Material Science: Properties, Bonding, and Mechanics

Vocabulary practice flashcards covering material design constraints, thermal behavior, interatomic bonding curves, and mechanical stress-strain relations.

Cost

The amount of money required to manufacture and deliver a product to the consumer.

Price

The amount a consumer pays for a product, determined by supply and demand, commodity speculation, geopolitical influences (such as tariffs), cost to produce, scarcity of raw materials, and strategic importance.

Value

What a product is worth to the consumer, adhering to the standard economic hierarchy: $\text{Cost} < \text{Price} < \text{Value}$.

Materials Science Paradigm

The framework describing the relationship: $\text{Process} \rightarrow \text{Structure} \rightarrow \text{Properties} \rightarrow \text{Performance}$, where microstructure and atomic structure govern the material properties.

Hybrids (Composites)

A class of materials made of a mixture of two or more distinct materials whose properties can be tailored, typically more expensive, with density calculated as $\rho = \rho_1 f_1 + \rho_2 f_2$.

Archimedes' Principle

The principle stating that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced, enabling density determination via $\rho = \rho_{\text{fluid}} \frac{m_1}{m_1 - m_2}$, where $m_1$ is the mass in air and $m_2$ is the mass in fluid.

Sensible Heat

Heat energy transferred to or from a body that is associated with a change in temperature and results in the vibration of atoms.

Latent Heat

Heat energy transferred during a phase change that alters the entropy (randomness of atomic arrangement) of a material without changing its temperature.

Equilibrium Interatomic Distance

The interatomic separation distance where the net force between two adjacent atoms equals zero ($F_{\text{net}} = F_{\text{att}} + F_{\text{rep}} = 0$), corresponding to the minimum potential energy.

Bond Strength

A property determined by the peak of the interatomic net force curve or the depth of the potential energy well; stronger bonds lead to lower coefficient of thermal expansion, higher Young's modulus, and higher melting temperature.

Bond Stiffness

A measure of the energy required to overcome the restoring force and displace an atom from equilibrium, indicated by the steepness of the slope of the force curve at $F = 0$ and the depth of the energy trough.

Thermal Expansion (Atomic Potential Well Model)

Expansion resulting from the asymmetry of the potential energy trough; as thermal energy increases, atoms vibrate between $r_{\min}$ and $r_{\max}$, shifting the average interatomic distance to higher values: $r_T = \frac{r_{\min} + r_{\max}}{2}$.

Coefficient of Thermal Expansion ($\alpha$)

A measure of how much a material expands when heated, defined by the relationship $\Delta L = L_0 \alpha \Delta T$.

Phonon

A quantum of thermal vibration propagating as an elastic wave at the speed of sound ($c_s = \sqrt{\frac{E}{\rho}}$) through the crystal lattice of a solid.

Mean Free Path ($\ell_m$)

The average distance a heat carrier (such as a phonon or free electron) travels between scattering events from imperfections (vacancies, impurities, or grain boundaries); longer mean free paths result in higher thermal conductivity.

Homologous Temperature Scale ($T_H$)

A dimensionless temperature scale defined as $T_H = \frac{T}{T_m}$, which normalizes a material's actual temperature by its absolute melting temperature to allow direct comparison of temperature-dependent behaviors.

Steady-State Heat Transfer

A thermal condition where the temperatures of atoms throughout a material remain constant over time while heat continuously flows at a uniform rate described by Fourier's law.

Transient Heat Transfer

A time-dependent, two-stage thermal process during which the temperatures of atoms change over time as heat is transmitted to colder atoms and raises the internal energy of the material.

Normal Stress ($\sigma$)

The intensity of internal force acting perpendicular to the surface of a cross-sectional area, defined as $\sigma = \frac{F}{A_0}$ in units of Pascals ($\text{Pa}$).

Shear Stress and Strain

Mechanical responses produced when a force acts parallel to a surface, where shear stress is $\tau = \frac{F}{A_0}$ and shear strain is $\gamma = \frac{\Delta x}{y}$.

Hydrostatic Stress ($p$)

A stress state resulting from equal normal forces exerted in three orthogonal directions by a fluid at rest, defined as $p = -\frac{F}{A}$ (negative because it is compressive).

Hydrostatic Strain (Dilation, $\Delta$)

The unitless volumetric strain produced under hydrostatic pressure, defined as $\Delta = \frac{\Delta V}{V_0}$.

Bending

A mode of loading where a transverse load is applied perpendicular to the longitudinal axis of a member, causing compressive stress on one face, tensile stress on the opposing face, and shear throughout the cross section.

Engineering Stress-Strain Curve

A curve plotting tensile stress against strain that identifies elastic modulus ($E$), yield strength ($\sigma_y$), $0.1\%$ proof stress ($\sigma_{0.1\%}$), tensile strength ($\sigma_{TS}$), the onset of necking, and fracture strain ($\varepsilon_f$).

Tensile Test Specimen

A standardized test sample designed with enlarged grip ends, smooth transition shoulder fillets (e.g., $10\,\text{mm R}$) to avoid stress concentrations, and a reduced gauge length (e.g., $50\,\text{mm}$) where elongation is recorded.

Free Variable (Material Selection)

A geometric or design variable that is not strictly constrained and is shared between the objective and constraint equations, allowing it to be algebraically eliminated to formulate a material performance index.