Materials Science Midterm
Covalent bonding mechanism
Adjacent atoms share electrons -> directional: each atom assumes a geometry to minimize repulsion between electrons
Torsion Loading
is applied through shafts, and twists the central component (force applied like revving a motorcycle).
Pressure Loading
is applied through shells or pressure vessels (liked compressed gas in a dive tank).
Bending Loading
applied through beams or panels, and either pulls away or compresses the central portion of the sample (like snapping a pencil)
Tension Loading
applied through a tie or cable, and pulls outwards
Compression Loading
is applied in columns, through pressing inwards
Predominant bond type for polymers
(Non-metals). adjacent atoms share electrons. Has directionality if polar. Hybrid orbitals of covalent bonding enable complex geometry (all working to minimize electron cloud repulsion).
Predominant bond type for ceramics
(nonmetals + metal) ionic bonding, electrostatic attraction between ions of opposite charges. Bond is non-directional.
Vickers hardness to yield strength
9.807 HV = 3 (yield strength)
Material Property
A material property describes the kind and magnitude of a response to an imposed stimulus. It can be either intrinsic or attributive. Mechanical properties, specifically, are responses to applied loads.
How does bonding Influence Properties
A stronger bond leads to a seep, narrow(more symmetric) well with high melting temperature (T_m), high Young's modulus (E), and low coefficient of thermal expansion (CTE)
State the steps in an annealing process (recovery, recrystallization and growth), the conditions under which annealing takes place, and the microstructural and mechanical property changes that occur during each step
Annealing is heat treatment to relieve internal stress and strain, which alters the microstructure and restores pre-cold worked properties. Is only done following plastic deformation.
Coefficient of thermal expansion, alpha
Arises because of the asymmetry of the potential energy well. If the well is symmetric, there is no thermal expansion
Influence of temperature
As temperature increases, Yield strength decreases (strength_0.2%, y) , tensile strength decreases (stress_UTS), and Ductility (%EL) increases
Use polymer density to determine degree of crystallinity.
Ceramic density is the mass of everything fully contained within the unit cell divided by the volume of the unit cell. Polymers can exhibit local packing of chains in an ordered arrangement. A greater % crystallinity means more efficient packing, meaning a higher density.
Describe how Ionic ceramics arrange into 3D solids
Ceramic unit cells are often based on metallic crystal structure with smaller atoms or ions in interstitial sites
Ceramic Stress Strain Curve
Ceramics ( like concrete) are typically tested w/ compression, not tension. They are susceptible to brittle fracture due to flaws in material. They break very quick
H_c
Cohesive energy, energy per mole to separate the atoms of a solid completely. Greater cohesive energy = stronger bond
Define density
Density is mass per unit volume. To measure it, weigh the sample in air, then weigh it again submerged in fluid.
Define dislocation density
Dislocation density is a measure of the concentration of dislocations in a crystalline material (units: 1/m^2)
Draw a series of sketches to show how an edge dislocation moves through a crystal, and describe how dislocations facilitate plastic deformation (slip)
Dislocations break lines of bonds each time, rather than a whole plane. Edge dislocations are distortions about an extra half plane of atoms. For ceramics specifically, it is hard for dislocations to form or move, corresponding to a high strength but highly brittle material (no plastic deformation). Metals make it easy for dislocations to form and move, making them ductile. Dislocation motion occurs on specific slip planes, which are the most densely packed atomic planes in the structure. Dislocations move on these planes in a direction along which atoms are touching (a close packed direction).
Define ductility and work of fracture and examine stress strain curves from different materials to compare them based on these properties.
Ductility is the degree of plastic deformation at fracture, expressed as percent elongation. Work of fracture is the ability of a material to absorb energy and plastically deform prior to fracture (area under stress-strain curve up to point of fracture). Work of Fracture:
Material Sub families
Elastomers are a subfamily of polymers, and glasses are an amorphous subfamily of ceramics. Hybrids are composites of the other material families.
Ionic Bonding mechanism
Electrostatic attraction between ions of opposite charge -> non directional
Calculate engineering stress from applied load and cross-sectional area.
Engineering stress is also called nominal stress. Divide force by area, units are in pascals, typically reported in megapascals. Compression is the inverse of tension, w/ a negative sign in front of it.
Differentiate between an engineering stress-strain curve and a true stress-strain curve
Engineering/nominal stress and strain are calculated using initial sample dimensions. In reality, the sample dimensions are changing during the test, and true stress and strain are based on instantaneous sample dimensions. The true stress strain curve is higher. True stress and strain is only valid until necking AKA until the plastic deformation AKA until the yield point
r_0
Equilibrium atomic seperation distance
Rank the packing efficiency of common crystal structures (FCC, HCP, BCC)
FCC (74%) = HCP (74%) > BCC (68%), in terms of efficiency. Face centered cubic and hexagonal close packed have the same packing efficiency in 3D space, just ABCABC (FCC) versus ABAB (HCP). Body centered cubic is not closely packed.
Calculate theoretical density and volume for metals with cubic crystal structures.
FCC n = 4 atoms in unit cell. Lattice parameter// Volume of a unit cell= 2(sqrt(2))* R for FCC
primary mode of loading in a component
Five Types: Tension, Compression, Bending, Torsion, Pressure
State Hooke's law and use it to relate stress and strain in the elastic region
For linear elastic materials, stress is proportional to strain in the elastic (reversible) region. This linear relationship is stress = young's modulus * (strain), which is Hooke's law.
Explain how grain boundaries influence the strength of a crystalline material
Grains deform in the same way the bulk metal deforms. Grain boundaries are obstacles to dislocation motion. Grain boundaries are sources of dislocations.
Describe and/or sketch how grain structure changes during an annealing treatment and explain the driving force for the change
Grains go from elongated to equiaxed in the annealing process. Most significant changes occur during recrystallization.
Growth
Growth is when the grains grow to reduce grain boundary area. Some grains grow at the expense of others.
Vickers indentation to hardness calculation
HV = 1854.4 (F/ d^2)
Define hardness and describe how hardness is measured
Hardness is the measurement of localized resistance to plastic deformation. Can be measured with an indentation test, where an indenter penetrates the sample surface and the size of the indent mark indicates resistance to plastic deformation. Brinell hardness testing uses a spherical indenter (diameter of indent impression used to calculate hardness), whereas Vickers uses a diamond indenter with a pyramid shape (average of impression diagonals used to calculate hardness). Moh's hardness scale depends on what scratches what (hardest is diamond).
Hydristatic pressure and bulk Modulus(?_
Hydrostatic pressure - pressure (p)= bulk modulus (K)* dilation/volume change (represented by delta). Bulk modulus is inverse of compressibility Modulus can also be measured by finding the speed of sound in the material.
How to sketch a schematic bond energy curve...
If the cohesive energy is high that means the well is really deep, and if the thermal expansion coefficient is high then the well is more asymmetric
Use the Hall-Petch relationship to calculate changes in strength as a function of grain size
In general, hardness and strength increase as grain size decreases. Ductility increases as grain size increases. ** relationship breaks down at nanoscale.
Elastic Deformation
Initial -> Bonds stretch -> Return to initial The material reverts back to its original shape and size
Describe strain hardening and the underlying mechanism by which crystalline materials become stronger as they are plastically deformed
Intrinsic strength is a measure of how difficult it is for a dislocation to move in a material. Strain hardening takes advantage of the fact that plastic deformation increases dislocation density, thus resistance to dislocation motion in a material. Before strain hardening, specifically cold rolling, a material is equiaxed, and afterwards it is elongated.
Metallic bonding Mechanism
Ion cores surrounded by a sea of electron glue -> non-directional
design/safety factors in determining appropriate materials to use for a given loading scenario
Material properties are not exact, and they are typically expressed as an average or range. So a safety design factor is applied to the stress. Safety factor (N) must be greater than 1. Calculated stress * design factor = design stress yield stress/ safety factor = safety(working) stress
Explain why engineering stress and strain values are more commonly used in engineering practice.
Mechanical properties are easier to determine from engineering stress-strain curves. Below the yield strength, there is a negligibly small difference between engineering and true stress/strain.
Define the properties of melting temperature
Melting temperature is proportional to cohesive energy, which is related to the total effects of secondary bonding.
Describe how metallic atoms arrange into 3D solids
Metallic bond is nondirectional and delocalized, and forms multiple close-packed layers. The unit cell is the symmetry element, and the lattice parameter, a, is the edge length of the unit cell. Smallest interatomic spacing results in lower energy and higher bond strength
Describe the basic differences between the crystal structures of metals and ceramics
Metals tend to be densely packed, and are often a single atom or atoms of a similar size. Smallest interatomic spacing results in the lowest energy and highest bond strength. Ceramics tend to have more complex unit cells than metals because of fixed bond angles. Ceramic unit cells based on metallic crystal structure, but smaller atoms or ions are in interstitial sites. exception to this is glass is an amorphous ceramic, which is non crystalline with no periodic order/symmetry
Net force between atoms
Net Force = Attractive force + Repulsive Force
Describe the molecular structure of polymers and use repeat unit notation to represent a polymer
Notation to write polymers is 'repeat unit notation' w/ an n or number of monomers in bottom corner. Typically derived from petroleum products, carbon-based, w/ nonmetals.
Define the term "recrystallization temperature"
Recrystallization temperature is where recrystallization is complete after one hour in a highly deformed sample. Typical annealing temperatures are between 0.4 and 0.6 of the melting temperature, and held for a few hours.
Use Poisson's ratio to calculate transverse strains under given loading conditions
Poisson's ratio is the ratio of induced transverse elastic strain to axial elastic strain. Assumes that materials are isotropic, meaning that properties are same in all directions (meaning strain in x direction is same as strain in y direction). When you stretch something, it gets narrower (think piece of gum). Poissons' ratio = -Ex/Ez = -Ey/Ez For metals, Poissons' is approximately ⅓. For ceramics, Poissons' is approximately ¼. For polymers, Poissons' is approximately ⅖. For elastomers, Poissons' is approximately ½. Watch out for the negatives
Explain why polycrystalline materials are typically stronger than single crystals
Polycrystalline materials are less favorably oriented for slip - as multiple slip systems can be activated. Each grain has a different orientation to the tensile axis.
Describe how plastic deformation occurs in polymers
Polymer properties depend on temperature and strain rate. Drawing (permanent/plastic) deformation straightens and aligns polymer chains in the direction of applied load.
Recovery
Recovery is where dislocations vertically align, and some cancel out in dislocation annihilation. Vertically aligned dislocations cause less distortion, and have a lower elastic strain energy than a random arrangement.
Recrystallization
Recrystallization is when new grains grow from previously deformed grains. Nucleate at grain boundaries and regions of high dislocation density.
Shear stress
Shear stress, represented by tau, is force applied parallel. Shear stress (tau) = shear modulus (G) * shear strain (represented by lowercase gamma).
Describe the differences in atomic arrangement between single crystals, polycrystalline materials, and amorphous materials
Single crystals are anisotropic, with one crystal structure and one orientation. Polycrystalline materials have one crystal structure, but many random orientations and are isotropic.
Describe how the presence of solute atoms alters the strength of a crystalline material
Solute atoms move to the dislocation line, ease internal strains and pin dislocations. Oversized solute atoms go below the dislocation line, undersized solutes go above. Strength increases with the concentration of the alloying element.
Calculate engineering strain based on deformation, and vice versa
Strain is unitless. It is the change in length over the initial length. Engineering strain is the same as nominal strain. Strain is calculated by putting the change in length over the initial length
what is happening physically to a sample at points of interest on a stress strain curve?---> Metals
Stress < yield strength -> Reversible, uniform deformation Yield strength < stress < tensile strength -> Uniform permanent deformation Stress > tensile strength -> At UTS neck develops, nonuniform permanent deformation Then fracture
Tensile test method and data
Tensile tests are destructive, collecting data on load/force and position/extension using dogbone shaped samples. Values are dependent on the sample size, and the initial displacement is called the gauge length.
Define the properties of the coefficient of thermal expansion
The coefficient of thermal expansion (alpha), arises because of the asymmetry of the potential energy well. It relates to the ability of a material to adjust to temporary volume changes.
Transverse strain
The elastic strain on the x and y axis which are equal to one another The change in width over the initial width
Axial Strain
The elastic strain on the z-axis or vertical axis Change in length over the initial length
Describe how each of the following factors relates to annealing: time, temperature, strain (%CW or %R)
The longer time in a furnace, the greater the effect of annealing. The higher the temperature of annealing, the faster annealing occurs. The greater the percent cold work or percent reduction, the greater the driving force for recrystallization, so the faster the annealing process occurs. A minimum strain is required for recrystallization to occur.
Explain why the real strength of metals is dramatically lower than the theoretical strength
The presence of dislocations is the reason real strength is so much lower than ideal strength in metals. There are numerous edge dislocations throughout a metal, which is true of all polycrystalline metals.
What happens physically at the ultimate tensile strength
There is a large portion of necking in the sample
Describe general relationships between the following properties: strength, hardness, ductility
Yield strength is the resistance to plastic deformation. Hardness is the resistance to localized deformation. Ductility is the extent of plastic deformation at fracture. Strength and hardness are proportional to one another, and ductility is inversely proportional to strength and hardness.
Through analysis of a tensile stress strain curve, determine: the Young's modulus of a material, its yield strength, ultimate tensile strength, and strength/strain at failure.
Young's modulus is the slope of the elastic region. The yield strength is the point at which the graph switches from linear to nonlinear, which can be approximated (proportional limit, 4% change in slope) or mapped with a 0.02 line (where initial strain is 0.2% and E is the slope, pick a random point later on in the graph, find intersection of stress-strain curve with 0.02 line. Called offset yield). The ultimate tensile strength is the maximum point on the curve. The strength and strain at failure are the values right before a steep drop further along the curve. Yield strength is the measure of resistance to permanent deformation.
Relate each property to features on a bond force and/or bond energy curve: Young, Alpha, Cohesive energy
Young: slope of bond-force curve. Alpha: measure of well's asymmetry Cohesive energy: depth of energy well
Estimate the Young's modulus of a material from tensile test data
Youngs' modulus is equal to stress over strain, which is typically reported in gigapascals. Youngs' modulus is a measure of the change of shape that is elastic. It is a measure of stiffness and is size independent. Determine this from tensile test data by figuring out the slope of the stress-strain curve in the elastic region.
Define the properties of Young's modulus
Youngs' modulus is relative stiffness of a material, and is the slope of the bond-force curve at r sub 0.
Describe how Network Covalent ceramics arrange into 3D solids
ceramic unit cells are often based on metallic crystal structure with smaller atoms or ions in interstitial sites
similarities across material families
mechanical (response to applied load), thermal (heat capacity/thermal expansion/etc.), electrical (dielectric constant/conductivity), magnetic (remanence), optical (refraction/absorption), and chemical (corrosion resistance). Metals and ceramics are both crystalline.
Predominant bond type for metals
metallic bonding, where metallic elements shed valence electrons. Ion cores are surrounded by a sea of electron glue. Bond is non-directional.
Main material families
metals, ceramics, and polymers
Polymer tensile stress-strain curve behavior
necking happens at the yield strength, not the tensile strength. Polymers, generally, have a low strength and high ductility
What to consider when brainstorming property requirements
price and availability, Resistance to pressure, strength, flexibility, temperature resistance, all are potential driving factors Examples from class: Two given in class examples: soda cup and coffee cup. For a soda cup, it needs to be watertight, withstand pressure, and relatively inexpensive. For a coffee cup, needs to be temperature resistant (not burn hands), hold liquid, have an open top, and also be relatively inexpensive.
