Chapter 7: Mechanical Properties

Vocabulary practice flashcards covering mechanical properties of materials, stress-strain behavior, elastic and plastic deformation, tensile testing, and hardness measurements.

Engineering Stress ($\sigma$)

The instantaneous tensile force ($F_t$) applied normal to a specimen divided by its original cross-sectional area ($A_0$) prior to loading, expressed with the formula $\sigma = \frac{F_t}{A_0}$ in units of $N/m^2$.

Shear Stress ($\tau$)

The shear force ($F_s$) applied parallel to a plane divided by the original cross-sectional area ($A_0$), expressed with the formula $\tau = \frac{F_s}{A_0}$ in units of $N/m^2$.

Engineering Strain ($\epsilon$)

The change in length ($\Delta L$) of a specimen subjected to tensile stress divided by its original gauge length ($L_0$), given by $\epsilon = \frac{\Delta L}{L_0}$, which is a dimensionless quantity.

Shear Strain ($\gamma$)

The tangent of the shear displacement angle ($\theta$) produced under shear stress, expressed as $\gamma = \frac{\Delta x}{y} = \tan(\theta)$, which is a dimensionless quantity.

Elastic Deformation

A reversible deformation in which interatomic bonds stretch under a small applied load and return completely to their original positions upon unloading.

Plastic Deformation

A permanent deformation in which stress causes interatomic bonds to stretch and atomic planes to shear, leaving permanent strain ($\delta_{\text{plastic}}$) after the load is removed.

Modulus of Elasticity ($E$)

Also called Young's modulus; the constant of proportionality representing a material's stiffness, measured as the slope of the linear-elastic region of a stress-strain curve in units of $GPa$.

Hooke's Law

The linear relationship between stress and strain within the elastic deformation regime, expressed mathematically as $\sigma = E \epsilon$.

Elastic Shear Modulus ($G$)

The slope of shear stress versus shear strain in the linear elastic regime ($\tau = G \gamma$), which for isotropic materials relates to Young's modulus via $G = \frac{E}{2(1 + \nu)}$.

Poisson's Ratio ($\nu$)

The negative ratio of lateral strain ($\epsilon_L$) to axial tensile strain ($\epsilon$), expressed as $\nu = -\frac{\epsilon_L}{\epsilon}$, which is dimensionless with approximate values of $0.33$ for metals, $0.25$ for ceramics, and $0.40$ for polymers.

Yield Strength ($\sigma_y$)

The stress level at which noticeable plastic deformation occurs, conventionally measured in $MPa$ at a plastic strain offset of $\epsilon_p = 0.002$.

Tensile Strength ($TS$)

The maximum engineering stress on a stress-strain curve in $MPa$, corresponding to the onset of noticeable necking in metals or alignment and fracture of backbone chains in polymers.

Ductility

A measure of the degree of plastic deformation sustained by a material prior to fracture, quantified as percent elongation ($\%EL = \frac{L_f - L_0}{L_0} \times 100$) or percent reduction in area ($\%RA = \frac{A_0 - A_f}{A_0} \times 100$).

Toughness

The capacity of a material to absorb energy up to fracture per unit volume ($J/m^3$), represented geometrically by the total area under the engineering stress-strain curve.

Modulus of Resilience ($U_r$)

The capacity of a material to absorb energy per unit volume when deformed elastically and release it upon unloading ($J/m^3$), given by $U_r = \int_0^{\epsilon_y} \sigma\,d\epsilon \cong \frac{1}{2} \sigma_y \epsilon_y$.

True Stress ($\sigma_T$)

The applied load divided by the instantaneous cross-sectional area of a specimen, related to engineering stress and strain before necking by $\sigma_T = \sigma(1 + \epsilon)$.

True Strain ($\epsilon_T$)

The natural logarithm of the ratio of instantaneous length to original length, related to engineering strain by $\epsilon_T = \ln(1 + \epsilon)$.

Hardness

A measure of a material's resistance to localized permanent surface indentation or scratching, where smaller indentations denote higher hardness values.

Brinell Hardness ($HB$)

A hardness testing method using a $10\text{ mm}$ sphere indenter made of steel or tungsten carbide subjected to a load between $500$ and $3000\text{ kg}$, related to tensile strength by $TS\text{ (MPa)} = 3.45 \times HB$.

Rockwell Hardness Test

A hardness testing technique that uses minor ($10\text{ kg}$) and major ($60$, $100$, or $150\text{ kg}$) loads with a diamond cone or steel sphere indenter across calibrated scales (such as A, B, and C).

Factor of Safety ($N$)

A structural design factor, typically chosen between $1.2$ and $4$, used to calculate safe working stress from yield strength via $\sigma_{\text{working}} = \frac{\sigma_y}{N}$.