Langford Analytic · Knowledge Base
Fatigue & Damage Tolerance
How repeated loading creates progressive structural damage — from S–N and strain-life fatigue through cumulative damage, variable-amplitude loading, crack growth, fracture mechanics, residual strength and damage tolerance assessment. Advanced fracture coverage includes elastic-plastic fracture mechanics, J-integral and CTOD, constraint, mixed-mode loading, short-crack and closure behaviour, full-range crack-growth modelling, multiple-site damage, environment-assisted growth, welded-flaw assessment, fracture FEA and crack-arrest/fail-safe verification.
Fatigue Fundamentals
Fatigue FundamentalsHow repeated loading creates progressive structural damage even when individual loads remain below static strength limits.Cyclic Stress, Stress Range & Stress RatioUnderstanding the stress quantities that define a fatigue cycle and why maximum stress alone is not enough.S–N Fatigue AnalysisUsing stress-life data to estimate fatigue life under predominantly elastic cyclic loading.Mean Stress EffectsWhy fatigue behaviour depends upon both alternating and mean stress and how common correction methods are interpreted.Strain-Life & Low-Cycle FatigueAssessing fatigue where local cyclic plasticity makes strain-based methods more appropriate than conventional stress-life analysis.
Load History & Damage
Cumulative Damage & Miner’s RuleHow fatigue damage from different cyclic stress levels is combined and where linear damage accumulation becomes limited.Variable-Amplitude Loading & Load SpectraRepresenting the changing loads experienced in real operation rather than idealised constant-amplitude cycles.Rainflow Cycle CountingConverting complex stress histories into fatigue-relevant cycles with range, mean and occurrence information.Vibration Fatigue — Damage Tolerance PerspectiveHow dynamic stress response from harmonic or random vibration accumulates fatigue damage.
Local Detail & Manufacturing
Stress Concentrations, Notches & FatigueHow holes, fillets and geometric discontinuities alter local cyclic behaviour and fatigue performance.Surface Finish, Size & Manufacturing EffectsWhy the fatigue performance of a manufactured component can differ significantly from polished material-test data.Fatigue of Bolted & Mechanical JointsHow preload, joint stiffness, fastener holes, fretting and local load transfer influence joint fatigue.Fatigue FEA, Hot-Spots & Local Stress MethodsSelecting fatigue-relevant stress or strain from finite element models without simply using the highest numerical peak.
Fracture Mechanics & Crack Growth
Fracture Mechanics FundamentalsHow crack size, geometry, stress and material toughness determine the behaviour of an already-cracked structure.Stress Intensity Factor & Crack Driving ForceUnderstanding the parameters that describe crack-tip loading and control fracture and fatigue crack growth.Fatigue Crack GrowthHow cyclic loading extends an existing crack and how crack-growth rate changes as the crack develops.Residual Strength & Critical Crack SizeDetermining the remaining load capability of damaged structure and the crack size at which structural integrity becomes unacceptable.
Damage Tolerance & Substantiation
Damage Tolerance PhilosophyHow crack growth, residual strength and inspection are combined to manage structural defects safely.Inspection Intervals & Detectable Flaw SizeHow inspection capability and crack-growth behaviour influence allowable inspection intervals.From Load Spectrum to Life & Damage-Tolerance SubstantiationTurning operational loads, structural analysis, material data and crack-growth behaviour into a traceable fatigue assessment.
Advanced Fracture Mechanics
Elastic-Plastic Fracture Mechanics — J, CTOD & R-CurvesHow J-integral, CTOD and tearing-resistance curves extend fracture assessment beyond small-scale yielding, and how to decide when stable tearing can or cannot be credited.Fracture Constraint, Thickness & Crack-Tip TriaxialityWhy the same material can appear to have different fracture resistance in thin and thick sections, shallow and deep cracks, and low- versus high-constraint geometries.Mixed-Mode Fracture & Crack-Path AssessmentHow combined opening, sliding and tearing modes affect crack driving force, propagation direction and structural interpretation when Mode I alone is insufficient.Short Cracks, Crack Closure & Threshold BehaviourWhy small cracks can grow faster than long-crack data predict, how closure affects effective ΔK and how threshold assumptions should be used in damage-tolerance assessments.Advanced Fatigue Crack-Growth Models & Sequence EffectsHow Walker-, Forman- and closure/retardation-type models extend Paris-law growth for stress-ratio effects, near-fracture acceleration and variable-amplitude sequence effects.
Damage Tolerance & Advanced Assessment
Multiple-Site Damage, Crack Interaction & CoalescenceHow nearby cracks change one another’s driving force, when separate flaws must be treated as interacting, and how widespread fatigue damage can erode fail-safe assumptions.Environment-Assisted Crack Growth in Damage-Tolerance AssessmentHow stress-corrosion, hydrogen-assisted and corrosion-fatigue growth are incorporated into fracture and life assessment without duplicating the underlying corrosion chemistry.Fracture Assessment of Welded Structures & Residual StressHow weld geometry, HAZ toughness, residual stress, misalignment and flaw location combine in fracture and damage-tolerance assessment of welded structures.Fracture Mechanics FEA — Contour Integrals, Crack Fronts & Mesh VerificationHow to build and verify cracked finite-element models for K, J and mixed-mode parameters without confusing numerical convergence with physical correctness.Crack Arrest, Fail-Safe Load Paths & Residual-Strength VerificationHow structural details can stop or redirect cracking, how alternate load paths are verified after damage, and why crack arrest must be substantiated rather than assumed.