Residual Stress

A stress with no external load

Most stress in engineering is the response to something you do to a part — a bolt pulls, a beam carries a floor, a shaft transmits torque. Residual stress is different. It is locked in. Set the part on a bench, remove every external force, and the stress is still there, in static balance with itself. It got there because at some moment in the part's history one region was forced to take a different permanent (plastic) strain than its neighbours, and once everything returned to the same temperature and the same shape, those mismatched regions had to share the leftover elastic strain among themselves.

The defining property is equilibrium. A residual-stress field acting on a free body can exert no net force and no net moment, because nothing outside the body is reacting them. For a cross-section that means:

Force balance:   ∫ σ_res dA = 0
Moment balance:  ∫ σ_res · y dA = 0

  σ_res = residual stress at a point  (Pa)
  A     = cross-sectional area  (m²)
  y     = distance from the centroid  (m)

This is why residual stress always comes in pairs of opposite sign. If the surface of a quenched bar is in compression, the core must be in tension, and the two integrate to zero. Cut the part — by machining, sawing or even drilling a small hole — and you break that balance. The remaining material springs to a new equilibrium shape: the bar bows, the plate cups, the machined slot opens or closes. That spring-back is exactly the signature exploited by hole-drilling and contour-method measurements.

Where residual stress comes from

Almost any non-uniform permanent deformation will do it. The common industrial origins are:

• Thermal gradients (quenching). A hot part plunged into oil or water cools from the outside in. The surface contracts while the core is still hot and soft; the core later contracts against an already-rigid shell. The mismatch locks in stress.
• Phase transformation. In hardenable steels the austenite-to-martensite change is accompanied by a roughly 1–4% volume expansion. If the surface transforms before the core, that local expansion adds — and can reverse — the purely thermal stresses.
• Welding. The weld bead and heat-affected zone melt and then shrink on solidification while clamped by cold surrounding metal. The weld line ends up in high longitudinal tension, often near yield, with balancing compression in the plate.
• Mechanical working. Shot peening, rolling, autofrettage, bending, drawing and forging all impose non-uniform plastic strain. These are the controllable sources used to engineer beneficial compression.
• Machining. Cutting and grinding plastically smear and heat a thin surface layer; abusive grinding can leave a tensile surface skin that ruins fatigue life even on an otherwise good part.
• Casting and additive manufacturing. Solidification shrinkage and the steep, repeated thermal cycles of laser powder-bed fusion build up large layer-by-layer residual stresses that can crack parts or lift them off the build plate.

Quenching: the canonical case

Quenching shows the mechanism cleanly because two effects fight each other. Consider a cylinder of plain-carbon steel heated uniformly and then water-quenched.

Stage 1 — thermal contraction. The surface cools first and tries to contract, but the hot interior holds it back. The surface goes into tension and, because hot steel is weak, yields in tension (stretches plastically). Meanwhile the core is in compression.

Stage 2 — the core catches up. Now the surface is cold and stiff while the core finally cools and contracts. The contracting core pulls the surface inward, but the surface, having already been plastically stretched, resists. The signs flip: the final purely-thermal state is compression at the surface, tension in the core.

For a hardenable steel a transformation effect is layered on top. Martensite occupies more volume than the austenite it replaces. Because the surface usually transforms first, its expansion can over-ride the thermal pattern and, in severe cases, leave dangerous tension at the surface — the classic recipe for quench cracking. Real heat-treatment practice (interrupted quenches, martempering, choosing oil over water, tempering immediately) is largely about steering this competition. The visible symptoms of getting it wrong are distortion (a shaft that bows out of straightness) and cracks that appear hours after the part has cooled.

Welding: tension where you least want it

A weld is a tiny casting clamped inside a cold, rigid plate. As the molten bead and the heat-affected zone (HAZ) solidify and cool, they want to shrink, but the surrounding metal will not let them. The result is longitudinal residual tension running along the weld line, commonly reaching the yield strength of the material, balanced by compression in the parent plate further away. Transverse stresses and through-thickness stresses add a fully three-dimensional field.

This matters because welds also concentrate stress geometrically (the toe of the weld) and metallurgically (a hardened, sometimes brittle HAZ). High tensile residual stress at exactly that location is why fatigue cracks so often start at weld toes, and why design codes for welded structures use such conservative fatigue curves. Mitigations include post-weld heat treatment (PWHT) for stress relief, weld-toe grinding or remelting (TIG dressing), and — bringing the story full circle — friction stir welding, whose lower peak temperatures and solid-state joining leave a much gentler residual-stress field than fusion welding.

Shot peening: residual stress as a defense

The same phenomenon that cracks quenched parts can be turned into one of the cheapest fatigue defenses available. Shot peening blasts a surface with thousands of small hardened beads (steel, ceramic or glass) travelling at roughly 20 to 100 m/s. Each impact plastically stretches a shallow dimple at the surface. The elastic bulk underneath, which was not stretched, squeezes that worked layer back when the shot bounces off. The net result is a thin compressive layer, typically 0.1 to 0.5 mm deep, with peak compression often 50 to 100% of the material's yield strength, balanced by a small tension a little deeper in.

Because fatigue cracks only propagate under tensile opening stress, this compressive skin must first be cancelled by the applied load before the surface ever feels tension. Initiation is delayed, early growth is suppressed, and measured fatigue lives commonly improve by 3 to 10 times for springs, gears, crankshafts, turbine blades and aircraft landing gear. Peening intensity is controlled with the Almen test: a thin steel strip is peened on one side and the arc height it bows to (in thousandths of an inch, e.g. an "8A" or "12C" value) calibrates the process. Coverage — the percentage of the surface dimpled — is verified separately, usually requiring 100% or more.

Carburizing and nitriding ride on the same idea by metallurgical rather than mechanical means: the diffused surface layer transforms with a volume increase, leaving the hardened case in compression. Autofrettage pressurizes a thick-walled tube (gun barrels, high-pressure fittings) beyond yield at the bore so that, on release, the bore is left in compression and can survive far higher operating pressures.

Comparing the major sources

Source	Mechanism	Surface sign	Typical depth / extent	Effect on fatigue	Control / fix
Quenching (thermal)	Surface cools/contracts before core	Compressive (thermal-only)	Through-thickness	Beneficial if compressive	Quench medium, martempering
Quenching (transformation)	Martensite volume expansion	Can reverse to tensile	Through-thickness	Risk of quench cracking	Temper immediately, interrupt quench
Fusion welding	Restrained shrinkage of bead + HAZ	Tensile, near yield at weld line	Whole joint, 3D field	Detrimental (weld-toe cracks)	PWHT, toe grinding, FSW
Shot peening	Plastic dimpling of surface skin	Compressive, 50–100% σ_y	0.1–0.5 mm	Strongly beneficial (3–10×)	Almen intensity + coverage spec
Carburizing / nitriding	Diffused case transforms w/ expansion	Compressive	0.2–2 mm case	Beneficial	Case-depth and temperature control
Abusive grinding	Localized heating + tempering of skin	Tensile (with burns)	10–100 µm	Detrimental	Lower feed, coolant, gentle grinding
Additive (L-PBF)	Repeated steep thermal cycles per layer	Tensile near top surface	Whole part	Detrimental; can crack/warp	Build-plate heating, post-build HT

Measuring what you cannot see

Because residual stress carries no external load, you cannot read it with a force gauge. Every method instead measures a consequence — usually either the strain released when you cut the balance, or the change in atomic lattice spacing that the stress produces.

• Hole-drilling (ASTM E837). A strain-gauge rosette is bonded, a small hole is incrementally drilled at its center, and the relaxation strains are inverted into a near-surface stress profile. Semi-destructive, fast, depths to ~1–2 mm.
• Contour method. The part is cut in two; the relaxed cut face is mapped with a coordinate-measuring machine, and the displacement is back-computed into the stress that used to hold the face flat. Gives a full 2D map on the cut plane.
• X-ray diffraction (XRD). Measures elastic lattice strain from diffraction-peak shifts in the top few microns. Non-destructive, excellent for surface and peened layers; needs layer removal to go deeper.
• Neutron diffraction. Same lattice-spacing principle but neutrons penetrate centimetres, giving true 3D bulk maps. Requires a reactor or spallation source.
• Ultrasonic & magnetic Barkhausen. Indirect, fast, portable; sensitive to stress through acoustoelastic and magneto-mechanical effects but need careful calibration.

Failure modes and trade-offs

• Quench / cold cracking. Tensile residual stress (often combined with hydrogen and a brittle martensitic structure) splits parts hours or days after processing. Counter with tempering and slower quenches.
• Distortion and dimensional instability. A balanced field is fine until you machine it asymmetrically; removing material on one side unbalances the part and it warps. Precision parts are often rough-machined, stress-relieved, then finish-machined.
• Stress-corrosion cracking (SCC). Tensile residual stress plus a corrosive environment cracks alloys (e.g. austenitic stainless steel in chlorides) at stresses far below yield. Stress relief or peening to compression is a standard mitigation.
• Fatigue, both ways. Tensile surface stress (weld toes, ground burns) cuts life; compressive surface stress (peening, carburizing) extends it. The single largest lever on real-component fatigue is often the sign of the residual stress, not the nominal stress range.
• Relaxation in service. Beneficial compression is not permanent. High temperature (creep), large overloads, or excessive tempering after peening can fade the compressive layer, so it must be protected — heat treatment after peening is deliberately limited.
• Buckling of thin welded panels. Compressive residual stress in the parent plate around a weld lowers the load at which thin plates buckle, a real concern in ship and bridge deck design.

Designing with it on purpose

Mature design treats residual stress as a budget to be spent. You add a deep, controlled compressive layer exactly where cracks would start — the fillet of a crankshaft journal, the root of a gear tooth, the bore of a pressure vessel — and you remove harmful tension everywhere you can with stress relief, gentler processes, or geometry that lowers stress concentration. The art is that the two integrals must still balance: every bit of beneficial compression you install at the surface is paid for by tension somewhere below it, so peening too aggressively can simply move the crack-initiation site to the subsurface tensile peak. Like most of engineering, it is bookkeeping with consequences.