even below the yield strength. Creep – diffusional deformation at a stress below the yield strength – it is a time dependent deformation due a long term exposure to loads even below the yield strength – its rate depends on the temperature and the stress – it is slower in single crystal compare to polycrystalline (reverse of Hall-Petch relation).
Strength: the ability to withstand load
Hardness: the ability to resist plastic deformation
Toughness: the ability to absorb energy
Ductility: the ability to deform without fracture.
Nanoindentation: system configuration to meet individual needs
Phase – form of matter that has distinct properties from other phases – it is a state of a matter such as gas, liquid or solid.
Phase diagram – graphical representation, representing different states of a matter under various conditions. The phase diagram provides in different conditions, a variety of information of the matter (such as phases, composition, concentration, melting, etc.)
Solidus – phase boundary separating the solid from a solid plus liquid system – a temperature at which a material will starts to melt – anything below the solidus line is solid. Liquidus – phase boundary separating the liquid from a solid plus liquid system – a temperature at which a material starts to solidify – anything above that line is liquid. Don't forget about the age old question of What is the definition of business trust?
Tie line is the line drawn in a 2 phases region – it intersects both liquidus and solidus – it is helpful in determining the composition of the components in the system.
Concentration is how much of the different phases are present in the system – this concentration can be determined by the Lever Rule.
Let’s Xα and Xβ be the concentration respective of the components α and β. C0 is the composition at eutectic point on the diagram.
First draw the tie line and determine the C’s in the formula on the graph and calculate the X’s. Xα = (Cβ – C0) / (Cβ – Cα) If you want to learn more check out What is the definition of catatonia?
Xβ = (C0 – Cα) / (Cβ – Cα)
Composition is different from Concentration. Composition is found on the diagram and Concentration is calculated using lever rule and the values of different compositions.
There are different types of phase diagrams
- Unary phase diagram: diagram for one component then it is for pure substance – temperature and pressure are variable parameters.
- Binary phase diagram: phase diagram containing two components – temperature and composition are variable parameters and pressure is constant.
Eutectic phase diagram
Eutectic point is the lowest temperature at which a specific composition of alloy melts. It is an invariant point because at eutectic, the number of degree of freedom F is 0, i.e. it occurs at a specific composition and temperature in a given system.
Degree of freedom- Gibbs Phase Rule – In general, F = C – P + 2
F = C – P + 1 if the pressure is constant (this is the case in our course).
F = degree of freedom = number of variables independent
C = number of components
P = number of phases
Alloys at the left (hypoeutectic) or at the right (hypereutectic) of the eutectic concentration form the proeutectic phase.
Eutectic reaction is a 3-phase reaction at which a liquid transforms by cooling to solid1 and solid2 at the same time.
Eutectoid reaction is like eutectic reaction – it is a 3-phase reaction at which a solid1 transforms by cooling to solid2 and solid3 at the same time.
Peritectic reaction is a reaction at which a solid1 and a liquid transform by cooling to solid2 at specific composition and temperature.
Peritectoid reaction is a reaction at which a solid1 and a solid2 transform by cooling to solid3 at specific composition and temperature.
Carbon is the most important element for strength and hardness. Increase in carbon increases tensile strength and hardness. Carbon is essential for the formation of microstructures.
Austenite is formed above eutectoid temperature of 727°C and has fcc (face centered cubic) structure.
Pearlite in steel is the mixture of cementite and ferrite respectively 12% and 88%. It is formed by eutectoid transformation of austenite cooled below a certain temperature. Bainite in steel is formed at temperatures between 250 and 550°C. It is like the pearlite but stronger with very fine layers.
Martensite is a metastable phase. Martensite is a body centered tetragonal non cubic structure. It is formed by rapid cooling (quenching) of the austenite. Martensite as quenched may be too hard so that it is brittle. Therefore, tempering is applied to reduce the concentration of martensite by the application of heat because too much martensite makes the sample brittle and too little makes it soft. The amount of martensite must be monitored to get an alloy with wanted properties.
Spheroidite like pearlite and bainite consists of ferrite and cementite phases but is in shape of spheroidal particles
Austenite (solid) – ductile – gamma is representation symbol
Ferrite (solid) – ductile – alpha is representation symbol
Cementite or carbide (compound Fe3C) – hard and brittle ceramic
Controlling factors of the kinetic of phase transformation
∙ Thermodynamic driving force
∙ Diffusion coefficient
These two factors control the kinetic of phase transformation. At low temperatures, the driving force raises and the diffusion coefficient decreases.
Transformation starts at low rate at the beginning and the end but rapid in between. At fixed temperature, the transformation approximately follows the Avrami equation F 1 - exp (-ktn)
F is the fraction of gamma transformed
K and n are constant
t is time of transformation
Process of precipitation hardening (Another approach to make fine distribution of particles in a metal without using eutectoid transformation)
1. Choose right alloy – 2 phases at room temperature, one phase solid at high temperature. 2. Solutionize heat to temperatures where metal is one phase
3. Quench to make soft – supersaturated alloy may form
4. Age – heat to temperature in two phase-regions where second phase particle can form. Hardness versus time during aging increases, goes through a maximum and then decreases due to overaging.
Ferrous alloys: 10xx steel has 0.xx% C – for alloy first two numbers are 10 Jominy end quench test measures the hardenability of steels
Hardenability: how deep the steel is hardened upon quenching from high temperature. Do not confuse with hardness.
Annealing is a heat treatment that changes electrical and mechanical properties of the material by altering the microstructures. In ferrous alloys, this process reduces its hardness (less brittle) and increases its ductility, also makes a uniform fine grained structure.
Microstructures are very small scale structure of a material.