Electronics Guide

Stress-Life Approach

The stress-life (S-N) approach represents the oldest and most widely used fatigue analysis method, relating applied stress amplitude to the number of cycles until failure. S-N curves, developed through extensive testing of material specimens, plot stress amplitude against cycles to failure on logarithmic scales. For ferrous metals, these curves often exhibit an endurance limit below which infinite life is theoretically possible; non-ferrous metals typically show continued strength reduction even at very high cycle counts.

Applying S-N data to real components requires accounting for factors that differ from laboratory test conditions. Surface finish, size effects, loading type, temperature, and reliability requirements all modify the baseline S-N curve. Modification factors quantify these effects, reducing the allowable stress amplitude from test specimen values to those appropriate for actual component conditions. Conservative factor selection ensures adequate safety margins for critical applications.

Variable amplitude loading, typical in service conditions, complicates fatigue analysis because different stress levels contribute differently to damage accumulation. Miner's rule provides a simple damage summation approach, treating damage as linearly additive regardless of load sequence. While Miner's rule has known limitations, particularly for load sequences where high stresses precede low stresses, its simplicity makes it the standard starting point for variable amplitude fatigue analysis.

Strain-Life Approach

The strain-life approach addresses low-cycle fatigue where plastic deformation occurs during each loading cycle. This regime, typically below 10,000 cycles to failure, characterizes highly loaded components such as pressure vessel nozzles, turbine blade roots, and structural joints. The strain-life method separates total strain into elastic and plastic components, each following distinct relationships with fatigue life.

The Coffin-Manson relationship describes plastic strain amplitude versus cycles to failure, while Basquin's equation handles the elastic strain component. Combining these relationships yields the total strain-life curve, enabling prediction across the entire fatigue regime from low-cycle plastic-dominated failure to high-cycle elastic-dominated failure. Material constants for these equations derive from strain-controlled fatigue testing under fully reversed loading conditions.

Mean stress effects significantly influence strain-life predictions. Tensile mean stresses reduce fatigue life by holding cracks open, while compressive mean stresses extend life by keeping cracks closed. The Morrow and Smith-Watson-Topper (SWT) parameter methods incorporate mean stress effects into strain-life calculations, with the SWT approach generally providing better predictions for materials sensitive to mean stress.

Cycle Counting Methods

Rainflow counting is the standard method for extracting fatigue cycles from complex service loading histories. The algorithm identifies closed hysteresis loops in the stress-strain response, extracting the range and mean stress of each cycle. Named for its resemblance to rain flowing down pagoda roofs, the method correctly handles loading sequences where small cycles are superimposed on larger cycles, a common occurrence in service loading.

Implementation of rainflow counting requires decisions about range pairing rules and residual handling. The three-point and four-point algorithms represent the most common implementations, differing in how they pair range extremes. Residual cycles remaining after processing the main history require special treatment, typically by repeating the history or applying conservative assumptions about the worst-case completion of partial cycles.

Alternative counting methods serve specific applications. Level crossing counting and peak counting provide simpler approaches suitable for preliminary analysis. Range-mean counting directly extracts the information needed for fatigue calculations. The choice of counting method can significantly affect predicted fatigue life, making consistency between analysis and validation testing essential.

Linear Elastic Fracture Mechanics

Linear elastic fracture mechanics (LEFM) characterizes crack behavior in materials where plastic deformation remains confined to a small region near the crack tip. The stress intensity factor K quantifies the stress field surrounding a crack, depending on applied stress, crack size, and component geometry. When K reaches the material's fracture toughness KIC, unstable crack propagation occurs, leading to sudden failure.

Stress intensity factor solutions exist for numerous standard geometries including through cracks, surface cracks, corner cracks, and embedded cracks in plates, cylinders, and other shapes. Handbooks compile these solutions as functions of crack dimensions and component geometry. For complex geometries, finite element analysis with specialized crack tip elements provides accurate stress intensity factor calculations.

LEFM validity requires that plastic zone size remains small compared to crack length, component thickness, and distance to boundaries. The small-scale yielding requirement typically limits LEFM applicability to high-strength materials or large components. When plastic zone size becomes significant, elastic-plastic fracture mechanics methods such as J-integral or crack tip opening displacement (CTOD) approaches become necessary.

Fatigue Crack Growth

Fatigue crack growth analysis predicts how long a crack will take to grow from an initial size to a critical size causing fracture. The Paris law relates crack growth rate da/dN to stress intensity factor range, with material constants C and m determined through testing. This power-law relationship applies in the stable crack growth regime, Region II of the crack growth curve, where growth rate depends primarily on stress intensity factor range.

Below a threshold stress intensity factor range, cracks grow at negligible rates or arrest entirely. This threshold behavior has significant implications for damage tolerance design, as cracks below threshold may be safely left in service indefinitely. Above the Paris regime, crack growth accelerates as the maximum stress intensity factor approaches fracture toughness, leading to rapid failure. Complete crack growth analysis must address all three regions.

Mean stress effects in crack growth are characterized by the stress ratio R, the ratio of minimum to maximum stress intensity factor. Higher R ratios typically produce faster crack growth at the same stress intensity factor range. The Walker equation and other modifications to the Paris law account for R-ratio effects, improving prediction accuracy across different loading conditions.

Damage Tolerance Design

Damage tolerance design philosophy assumes that cracks or crack-like defects exist in all structures and demonstrates that these flaws will not grow to critical size during the inspection interval. This approach, mandatory in aircraft structures since the 1970s, requires characterizing initial flaw sizes, predicting crack growth under service loading, establishing inspection intervals, and demonstrating that critical crack sizes exceed those expected at inspection.

Initial flaw size assumptions significantly impact damage tolerance analysis results. For metallic structures, initial flaws typically represent the largest defect likely to escape detection during manufacturing inspection. Non-destructive inspection capability determines detectable flaw sizes, which in turn establish analysis starting points. Conservative assumptions about initial flaw size provide margin for inspection variability and unusual defect configurations.

Inspection interval determination balances safety, inspection cost, and operational availability. Intervals must ensure that cracks remain detectable and well below critical size, providing two opportunities for detection before failure. The factor of two on growth life provides margin for analysis uncertainties, inspection reliability, and the possibility that damage may begin growing between inspections. Risk-based approaches optimize intervals by considering failure consequences and detection probability.

Wear Mechanisms

Adhesive wear occurs when contacting surfaces form localized bonds that subsequently shear, transferring material between surfaces. This mechanism dominates when similar metals slide against each other without adequate lubrication. The Archard wear equation relates wear volume to normal load, sliding distance, and material hardness, providing a framework for estimating adhesive wear rates. Surface treatments, coatings, and proper lubricant selection minimize adhesive wear.

Abrasive wear results from hard particles or asperities plowing through softer surfaces. Two-body abrasion occurs when a hard rough surface slides against a softer one; three-body abrasion involves loose hard particles between surfaces. Abrasive wear rates depend on particle hardness, shape, and size relative to surface hardness. Hardening surfaces, filtering contaminants from lubricants, and using wear-resistant materials combat abrasive wear.

Erosive wear occurs when particles impacting a surface cause material removal. Impact angle, particle velocity, particle properties, and target material characteristics determine erosion rates. Ductile materials suffer maximum erosion at shallow impact angles where particles cut and plow; brittle materials erode fastest at normal impact where cracks form and intersect. Erosion-resistant designs minimize particle impingement or use appropriate materials for expected impact conditions.

Surface fatigue wear develops under repeated contact loading, producing pitting and spalling as subsurface cracks propagate to the surface. This mechanism limits life in rolling element bearings, gears, and cams where high contact stresses cycle repeatedly. Contact fatigue life depends on applied loads, material fatigue properties, surface finish, lubrication, and contamination. Proper design maintains contact stresses below levels causing unacceptable fatigue damage.

Lubrication Principles

Hydrodynamic lubrication separates surfaces with a continuous fluid film generated by relative motion and geometry. The converging gap between surfaces draws lubricant into the contact zone, building pressure that supports applied loads. Film thickness depends on speed, viscosity, load, and geometry, with thicker films providing better surface separation. Journal bearings, thrust bearings, and slider bearings operate primarily in the hydrodynamic regime.

Elastohydrodynamic lubrication (EHL) occurs in concentrated contacts such as rolling element bearings and gear teeth where high contact pressures cause elastic deformation of the surfaces and dramatic increase in lubricant viscosity. Despite apparent metal-to-metal contact geometry, thin EHL films form that provide effective separation. EHL film thickness depends on speed, lubricant properties, and material elastic properties, with typical values measured in micrometers.

Boundary lubrication operates when conditions prevent full fluid film formation, leaving surfaces separated only by molecular layers of lubricant or additives. This regime occurs during starting, stopping, and at low speeds or high loads. Boundary lubricant additives form protective surface films that reduce friction and wear when metal contact occurs. Extreme pressure additives react chemically with surfaces under high contact stress to prevent seizure and severe wear.

Mixed lubrication represents the transition between hydrodynamic and boundary regimes, where partial fluid film supports some load while asperity contact carries the remainder. Most machine elements operate in mixed lubrication during portions of their operating cycle. Surface roughness, combined with hydrodynamic and boundary film properties, determines mixed lubrication performance. Surface engineering and lubricant optimization improve mixed regime operation.

Surface Engineering

Surface hardening processes increase near-surface hardness to improve wear resistance while maintaining tough, ductile cores for impact resistance. Carburizing diffuses carbon into steel surfaces followed by quenching to form hard martensite. Nitriding produces hard nitride layers without requiring quenching, minimizing distortion. Induction hardening and flame hardening provide localized surface hardening for specific wear areas.

Coating technologies apply wear-resistant materials to component surfaces. Hard chrome plating provides excellent wear resistance for hydraulic cylinders and similar applications. Thermal spray coatings apply metallic, ceramic, or cermet materials for wear, corrosion, or thermal protection. Physical vapor deposition (PVD) and chemical vapor deposition (CVD) produce thin, hard coatings for cutting tools and precision components.

Surface texture engineering optimizes roughness, waviness, and lay for tribological performance. Smoother surfaces generally reduce wear and friction but may lose lubricant retention capability. Deliberate texturing with pockets or grooves can improve lubrication by providing lubricant reservoirs and generating hydrodynamic pressure. Surface engineering integrates hardening, coating, and texturing to achieve optimal tribological performance.

Rolling Element Bearing Life

Rolling element bearing life prediction uses the basic rating life calculation from ISO 281, relating life to the ratio of dynamic load rating to applied load raised to a power. The exponent is 3 for ball bearings reflecting point contact fatigue, and 10/3 for roller bearings with line contact. This L10 life represents the number of revolutions at which 10% of a population would fail, with 90% surviving.

The basic rating life calculation assumes specific operating conditions that rarely match actual applications. The modified rating life calculation applies adjustment factors for reliability levels other than 90%, for material and processing improvements over reference bearings, and for lubrication and contamination conditions. These factors can extend calculated life by factors of 10 or more compared to basic rating life.

Lubrication quality critically affects bearing life. The viscosity ratio compares actual lubricant viscosity at operating temperature to the minimum required for adequate film formation. Viscosity ratios above 1 indicate full film lubrication with potential for extended life; values below 1 indicate boundary lubrication with reduced life. Contamination particles in the lubricant cause surface damage that initiates fatigue, making filtration and sealing essential for long life.

Plain Bearing Analysis

Plain bearing design ensures adequate hydrodynamic film formation while managing heat generation, wear, and stability. The Sommerfeld number combines speed, viscosity, load, and geometry into a dimensionless parameter that determines bearing performance characteristics. Design charts relate Sommerfeld number to minimum film thickness, friction coefficient, oil flow, and temperature rise, enabling rapid bearing sizing.

Minimum film thickness must exceed the combined surface roughness of shaft and bearing to prevent metal contact. Design minimum film thickness of three to four times composite surface roughness provides margin for manufacturing variations and transient conditions. Insufficient film thickness leads to boundary lubrication, elevated friction, heat generation, and accelerated wear.

Bearing materials must accommodate the sliding contact that occurs during starting, stopping, and boundary lubrication conditions. Babbitt alloys provide excellent embedability for contaminants and conformability to shaft misalignment but have limited load capacity and temperature capability. Bronze alloys offer higher strength for more demanding applications. Polymer and composite materials serve in applications requiring self-lubrication or chemical resistance.

Bearing Failure Analysis

Contact fatigue manifests as pitting or spalling on rolling element and raceway surfaces. Subsurface-initiated fatigue begins at inclusions or microstructural irregularities below the surface, propagating until material flakes away. Surface-initiated fatigue results from surface damage caused by contamination, inadequate lubrication, or handling damage. Examination of fatigue spall characteristics reveals whether failure originated at surface or subsurface.

Wear patterns on bearing surfaces indicate operating conditions and failure causes. Abrasive wear from contamination produces scratched, polished surfaces. Adhesive wear from inadequate lubrication creates material transfer and surface damage. Corrosive wear from moisture or chemical attack shows etched or pitted surfaces. Electrical discharge damage from stray currents produces characteristic cratering patterns.

Systematic bearing failure analysis examines operating conditions, maintenance history, lubricant condition, and physical evidence to identify root causes. Visual examination categorizes damage type and location; metallurgical analysis reveals material condition and damage mechanisms; lubricant analysis indicates contamination and degradation. Effective analysis prevents recurrence by addressing root causes rather than symptoms.

Gear Tooth Bending Fatigue

Gear tooth bending fatigue occurs when cyclic root stresses exceed material fatigue strength. The Lewis equation provides basic bending stress calculation, treating the tooth as a cantilever beam loaded at its tip. Modern gear rating standards such as AGMA 2001 and ISO 6336 refine this approach with geometry factors accounting for load sharing, stress concentration, and actual load position during mesh engagement.

Dynamic effects increase tooth loads above those calculated from transmitted torque. Gear quality grade determines profile and spacing errors that cause velocity variations and impact loading. The dynamic factor relates actual tooth loads to ideal smooth-running loads, with higher quality gears experiencing lower dynamic factors. Proper gear accuracy specification balances cost against dynamic load reduction.

Material and heat treatment selection determines allowable bending stress. Case-hardened gears achieve the highest strength through hard, fatigue-resistant surfaces with tough cores. Through-hardened gears offer simpler processing for moderate-duty applications. Material grade factors in rating standards account for cleanliness and quality variations between material sources and processing methods.

Gear Tooth Surface Durability

Surface durability, or pitting resistance, limits gear capacity when contact stresses cause fatigue of tooth surfaces. Hertzian contact stress calculation determines the maximum stress at the pitch line, where pure rolling occurs, and at points of sliding contact along the tooth profile. Pitting typically initiates in regions of combined high contact stress and sliding, particularly in the dedendum where sliding opposes rolling.

Surface hardness, finish, and lubrication determine allowable contact stress. Harder surfaces support higher contact stresses without fatigue damage. Smoother surfaces distribute contact over larger areas, reducing peak stresses. Adequate EHL film thickness separates surfaces, eliminating metal contact and extending surface life. Rating standards incorporate these factors through material, surface condition, and lubrication factors.

Micropitting represents a surface distress mode becoming increasingly important as gear designs push performance boundaries. Fine surface pitting in regions of high sliding creates frosted appearance and can progress to macro-pitting or tooth profile degradation. Proper lubricant selection, including appropriate additive packages, and controlled surface roughness minimize micropitting risk.

Gear System Reliability

Gear system reliability encompasses not just individual gear pair life but also bearing life, lubrication system reliability, housing integrity, and seal performance. System reliability is the product of component reliabilities, making the weakest component the limiting factor. Balanced design ensures no single component dominates system failure probability, optimizing overall cost-effectiveness.

Condition monitoring extends gear system reliability through early fault detection. Vibration analysis detects mesh frequency changes, sidebands, and other signatures indicating developing problems. Oil analysis reveals wear particle generation, contamination ingress, and lubricant degradation. Temperature monitoring identifies thermal anomalies suggesting inadequate lubrication or excessive loading. Integrated monitoring enables predictive maintenance that prevents failures while minimizing unnecessary interventions.

Design for reliability considers not just rated capacity but also overload capability, contamination tolerance, and degraded-mode operation. Gear systems with adequate design margins tolerate occasional overloads, temporary lubrication problems, and minor damage without immediate failure. This robustness provides time for condition monitoring to detect problems and for maintenance to be scheduled conveniently.

Static Seal Design

O-rings remain the most common static sealing elements due to their simplicity, low cost, and effectiveness across wide pressure and temperature ranges. Proper O-ring design requires adequate squeeze compression to establish initial sealing contact, sufficient gland fill to prevent extrusion, and appropriate material selection for the service environment. Standard groove dimensions from industry specifications ensure reliable sealing for most applications.

Gasket design balances sealing effectiveness against joint assembly requirements. Sufficient gasket stress must develop to fill surface irregularities and create effective sealing, but excessive stress can damage gaskets or distort flanges. Gasket factors and maintenance factors from ASME standards guide bolting and flange design to achieve required sealing stress under all operating conditions including bolt relaxation and thermal cycles.

Material compatibility determines seal life in chemical service. Elastomers swell, shrink, harden, or degrade when exposed to incompatible fluids or temperatures. Chemical resistance charts guide material selection, but testing in actual service fluids remains advisable for critical applications. Temperature limits vary significantly between materials, with some elastomers suitable from cryogenic to several hundred degrees while others span much narrower ranges.

Dynamic Seal Analysis

Rotary shaft seals, commonly called lip seals, prevent leakage around rotating shafts while minimizing friction and wear. The seal lip contacts the shaft with controlled radial force, creating a sealing interface that must exclude contaminants while allowing a thin lubricant film to prevent dry running. Seal life depends on shaft speed, surface finish, misalignment, lubrication, and contamination environment.

Mechanical seals provide superior sealing for demanding rotary applications such as pumps and compressors. Two precision-lapped faces, one rotating and one stationary, maintain a thin fluid film between them that provides both sealing and lubrication. Face materials, spring loading, secondary seals, and cooling provisions all affect mechanical seal reliability. Proper selection, installation, and operation are essential for achieving design life.

Reciprocating seals for hydraulic and pneumatic cylinders must seal during both extension and retraction strokes while minimizing friction. Piston seals prevent bypass across the piston; rod seals prevent external leakage and exclude contaminants. Seal geometry, material, and surface finish optimization balances sealing, friction, and wear for long service life under cyclic pressure loading.

Seal Failure Modes

Extrusion occurs when seal material is forced into clearance gaps under pressure. Excessive clearance, inadequate material hardness, or overpressure relative to seal design allows extrusion. Anti-extrusion backup rings protect soft seal materials in high-pressure applications. Proper gap specification and seal material selection prevent extrusion failure.

Chemical attack degrades seal materials through swelling, shrinking, hardening, cracking, or dissolution. Compatibility testing validates material selection for specific service fluids. Even compatible materials eventually degrade through cumulative chemical exposure, establishing chemical attack as a wear-out failure mode requiring periodic seal replacement.

Thermal damage manifests as hardening, cracking, or loss of elastic properties. Continuous operation near material temperature limits accelerates aging; brief excursions above limits can cause immediate permanent damage. Heat generated by friction at seal interfaces adds to ambient temperature, potentially exceeding material limits even when fluid temperatures appear acceptable.

Mechanical damage includes cuts, tears, abrasion, and installation damage. Sharp edges on mating hardware cut seals during assembly; contamination particles abrade sealing surfaces; excessive compression crushes or permanently deforms seal profiles. Proper installation procedures, surface preparation, and contamination control prevent mechanical seal damage.

Spring Fatigue Design

Spring fatigue life depends on stress range, mean stress, surface condition, and material properties. Helical compression springs experience torsional stress in the wire, with maximum stress occurring at the inner diameter of the coil where curvature effects add to basic torsional stress. The Wahl factor or Bergstrasser factor accounts for this curvature effect and direct shear stress contribution.

Spring fatigue diagrams, analogous to Goodman diagrams for axial loading, relate alternating stress to mean stress for various life requirements. Shot peening induces beneficial compressive residual stresses in spring surfaces, significantly extending fatigue life, particularly at high mean stresses. Preset or scragging removes the detrimental effect of unfavorable residual stresses from manufacturing, improving fatigue performance.

Environmental factors affect spring fatigue life. Corrosion creates stress concentrations that initiate fatigue cracks; corrosion-resistant materials or protective coatings address this concern. Elevated temperatures reduce material strength and may allow stress relaxation. Hydrogen embrittlement affects high-strength spring materials exposed to hydrogen sources, requiring material and process controls for susceptible applications.

Spring Relaxation and Set

Stress relaxation in springs causes gradual load loss at constant deflection, important in applications such as bolted joints and interference fits where springs maintain clamping force. Relaxation depends on temperature, time, and stress level, with higher values of each accelerating relaxation. Material selection for relaxation resistance becomes critical for elevated-temperature applications requiring maintained spring force.

Set refers to permanent deformation that occurs when springs are stressed beyond their elastic limit. Initial set during manufacturing is removed by presetting; subsequent set during service indicates overstressing. Proper design ensures operating stresses remain below set limits, maintaining spring performance throughout service life. Specifying solid height at coil bind prevents overstress from bottoming.

Creep in springs produces time-dependent dimensional changes under sustained loading. While typically minor at room temperature, creep becomes significant at elevated temperatures, particularly in materials with low creep resistance. Applications requiring stable spring dimensions at temperature must select appropriate materials and limit operating stresses to prevent unacceptable creep accumulation.

Bolted Joint Design

Proper bolted joint design ensures that external loads are carried primarily by joint clamping force rather than bolt tension changes. The joint diagram illustrates how preload establishes clamping force and how external loads distribute between bolt stretch and joint compression relief. High preload relative to external loads minimizes bolt stress fluctuation, maximizing fatigue life while maintaining joint integrity.

Preload target setting balances joint requirements against fastener strength. Minimum preload must maintain clamping under all service conditions including thermal expansion differences, embedment relaxation, and maximum external loading. Maximum preload is limited by fastener yield strength and the requirement to avoid crushing joint members. The torque-tension relationship, though highly variable, enables controlled preload application through proper specification of friction coefficients and tightening procedures.

Joint stiffness affects load distribution between bolt and joint members. Stiff joints direct most external load through compression relief of joint members, minimizing bolt load variation. Compliant joints transfer more load to bolt stretching, increasing bolt stress variation. Joint stiffness depends on grip length, clamped area, and member materials, enabling design optimization for fatigue-critical applications.

Fastener Fatigue

Thread root stress concentration limits fastener fatigue strength. Rolled threads provide superior fatigue performance to cut threads due to beneficial residual stresses and improved surface finish at the root radius. Thread engagement length and nut design affect stress distribution among engaged threads, with the first engaged thread carrying disproportionate load in conventional designs.

Fastener fatigue testing under representative loading conditions validates calculated fatigue life. Standard fatigue tests apply axial loading to the fastener, but actual service may include bending from joint prying or misalignment. Preload level affects the stress range experienced under external loading; testing should represent actual preload conditions rather than zero mean stress conditions.

Design features improve fastener fatigue performance. Reduced shank diameter concentrates stretch in the shank rather than threads, reducing thread stress. Large thread root radii reduce stress concentration. Tension-nut designs distribute load more uniformly among engaged threads. These features enable reliable fastener performance in high-cycle fatigue applications.

Loosening Prevention

Vibration-induced loosening occurs when transverse joint motion overcomes thread friction, allowing gradual bolt rotation and preload loss. This mechanism, demonstrated by Junker testing, represents the primary loosening mode in dynamic applications. Prevention requires either maintaining friction above applied forces or physically preventing rotation through locking features.

Friction-based locking methods include thread-locking compounds, prevailing torque nuts, and serrated bearing surfaces. Thread-locking compounds fill thread clearances and cure to resist rotation. Prevailing torque nuts use deformed threads or polymer inserts to maintain friction independent of clamping force. Serrated surfaces increase rotational resistance through mechanical interference.

Positive locking physically prevents rotation regardless of friction. Lock wire threads through bolt heads, preventing rotation without wire failure. Cotter pins through castle nuts and drilled bolts similarly require pin failure for loosening. Tab washers bent against bolt heads and joint surfaces prevent rotation through deformation resistance. Critical applications often require positive locking methods for assured retention.

Design Codes and Standards

Pressure vessel design codes such as ASME Boiler and Pressure Vessel Code Section VIII establish minimum requirements for materials, design, fabrication, inspection, and testing. Design by rule provides formulas for common geometries and loadings, enabling straightforward compliance for standard configurations. Design by analysis permits optimization through detailed stress analysis demonstrating adequate safety margins.

Design pressure and temperature establish the service conditions for which the vessel is rated. These values include appropriate margins above expected operating conditions to accommodate transient excursions, instrument accuracy, and regulatory requirements. Maximum allowable working pressure (MAWP), calculated from actual material properties and dimensions, must equal or exceed design pressure.

Material selection considers strength, ductility, toughness, corrosion resistance, and fabricability. Allowable stresses derive from material properties with safety factors specified by the applicable code. Material certifications document mechanical properties and chemistry for traceability. Impact testing requirements ensure adequate toughness to prevent brittle fracture at minimum operating temperatures.

Fatigue Assessment

Pressure vessel fatigue analysis addresses cyclic stresses from pressure variations, thermal transients, and mechanical loading. Fatigue curves in design codes relate allowable stress amplitude to cycles for the design life, with safety factors accommodating scatter in material properties and the effects of mean stress. Cycle counting methods extract individual cycles from complex loading histories.

Thermal stress from temperature gradients and differential expansion contributes significantly to fatigue damage in process vessels. Startup and shutdown transients often produce the most severe thermal stresses, making the number of such events a primary fatigue life determinant. Thermal analysis identifies stress concentrations at geometric discontinuities and material transitions where thermal fatigue cracking initiates.

Cumulative fatigue damage assessment applies Miner's rule to sum damage from different cycle types. Each cycle type contributes damage equal to the ratio of actual cycles to allowable cycles at that stress level. When cumulative damage reaches unity, the design fatigue life is exhausted. Conservative practice limits cumulative damage to values below unity to provide margin for analysis uncertainties.

Fitness for Service

Fitness-for-service evaluation determines whether vessels with flaws or damage can continue operating safely. API 579-1/ASME FFS-1 provides systematic assessment procedures for common damage types including corrosion, pitting, cracking, dents, and bulges. Level 1 assessments use simple screening criteria; Level 2 applies standardized calculations; Level 3 requires detailed analysis for complex situations.

Remaining life assessment predicts how long a degraded vessel can operate before requiring repair or retirement. Corrosion rate trends project future wall thickness; crack growth analysis predicts time to critical flaw size; creep-life fraction consumption estimates remaining service at elevated temperatures. These assessments support run-repair-replace decisions and inspection interval determination.

Repair and alteration procedures restore vessel integrity when damage exceeds acceptable limits. Weld repairs must follow qualified procedures with post-weld heat treatment as required. Code compliance documentation demonstrates that repaired vessels meet original construction standards. Re-rating to lower pressure or temperature may enable continued service when repair is impractical.

Pipe Stress Analysis

Piping stress analysis ensures that sustained, occasional, and cyclic loads remain within allowable limits. Sustained loads from pressure and weight must not exceed allowable stress at design temperature. Occasional loads from wind, earthquake, and relief valve thrust are allowed higher stresses for their brief duration. Displacement stresses from thermal expansion and anchor movements are limited based on fatigue considerations.

Flexibility analysis determines displacement stresses in piping systems constrained by equipment connections, supports, and anchors. Thermal expansion of pipe runs between fixed points creates displacement stresses that cycle with temperature changes. Adequate flexibility through pipe routing, expansion loops, and flexible joints maintains stresses within allowable limits while supporting the system properly.

Support design affects both stress distribution and vibration behavior. Proper support locations and types guide loads to structure while allowing thermal movement. Spring supports accommodate vertical thermal displacement; sliding supports permit horizontal movement. Vibration dampers and snubbers control dynamic response to flow-induced and mechanical excitation.

Flow-Induced Vibration

Flow-induced vibration causes fatigue failures at pipe welds, supports, and small branch connections. Turbulent flow generates broadband excitation that can excite piping natural frequencies. Two-phase flow produces slug and plug flow patterns with severe dynamic loading. Proper flow velocity limits, pipe sizing, and support spacing minimize flow-induced vibration problems.

Acoustic fatigue occurs when high-frequency pressure fluctuations excite structural vibration modes. Control valve cavitation, pressure relief, and safety valve operation produce high-intensity noise that can fatigue thin-walled downstream piping. Acoustic treatment, piping reinforcement, or noise source mitigation addresses acoustic fatigue risks.

Vortex shedding from obstructions in the flow stream creates periodic excitation at frequencies determined by flow velocity and obstruction geometry. When shedding frequency matches piping natural frequency, resonant vibration amplifies response dramatically. Design modifications including strakes, shrouds, or geometry changes disrupt coherent vortex shedding, preventing resonant excitation.

Corrosion Management

Internal corrosion in piping systems depends on fluid chemistry, temperature, flow velocity, and pipe material. Corrosion allowance in pipe wall thickness accommodates expected corrosion over design life. Material selection matches corrosion resistance to service conditions; austenitic stainless steels, nickel alloys, and non-metallic materials serve aggressive chemical services.

External corrosion attacks pipe surfaces exposed to atmospheric moisture, soil, or process spills. Coating systems protect external surfaces; cathodic protection supplements coatings for buried piping. Corrosion under insulation poses particular challenges because moisture trapped beneath insulation contacts warm pipe surfaces, accelerating attack while hiding damage from visual inspection.

Inspection and monitoring programs detect corrosion damage before failure occurs. Ultrasonic thickness measurement at designated monitoring locations tracks wall loss trends. Radiography and guided wave testing screen larger pipe sections. Corrosion rate data support remaining life assessment and inspection interval optimization.

Rotor Dynamics

Rotor dynamics analysis ensures that rotating machines operate reliably without excessive vibration. Critical speeds occur where rotational frequency coincides with lateral natural frequencies of the rotor system, causing resonant response to unbalance forces. Design targets operation sufficiently removed from critical speeds to limit vibration amplitude even with manufacturing unbalance variations.

Bearing stiffness and damping significantly affect rotor dynamic behavior. Fluid film bearings provide both support stiffness and energy dissipation that attenuate rotor response. Rolling element bearings offer high stiffness but minimal damping, often requiring external damping provisions. Bearing selection and design must consider rotor dynamic requirements alongside load capacity and life.

Stability analysis evaluates potential for self-excited vibration that can grow without bound. Internal friction, fluid forces in seals and bearings, and aerodynamic effects can all drive instability under certain conditions. Stability threshold speed represents the maximum safe operating speed; machines intended for operation above this speed require design modifications to improve stability margins.

Balancing Requirements

Rotor balancing reduces unbalance forces to acceptable levels for smooth operation and long bearing life. Rigid rotor balancing in two planes corrects static and couple unbalance for rotors operating well below their first critical speed. Flexible rotor balancing addresses mode shapes excited at operating speed, requiring correction at multiple speeds and planes.

Balance quality grades per ISO 1940 specify permissible residual unbalance based on rotor mass and operating speed. Grade G2.5 suits most industrial rotating equipment; precision applications such as machine tool spindles require G1 or better; large slow-speed rotors may accept G6.3 or higher. Proper grade selection balances manufacturing cost against vibration requirements.

Balance change in service results from deposit accumulation, erosion, thermal bowing, component loosening, or coupling misalignment. Routine vibration monitoring detects balance deterioration before damage occurs. In-place balancing capabilities enable correction without disassembly, minimizing downtime for applications prone to balance change.

Vibration Diagnostics

Vibration analysis detects developing faults in rotating equipment before failure occurs. Vibration signatures contain frequency components related to rotating speed, bearing geometry, gear mesh, and structural resonances. Changes in amplitude, frequency, or phase indicate developing problems whose character reveals likely causes.

Unbalance produces vibration at running speed with amplitude proportional to speed squared. Misalignment generates running speed vibration with strong axial component and harmonics at twice running speed. Bearing defects create signatures at frequencies calculated from bearing geometry and running speed. Rolling element defects produce distinct frequencies for inner race, outer race, ball, and cage faults.

Trend analysis tracks vibration levels over time to detect gradual deterioration. Alarm levels trigger investigation when vibration exceeds normal operating range. Shutdown levels prevent operation at vibration levels risking imminent failure. Effective trending requires consistent measurement conditions and proper statistical treatment of measurement variability.

Load and Resistance Factor Design

Load and resistance factor design (LRFD) provides a rational framework for structural reliability. Load factors increase design loads to account for uncertainty in load magnitude and combinations. Resistance factors reduce nominal strength to account for material variability, fabrication tolerances, and model uncertainty. The relationship between factored loads and factored resistance determines reliability level.

Calibration of load and resistance factors targets consistent reliability across different structural elements and failure modes. First-order reliability methods (FORM) compute probability of failure for given factor combinations. Target reliability indices, typically around 3.0 for member design and higher for connections, establish acceptable failure probabilities. Calibration studies ensure that code-specified factors achieve target reliability.

Reliability-based assessment of existing structures applies LRFD principles to structures designed to earlier codes or exhibiting deterioration. Reduced resistance factors may be appropriate when actual material properties are measured rather than estimated. Load factors may be reduced when loads are better characterized than code assumptions. This flexibility enables rational decisions about existing structure adequacy.

Fatigue and Fracture Reliability

Probabilistic fatigue analysis accounts for uncertainty in loading, material properties, and damage models. Instead of single-valued life predictions, probabilistic methods produce failure probability as a function of time or cycles. This information supports risk-based decisions about inspection intervals, replacement timing, and acceptable operating conditions.

Fracture reliability analysis incorporates uncertainty in flaw size distribution, crack growth parameters, and fracture toughness. Initial flaw size distributions derive from non-destructive inspection probability of detection curves. Monte Carlo simulation propagates these uncertainties through crack growth calculations to predict failure probability over time. The results inform inspection program design and risk management decisions.

System reliability considers multiple potential failure locations and failure mode interactions. Series system reliability, where any component failure causes system failure, yields system reliability lower than any component reliability. Parallel systems with redundancy achieve higher reliability than individual components. Realistic structural systems often combine series and parallel elements requiring sophisticated analysis.

Composite Failure Modes

Composite materials fail through mechanisms distinct from metallic materials, requiring specialized analysis approaches. Fiber failure occurs when tensile or compressive loads exceed fiber strength; this typically represents catastrophic failure with little warning. Matrix failure includes cracking parallel to fibers that may or may not propagate depending on loading and layup. Delamination separates plies, reducing compression strength and enabling damage growth.

Failure criteria predict composite failure under combined loading. Maximum stress and maximum strain criteria evaluate each stress or strain component against allowable values. Interactive criteria such as Tsai-Wu and Hashin consider stress interactions that affect failure. Different criteria suit different failure modes and loading conditions; no single criterion adequately predicts all composite failure behaviors.

Progressive damage analysis models the gradual accumulation of matrix cracks, fiber failures, and delaminations leading to ultimate failure. Material properties degrade as damage accumulates, redistributing loads to undamaged regions. This behavior provides damage tolerance in properly designed composites, with substantial load-carrying capability remaining even after initial damage occurs.

Environmental Effects

Moisture absorption affects polymer matrix composite properties over time. Absorbed moisture plasticizes the matrix, reducing stiffness, strength, and glass transition temperature. Thermal spiking combined with moisture can cause matrix microcracking. Design allowables based on hot-wet conditioned specimens ensure adequate properties throughout service life even under adverse moisture conditions.

Ultraviolet radiation degrades polymer matrix surfaces, causing chalking and erosion that can penetrate to structural fibers over extended exposure. Protective coatings, including pigmented paints and UV-absorbing clear coats, prevent UV damage. Surface erosion from rain, sand, or other particles requires additional protective provisions for exposed composite structures.

Temperature effects include thermal expansion mismatch stresses, matrix property changes, and potential thermal damage. Composites with different fiber and matrix thermal expansion coefficients develop internal stresses during temperature changes, potentially causing microcracking. Operating temperature limits derive from matrix glass transition temperature with appropriate margins for hot-wet conditions.

Damage Tolerance

Impact damage represents a primary threat to composite structure integrity. Low-velocity impacts from dropped tools or runway debris create internal delaminations and matrix cracks with minimal visible surface indication. This barely visible impact damage (BVID) can significantly reduce compression strength while escaping detection during routine visual inspection.

Damage tolerance design ensures that structures with undetected damage maintain required strength until damage is found through detailed inspection. Design to discrete source damage levels establishes allowable stress accounting for expected damage. Inspection intervals ensure damage does not grow to critical size between examinations. Structural health monitoring offers potential for continuous damage detection.

Repair methods restore strength to damaged composite structures. Bonded patch repairs cover damage regions with additional material bonded to the parent structure. Bolted repairs attach metallic or composite patches with mechanical fasteners, avoiding bonding concerns but adding weight. Scarf repairs replace damaged material with new layup at tapered angles, achieving full strength restoration for properly executed repairs.

Process-Induced Variability

Additive manufacturing processes introduce unique variability sources affecting part reliability. Layer-by-layer fabrication creates anisotropic properties with strength differences between build directions and within-plane directions. Residual stresses from rapid heating and cooling cycles cause distortion and affect fatigue performance. Porosity from incomplete fusion, keyhole collapse, or trapped gas creates stress concentrations and initiation sites.

Process parameter control critically affects part quality. Laser power, scan speed, layer thickness, hatch spacing, and build orientation all influence density, microstructure, and properties. Parameter development establishes processing windows producing acceptable quality; robust parameter sets tolerate normal process variation without quality degradation. In-process monitoring enables detection of anomalies during fabrication.

Surface roughness in as-built additive parts significantly exceeds machined surfaces. Stair-stepping on inclined surfaces, partially melted powder particles, and surface irregularities create stress concentrations affecting fatigue performance. Post-processing including machining, polishing, and shot peening improves surface condition for fatigue-critical applications.

Qualification Approaches

Qualification of additive manufactured parts demonstrates that specific parts produced by specific processes meet application requirements. Point qualification tests each unique part configuration, requiring extensive testing for every design. Process qualification establishes that a controlled process produces acceptable parts, reducing part-specific testing requirements once the process is validated.

Statistical process control monitors additive manufacturing to ensure continued operation within qualified parameters. Control charts track process inputs and outputs, detecting drift before out-of-specification parts result. Machine maintenance, powder management, and environmental controls maintain consistent processing conditions. Documentation provides traceability from raw material through finished part.

Equivalency demonstration compares additive manufactured parts against traditionally manufactured counterparts. When additive parts meet or exceed conventional part performance, existing design allowables may be applicable. Differences in microstructure, defect populations, or property distributions may require development of additive-specific allowables based on representative testing.

Inspection and Quality Assurance

Non-destructive inspection of additive manufactured parts addresses unique defect types and challenging geometries. Computed tomography (CT) scanning reveals internal porosity, inclusions, and geometric accuracy. Ultrasonic inspection detects lack of fusion and other planar defects. Surface inspection methods including dye penetrant and eddy current find surface-connected flaws.

In-process monitoring captures quality indicators during fabrication. Melt pool monitoring using thermal imaging or photodiodes detects anomalies in real time. Layer imaging systems photograph each layer for post-build analysis. Acoustic monitoring may detect cracking or porosity formation. These methods offer potential for part-specific quality assessment without post-build inspection.

Mechanical testing validates that as-built properties meet design requirements. Witness specimens fabricated alongside production parts characterize batch properties. Destructive testing of production parts provides direct property measurement at the cost of part consumption. Test programs balance property knowledge needs against testing costs and part availability.