# Residual stress

Self-equilibrated internal stress: manufacturing origins, distortion and service effects, measurement depth and reference-state limits, redistribution and stress relief.

Reviewed: 2026-11-02

Tags: production, process-effects, residual-stress, dimensional-stability

In an ideal unloaded **10 × 6 mm** strip, each **1 mm** surface layer carries **+200 MPa** tension and contributes **+2,000 N**. The **4 mm** core carries **−100 MPa** compression and contributes **−4,000 N**. The symmetric longitudinal stress field balances to zero net force and bending moment away from the ends. The local stresses remain nonzero. This is an assumed distribution, separate from measuring stress or flatness.

Residual stresses persist after external loads are removed. TWI describes self-balance arising from incompatible internal strains, including tension near welds balanced by compression elsewhere. [TWI, Residual Stress: prediction and measurement](https://www.twi-global.com/what-we-do/services-and-support/asset-management/engineering-critical-assessment/residual-stress)

Report stress component, location, depth and material state.

## Origins and relationship to distortion

Uneven plastic deformation, nonuniform heating/cooling and constrained dimensional changes can leave regions with incompatible stress-free shapes. During welding, hot and cooler material constrain one another; cooling does not necessarily return every region to its original unstressed condition. The resulting field depends on geometry, restraint, sequence and material behavior.

Manufacturing can both introduce stress and redistribute an existing field. Bodycote identifies machining, cutting and plastic deformation as sources of stresses associated with later dimensional change, and describes stress relief as a means of reducing that risk. This is a process explanation, not a universal requirement to heat-treat every machined component. [Bodycote, Stress relieving](https://www.bodycote.com/what-we-do/precision-heat-treatment/stress-relieving-atmosphere-vacuum/)

Distortion is a change in shape; residual stress is internal stress. They are related but not interchangeable measurements. A component can remain straight while containing a balanced stress field. Removal of material or restraint can change that balance and produce movement. Conversely, a bent part can be relatively low in residual stress after deformation and relaxation.

Elastic clamping can temporarily hold a part to a reference surface without eliminating its internal stress. Dimensions while restrained and dimensions after release describe different mechanical states. Subsequent machining also creates a new boundary and can remove the regions that previously supplied balancing forces and moments.

## Why tension and compression matter differently

TWI associates tensile residual stress with possible adverse effects on fatigue, environmental damage and brittle-fracture behavior. It notes that compression can be beneficial but can also reduce buckling capacity. The sign alone therefore does not establish suitability for every loading mode. [TWI, performance effects](https://www.twi-global.com/what-we-do/services-and-support/asset-management/engineering-critical-assessment/residual-stress)

Explanatory synthesis: within an applicable linear-elastic model, residual and service stress components can be superposed at the same point and direction. That approximation loses validity when plasticity, contact changes or relaxation redistribute the field. A local compressive surface layer can reduce a tensile surface component while balancing tensile stress remains elsewhere.

Residual stress also differs from hardness, cold-work level and surface roughness. Those observations may be related to a process history, but none independently supplies the magnitude and direction of the residual-stress tensor. A treatment that improves one surface property is not automatically evidence of a favorable through-thickness stress state.

## Original self-equilibrium example

Assume a long, unloaded rectangular strip with **10 mm width** and **6 mm thickness**. Away from end effects, consider an idealized longitudinal residual-stress distribution:

| Region | Cross-sectional area | Assumed longitudinal stress | Axial resultant |
| --- | --- | --- | --- |
| Upper 1 mm layer | 10 mm² | +200 MPa tension | +2,000 N |
| Middle 4 mm core | 40 mm² | −100 MPa compression | −4,000 N |
| Lower 1 mm layer | 10 mm² | +200 MPa tension | +2,000 N |
| Total | **60 mm²** | Area-weighted mean **0 MPa** | **0 N** |

Here **1 MPa = 1 N/mm²**. The symmetric distribution also has zero resultant bending moment about the mid-thickness. Zero net force and moment coexist with local stresses of +200 and −100 MPa; an average of zero does not describe the local extremes.

If the upper layer is removed, the old stress distribution on the remaining material would sum to **−2,000 N**. That is a calculation on the *unrelaxed remainder*, not a new external compressive load. The free remainder cannot retain that distribution unchanged: stress must redistribute, potentially with shortening and curvature. This original model supplies no predicted distortion, allowable stress or machining sequence; those require material behavior, geometry and a compatible deformation analysis.

## Measurement techniques see different evidence

Diffraction measures lattice spacing rather than directly reading a stress gauge. NIST explains that neutron measurements average lattice spacing over a defined gauge volume and that specimen orientation determines the stress direction being investigated. Neutrons can penetrate millimeters to centimeters in many engineering materials, enabling internal measurements that conventional laboratory X-ray methods cannot generally reproduce. [NIST, Principles of Neutron Stress Measurements](https://www.nist.gov/ncnr/principles-neutron-stress-measurements)

NPL's **Measurement Good Practice Guide 52, Issue 2, September 2005**, describes X-ray diffraction measurements on crystalline materials and the effects of specimen and measurement conditions. Its depth-profiling treatment distinguishes a near-surface measurement from a profile obtained after material removal. The physical depth sampled depends on the material, radiation and measurement geometry; “XRD” does not imply one universal penetration depth. [NPL, Determination of Residual Stresses by X-ray Diffraction, Issue 2](https://www.npl.co.uk/special-pages/mgpg52)

| Technique family | What limits the interpretation |
| --- | --- |
| Laboratory X-ray diffraction | Sampled near-surface region, crystallographic response and measurement direction |
| Neutron diffraction | Gauge volume, accessible geometry, lattice reference and directional sampling |
| Hole drilling or other local relaxation | Stress relieved by the introduced geometry and the inverse mechanical model |
| Sectioning or contour methods | Cutting-induced relaxation and the component reconstructed from it |

The table is explanatory synthesis, not a ranking of universal accuracy. Different techniques may answer different questions rather than contradict one another. A surface result cannot establish the interior field; a bulk volume average can miss a steep local gradient.

## Reference states and uncertainty

NPL's guide discusses X-ray elastic constants, stress analysis assumptions and uncertainty. In its discussion of deeply penetrating measurements with nonzero surface-normal stress, knowledge of the stress-free lattice parameter becomes necessary. Texture, grain sampling, phase composition and depth gradients can also affect the relationship between a diffraction observation and the intended engineering stress. [NPL, GPG52 Issue 2, measurement and analysis limitations](https://www.npl.co.uk/special-pages/mgpg52)

Mechanical relaxation methods infer the original stress from deformation caused by a cut or hole. Their result depends on the geometry, constitutive assumptions and reconstruction, and the measurement changes the specimen. “Non-destructive,” “semi-destructive” and “destructive” describe different kinds of intervention; they do not establish equal spatial resolution or uncertainty.

TWI explains that numerical predictions and measurements both have limitations and are often combined. Agreement at measured locations supports a model within that evidence, but does not independently validate every unmeasured location, load history or altered manufacturing route. [TWI, prediction and measurement limitations](https://www.twi-global.com/what-we-do/services-and-support/asset-management/engineering-critical-assessment/residual-stress)

## Stress relief changes the material state

Thermal stress relief aims to reduce residual stress through an alloy- and condition-dependent treatment. Bodycote describes its use after rough machining and before final finishing, and distinguishes treatment considerations for previously hardened and tempered parts. Its general process descriptions do not establish a universally safe temperature or a guarantee of zero remaining stress. [Bodycote, stress-relieving process and material scope](https://www.bodycote.com/what-we-do/precision-heat-treatment/stress-relieving-atmosphere-vacuum/)

Heat treatment may also affect strength, hardness, microstructure, surface condition and dimensions, depending on the alloy and prior condition. Mechanical treatments that introduce compression likewise redistribute rather than abolish stress. Stability after one treatment does not guarantee stability after additional material removal, heating or service loading.

The engineering significance of a residual-stress result is consequently tied to the actual stress component, spatial scale, material state and failure or dimensional mechanism. No single measurement value or generic stress-relief label establishes a component's fatigue life, fracture resistance or final dimensional stability.

## Source versions

Reviewed **2026-11-02 PST**. The downloaded NPL PDF's internal publication page states **September 2005**, **© Crown copyright 2005**, and **Issue 2**; its hosting page's February 2020 date is not treated as the guide's edition. NIST marks its page **Created February 15, 2023**; that is page metadata rather than a separate technical edition. No separate technical issue date was verified for the cited TWI or Bodycote live pages. The strip calculation and comparative synthesis are original, bounded explanations.

## Related reference

[Manufacturing process references](../../processes/index.md)