residual-stress-measurement

name	residual-stress-measurement
description	Residual stress measurement — X-ray diffraction (sin²ψ method, Bragg's law), neutron diffraction (bulk measurement, d-spacing), hole drilling (ASTM E837, stress relaxation coefficients a/b), blind hole vs. through hole, incremental blind hole, contour method, Vickers hardness estimation, Barkhausen noise, synchrotron diffraction, biaxial stress state, residual stress in welds (tensile at fusion zone), shot peening compressive layer, and residual stress effect on fatigue life.
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Residual Stress Measurement — Complete Skill

Fundamentals of Residual Stress

Sources and Types

Residual stress: stress remaining in material after manufacturing, in absence of external loads Macro-residual stress (Type I): extends over many grains; measurable by hole drilling, XRD; affects structural performance Micro-residual stress (Type II, III): between grains or within grains; affects hardness, yield; measured by XRD line broadening

Common sources: Welding: tensile residual stress at fusion zone (up to σ_y); compressive in surrounding material Shot peening: compressive surface layer (-400 to -800 MPa in steel) Machining: surface tensile or compressive depending on cutting conditions (ground: usually compressive; hard-turned: depends) Quenching: compressive surface (carbon steel); tensile surface (stainless, aluminum in some conditions) Press fitting/interference: compressive in hub bore; tensile in shaft at fit zone

Effect on fatigue: Compressive residual: shifts mean stress negative → extends fatigue life (Goodman-beneficial) Tensile residual: shifts mean stress positive → reduces fatigue life Example: Shot-peened steel: fatigue limit improvement 20–60%; tensile weld stress: reduces fatigue limit 30–50%

X-Ray Diffraction (XRD) — sin²ψ Method

Bragg's Law

Bragg's condition: nλ = 2 × d × sin(θ) [n = integer; λ = X-ray wavelength; d = d-spacing; θ = Bragg angle] Residual stress changes d-spacing → measured as shift in Bragg peak 2θ

sin²ψ method (biaxial surface stress): ε_ψ = (d_ψ - d₀) / d₀ [strain at tilt angle ψ; d₀ = unstressed d-spacing] d_ψ = d₀ × [1 + (1+ν)/E × σ × sin²ψ - 2ν/E × (σ_x + σ_y)] [plane stress assumption]

sin²ψ plot: Linear relationship: d_ψ = f(sin²ψ) → slope gives residual stress Slope = d₀ × (1+ν)/E × σ [for equi-biaxial: σ_x = σ_y = σ; σ_x from rotating sample] σ = (E/(1+ν)) × (∂d/∂sin²ψ) / d₀

Typical XRD parameters: Steel: Cr Kα radiation (λ = 0.2291 nm); {211} reflection (2θ ≈ 156°); penetration depth ≈ 5 μm Aluminum: Cu Kα (λ = 0.1542 nm); {311} reflection; penetration ≈ 20 μm Nickel superalloy: Cr Kα; {311} Depth profiling: combine electrochemical polishing (material removal in steps) + XRD at each depth → σ(z) profile

Accuracy: Typical accuracy: ±20–50 MPa for steel; ±10–30 MPa for aluminum Instrument calibration: stress-free powder standard (silicon Si 640c NIST); measure peak center

Non-destructive for surface (< 20 μm); destructive for depth profiling (electropolishing)

Laboratory vs. Portable XRD

Laboratory XRD: high accuracy; stable geometry; requires sample removal; goniometer Portable XRD (iXRD, Proto LXRD): field measurements on large components; welds, turbine blades; accuracy ±30 MPa

Hole Drilling Method (ASTM E837)

Principle

Semi-destructive: drill small blind hole into surface; measure strain relief with strain gauge rosette Strain gauges measure relaxed strains ε₁, ε₂, ε₃ as material is removed → calculate principal stresses

Standard rosette (ASTM E837 Type A or B): Three strain gauges at 0°, 45°, 135° (or 0°, 45°, 90° for B) Gauge radius a = D_hole/2; hole diameter = 1.8 mm standard (A-type 1.8 mm; B-type 3.8 mm)

Calculation (uniform stress): P = (ε₁ + ε₃) / (2A) [A = calibration coefficient for equibiaxial] Q = (ε₁ - ε₃) / (2B); T = (2ε₂ - ε₁ - ε₃) / (2B) [B = shear calibration coefficient] σ_max, σ_min = P/2 ± √(Q² + T²)/2 [principal stresses]

Calibration coefficients A and B: From ASTM E837 tables as function of hole diameter/gauge mean radius ratio and z/D (depth/diameter) Depend on: geometry, elastic modulus E, Poisson's ratio ν; given in ASTM E837 Table 3

Hole drilling depth: Shallow (0.3–1.0 mm): uniform stress assumption; full depth = gauge mean diameter Incremental: drill in small steps (0.05–0.2 mm increments); measure strain at each depth → σ(z) profile Integral method (Schajer): uses strain data from all increments simultaneously → improved depth resolution

Limitations: Applicable range: σ < 60% σ_y (non-plastic; plastic deformation at hole invalidates analysis) Accuracy: ±10–20 MPa typical; ±5 MPa with careful calibration Minimum component thickness: ≥ 5 × hole diameter for semi-infinite assumption

Neutron Diffraction

Principle: same as XRD but λ_neutron ≈ 1–2 Å; deeply penetrating (mm to cm in steel vs. μm for XRD) Non-destructive bulk measurement: measure d-spacing inside thick components (e.g., weld cross-section, pressure vessel wall) d-spacing from time-of-flight or angle measurement: ε_gauge = (d_hkl - d₀)/d₀ for each crystal plane direction

Gauge volume: defined by slits; typically 1 mm³ to 10 mm³; spatial resolution ~1 mm Facilities: NIST Center for Neutron Research (NCNR); Oak Ridge SNS; ISIS (UK); ILL (France) Access: facility-based; expensive; long lead times; used for critical aerospace, nuclear, automotive components

Measurement time: 1–8 hours per point; typical scan 50–200 points for residual stress map Accuracy: ±10 MPa typical; ±5 MPa with good d₀ reference

Contour Method

Principle: Cut specimen in half using wire EDM (precise planar cut) → record surface topography of cut face (CMM or profilometry) Surface deformation = elastic springback from residual stress relief → solve backwards for stress using FEA

Results: full-field 2D map of stress normal to cut plane; single measurement per component Accuracy: ±20–50 MPa; depends on cut quality and CMM accuracy Application: welds, friction stir welds, forgings, large complex geometry Destructive: component sectioned; cannot be used in-service

Other Methods

Barkhausen Noise (BN): Ferromagnetic steel: magnetic domains move under applied AC field; BN amplitude correlates with stress and hardness Non-destructive surface method; qualitative to semi-quantitative Sensitivity: detects compressive vs. tensile; calibration required per material condition Depth: 0.01–0.5 mm (frequency dependent)

Synchrotron XRD: Brilliant X-ray beam from synchrotron; penetration 1–10 mm in steel (tunable energy) High spatial resolution (0.1 mm); fast acquisition (seconds per point); access at APS, ESRF, SPring-8 Used for titanium engine components, hardened steel gears, pressure vessel components

Ultrasonic (acoustoelastic): Speed of sound changes with stress state: V(σ) = V₀ × (1 + K × σ); K = acoustoelastic constant Requires calibration on stress-free sample; accuracy ±30–100 MPa; non-destructive bulk

Residual Stress in Welds

Weld Residual Stress Distribution

Typical butt weld (single pass): At fusion zone: σ_longitudinal ≈ +σ_y (tensile; material contracts on cooling) At distance 2–5× bead width: σ_longitudinal compressive (balance equilibrium) Transverse stress: lower; peaks at ends of weld

Multi-pass welds: More complex distribution; intermediate passes partially re-anneal previous pass stress Through-thickness: may be tensile through full thickness in thick welds

Post-weld heat treatment (PWHT): Reduces σ_residual to < 0.3 × σ_y; temperature: 600–650°C for carbon steel 1 hr/25 mm thickness Required by ASME B31.3 for critical piping; ASME VIII for pressure vessels above certain thickness

Standards and References

Standard	Scope
ASTM E837	Standard test method for determining residual stresses by hole-drilling strain-gauge method
EN 15305	Non-destructive testing — XRD residual stress analysis
SAE HS784	Residual stress measurement by X-ray diffraction
ASTM E2860	Residual stress measurement by neutron diffraction
ASTM E2592	Barkhausen noise residual stress measurement
BS EN ISO 6507	Vickers hardness test (indirect hardness-stress correlation)

Output

Provide: component description (material; heat treatment; manufacturing history; expected stress type), measurement method selected (XRD/hole drilling/neutron/contour; justification based on depth, geometry, accuracy need), XRD parameters (radiation; crystal plane; penetration depth [μm]; portable vs. laboratory), sin²ψ data summary (d₀ [Å]; slope ∂d/∂sin²ψ; σ_x and σ_y [MPa]; biaxial equibiaxial or principal), hole drilling results (gauge type; A and B coefficients; ε₁/ε₂/ε₃ [μstrain]; σ_max and σ_min [MPa]; angle of principal plane), depth profile σ(z) [MPa vs. mm depth] (from electropolishing + XRD or incremental hole drilling), weld residual stress map (if applicable: longitudinal σ_L [MPa] distribution across weld; compressive balance zone), impact on fatigue life (Goodman correction: σ_a_eff vs. unmodified; fatigue limit shift [MPa or %]), post-weld or surface treatment assessment (PWHT effectiveness; shot peening depth and σ_compressive [MPa]), and applicable standard (ASTM E837, EN 15305, SAE HS784).