ENS 167: Properties of Materials

• ENS 167: Fundamentals of Materials Science and Engineering covers the properties of materials
• Prepared by PROF. JOSHUA B. ZOLETA, PHD

Properties of Materials

• Mechanical, electrical, electronic,magnetic and thermal properties of materials are investigated

Mechanical Properties of Materials

• The mechanical properties reflect a material's response to applied loads or forces
• These are determined through controlled laboratory experiments that simulate service conditions
• Processing impacts structure, which in turn dictates properties and ultimate performance
• The American Society for Testing and Materials (ASTM) promotes consistency in testing and results interpretation
• ASTM publishes standardized testing techniques

Four Principal Ways of Load/Force Applications

• Tension produces elongation
• Compression produces contraction
• Shear is similar to frictional force
• Torsion produces rotational motion

Tension Tests

• Tension tests help ascertain mechanical properties important for design
• Load application is uniaxial along the specimen's long axis
• The specimen experiences deformation to fracture under gradually increasing tensile load
• These tests are destructive as the test specimen is permanently deformed and fractured, and typically take several minutes

Mechanical Properties

• Engineering stress (σ) is the instantaneous load (F) applied perpendicularly to the specimen's cross-sectional area (A₀), measured in Pascals (Pa) or pounds per square inch (psi)
  • 1 Pa equals 1 N/m²
  • 1 psi equals 1 lb/in²
• Engineering strain (€) is defined as (li - l₀) / l₀ = Δl / l₀, using original length (l₀), instantaneous length (li), and change in length (Δl)

Compression Tests

• Similar to tensile tests, but applies compressive force
• Specimens contract along the stress direction
• Materials brittle in tension are usually tested
• Compressive force is taken to be negative in calculations

Shear Tests

• Shear stress (τ) equals F/A₀, where F is the load applied parallel to the upper and lower faces, and A₀ is the area under consideration
• Shear strain (γ) can be calculated: γ = tan θ

Elastic vs. Plastic Deformation

• Elastic deformation sees stress and strain being proportional
• It is non-permanent
• When the load is removed, the piece returns to its original shape
• Elastic deformation obeys Hooke’s Law: σ = E€
  • σ = stress
  • € = strain
  • E = Young's modulus
• Higher the E value means a stiffer material
• Plastic deformation sees stress no longer being proportional to strain
• It is permanent and the piece will not return to its original shape when the stress is removed
• Atoms do not return to their original positions

Definitions of material strengths

• Proportional Limit (P) is the point of yielding, or the initial departure from linearity in the stress-strain curve
• Yield Strength (σy) gives a more precise point of yielding
  • Found by drawing a parallel line to the elastic portion of the stress-strain curve at 0.002 strain offset
  • A measure of a material's resistance to plastic deformation
• Tensile Strength (TS) is the stress at the maximum on the stress-strain curve
  • It corresponds to the maximum stress a structure can withstand in tension
• Fracture Point (F) is when the material finally fractures

Ductility, Resilience, Toughness and Hardness

• Ductility measures the degree of plastic deformation at fracture
• Brittle materials experience very little plastic deformation
• Resilience measures a material's capacity to absorb energy during elastic deformation and release it upon unloading
• Toughness measures a material's ability to absorb energy up to fracture
• Hardness measures a material's resistance to localized plastic deformation, like dents or scratches. It is the ability of a material to scratch another material that is softer
• The Mohs Scale of Hardness ranks materials from 1 (Talc) to 10 (Diamond)

Electrical Properties of Materials

• Describes how a material responds to an applied electric field
• Ohm's Law relates current (I) to applied voltage (V) using the equation V = IR, where R is resistance
  • V is measured in Volts (J/C)
  • I is measured in Amperes (C/s)
  • R is measured in Ohms (V/A)
• Electrical conductivity (σ) is the reciprocal of resistivity (ρ) and specifies a material's electrical character
• Conductivity indicates the ease with which a material conducts electric current

Resistivity

• Resistivity (ρ) is defined as RA/l, where R is resistance, A is cross-sectional area, and l is the distance between voltage measurement points

Conductivity Classification

• Conductors have conductivity values around ~10⁷ (Ω-m)⁻¹
• Semiconductors have intermediate conductivity around ~10⁻⁶ to 10⁴ (Ω-m)⁻¹
• Insulators have low conductivity values around ~10⁻¹⁰ to 10⁻²⁰ (Ω-m)⁻¹
• Electrical properties depend on electron band structure and electron arrangement
• Electron energy band is a series of closely spaced electron states in the material

Band Types

• In metals such as copper, a partially filled outermost band allows electron states above and adjacent to filled states
• Insulators have a filled valence band separated by a large band gap (> 2eV)
• Semiconductors have a similar structure to insulators but has a narrow band gap (< 2eV)

Conduction

• In conductors, minimal energy is needed to move electrons to vacant states
• An electric field is sufficient to excite many electrons into conducting states
• Insulators and semiconductors require electrons to jump the energy band gap to reach conducting states
• Matthiessen's Rule says total resistivity equals thermal resistivity plus impurity resistivity and plus plastic deformation resistivity

Magnetic Properties of Materials

• Magnetism is the phenomenon where materials exert attractive or repulsive forces on other materials
• All substances, including iron, are influenced to some degree by magnetic fields
• Magnetism is generated by moving electrically charged particles

Diamagnetism

• A weak, nonpermanent form of magnetism present only with an external magnetic field
• Caused by changes in electron orbital motion
• Materials are attracted to regions where the magnetic field is weak between strong electromagnet poles
• Present in all materials but only observed when other types of magnetism are absent
• Dipoles are induced opposite to the field direction when in the presence of a field,
• No dipoles exist in the absence of an external field

Paramagnetism

• Results when atomic magnetic moments align with an external field
• Magnetic moments are random in the absence of an external field
• Dipoles preferentially align with the field when in the presence of a field
• Both diamagnetic and paramagnetic materials are considered non-magnetic and exhibit magnetization only in the presence of external field

Ferromagnetism

• Characterized by a permanent magnetic moment, even without an external field
• Exhibits very large magnetic susceptibilities and permanent magnetizations
• Examples: BCC iron, cobalt, and nickel

Influence of Temperature

• Raising temperature increases thermal vibrations, which randomizes aligned magnetic moments

Ferromagnetic Materials

• Soft magnets are used in devices needing low energy losses in alternating magnetic fields, such as transformer cores
• Hard magnets are used in permanent magnets and are resistant to demagnetization

Thermal Properties of Materials

• Describes the way a material responds to heat application
• Solid materials see rising temperatures and increased dimensions as they absorb heat
• Thermal properties of solids include heat capacity, thermal expansion, and thermal conductivity

Thermal capacity

• Heat capacity (C), measured in J/mol·K is dQ/dT
• It describes a material's ability to absorb heat from its surroundings
• It represents the energy required to raise the temperature by 1°
• dQ is the energy used to produce a dT temperature change
• Cv is heat capacity measured at constant volume
• Cp is heat capacity at constant external pressure

Thermal Expansion and Stress

• Thermal expansion is the change in length of a solid material with temperature, expanding when heating and contracting when cooling
• Linear coefficient of thermal expansion (αt) indicates how much a material expands upon heating
  • units: (°C)⁻¹ or (°F)⁻¹
• Equation of thermal expansion:
• Metals: intermediate values from 5x10-6 to 25x10-6 (°C)-1
• Ceramics: low (0.5x10-6 to 15x10-6 (°C)-1) due to relatively strong interatomic bonding forces
• Polymers: very large (50x10-6 to 400x10-6 (°C)-1) due to weak intermolecular bonds

Thermal Conductivity

• Describes the transport heat from high to low temperature regions in a material
• Characterizes a material's ability to transfer heat, q = -k(dT/dx)
  • (-) sign indicates the heat flows down the temperature gradient
  • q = heat flow per unit time per unit area (W/m²)
  • k = thermal conductivity (W/m-K)
  • dT/dx = temperature gradient
• Thermal stress is induced in a body due to temperature change or as a result of restrained thermal expansion and contraction
  • Equation: σ = Eαt(T₀ - Tf ) = EαtΔT
• Upon heating, if Tf > T₀, stress is compressive (σ < 0)
• Upon cooling, if Tf < T₀, tensile stress is imposed (σ > 0)