Engr 45: Fatigue, Creep, and Phase Diagrams

Vocabulary flashcards covering the concepts of fatigue, creep, and binary phase diagrams from Materials Science and Engineering lecture notes.

Rotating-Bending Beam Test

The most common mechanical test for evaluating fatigue, used to plot the maximum stress amplitude versus the number of cycles to failure ($N$).

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

The limiting stress amplitude below which fatigue failure will not occur regardless of the number of cycles ($S < S_{\text{fat}}$), typically ranging between $35\%$ and $60\%$ of the tensile strength.

Fatigue Strength

The stress level at which fatigue failure occurs for a specified, predetermined number of loading cycles.

Stages of Fatigue Failure

The three successive steps in fatigue failure: crack initiation (almost always starting from surface defects), crack propagation (involving plastic deformation at crack tips), and final failure.

Paris' Law

A relationship used to estimate fatigue crack growth: $\frac{da}{dN} = C(\Delta K)^m$, where $\frac{da}{dN}$ is the increase in crack length per cycle, $C$ and $m$ are material-specific constants (with $m$ typically ranging from $1$ to $6$), and $\Delta K \sim (\Delta\sigma)\sqrt{\pi a}$.

Shot Peening

A surface treatment that imposes residual compressive surface stresses onto a component to suppress surface cracks from initiating and growing, thereby improving fatigue life.

Creep

The time-dependent slow flow or deformation of a material subjected to mechanical stress below the yield strength ($\sigma < \sigma_y$) at elevated homologous temperatures ($T > 0.4 T_m$).

Primary Creep

The initial, transient stage of creep deformation during which the creep rate (slope of the strain-time curve) continuously decreases with time.

Secondary Creep

The steady-state stage of creep where the strain rate ($\dot{\varepsilon}_s$) remains constant because strain hardening is balanced by recovery.

Tertiary Creep

The final stage of creep deformation where the creep rate accelerates with time until rupture occurs, primarily by cavitation along grain boundaries.

Larson-Miller Parameter

A parameter ($m$) used to estimate the time to creep rupture ($t_r$), expressed by the equation $m = T(C + \log(t_r))$, where $T$ is temperature and $C$ is a material constant typically around $20$.

Component

A distinct chemical element or compound present in an alloy system or mixture, such as $\text{Al}$, $\text{Cu}$, or $\text{Ni}$.

Phase

A physically and chemically distinct, homogeneous region of a material system, conventionally denoted by Greek letters such as $\alpha$ and $\beta$.

Solubility Limit

The maximum concentration of solute that can dissolve in a solvent to form a single-phase solution before an additional phase precipitates.

Phase Diagram

A graphical map showing the equilibrium phases present in an alloy system as a function of temperature ($T$), composition ($C_0$), and pressure ($P$).

Hume-Rothery Rules

A set of empirical rules predicting solid solubility, stating that elements with the same crystal structure, similar electronegativities, and similar atomic radii have high mutual solubility (such as complete miscibility in the $\text{Cu-Ni}$ system).

Liquidus Line

The boundary line on a phase diagram above which only the equilibrium liquid phase ($L$) exists.

Solidus Line

The boundary line on a phase diagram below which only the equilibrium solid phase ($\alpha$) exists.

Tie Line

An isothermal horizontal line constructed across a two-phase region of a phase diagram to connect the equilibrium compositions of the coexisting phases.

Lever Rule

A mathematical method used to calculate the relative weight fraction or percentage of each phase in a two-phase field: $\text{Phase \%} = \frac{\text{opposite arm of lever}}{\text{total length of tie line}} \times 100$.

Isomorphous System

A two-component alloy system exhibiting complete liquid and solid solubility across all composition ranges from $0\,\text{wt}\%$ to $100\,\text{wt}\%$, such as the $\text{Cu-Ni}$ system.

Cored Structure

A non-equilibrium microstructural segregation within grains caused by fast cooling, where the first solid to form is enriched in the higher-melting-temperature element and subsequent layers have lower-melting compositions.

Equilibrium Structure

A homogeneous microstructure formed through sufficiently slow cooling that provides adequate diffusion time for uniform composition across each phase.

Binary Eutectic System

A two-component alloy system displaying limited solid solubility and containing a special composition with the lowest melting temperature of the entire system.

Eutectic Composition ($C_E$)

The specific alloy composition having the lowest melting point in a eutectic system, which solidifies at a single invariant temperature rather than across a melting range.

Eutectic Reaction

An invariant, isothermal reversible transition upon cooling where a liquid of eutectic composition freezes into two separate solid phases: $L(C_E) \rightleftharpoons \alpha(C_{\alpha E}) + \beta(C_{\beta E})$.