ENGR Midterm Revioew

I: Stress-Strain Diagrams

• Label mechanical properties at every notable point on the stress-strain curve.

  • Key points include:

  • Proportional Limit: Point where Hooke's Law is valid.

  • Elastic Limit: Maximum stress that can be applied without permanent deformation.

  • Yield Point: Stress at which a material begins to deform plastically.

  • Ultimate Tensile Strength (UTS): Maximum stress a material can withstand.

  • Fracture Point: Stress at which the material breaks.

• Write the equations for each of the following and label the terms.

  • Engineering Stress (σ): $ext{σ} = rac{F}{A}$

  • where F = force (N), A = original cross-sectional area (m²)

  • Engineering Strain (ε): $ext{ε} = rac{ ext{Δ}L}{L_0}$

  • where ΔL = change in length (m), L₀ = original length (m)

  • Hooke’s Law: $ext{σ} = E imes ext{ε}$

  • where E = modulus of elasticity (Pa)

  • Percent Elongation: ext{Percent Elongation} = rac{ ext{Δ}L}{L_0} imes 100 ext{%}

  • Percent Reduction Area: ext{Percent Reduction} = rac{(A0 - Af)}{A_0} imes 100 ext{%}

  • where A₀ = original area, A_f = final area

  • Poisson’s Ratio (ν): $<br>u = - rac{ ext{ε}<em>t}{ ext{ε}</em>l}$

  • where εₜ = transverse strain, εₗ = longitudinal strain

• Identify what the images in (2a) depict.

  • Curves showing relationship between stress and strain for different materials (e.g., ductile vs. brittle).

• What kinds of materials could create the stress-strain curves in (2b)?

  • Ductile materials (e.g., metals like aluminum or steel) exhibit significant plastic deformation; brittle materials (e.g., glass, ceramics) break with little deformation.

  • Stronger Material: Higher UTS.

  • Tougher Material: More area under the curve (greater energy absorption before fracture).

• Label where strain hardening would occur in figure (2b).

  • Strain hardening occurs after yield point, within the plastic deformation region.

• Given an engineering stress-engineering strain diagram for an aluminum alloy, calculate:

  • Modulus of Elasticity (E): Slope of the initial linear portion of the curve.

  • Elongation (ΔL) when a load of 25 kN is applied.

II: Dislocations, Slip Systems, & Strengthening Mechanisms

• Main Vocabulary:

  • Match terms with definitions:

  • a) Slip: A. Motion of dislocations in response to an externally applied shear stress.

  • b) Slip Plane: B. The plane that has the densest atomic packing.

  • c) Slip Direction: C. The direction in the slip plane that is most densely packed with atoms.

  • d) Strain Hardening: F. Increase in strength (decrease in ductility) of a metal as it is deformed plastically.

  • e) Grain Size Reduction: D. Increasing the strength of a metal by increasing the grain boundary area, which provides more barriers to dislocation motion.

  • f) Precipitate Hardening: E. Strengthening of a material through heat treatment resulting in precipitates.

• Identify the 3 mechanisms of strengthening:

  • Precipitate Hardening, Grain Size Reduction, and Strain Hardening.

  • All involve a decrease in dislocation motion.

III: Electronic Properties

• Fill out the electrical equations:

  • Ohm’s Law: $V = IR$

  • where V = voltage (V), I = current (A), R = resistance (Ω)

  • Resistivity: $ρ = R rac{A}{L}$

  • where R = resistance (Ω), A = cross-sectional area (m²), L = length (m)

  • Conductivity: $σ = rac{1}{ρ}$

  • Current Density: $J = rac{I}{A}$

  • Electric Field: $E = rac{V}{L}$

• Calculate minimum diameter of the aluminum wire:

  • Use the resistivity equation to find required diameter for voltage drop of less than 1.0V at 5A current.

• Electric Field Calculation for 12-gauge copper wire carrying 10A current:

  • $E = rac{I}{σA}$

  • where I = current (A), σ = conductivity (S/m), A = area (m²).

IV: Doping

• General equation for conductivity in semiconductors:

  • $σ = q(n + p)$

  • where q = charge of carriers, n = electron concentration, p = hole concentration.

• Fill in table for semiconductor types:

  • Intrinsic, Extrinsic n-type, and Extrinsic p-type.

  • Doping: Presence of donor or acceptor atoms modifies conductivity.

  • Modified conductivity equations vary for n-type and p-type.

• Calculate electron concentration in silicon:

  • Given room-temperature electrical conductivity and hole concentration.

  • Determine if material is intrinsic, n-type, or p-type.

• Types of Polarization influence:

  • Ionic polarization, orientation polarization, and electronic polarization can occur due to applied electric fields.

V: Dielectrics & Polarization

• Polarization Types and Their Explanations:

  • Ionic, orientation, and electronic polarizations demonstrate how materials respond to electric fields.

• Using dielectric materials:

  • Compare capacitors with different shapes/structures filled with same dielectric to assess capacitance differences.

• Capacitance Calculation with given values:

  • $C = rac{εA}{d}$

  • where C = capacitance (F), ε = permittivity, A = area (m²), d = distance between plates (m).

VI: Thermal Properties

• Heat Needed and Thermal Expansion Equations:

  • Amount of heat needed to raise temperature and volumetric thermal expansion calculations.

  • The amount of heat required can be calculated using the formula Q = mc∆T, where Q is the heat energy (J), m is the mass (kg), c is the specific heat capacity (J/kg·K), and ∆T is the change in temperature (K). Additionally, volumetric thermal expansion can be determined using the equation ( \Delta V = V0 \beta \Delta T ), where ( \Delta V ) is the change in volume, ( V0 ) is the original volume, ( \beta ) is the coefficient of volumetric thermal expansion, and ( \Delta T ) represents the change in temperature.

• Thermal Conductivity Contributions:

  • Examine how thermal conductivity is derived from various factors (e.g., electron and phonon contributions). The thermal conductivity (k) of a material is influenced by its structure and composition, where contributions from both free electrons and lattice vibrations (phonons) play a crucial role in the effective transport of heat.