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Fatigue Behavior Under Cyclic Loading

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Yield Strength and Tensile PropertiesFatigue: Cyclic Loading and Failure→
fatigue stress-cycles s-n-curves endurance-limit

Core Idea

Fatigue is progressive damage accumulation and crack growth under cyclic loading, causing failure at stresses far below static yield strength. The S-N curve (stress vs. number of cycles) characterizes fatigue behavior, with many materials exhibiting an endurance limit below which they theoretically survive infinite cycles. Fatigue failure initiates at stress concentrations (notches, defects) and propagates through dislocation motion and microcrack coalescence.

Explainer

Static tensile testing, which you know from yield strength and tensile properties, measures a material's resistance to a single monotonically increasing load. Fatigue asks a fundamentally different question: what happens when a smaller stress is applied and removed thousands — or millions — of times? The answer is counterintuitive: materials fail at stresses well below the yield strength, through progressive, often invisible damage that accumulates until sudden fracture. A shaft that easily withstands a static load of 200 MPa may fracture after 10⁶ cycles at only 80 MPa.

The S-N curve (Wöhler curve) is the primary characterization tool. On a semi-log or log-log plot of applied stress amplitude S versus cycles to failure N_f, the curve slopes downward: higher stress amplitude produces fewer cycles to failure. For ferrous metals — steel and cast iron — the S-N curve typically flattens at high cycle counts, becoming horizontal at the endurance limit S_e (roughly 0.4–0.5 × tensile strength for steels). Below this stress, the material is assumed to survive indefinitely. Nonferrous metals (aluminum, titanium, copper alloys) show no true horizontal asymptote; their S-N curves continue declining, so fatigue design uses a fatigue strength at a specified life, typically 10⁷ or 10⁸ cycles. The engineering implication: for aluminum aircraft components, every cycle counts, and there is no stress low enough to guarantee infinite life.

Fatigue damage initiates at stress concentrations — locations where the local stress significantly exceeds the nominal (average section) stress. Notches, holes, fillet radii, weld toes, machining marks, and internal voids all act as stress raisers. The stress concentration factor K_t quantifies the amplification: if K_t = 2 and the nominal stress is 100 MPa, the local stress is 200 MPa. Fatigue responds to local stress, not nominal stress, so even a small K_t at a sharp notch can elevate local stress above the endurance limit while the bulk of the component remains elastic. This is why fatigue design focuses on surface finish, avoiding sharp corners, and minimizing geometric discontinuities — a smooth, polished specimen may have an endurance limit twice that of the same material with a notch.

Once a crack initiates (Stage I), it propagates under the tensile portion of each stress cycle (Stage II). Each cycle advances the crack tip by a small increment, leaving a characteristic beach mark or fatigue striation on the fracture surface — each striation corresponds to one cycle of crack advance, making striations visible evidence of cyclic loading history. Crack propagation continues until the remaining net section can no longer support the peak load in the cycle, at which point sudden final fracture (Stage III) occurs. The final fracture zone is rough and granular (typical of fast fracture), clearly distinguishable from the smooth, striated crack propagation zone. This fracture surface morphology is the forensic signature of fatigue failure and is the starting point of any failure analysis investigation involving cyclic loading.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → Quantum Entanglement → Bell Theorem and Bell Inequalities → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Covalent Bonding → Electronegativity and Bond Polarity → Ionic Bonding → Lewis Structures → Polar Covalent Bonds and Dipole Moments → Classification of Bonds: Ionic, Covalent, and Metallic → Metallic Bonding and Properties of Metals → Crystal Structures and Solid Properties → Crystal Structure and Unit Cells → Crystal Systems and Bravais Lattices → Miller Indices: Crystallographic Planes and Directions → Plastic Deformation and Slip Systems → Dislocation Types and Motion → Dislocation Motion and Slip Systems → Plastic Deformation and Yielding → Toughness, Ductility, and Brittle Behavior → Fracture Mechanics: Brittle and Ductile Failure → Fatigue: Cyclic Loading and Failure → Fatigue Behavior Under Cyclic Loading

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