MAT E 273: Exam #2
Hooke's Law
(stress)=E(strain)
Types of Loading
*Tension (Pull) *Compression (Press) Shear (Shift) Torsion (Twisting)
HCP Slip System
1 distinct {001} planes in an HCP crystal. x 3 independent <1120> directions per {001} plane. ------------------------------------------------------ =3 independent slip systems
Dislocation Generation
1.) Generation of a surface step due to shear stress. 2.) Splitting of existing dislocations
Earth's 8 Big Elements Ranked By wt%
1.) Oxygen (O)- 46% 2.) Silicon (Si)- 27% 3.) Aluminum (Al)- 8% 4.) Iron (Fe)- 6% 5.) Calcium (Ca)- 5% 6.) Magnesium (Mg)- 2.9% 7.) Sodium (Na)- 2.3% 8.) Potassium (K)- 1.5%
Factors That Influence Fatigue
1.) Stress Amplitude 2.) Mean Stress
FCC Slip System
4 distinct {111} planes in an FCC crystal. x 3 distinct <110> directions per {111} plane. --------------------------------------------- =12 independent slip systems
BCC Slip System
6 distinct {110} planes in an BCC crystal. x 2 independent <111> directions per {110} plane. ---------------------------------------------------- =12 independent slip systems
Aluminum (Al)
8% of Earth's crust (most abundant metal in crust) Lighter than steel Great for casting (low melting temp, good fluidity) Soft/high ductility Good conductor of heat and electricity Relatively inexpensive Excellent corrosion resistance Aluminum alloys are superior to pure aluminum in terms of yield strength Pure aluminum is most ductile Prized for corrosion resistance Highly reflective
Sterling Silver
92.5 wt% Ag - 7.5 wt% Cu
Flaw Orientation
A flaw whose major axis is parallel with an applied tensile stress is likely to be inactive and possibly"healed" while the stress is applied. A flaw whose major axis is perpendicular to an applied tensile stress is likely to grow (propagate). Opposite for compression
Toughness
A measure of how much energy a material can absorb before fracture. Proportional to the area under the stress-strain curve up to fracture.
Ductility
A measure of how much plastic deformation a material can sustain before fracture. Higher the strain = higher ductility
Hardness
A measure of how well a material resists local indentation, abrasion, wear, etc. Given by σy or scratch / indention measures (Moh's Scale, Brinell, Rockwell, Vickers).
Stainless Steel
A metal alloy of steel, chromium(> 11 wt% Cr), and sometimes Ni and Mo which is used in casket construction; noted for its ability to resist rust. Hard to repair Work hardens
Magnesium (Mg)
A metal that is quite similar to aluminum, but is less ductile and highly susceptible to corrosion. Impurities such as Fe further reduce corrosion resistance 1/2 of Mg produced is alloyed with Aluminum
Bainite
A microstructure that consists of the ferrite and cementite phases ( α and Fe3C).
Titanium (Ti)
A relatively low-density but high-strength metal that has excellent corrosion resistance as a cool solid, but not as a very hot solid or liquid. The thermal conductivity of this metal is very low, making it difficult to machine since it doesn't effectively dissipate the heat produced at the cutting tool location. It's oxide is more commonly produced (approximately 60x more by weight). The identity of this oxide mineral is rutile.
Chromium (Cr)
A shiny metal that is completely brittle below 300 degrees C.It is added to steels to drastically improve their corrosion resistance. Austenite de-stabilizer.
Eutectic Point
A specific composition associated with a minimum melting temperature and useful solidification pathway
Fatigue
A specimen is subjected to dynamic or cyclic stresses. Cause: Localized pile-up of dislocations during cyclic straining. Effect: Local embrittlement as the cyclic loading proceeds.
Secondary Phase Strengthening
Additional phases (more crystallographic boundaries) will also impede dislocation motion.
Tensile Testing
Applies constant force to a material and measures the specimen's response to the stress.
IT Diagram
Applies to one composition and describes the time dependence of a phase transformation.
Ductile-to-Brittle Temperature Dependency
As temperature decreases, ductility and toughness decrease because bonds "seem" stronger since thermal energy doesn't act to weaken / break the bonds.
Yield Point
Beyond this point, some strain will be permanent in the material
Tempered Martensite
Briefly annealing martensite converting it from ultra-fine needles of BCT ferrite to very small spheres of cementite in BCC ferrite. A less brittle and ultra-fine spheroidite-like structure formed by annealing martensite to reduce internal stress / strain.
Alkali Metal Compound Applications
CO2 Scrubbers, Sode-Lime Glass, Lithium Ion Batteries, Chemical Strengthening of Glass - Ion Exchange, Na-K Eutectic Alloy Composition (Thermal Conductivity, High* Boiling Point, Low* Vapor Pressure *compared to water)
Slip System
Combination of slip plane and slip direction For systems that offer close-packed planes and close-packed directions, these will be preferred
Martensite
Diffusionless transformation. Transformation only depends of temperature. Any austenite that is quenched to room temperature transforms to martensite. Forms BCT phase, very brittle but strong. Formation of martensite is more difficult for higher carbon content steel
Dislocation and Strength Trade off
Dislocation motion needs to be easy for metals to be ductile, but strength is derived making dislocation motion difficult.
Slip
Dislocation movement/motion Slip allows a material to deform through incremental breaking of bonds (inch worm) Easy is metals, difficult in covalent/ionic systems
Steel Designations/Grades
Ex: 1045 Steel 10- Plain Carbon Steel 45- 0.45wt% C
Silver (Ag)
Excellent thermal and electrical conductivity Liquid Ag extremely soluble of oxygen Second most ductile metal behind Au Higher cost
Ductile Failure
Extensive gross plastic deformation or strain prior to failure. Crack growth is slow and non-catastrophic. Preferred over brittle failure.
Predicting Failure
Failure=cycles/time
Engineering Stress
Force divided by the original cross sectional area
Strain Hardening (Cold-working or work-hardening)
Generation of dislocations (and their subsequent interactions). The yield strength and tensile strength increase and ductility decreases.
Alkali Metals
Group 1 From Na on, a filled p shell shields the single valence electron very well, resulting in a weakly bound valence electron and extreme behavior: Easily ionized (reactive), Low melting / boiling points, Extremely soft & ductile The largest atoms of the elements
Alkaline Metals
Group 2, Be & MG-Lowest density structural metals Ca, Sr, Ba, Ra- Weaker and reactive in normal air. Useful as alloying elements.
Solid Solution Strengthening
Hardening and strengthening of metals that result from alloying in which a solid solution is formed. The increased presence of impurity atoms restricts dislocation mobility. Cause stress strain in host lattice.
Annealing
Heating enhances atomic diffusion in order to remove local dislocations/strain and certain grains will grow and "consume" surrounding grains (recrystallization).
Coarse Pearlite
High Temperatures. Diffusion is fast so the carbon diffuses further in a given amount of time. Therefore, the carbon-rich cementite plates form further apart.
Alkali Metal Thermal Conductivity
High reactivity and low melting points preclude their use as room temperature conductors, but liquid alkali metals are useful as coolants in nuclear reactors.
Alkali Metals Corrosion Properties
High-purity Li, Na, and K form a thin protective oxide in ultradry high purity O2 In normal air they react with, H2O, O2, CO2, and N2 to form a complicated mixture of hydrides, oxides, carbonates, bicarbonates (and for Li a nitride) that are non-protective. Exhibit very low electronegativities and therefore highly reactive and must be stored in mineral oil or inert gas. Thick specimens of Na and K corrode to nonmetallic compounds within days. Alkali metals can even attack glass, reducing SiO2 to pure Si. The reactivity increases down the group, as the ionization energy decreases.
Gold (Au)
Highest electronegativity (2.4 Paulings) Can be purified by bubbling 02 through molten Au, oxidizes impurities which rise to top Most ductile metal
Microstructure Development Near Eutectoid Temperature(Fe-Fe3C
Hypoeutectoid- Proeutectoid Ferrite & Pearlite Eutectoid- Pearlite Hypereutectoid- Proeutectoid Cementite & Pearlite
Mechanical Properties of Steels
Increasing hardness, strength, brittleness Decreasing ductility Spherodite, Pearlite (+pro-eutectoid), Bainite, Tempered Martensite, Martensite
An equation that relates the stress required for crack propagation and the size of a flaw to a material property that describes resistance to brittle failure:
KIC=Yσc(πa)^(1/2) KIC - Plane Strain (Mode I) Fracture Toughness a - Half of the major axis of the elliptical flaw Y - A parameter describing the specimen geometry. (given or solvable)
Brittle Failure
Little to no plastic deformation prior to fracture. Crack growth is rapid, unstable and catastrophic.
Fine Pearlite
Low Temperatures. Diffusion is slow so the carbon diffuses less in a given amount of time. Therefore, the carbon-rich cementite plates form closer together.
Hardness Test
Measuring the depth of indentation
Compressive Stresses
Negative stress
Athermal (Diffusionless) Phase Transformation
No change in composition. (No diffusion required.) Cooperative and local rearrangement to form a new crystal structure. The extent of transformation is temperature dependent. Relatively fast upon activation. Ex: γ→α' (martensite)
Copper (Cu)
One of few elements found in metallic state in Earth's crust About as dense as Fe Excellent conductor of heat and electricity Relatively low cost Great ductility Work hardens very easily as room temp Used in electrical parts (wires) Forms non-protective layer above 200*C Forms protective layer below 200*C (green tarnish) Brass= Cu+Zn (Higher strength) Bronze= Cu+Sn (Low melting, easy to cast, brittle)
Tensile Stresses
Positive stress
Diffusion Controlled Phase Transformation
Product phase(s) are a different composition, and likely a different crystal structure. Thermally activated, meaning the transformation rate is temperature dependent. Ex: γ→α + Fe3C
Platinum Group Metals
Ru, Os, Rh, Ir, Pd, Pt 6 of the 10 most rare elements Extremely corrosion resistant Don't rely on protective oxide layers Large number of unpaired d electrons available for bonding, resulting in high moduli, high melting points, low thermal expansion, and short bond lengths (high densities). Low electrical conductivities
Failure/Fracture
Separation of a material to generate new and undesirable surfaces.
Nickel (Ni)
Similar properties as Fe Austenite stabilizer Nickel-based superalloys feature remarkable strength and corrosion resistance up to 1100*C Susceptible to corrosion when it contains chromium impurities or is exposed to environments with sulfur. >0.01wt% Ni in Earth's crust, mainly in core
Magnified Stress
Small and sharp flaws amplify/concentrate stress. σm=2(σo)(a/ρt)^(1/2) σm = magnified stress σo = original stress ρt = Crack tip radius a = Half of the major axis of the ellipse
Grain Size Reduction
Smaller grains (larger grain count) means more barriers to dislocation motion means harder / stronger (less ductile). Grain boundaries act as a "fence" for dislocations.
Spherodite
Spheroidite forms when a eutectoid steel (pearlite, bainite, or martensite) is held near eutectoid temperature for a very long time (> 100 hours for typical sized parts).
Martensite Application
Surface hardening of steel. Obtaining a high-carbon martensitic case (hard) on a tough low-carbon steel core (ductile) through carburization.
Elastic Region
The area of a stress-strain curve before the yield point. All strain in reversible. Atomic bonds are stretched.
Non-Uniform Plastic Region
The area of a stress-strain curve between the tensile strength point and the point of failure. Some strain is non-reversible and occurs locally in the specimen (at the necked cross section).Atomic bonds are broken/reformed. Dislocation is becoming difficult.
Uniform Plastic Region
The area of a stress-strain curve between the yield point and tensile strength point. Some strain is non-reversible and occurs throughout the specimen. Atomic bonds are broken/reformed. Dislocations begin to move.
Slip Direction
The crystallographic direction along which a dislocation moves
Slip Plane
The crystallographic plane along which a dislocation moves
Tungsten (W)
The highest melting point pure metal. 7th most dense metal (19.25g/cm^3). A metal that forms a very hard ceramic carbide for cutting tools and wear resistant coatings. Most of the annual extraction of this metal from the earth is utilized to form its carbide.
Elastic Deformation
The material will return to its original shape when the load is removed. Slope is the "spring constant", called the Young's Modulus, E
Tensile Strength
The maximum force that a specimen will endure. Necking begins to occur if more force is applied.
Failure/Fracture Point
The point at which the material breaks
Lever Law
The weight fraction of a phase is given by the length of the *OPPOSITE* lever arm over the entire length of both arms.
Creep
Time-dependent plastic deformation of a material subjected to a load at elevated temperatures
Hypoeutectic
To the left of the eutectic point
Hypereutectic
To the right of the eutectic point
Beryllium (Be)
Toxic, rare in Earth's crust, great for x-ray windows
Brittle
Very strong materials but not very ductile. Doesn't have a prominent yield point. Fail under elastic load after little to no plastic deformation.
Twinning
When separate crystals share a common set of lattice points. Can manifest during crystallization and during mechanical deformation. Mechanical twinning produces audible acoustic waves
Hot Working
Working or shaping a metal above its recrystallization temperature. Dislocations anneal out / heal as they form. Material does not strain harden and remains fairly ductile. Saves energy / allows for extreme deformations without fracture.
Cold Working
Working or shaping a metal below its recrystallization temperature. Material strain hardens, so strength and hardness increase. Limits shaping. Often requires post process annealing.
Dislocations and their purposes
[1] Crystalline materials generally feature many dislocations. [2] Dislocations can move (slip) in response to local shear stress. This is a good thing, since it makes deformation of metals relatively easy. [3] Dislocations can interact with each other and other defects(grain / phase boundaries, free surfaces, impurities, etc.)These interactions form the basis of strengthening mechanisms in metals. [4] Dislocations can be generated / multiplied in a number of ways in the material. More dislocations means more interactions ... means a stronger material. [5] Dislocation mobility typically* dictates mechanical properties of metals. Easy dislocation motion allows deformation to occur with fairly low stress. Dislocation pinning (or blocking) means a higher stress is required for deformation. aka. the material is stronger.
Engineering Strain
the change in length of sample divided by the original length of the sample
Poisson's Ratio
v= -(lateral strain)/(axial strain)
Fe-Fe3C Phase Diagram Classifications
wt%C < 0.022 = (Irons) Pure Iron or single phase α 0.022 < wt%C < 2.14 = (Steels) Often a two-phase mixture of α and Fe3C 2.14 < wt%C < 6.7 = (Cast Irons) Two or three-phase mixtures of α, Fe3C, and/or graphite.
Mean Stress
σ(m) = (σ(max) + σ(min))/2
Stress Amplitude
σa=abs[(σmax−σmin)/2]
An equation that relates the stress required for crack propagation to the "energy cost" associated with creating exposed surfaces during crack growth:
σc=(2Eγs/πa) σc= Stress required for crack propagation a - Half of the major axis of the elliptical flaw E - Young's modulus γs - Surface Energy = energy required to form free (unbonded) surfaces
An equation that relates the theoretical strength of a material to the magnified stress at a flaw.
σth=σm=2(σo)(a/ρt)^(1/2) σth = theoretical strength σm = magnified stress σo = original stress ρt = Crack tip radius a = Half of the major axis of the ellipse
Resolved Shear Stress
τR=σ(cosφcosλ) φ- Angle between the normal vector of the plane of interest (often the slip plane) and the loading axis. λ- Angle between the direction of interest on the plane (often the slip direction) and the axis of loading.
