Stress Concentration: Notches, Fillets and Fatigue

What is Stress Concentration: Notches, Fillets and Fatigue?

Stress concentration is the local rise in stress caused by a geometric discontinuity such as a shoulder, keyway, hole, groove, thread, weld toe or abrupt thickness change. The nominal stress from a hand calculation or finite-element model is not automatically the stress that initiates a crack. Local elastic stress can be many times higher at a sharp re-entrant feature, especially when the component is cyclically loaded.

The elastic stress-concentration factor Kt is the ratio of peak elastic stress to nominal stress for a defined geometry and load. In fatigue work the effective fatigue notch factor Kf may be lower than Kt because materials have different notch sensitivity; surface condition, residual stress, size, corrosion and mean stress still determine the actual endurance. A generous radius, smooth transition and a load path that avoids abrupt eccentricity are normally more valuable than simply increasing plate thickness.

Why this topic needs a component-level basis

Stress Concentration: Notches, Fillets and Fatigue 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

The elastic stress-concentration factor Kt is the ratio of peak elastic stress to nominal stress for a defined geometry and load. In fatigue work the effective fatigue notch factor Kf may be lower than Kt because materials have different notch sensitivity; surface condition, residual stress, size, corrosion and mean stress still determine the actual endurance. A generous radius, smooth transition and a load path that avoids abrupt eccentricity are normally more valuable than simply increasing plate thickness.

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. Kt = local elastic stress / nominal stress for a stated geometry and loading. 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. Kf relates the fatigue penalty to notch sensitivity and must not be assumed equal to Kt. 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. fatigue assessment uses the local alternating and mean stress, not only the gross-section stress. 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. a weld toe or attachment should be assessed using an accepted fatigue detail category where applicable. 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

• dimensioned geometry including radii, hole edge distance and thickness transition
• load spectrum: steady, start-stop, reversing, shock and accidental cases
• material strength, surface finish, corrosion allowance and manufacturing route
• location of welds, grinding, peening or other local improvement
• inspection history, crack location and any previous repair

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

1. Review 1. replace sharp internal corners with controlled fillets wherever the function permits
2. Review 2. move holes, keyways and attachments away from the highest bending or torsional section
3. Review 3. align transitions with the force path and avoid sudden stiffness changes
4. Review 4. use local finite-element refinement only after the global boundary conditions are credible
5. Review 5. state whether the assessment is static yield, brittle fracture, fatigue or all three

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. replace sharp internal corners with controlled fillets wherever the function permits. 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. move holes, keyways and attachments away from the highest bending or torsional section. 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. align transitions with the force path and avoid sudden stiffness changes. 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. use local finite-element refinement only after the global boundary conditions are credible. 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. state whether the assessment is static yield, brittle fracture, fatigue or all three. 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

For a stepped shaft carrying a pulley, the bending moment is often highest near the shoulder where the diameter changes. The review should compare a generous shoulder radius, a relief groove, a moved keyway and a larger transition length. The preferred solution is the one that reduces local alternating stress without creating an assembly, bearing-fit or manufacturability problem.

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

Stress Concentration: Notches, Fillets and Fatigue is relevant to shafts, pressure parts, platework, lifting lugs, frames, pipe supports, welded attachments and bolted-machine components. 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 high theoretical Kt can be hidden by a coarse finite-element mesh
• grinding marks, corrosion pits and undercut can create a more severe notch than the drawing shows
• a repair weld can alter local residual stress and fatigue detail category
• increasing nominal section can shift the crack to a nearby attachment instead of removing the cause

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 Stress Concentration: Notches, Fillets and Fatigue, 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 dimensioned geometry including radii, hole edge distance and thickness transition. 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 load spectrum: steady, start-stop, reversing, shock and accidental cases. 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 material strength, surface finish, corrosion allowance and manufacturing route. 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 location of welds, grinding, peening or other local improvement. 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 history, crack location and any previous repair. 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

References

1. Khurmi, R. S. Strength of Materials. Supplied source library.
2. 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.

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