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Creep: Time-Dependent Deformation

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Stress-Strain Behavior and Elastic PropertiesDiffusion in Solids+1 moreCreep Deformation at Elevated Temperatures
creep high-temperature tertiary-creep steady-state dislocation-climb

Core Idea

Creep is the slow, time-dependent plastic deformation of a material under constant stress at elevated temperatures (typically above ~0.4 Tm, where Tm is the melting temperature in Kelvin). A creep curve shows three stages: primary (decreasing strain rate as the material strain hardens), secondary/steady-state (constant minimum strain rate governed by balance of hardening and recovery), and tertiary (accelerating strain rate leading to fracture). Mechanisms include dislocation climb (aided by diffusion), grain boundary sliding, and vacancy diffusion. Creep is critical for designing turbine blades, boilers, and other high-temperature structural components.

How It's Best Learned

Plot creep curves for different stress levels and temperatures, observing how both accelerate creep rate. Apply the Arrhenius relationship to the steady-state creep rate to extract activation energy and compare with diffusion activation energies.

Common Misconceptions

Explainer

From your study of stress-strain behavior, you know that metals deform elastically (reversibly) below the yield stress and plastically (permanently) above it. Both of these responses happen almost instantaneously when the load is applied. Creep reveals a third type of deformation that your basic stress-strain curve ignores: time-dependent plastic flow that occurs even at stresses well below the yield stress, but only when the temperature is high enough. Apply a constant load to a turbine blade at 800°C, come back a week later, and it will be permanently longer — even though the stress never exceeded the yield point you measured at room temperature.

The temperature threshold for creep is not absolute but relative. The relevant parameter is the homologous temperature T/Tm (temperature as a fraction of the melting point in Kelvin). Creep becomes significant above roughly 0.4 Tm for metals. This explains why lead creeps at room temperature (Tm ≈ 600K, so 0.4Tm ≈ 240K, below room temperature) while steel requires several hundred degrees Celsius. Your prerequisite on the Arrhenius equation explains why: the mechanisms that drive creep — primarily dislocation climb and grain boundary sliding — require thermal activation. Dislocation climb involves dislocations absorbing or emitting vacancies to bypass obstacles, and vacancy diffusion has an activation energy that makes the process exponentially more active at higher temperatures.

A creep curve plots strain versus time under constant stress and temperature, and it shows three characteristic stages. In primary creep, strain rate decreases over time as the material work-hardens: dislocations accumulate and interfere with each other's motion, making further deformation increasingly difficult. In secondary (steady-state) creep, hardening and thermally-assisted recovery (annihilation of dislocations by climb) reach a dynamic equilibrium, producing a roughly constant minimum strain rate — this is the stage engineers care most about for life prediction. In tertiary creep, internal damage accumulates (grain boundary cavities, necking), hardening can no longer keep pace with damage, and the strain rate accelerates until fracture. The steady-state creep rate follows an Arrhenius form: ε̇ = A·σⁿ·exp(−Q/RT), where Q is the activation energy (often close to the activation energy for self-diffusion you learned in diffusion in solids, confirming that diffusion controls the mechanism).

For design, creep limits manifest as two failure modes: creep rupture (the component eventually fractures) and creep deformation (blade tip clearances close, seals leak, structures sag). Engineers combat creep through microstructural strategies — fine coherent precipitates pin dislocations (as in nickel superalloys used in jet engine turbines), large grain size or single-crystal structures eliminate grain boundaries, and refractory alloying elements raise the effective Tm. Understanding that larger grain size *helps* against creep (by eliminating grain boundary sliding sites) while it *hurts* against fatigue and fracture is one of the fundamental tradeoffs in high-temperature materials design.

Practice Questions 5 questions

Prerequisite Chain

Understanding ZeroThe Number ZeroCounting to FiveCounting to 10Counting to 20Counting a Set of Objects Up to 20Cardinality: The Last Number CountedMatching Numerals to QuantitiesSubitizing Small QuantitiesAddition Within 10Number Bonds to 10Addition Within 20Doubles and Near DoublesDoubles Facts Within 10Near Doubles Facts Within 20Mental Math Strategies for AdditionMental Math: Adding and Subtracting TensAddition Within 100Repeated Addition as MultiplicationMultiplication as Equal GroupsMultiplication: ArraysBasic Multiplication Facts (0s, 1s, 2s, 5s, 10s)Multiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Multiplication and Division Fact FamiliesRelationship Between Multiplication and DivisionDivision Facts as Inverse of MultiplicationRemainders and Quotients in DivisionDivision Word ProblemsMulti-Step Word ProblemsSolving Multi-Step Word ProblemsMultiplication Word ProblemsDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueIntegers and the Number LineComparing and Ordering IntegersAbsolute ValueAdding IntegersSubtracting IntegersMultiplying IntegersDividing IntegersUnit RatesProportionsPercent ConceptConverting Between Fractions, Decimals, and PercentsOperations with Rational NumbersTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionSine, Cosine, and Tangent RatiosTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIndefinite IntegralsBasic Integration RulesRiemann SumsDefinite Integral DefinitionDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsWork and CirculationLine Integrals of Scalar and Vector FunctionsFundamental Theorem for Line IntegralsConservative Vector FieldsConservative Vector Fields and Potential FunctionsCurl and Divergence of Vector FieldsCurl and DivergenceDivergence TheoremElectric Flux and Divergence TheoremGauss's Law: Integral Form and MeaningSolving Problems with Gauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesPostulates of Special RelativityTime DilationLength ContractionLorentz TransformationRelativistic Velocity AdditionRelativistic Momentum and EnergyMass-Energy Equivalence and E=mc²Photons as Particles with Energy and MomentumPlanck-Einstein Relation: Energy and FrequencyPhotoelectric EffectThe Photon: Light as QuantaCompton ScatteringWave-Particle Dualityde Broglie WavelengthThe Schrödinger EquationState Vectors and WavefunctionsQuantum SuperpositionQuantum EntanglementBell Theorem and Bell InequalitiesPostulates of Quantum MechanicsObservables and Quantum OperatorsCommutators and Commutation RelationsQuantum Angular MomentumQuantum Mechanical Treatment of HydrogenSolving the Schrödinger Equation for Hydrogen AtomQuantum NumbersElectron ConfigurationPeriodic TrendsCovalent BondingElectronegativity and Bond PolarityIonic BondingLewis StructuresVSEPR Theory and Molecular GeometryMolecular Geometry and Electron Pair GeometryMolecular Polarity and Dipole MomentsIntermolecular ForcesStates of Matter and Phase Changes: Melting, Boiling, and SublimationGas Laws and the Ideal Gas EquationGas Stoichiometry and Volume-Volume CalculationsThermochemistry and EnthalpyHeat Capacity and CalorimetryEntropy and Molecular DisorderSpontaneity and ΔGEntropy and Gibbs Free EnergyChemical EquilibriumStatistical Mechanics: Ensembles and the Boltzmann DistributionPartition Function: Definition and PropertiesThe Canonical Partition Function and Thermodynamic DerivationMaxwell-Boltzmann Distribution and Classical LimitTransport Properties of GasesDiffusion and Fick's LawsDiffusion in SolidsCreep: Time-Dependent Deformation

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