Materials Science: Failure, Diffusion, and Strengthening Mechanisms

Vocabulary practice flashcards covering material failure, fracture mechanics, solid-state diffusion, and dislocation-based strengthening mechanisms.

Simple Fracture

The separation of a solid body into two or more pieces in response to a static applied stress.

Ductile Fracture

A mode of fracture characterized by slow crack propagation, substantial plastic deformation, high energy absorption, and visible warning prior to ultimate failure.

Brittle Fracture

A mode of fracture characterized by rapid crack propagation, little or no gross plastic deformation, and catastrophic failure without warning.

Cup-and-Cone Fracture

A distinctive fracture surface morphology observed in moderately ductile materials loaded in tension, consisting of an initial fibrous interior flat fracture and outer 45° shear lips.

Chevron Markings

V-shaped, fan-like ridges on brittle fracture surfaces that point back along the path of crack propagation toward the origin or crack initiation site.

Transgranular Fracture

A brittle fracture mechanism in which crack propagation cuts directly through individual crystal grains along specific crystallographic cleavage planes.

Intergranular Fracture

A brittle fracture mechanism characterized by crack propagation proceeding along the grain boundaries of a polycrystalline material.

Stress Concentration Factor ($K_t$)

The ratio of the maximum localized stress at a crack tip ($\sigma_m$) to the nominal applied macroscopic tensile stress ($\sigma_0$), expressed as $K_t = \frac{\sigma_m}{\sigma_0} = 2\left(\frac{a}{\rho_t}\right)^{1/2}$.

Critical Stress for Crack Propagation ($\sigma_c$)

The threshold applied stress required to cause rapid crack propagation in a brittle material containing a flaw of half-length $a$, given by $\sigma_c = \left(\frac{2 E \gamma_s}{\pi a}\right)^{1/2}$.

Fracture Toughness ($K_c$)

A mechanical property that measures a material's resistance to brittle fracture when a crack is present, defined as $K_c = Y \sigma_c \sqrt{\pi a}$.

Plane Strain Fracture Toughness ($K_{Ic}$)

The fundamental fracture toughness value measured under plane-strain conditions (specimen thickness much greater than crack dimensions) for tensile opening Mode I loading.

Charpy Impact Test

A dynamic impact test in which a weighted pendulum strikes a notched specimen to measure absorbed impact energy based on the height difference between swing release ($h$) and swing follow-through ($h'$).

Ductile-to-Brittle Transition Temperature (DBTT)

The critical temperature range exhibited by BCC metals (such as iron at $T < 914\,^\circ\text{C}$) and some polymers below which energy absorption drops sharply, causing normally ductile materials to fail in a brittle manner.

Fatigue

A form of material failure that occurs after repeated or cyclic stress fluctuations, often taking place at stress amplitudes below the yield strength ($\sigma_{\max} < \sigma_y$) and accounting for ~90% of mechanical engineering failures.

Fatigue Limit ($S_{\text{fat}}$/Endurance Limit)

The threshold stress amplitude ($S$) below which a material (such as steel) can withstand an infinite number of load cycles without experiencing fatigue failure.

Fatigue Life ($N_f$)

The total number of cyclic stress cycles required to cause fatigue failure of a material at a specified stress amplitude level.

Shot Peening

A surface treatment in which small round particles are fired at high velocity against a metal component to generate a plasticized outer layer with compressive residual stresses that suppress surface fatigue crack propagation.

Creep

Time-dependent permanent plastic deformation of a material subjected to a constant mechanical load or stress at elevated temperatures ($T > 0.4 T_m$ in Kelvin).

Secondary Creep

The intermediate steady-state stage of creep characterized by a constant minimum creep rate ($\dot{\varepsilon}_s = \frac{\Delta\varepsilon}{\Delta t}$), occurring because strain hardening is balanced by dynamic recovery.

Larson-Miller Parameter ($m$)

A time-temperature parameter defined as $m = T(C + \log t_r)$ (where $C \approx 20$) used to predict and extrapolate long-term creep rupture lifetime ($t_r$) from accelerated short-term, elevated-temperature tests.

Diffusion

The phenomenon of mass transport within solid, liquid, or gaseous matter governed by spontaneous, stepwise atomic motion.

Vacancy Diffusion

A solid-state diffusion mechanism where host or substitutional impurity atoms interchange lattice sites with adjacent vacant positions, depending on vacancy concentration and activation energy.

Interstitial Diffusion

A diffusion mechanism where relatively small solute atoms migrate directly between neighboring interstitial void sites within a host crystal lattice, occurring much faster than vacancy diffusion.

Case Hardening

An industrial diffusion treatment where carbon atoms are introduced into the outer surface layer of steel components at elevated temperatures to form a hard, wear-resistant case with fatigue-suppressing residual compressive stresses.

Doping

A processing technique involving the thermal diffusion of trace impurity atoms (such as phosphorus) into high-purity silicon to tailor its electrical and semiconductor characteristics.

Diffusion Flux ($J$)

The rate of mass transfer defined as the mass (or moles) of a substance diffusing perpendicularly through a unit cross-sectional area per unit of time: $J = \frac{M}{A t} = \frac{1}{A}\frac{dM}{dt}$.

Fick's First Law

The equation governing steady-state diffusion stating that diffusion flux is directly proportional to the spatial concentration gradient: $J = -D \frac{dC}{dx}$.

Concentration Gradient

The spatial rate of change of concentration with respect to position or distance ($\frac{dC}{dx}$), which acts as the driving chemical force for diffusion.

Diffusion Coefficient ($D$)

A kinetic rate constant representing the diffusivity of a species, which increases exponentially with temperature according to $D = D_0 \exp\left(-\frac{Q_d}{R T}\right)$.

Activation Energy for Diffusion ($Q_d$)

The threshold thermal energy barrier (expressed in $\text{J/mol}$ or $\text{eV/atom}$) required to activate the motion of one mole of atoms from one equilibrium site to another.

Fick's Second Law

The partial differential equation describing non-steady state diffusion in which concentration changes as a function of both time and spatial position: $\frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}$.

Gaussian Error Function ($\text{erf}(z)$)

A mathematical function used to solve Fick's second law for a semi-infinite solid with constant surface concentration, given by $\frac{C(x,t) - C_0}{C_s - C_0} = 1 - \text{erf}\left(\frac{x}{2\sqrt{D t}}\right)$.

Slip

The microscopic mechanism of plastic deformation in crystalline solids occurring via the stepwise motion of dislocations along specific crystallographic slip planes.

Slip Plane

The crystallographic plane along which dislocation slip occurs most easily, generally corresponding to the plane with the highest planar atomic packing density.

Slip Direction

The specific crystallographic direction within the slip plane along which dislocations move most readily, corresponding to the direction with the highest linear atomic packing density.

Slip System

The geometric pairing of a slip plane and a slip direction; in FCC metals, slip occurs on $\left\{111\right\}$ planes along $\langle 110\rangle$ directions, yielding a total of 12 independent slip systems.

Resolved Shear Stress ($\tau_R$)

The shear stress component acting on a designated slip plane and along a slip direction resulting from an applied tensile stress ($\sigma$), defined as $\tau_R = \sigma \cos(\lambda) \cos(\phi)$.

Critical Resolved Shear Stress ($\tau_{\text{CRSS}}$/$\tau_{\text{crss}}$)

The minimum shear stress required to initiate dislocation slip on the most favorably oriented slip system of a crystal, dictating the single-crystal yield strength as $\sigma_y = \frac{\tau_{\text{CRSS}}}{(\cos\lambda \cos\phi)_{\max}}$.

Hall-Petch Equation

The mathematical relationship describing grain size strengthening, stating that yield strength increases as average grain diameter ($d$) decreases: $\sigma_{\text{yield}} = \sigma_0 + k_y d^{-1/2}$.

Solid-Solution Strengthening

A strengthening mechanism in which impurity atoms (substitutional or interstitial) produce localized lattice strain fields that interact with and pin dislocation stress fields, raising the stress required for slip.

Precipitation Strengthening

The strengthening of an alloy achieved by precipitating fine, dispersed second-phase particles (such as intermetallics or ceramics) that act as pinning obstacles to gliding dislocations.

Strain Hardening (Cold Working)

The phenomenon whereby a ductile metal becomes stronger and harder as it plastically deforms at temperatures below its recrystallization temperature due to a dramatic increase in dislocation density and mutual repulsive dislocation interactions.

Dislocation Density ($\rho_d$)

The total length of dislocations per unit volume of material, which increases from $10^5 \text{--} 10^6\,\text{mm}^{-2}$ in annealed metals to $10^9 \text{--} 10^{10}\,\text{mm}^{-2}$ in heavily cold-worked metals.

Recovery

The initial stage of annealing cold-worked metals ($100 \text{--} 200\,^\circ\text{C}$) during which internal strain energy and dislocation density are reduced through atomic diffusion, dislocation climb, and dislocation annihilation.

Recrystallization

The second stage of annealing ($200 \text{--} 500\,^\circ\text{C}$) involving the nucleation and growth of new, strain-free, equiaxed grains with low dislocation density that consume and replace the cold-worked grain structure.

Recrystallization Temperature ($T_R$)

The temperature at which recrystallization just reaches completion within 1 hour, typically falling between $0.3 T_m$ and $0.6 T_m$ and decreasing with increasing cold work (%CW) or higher metal purity.

Grain Growth

The final stage of annealing ($> 500\,^\circ\text{C}$) where the average grain size increases over time as larger grains consume smaller grains to minimize the total grain boundary surface area and energy according to $d^n - d_0^n = K t$.

Hot Working

Mechanical plastic deformation carried out above a metal's recrystallization temperature ($T > T_R$), allowing recovery and recrystallization to occur continuously during deformation without strain hardening.