Mechanics-of-materials guide
Fatigue Design: S-N Curves, Mean Stress and Endurance
Fatigue Design: S-N Curves, Mean Stress and Endurance is a focused mechanics-of-materials guide within the Industrial Calculation Hub knowledge library. It explains the engineering purpose, physical basis, governing inputs, process or equipment interfaces, common failure mechanisms and the limits of preliminary use.
- Content type
- Mechanics-of-materials guide
- Canonical ID
- ICH-CAN-013
- Source basis
- Strength-of-materials and mechanical-engineering literature
- Last reviewed
- 31 August 2026
What is Fatigue Design: S-N Curves, Mean Stress and Endurance?
Fatigue design addresses cracking under repeated stress cycles, often at stresses well below the tensile strength. Rotating shafts, pressure cycling, vibrating supports, welded structures and repeatedly started equipment are governed by the number, size and sequence of cycles rather than by a single static load.
An S–N curve relates stress range or alternating stress to life for a particular material and specimen condition. The curve must be corrected for the real component: surface finish, size, notch, reliability, temperature, corrosion and mean stress change the usable endurance. Variable-amplitude service is commonly screened with cycle counting and a cumulative-damage rule, but that simplification does not replace a proper review of overloads, fretting and crack-growth behaviour.
Why this topic needs a component-level basis
Fatigue Design: S-N Curves, Mean Stress and Endurance is not reliably assessed by a single catalogue value or by one convenient operating condition. Geometry, material condition, assembly, load path, operating history and failure consequence must be recorded together. The objective is a repeatable engineering decision, not an over-precise calculation based on uncertain inputs.
Terms used in the assessment
- Design case
- The combination of geometry, material, load, speed, temperature and support condition used for the check.
- Service condition
- The actual operating state, including starts, process upsets, maintenance condition and environmental exposure.
- Acceptance evidence
- Measurements, inspection records, calculations and traceable documents supporting a decision.
Mechanics and governing relationships
An S–N curve relates stress range or alternating stress to life for a particular material and specimen condition. The curve must be corrected for the real component: surface finish, size, notch, reliability, temperature, corrosion and mean stress change the usable endurance. Variable-amplitude service is commonly screened with cycle counting and a cumulative-damage rule, but that simplification does not replace a proper review of overloads, fretting and crack-growth behaviour.
Check 1
alternating stress = (maximum stress − minimum stress) / 2
Check 2
mean stress = (maximum stress + minimum stress) / 2
Check 3
a Goodman- or other accepted mean-stress relation should use the material data appropriate to the component
Check 4
cumulative damage commonly compares actual cycle blocks with their allowed life, subject to the design standard
Use consistent units and state the source of each property. Where cyclic loading, a weld detail, a keyway, a contact interface or a support flexibility is present, the gross-section result is only the start of the review.
Applying the relationships responsibly
Relationship 1 in practice. alternating stress = (maximum stress − minimum stress) / 2. Before using it, define the section or component to which it applies, the load direction, material-temperature basis and whether the service is steady or cyclic. The relation is a check within the larger component model, not a replacement for the model.
Relationship 2 in practice. mean stress = (maximum stress + minimum stress) / 2. Before using it, define the section or component to which it applies, the load direction, material-temperature basis and whether the service is steady or cyclic. The relation is a check within the larger component model, not a replacement for the model.
Relationship 3 in practice. a Goodman- or other accepted mean-stress relation should use the material data appropriate to the component. Before using it, define the section or component to which it applies, the load direction, material-temperature basis and whether the service is steady or cyclic. The relation is a check within the larger component model, not a replacement for the model.
Relationship 4 in practice. cumulative damage commonly compares actual cycle blocks with their allowed life, subject to the design standard. Before using it, define the section or component to which it applies, the load direction, material-temperature basis and whether the service is steady or cyclic. The relation is a check within the larger component model, not a replacement for the model.
Information required before calculation or selection
- a realistic duty cycle including starts, stops, reversals and occasional upset loads
- stress ranges at weld toes, keyways, threads, holes and surface changes
- component material condition and actual surface treatment
- environmental exposure, corrosion, temperature and contact fretting
- inspection access and the consequence of a detectable versus sudden failure
Photographs can help confirm an installation, but they do not establish dimensions, material grade, preload, runout, stiffness or load spectrum. Obtain records and measurements that identify the actual component condition.
Practical design and verification method
- Review 1. separate the static-strength check from the fatigue-life check
- Review 2. reduce stress range at the source by balancing, alignment, support stiffness or process control
- Review 3. select recognised welded-detail categories instead of using parent-metal strength alone
- Review 4. avoid polishing or blending methods that damage coating or introduce new scratches
- Review 5. define the inspection interval from the credible initiation location and growth consequence
Recheck the component following manufacture, installation or operating change. Record the measurement position, instrument, temperature, speed or load condition and the acceptance criterion so the next inspection can be compared with a defensible baseline.
How design intent becomes a controlled installation
Control point 1. separate the static-strength check from the fatigue-life check. Assign the responsible discipline and inspection stage, then retain evidence that the as-built or as-installed condition satisfies the stated requirement. This avoids relying on a design intent that was not transferred to manufacture or maintenance.
Control point 2. reduce stress range at the source by balancing, alignment, support stiffness or process control. Assign the responsible discipline and inspection stage, then retain evidence that the as-built or as-installed condition satisfies the stated requirement. This avoids relying on a design intent that was not transferred to manufacture or maintenance.
Control point 3. select recognised welded-detail categories instead of using parent-metal strength alone. Assign the responsible discipline and inspection stage, then retain evidence that the as-built or as-installed condition satisfies the stated requirement. This avoids relying on a design intent that was not transferred to manufacture or maintenance.
Control point 4. avoid polishing or blending methods that damage coating or introduce new scratches. Assign the responsible discipline and inspection stage, then retain evidence that the as-built or as-installed condition satisfies the stated requirement. This avoids relying on a design intent that was not transferred to manufacture or maintenance.
Control point 5. define the inspection interval from the credible initiation location and growth consequence. Assign the responsible discipline and inspection stage, then retain evidence that the as-built or as-installed condition satisfies the stated requirement. This avoids relying on a design intent that was not transferred to manufacture or maintenance.
Example engineering review
A fan shaft that is satisfactory in static bending can still crack at a keyway after years of daily start-stop duty. The assessment needs shaft bending, torque fluctuation, keyway geometry, balance quality, bearing support stiffness and the actual number of starts; replacing the shaft without correcting the excitation may repeat the failure.
The example illustrates why replacement of a failed component alone is rarely sufficient. The review should identify the initiating mechanism, the feature that concentrated the response, the evidence that confirms it and the design or operating change that prevents recurrence.
Where it is used
Fatigue Design: S-N Curves, Mean Stress and Endurance is relevant to rotating machinery, crane parts, pressure vessels, fans, conveyors, structures, piping supports and welded fabrication. The same mechanics may apply in other industries, but material properties, environmental exposure, inspection rules and acceptable consequence of failure remain project-specific.
Common failure routes and warning signs
- a single “cycles per year” estimate can omit the damaging start-up or trip event
- compressive residual stress can be beneficial but should not be claimed after an uncontrolled repair
- corrosion fatigue can remove the apparent endurance limit
- a high cycle count with very small range may be less important than a few severe transient cycles
Failure route 1
a single “cycles per year” estimate can omit the damaging start-up or trip event. Treat this as a reason to inspect the underlying load path or duty before changing a part.
Failure route 2
compressive residual stress can be beneficial but should not be claimed after an uncontrolled repair. Treat this as a reason to inspect the underlying load path or duty before changing a part.
Failure route 3
corrosion fatigue can remove the apparent endurance limit. Treat this as a reason to inspect the underlying load path or duty before changing a part.
Failure route 4
a high cycle count with very small range may be less important than a few severe transient cycles. Treat this as a reason to inspect the underlying load path or duty before changing a part.
Trend information that is physically connected to the mechanism: torque, temperature, vibration, displacement, strain, leakage, bolt elongation, oil condition or crack indication. A measurement with a known location and operating state is more useful than a single visual judgement.
Inspection, maintenance and change control
Before altering Fatigue Design: S-N Curves, Mean Stress and Endurance, confirm isolation, stored energy, lifting, access, hot-work, guarding and process hazards. A modification to material, geometry, coating, lubrication, tightening method, speed, load, support, control logic or operating cycle can change the basis of the original assessment. Update the drawing, maintenance record and test result together.
Acceptance and reassessment record
1. Evidence item. Record a realistic duty cycle including starts, stops, reversals and occasional upset loads. It should be tied to the specific component and operating case, not copied from a nominal data sheet. This evidence changes the confidence in the final decision.
2. Evidence item. Record stress ranges at weld toes, keyways, threads, holes and surface changes. It should be tied to the specific component and operating case, not copied from a nominal data sheet. This evidence changes the confidence in the final decision.
3. Evidence item. Record component material condition and actual surface treatment. It should be tied to the specific component and operating case, not copied from a nominal data sheet. This evidence changes the confidence in the final decision.
4. Evidence item. Record environmental exposure, corrosion, temperature and contact fretting. It should be tied to the specific component and operating case, not copied from a nominal data sheet. This evidence changes the confidence in the final decision.
5. Evidence item. Record inspection access and the consequence of a detectable versus sudden failure. It should be tied to the specific component and operating case, not copied from a nominal data sheet. This evidence changes the confidence in the final decision.
Questions for the release review
Does the final condition match the documented geometry and material? Has the governing transient or fatigue case been included? Can inspection find the credible initiation location? Are the acceptance values measured under the conditions assumed by the design? If any answer is uncertain, state the limitation and assign the next action rather than declaring the component fully verified.
Frequently Asked Questions
Can tensile strength be used to predict fatigue life?
Not by itself. Fatigue performance is strongly influenced by local geometry, stress range, surface condition, mean stress, environment and the material test basis.
Which inputs should be confirmed for Fatigue Design: S-N Curves, Mean Stress and Endurance?
Information required before calculation or selection a realistic duty cycle including starts, stops, reversals and occasional upset loads stress ranges at weld toes, keyways, threads, holes and surface changes component material condition and actual surface treatment environmental exposure, corrosion, temperature and contact fretting inspection access and the consequence of a detectable versus. Confirm the source, condition and measurement basis for each input before treating a calculated or selected value as reliable.
How should Fatigue Design: S-N Curves, Mean Stress and Endurance be reviewed in practice?
Practical design and verification method Review 1. separate the static-strength check from the fatigue-life check Review 2. reduce stress range at the source by balancing, alignment, support stiffness or process control Review 3. select recognised welded-detail categories instead of using parent-metal strength alone Review 4. avoid polishing or blending methods that damage. Record the actual operating line-up and repeat the review at the condition most likely to challenge performance.
What warning signs deserve early attention?
Common failure routes and warning signs a single “cycles per year” estimate can omit the damaging start-up or trip event compressive residual stress can be beneficial but should not be claimed after an uncontrolled repair corrosion fatigue can remove the apparent endurance limit a high cycle count with very small range may. A trend linked to the physical mechanism is more useful than waiting for a single visible failure.
What evidence supports acceptance?
Acceptance and reassessment record 1. Evidence item. Record a realistic duty cycle including starts, stops, reversals and occasional upset loads. It should be tied to the specific component and operating case, not copied from a nominal data sheet. This evidence changes the confidence in the final decision. 2. Evidence item. Record stress. Keep the records traceable so later maintenance or a process change can be compared with the original basis.
When should Fatigue Design: S-N Curves, Mean Stress and Endurance be reassessed?
Reassess it after a change in duty, throughput, process material, temperature, pressure, geometry, maintenance condition, control logic or a recurring abnormal trend. The original result is valid only for the conditions it represented.
Can a typical value or handbook rule be used for final design?
Only as a preliminary screen. Final decisions for Fatigue Design: S-N Curves, Mean Stress and Endurance need the actual component or system data, applicable standard, supplier limits and qualified engineering review.
Where should an engineering investigation begin?
Start by defining the system boundary and current operating condition, then compare measured evidence with the design intent. Address the controlling mechanism before changing capacity, setpoints or hardware.
References
- Khurmi, R. S. Strength of Materials. Supplied source library.
- Roark. Formulas for Stress and Strain. Supplied source library.
Original educational summary informed by the supplied literature. It does not reproduce protected source text, figures, tables or standards material.