MENG 221: Materials Engineering - Failure, Fatigue, Creep, and Phase Diagrams

Vocabulary review flashcards covering ductile and brittle fracture, stress concentrations, fracture toughness, fatigue cycles and S-N curves, creep stages and kinetics, and binary isomorphous phase diagram concepts from MENG 221 Lessons 19 through 22.

Ductile Fracture

A mode of metal fracture characterized by substantial plastic deformation prior to breaking, occurring relatively slowly and displaying noticeable physical warning signs.

Brittle Fracture

A mode of metal fracture characterized by rapid and spontaneous crack propagation with little to no prior plastic deformation.

Cup-and-Cone Fracture

A characteristic ductile tensile fracture morphology where one mating half forms an indentation resembling a cup and the other forms a matching cone, indicative of necking and shear failure.

Chevron Markings

V-shaped fracture surface features typically observed in brittle fracture that point inward toward the crack initiation site.

Stress Raisers

Flaws, internal voids, sharp corners, or notches within a material that cause a localized amplification of applied stress near their periphery.

Stress Concentration Factor ($K_t$)

A dimensionless ratio of maximum localized tip stress to nominal applied stress, expressed for an elliptical crack as $K_t = \frac{\sigma_m}{\sigma_0} = 2\left(\frac{a}{\rho_t}\right)^{1/2}$, where $a$ is crack length and $\rho_t$ is tip radius of curvature.

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

A material property quantifying resistance to brittle fracture when a crack is present, measured under mode I opening conditions and thick-specimen plane-strain constraints.

Notch Toughness

A material's capacity to absorb mechanical energy during high-strain-rate impact loading before fracturing, commonly measured via Charpy and Izod tests.

Ductile-to-Brittle Transition Temperature (DBTT)

The temperature threshold below which a material undergoes a sharp change in failure mode from ductile, energy-absorbing fracture to catastrophic, low-energy brittle fracture.

Fatigue

A catastrophic mode of mechanical failure resulting from dynamic, fluctuating, or cyclic stresses, occurring at stress magnitudes well below a material's static tensile strength.

Reversed Stress Cycle

A cyclic loading state exhibiting a regular sinusoidal waveform that is symmetrical about zero stress, alternating between equal peak tensile and compressive stresses.

Repeated Stress Cycle

A sinusoidal cyclic loading mode that is asymmetrical about the zero-stress baseline, having unequal maximum and minimum stress values.

Random Stress Cycle

A loading sequence in which stress amplitude, frequency, and waveform fluctuate randomly over time without periodic symmetry.

Mean Stress ($\sigma_m$)

The algebraic average of the maximum and minimum stresses within a cyclic loading sequence, given by $\sigma_m = \frac{\sigma_{\max} + \sigma_{\min}}{2}$.

Stress Range ($\sigma_r$)

The algebraic difference between the highest and lowest stress values within a loading cycle, calculated as $\sigma_r = \sigma_{\max} - \sigma_{\min}$.

Stress Amplitude ($\sigma_a$)

One-half of the total stress range experienced in cyclic loading, defined by $\sigma_a = \frac{\sigma_r}{2} = \frac{\sigma_{\max} - \sigma_{\min}}{2}$.

Stress Ratio ($R$)

The dimensionless parameter calculated as the ratio of minimum stress to maximum stress in cyclic loading: $R = \frac{\sigma_{\min}}{\sigma_{\max}}$.

Fatigue Limit (Endurance Limit)

The limiting cyclic stress amplitude below which a material will theoretically endure an infinite number of load cycles without failing.

Fatigue Strength

The cyclic stress level at which fatigue failure is observed to occur after a specified number of cycles ($N$).

Fatigue Life ($N_f$)

The total cumulative number of stress cycles a component sustains under a specified cyclic stress amplitude before fracturing.

Corrosion Fatigue

A combined failure mechanism driven simultaneously by cyclic mechanical stresses and aggressive corrosive chemical attack from the operating environment.

Case Hardening

A surface-treatment process in which the surface layer of a steel component is enriched with carbon or nitrogen to increase hardness, induce compressive residual stresses, and retard fatigue crack initiation.

Creep

Time-dependent, permanent plastic deformation that takes place when a material is subjected to a constant mechanical load at elevated temperatures, typically exceeding $0.4\,T_m$ in metals.

Steady-State Creep Rate ($\dot{\varepsilon}_s$)

The constant rate of deformation with respect to time ($\frac{\Delta\varepsilon}{\Delta t}$) characteristic of the linear secondary stage of a creep strain versus time curve.

Rupture Lifetime ($t_r$)

The total elapsed duration from initial load application until final catastrophic mechanical separation in a creep test.

Activation Energy for Creep ($Q_c$)

The thermal energy barrier required to activate atomic diffusion mechanisms that mediate plastic flow during steady-state creep deformation.

Phase

A macroscopically homogeneous portion of a physical system possessing uniform physical and chemical attributes throughout its volume.

Solubility Limit

The maximum concentration of a solute component that can dissolve into a solvent phase at a specified temperature to create a single stable solution.

Phase Equilibrium

A thermodynamic state wherein the number, identities, compositions, and relative quantities of all coexisting phases remain invariant with time.

Liquidus Line

The boundary line on a phase diagram positioned above which all alloy mixtures exist exclusively as a homogeneous liquid ($L$) phase.

Solidus Line

The boundary line on a phase diagram positioned below which an alloy consists entirely of solid phase ($\alpha$).

Isomorphous System

A binary alloy system that demonstrates complete mutual solubility of both components in both the solid state and the liquid state across the entire composition range.

Tie Line

An isothermal horizontal line constructed across a two-phase equilibrium field on a phase diagram to identify the equilibrium chemical compositions of both coexisting phases.

Lever Rule

A mathematical relationship derived from mass balance principles utilized to calculate the relative mass fractions of two equilibrium phases within a two-phase field using tie-line segment lengths.