# Test 2 Flashcards

Weekly Test 2: Mechanical Properties (elastic, plastic, and ultimate tensile strength), Bonding and Crystal Packing

# Lecture 1: Mechanical Properties - Elastic Deformations

Q. When I pull or push on a sample of steel, is it possible that I am actually changing its overall volume? Am I expanding or contracting its volume or it constant?

### Uniaxial Tensile Test

• Common test — determines the relationship b/w load and deformation.
• Measures:
• Elastic Properties (Elastic Modules)
• Plastic Properties (Yield Stress)
• Failure Properties (Ultimate Tesnsile Stress)

### Typical Stress-Strain Curve

• Elastic is the linear region (similar to spring!)
• Steeper slope = stiffer spring/material
• Slope - modulus of elasticity

### Dimensional Change Under Elastic Deformation

• When materials are stretched, the areas of it changes.
• Volume is rarely constant under elastic deformation. Most materials will expand slightly and then return back after the stress is removed.
• Poisson Ration: (ratio of the lateral and axial strains under an applied stress)

### Measuring Young’s Modulus

• Tensile Test: An extremely large force is used for an extremely small extension. Usually will not give an accurate reading because of the room for error. Use entensometers for accuracy!
• Cantilever Test (Better)
• X-Section for moment of inertia is
• Use equation:

# Lecture 2: Mechanical Properties - Plastic Deformation

Q. Why does the stress strain curve stometimes start to go down? Is the material actually getting weaker as it deforms?

### Definition

Elastic Limit: Point at which permanent deformation begins.

Plastic Deformation: Permanent (irreversible deformation).

Yield Stress: Maximum stress before beginning plastic deformation.

• Work Hardening: The increase in stress to continue deformation beyond the elastic limit.
• Ultimate Tensile Stress: Maximum stress value a material can support.
• Failure or Fracture Stress: Stress value at the time of failure.
• Offset Yield Stress: Technique for defining the yield stress (used in homogenous materials) - see lab about this!

### Ductility

The amount of deformation a material will tolerate before failure.

It can be expressed as percent elongation or and percent reduction - related but not same value.

*QUESTION: What is the relationship between percent elongation and percent reduction?

### Necking

• Localized deformation in a small section in gauge length.
• Deformation is initially distributed through the sample and eventually leading to higher localized stresses due to decrease in material — leading to a localized area of higher stresses and then necking.
• Begins at Ultimate Tensile Strength. After this point, the sample deforms primarily at the region of necking.
• High stress in necking region - same tensile force but less area.
• a. Highly ductile fracture b.Moderately ductile fracture c. brittle fracture (no necking)

### Proportionality of Deformation

• Deformation before necking is linearly proportional as it varies with gauge length.
• Deformation ater necking is no longer proportional and will be somewhat the same as the previous length.

### Modulus of Resilience (MOR, Ur)

Measure of elastic energy storage.

Formula:

• Area up to the elastic deformation point.
• To increase stored energy - increase the yield stress or decrease the elastic modulus as long as the other value is constant.

### Toughness

Measure of energy absorbed before failure.

Formula:

• Total area under the stress and strain curve.
• Toughness increases if increase the yield, UT stress or strain of failure.

### Elastic Recovery after Plastic Deformation

• Elastic deformation continues to accumulate after plastic deformation.
• When undergoing elastic recovery - stays deformed at new plastic deformation (strain t). When load is reapplied, the curve follows the unload curve again can be elastically deformed.
• ADD MORE WHEN DONE TUTORIAL

### Heterogeneous Yielding in Steel

• Yielding (plastic deformation) does not accur uniformly over the length of the specimen.
• Yieleding is highly localized - deformation bands spread through the specimen competing between atom sizes.

### Hardness

• Measures material’s rsistacne to localized plastic deformations (dents/scratches)
• Affected by multiple mechanical properties (stiffness, yield strength, plastic characteristics)

Relationship b/w Hardness and Tensile

• Both values are proportional to each other
• Easier to conduct hardness test and then approximate the tensile strength

# Lecture 3: Interatomic Bonds

Q. What materials typically have a greater linear thermal expansion coefficients, ones with high melting points or ones with low melting points ()?

## A. Conceptual Bond Diagrams

• Attractive force FA (blue) is electrostatic attraction.
• Repulsive force FR(green) is the interference of electron clouds outside of the atom.
• Net force (red) can be attractive or repulse and will be 0 at the most stable diameter.
• Bottom Graph: Potential Energy Graph - emergy required bring ions together from infinite distance apart to distance r.
• At the minimal point or equilibrium, the optimal r is reached and this is where the attractive and repulsive forces balance out.

## B. Relative Physical Parameters from Conceptual Bond Diagrams

### Stiffness/Modulus of Elasticity

On an atomic level, when strecthing material - atoms are being stretch and then every atom returns to the same spot after load is removed.

• Value of E depends on the change of force with respect to interatomic radius (dF/dr) and total number of bonds.
• High slope results in high stiffness.
• All bonds are maintained and no atoms shift or change relative positions.

### Coefficient of Thermal Expansion

• In diagrams: E1 < E2 < E3 < E4 <E5
• Asymmetric: Meaning interatomic distance changes with the temperature. In diagram, meaning the distance is increasing with increasing temperature.
• Symmetric: means interatomic distance at the new energy level is constant with increasing temperature. For linear expansion .

### Melting Temperature

• Stronger bonds will have a lower thermal expansion coefficient and a higher-melting-point because increasing temperatures does not change bond distance as much.
• Therefore, more movement in bonds means lower-melting-point.

## C. Types of Bonds

### Primary Bonds

Intramolecular or chemical bonds.

Ionic Bonds

• Found both in metals and non-metals.
• Metal atoms give up their valence electron to non-metal (stolen electron)
• Metal becomes + charged and non-metal becomes - charged.
• Non-directional bonds so can form crystals.

Covalent Bonds

• In materials with a smaller difference in electronegatively.
• Sharing valence electrons (ie. orbital hybridization)
• Forms directional bonds between atoms. It will form molecules, chains, or crystal structures.
• Covalent Molecules: have shared electrons between different atoms (independent molecule units)
• Low melting and boiling points.
• Weak Van der Waal forces bewtween covalent molecular structures,
• Soft and Flexible.
• Covalent Networks: structures with continuous covalent bonds between atoms in a repeating pattern.
• High melting and boiling points.
• Only covalent bonds in a network structure.
• Very hard.

Metallic Bonds

• Found in metals and their alloys. Arranged in highly ordered crystal structures.
• Metals give up ther 1, 2, and 3 valence electron to a “sea of shared electrons”.
• Non localized electrons and non directional bonds.
• High electrical conductivity.
• Ductily of most metals

### Secondary Bonds

Intermolecular or physical bonds.

Van der Waals Bonds

• Dipoles from compounds causing attraction.
• London dispersion (permenent) is the weakest.
• Dipole-dipole (temporary) in polar molecules.

Hydrogen Bonds

• Strongest intermolecular bond.
• Hydrogen is bonded with lone electron from another atom with (F, O, N)

# Lecture 4: Crystal Structures, Directions and Planes

### Definitions

Crystal or Crystalline Solid: solid material arranged in highly ordered microscopic structure, forming a crystal lattice in all directions.

Polycrystalline Solid: solid composed of many grains in crystal structure.

Amorphous Solids: solid that is not organized into any definite lattice pattern.

Crystal Morphology: refers to the shape and size of crystals.

Microstructure: refers to he structure features of an alloy (grain or phase structure)

### Structure and Mechanical Properties

Each phase (same material), BCC and FCC, has a different crystal structures.

• The graph shows the volume changes and crystals form as iron is heated.
• Each different phase (crystal structure) may also have different mechanical, thermal, and electrical properties.

### Three Common Crystal Structures for Metals

Different crystals form due to different types of bonds, sometimes crystal structure will change due to environment (temeperature, pressure)

### Definitions

Unit Cell: minimum volumetric unit which repeats. Has a # of atoms per cell and length wrt atomic radius.

Coordination Number: # of atoms which are in constant with a one particular atom.

Atomic Packing Factor: fraction of unit cell value which is occupied by the hard-sphere atoms.

• APF = (volume of atoms in cell)/(unit cell volume)

### Summary of Crystals

Structure

Atoms/Unit Cell

Coordination #

APF

Lattice Parameter (a)

BCC

2

8

0.68

R

FCC (ABABAB)

4

12

0.74

R

HCP (ABCABC)

6

12

0.74

2R

### Density Calculation

= number of atoms per unit cell

= atomic weight g/mol

= unit cell volume =

= Avogardro’s Number = atoms/mol

### Crystal Directions and Planes

At scale of a single crystal, following mechanical properties depend on orientation wrt crystallographic planes.

• Brittle fractures can occur on specific planes.
• Permanent deformation occurs by sliding b/w crystal planes.

Defining Directions

1. Vector: passes through the origin of the coordinate system.
2. Length of Vector: is determined by length of unit cell dimensions a, b, and c.
3. Expressed as [u v w] such that u = x, v = y, w = z.
1. Negative gets bar on top

### Directionality

Anisotropic: Having different properties in different directions - usually in materials with smaller grains.

Isotropic: Properties are independent of direction.

### Crystallographic Planes (Miller Indices)

Crystallographic Planes are specified by 3 Miller Indices as [h k l], representing the normal vector to the plane.

Defining Planes

1. If plane passes through the selected origin pick a new origin to be established.
2. Determine the length of the plane finding where it intersects on x, y, and z.
3. Take the reciprocals of these numbers. A plane that parallels an axis may be considered an infinite intercept and thus, a zero reciprocal.
4. Change numbers to the smallest integers (get rid of the fractions).
5. Then specify them within the parentheses such that (h k l) - negative gets bar on top

# Lecture 5: Polycrystalline Strucutres and Disolcations

Q. Why are some pure metals inherently more ductile than others? What is it about their crystal structure which might be different?

## Types of Imperfections in Crystal Structures

Anything that disrupts the orderly pattern of unit cells in a crystal structure can be considered imperfect.

### 0. Point Defects

• Self Interstitial Atoms (extra atom)
• Squeezed into voids which are not normally occupied — can generate high stresses in the material.
• Does not happen commonly.
• Vacancies (atom is missing)
• N = # of atoms per unit volume.
• Qv = activation energy for vacancy formation.
• T = temperature.
• R = 8.31 J/K*mol
• As T increases, Nv increases.
• Most common.
• Vacancies allow atoms to move in the solid through a process of diffusion.
• Recrystallization, grain growth, phase transformations, creep.
• Rearrange atoms to get to lower energy configuration.
• Impurity Atoms (replacement atom)
• Solid Solutions are mixtures of 2 different types of atoms - solubility limit is the maximum amount of an element that can dissolve in another element.
• Substitutional: alloy atoms replace host atoms in the crystal structure (must be of similar size)
• Interstitial: small alloy atoms fit into spaces between host atoms (must be smaller atoms)

### 1. Line defects, aka Dislocations

• Edge Dislocation
• The presence of an extra half of the plane in the crystal structure.
• Can form when materials are deformed.
• Explains why yield stresses are lower compared to expected values.
• Screw Dislocation
• Bulk sample goes through partial shear.
• Shifted by 1 or more unit cells and two edges need to accommodate.

### 2. Planar interfaces

• Grain Boundaries
• These regions of atomic disorder and higher energy are more chemically active.
• The angle of misalignment can be found by finding the angle between the two high-density lines near the grain boundary.

Weekly Test 5: Strengthening Mechanisms, Failure (Fracture, Fatigue and Creep

Weekly Test 7: Phase Diagrams, Steel, Applications and Manufacturing Processes