phased-array-ultrasonic

name	phased-array-ultrasonic
description	Phased array ultrasonic testing (PAUT) — focal law calculation (delay laws for beam steering and focusing), electronic scanning (E-scan/S-scan/C-scan displays), near-field/far-field of phased array probes, aperture and element pitch, grating lobe conditions, sensitivity calibration (DAC/TCG curves), weld inspection (full matrix capture FMC/TFM), defect sizing (6 dB drop, tip diffraction TOFD), ASME Code Case 2541 and AWS D1.1 PAUT acceptance criteria.
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Phased Array Ultrasonic Testing (PAUT) — Complete Skill

Phased Array Fundamentals

Array Configuration

Linear array probe: N elements (typically 16–128); element pitch p = center-to-center spacing; element width w ≤ p; kerf (gap) between elements Array aperture: A = N × p [total active aperture; determines beam characteristics] Active aperture (subset): A_act = n_active × p [use n_active < N elements to form each beam]

Frequency selection: f = 2.5–10 MHz for welds (steel); f = 5–15 MHz for fine grain; f = 1–2.5 MHz for coarse grain/cast λ = v_L / f [v_L = 5900 m/s for steel; λ at 5 MHz = 1.18 mm]

Near-Field and Focusing

Near field (N₀) of array: N₀ = A² / (4λ) = (N×p)² / (4λ) [applies along probe axis; within N₀: complex beam; beyond N₀: diverges] Focal length: must be ≤ N₀ to achieve effective focusing Focus in near field: beam width at focus B_F ≈ λ × F / A [F = focal depth; B_F = −6dB beam width]

Example: N = 32; p = 0.6 mm; f = 5 MHz; A = 19.2 mm; λ = 1.18 mm N₀ = (19.2)² / (4 × 1.18) = 368.6 / 4.72 = 78 mm At F = 40 mm: B_F = 1.18 × 40 / 19.2 = 2.46 mm → lateral resolution ~2.5 mm at 40 mm depth

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Focal Laws (Delay Laws)

Beam Steering

Time delay for element i to steer beam to angle θ: Δt_i = x_i × sin(θ) / v [x_i = position of element i from array center; v = wave speed] For element i (numbered from 0 to N-1; center at x_c = (N-1)×p/2): x_i = i × p − x_c = (i − (N-1)/2) × p Δt_i = [(i − (N-1)/2) × p × sin(θ)] / v

Steering to focus (F, θ): Combined delay (steer + focus): t_i = (F − √(F² + x_i² − 2F × x_i × sin(θ))) / v + t_offset [exact geometric focusing delay] For small angles and x_i << F (paraxial approximation): t_i ≈ (x_i × sin(θ) − x_i² × cos²(θ) / (2F)) / v [steering + focusing combined]

Delay quantization: Delays quantized by digitizer clock; Δt_min = 1/f_sampling; sampling: 80–400 MHz Quantization error < λ/10 → negligible beam degradation Required: f_sampling > 10 × f_probe × sin(θ_max) / p (Nyquist for scanning)

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Scan Types

Electronic Scanning (E-scan)

E-scan (linear scan): moves active aperture along probe; same focal law; effectively moves virtual probe position without mechanical motion Resolution: equal to element pitch p in scan direction Used for: corrosion mapping, automated weld scanning at fixed angle

Sectorial Scan (S-scan): Fixed aperture; vary steering angle θ from θ_min to θ_max (e.g., 40°–70° for weld) Display: polar sector image showing all angles simultaneously Typical step: 1° or 2° between beams; gives "fan" of beams into material Most powerful tool for weld inspection: shows defects at all angles in single acquisition

C-scan (top view): Amplitude or depth mapped to XY coordinates from mechanical scanner Grid scan: 1 mm × 1 mm typically; full volumetric map of component

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Grating Lobes

Grating Lobe Condition

Grating lobe: spurious beam at angle θ_gl when array cannot distinguish constructive interference from adjacent periods Grating lobe condition: sin(θ_gl) = sin(θ_main) ± n × λ / p [n = 1,2,...; θ_gl = grating lobe angle] Grating lobes only occur if |sin(θ_main) ± λ/p| ≤ 1 [exists only if p > λ/(1 − sin(θ_max))]

Design rule to avoid grating lobes: p ≤ λ / (1 + sin(θ_max)) [strict limit; ensures no grating lobe for steering up to θ_max] For θ_max = 70°: p ≤ λ / (1 + 0.940) = λ / 1.940 ≈ 0.52λ At 5 MHz in steel (λ = 1.18 mm): p ≤ 0.61 mm → use p = 0.6 mm

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Sensitivity Calibration

DAC and TCG

DAC (Distance Amplitude Correction): curve drawn through amplitude peaks from SDH/FBH reference reflectors at various depths All signals compared to DAC level; signals > DAC level are recordable/reportable

TCG (Time Corrected Gain): electronic equivalent of DAC applied in hardware; amplifies signals from depth so reference reflector appears at same amplitude regardless of depth After TCG: uniform sensitivity throughout depth range (amplitude-depth independent)

Reference reflectors: ASME Code: #3 drill bit SDH (Side-drilled hole) or #2 FBH (Flat-bottom hole); sizes per code AWS D1.1: 1.6 mm SDH at various depths (for weld inspection) Calibration: set system sensitivity so SDH gives 80% full screen height; record calibration file

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Full Matrix Capture (FMC) and TFM

Full Matrix Capture

FMC: fire each element individually; receive on all N elements → N² A-scans stored Data set: H matrix [N×N×time]; complete dataset for post-processing reconstruction Advantages: no fixed focal laws; retrospective focusing to any point in volume

Total Focusing Method (TFM): Coherent sum of all FMC data focused at every pixel (x,z) in image: I(x,z) = |Σᵢ Σⱼ H_ij(t_ij(x,z))| [H_ij = A-scan; t_ij = time of flight transmit element i → pixel → element j] Result: optimally focused image at every depth simultaneously; better than any fixed focal law S/N improvement: √(N) vs. single element; resolution: λ/2 approximately

Processing requirements: N² A-scans; e.g., N = 64 → 4096 A-scans per shot; computationally intensive → real-time requires GPU

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Defect Sizing

6 dB Drop Method

6 dB drop technique: Peak the signal on defect; scan until signal drops to half amplitude (−6 dB = 50%); mark position Defect edge to edge = measured width; works for defects larger than beam width Sizing accuracy: ±1–3 mm (beam width dependent)

Maximum Amplitude Method: Find maximum amplitude position → tip of defect; compare to DAC curve → depth estimation from transit time Less accurate than echo-dynamic and TOFD for sizing

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ASME and AWS Standards

Code Acceptance Criteria

ASME Code Case 2541 (PAUT for weld inspection): Qualification: demonstrated capability (POD ≥ 90% at 90% confidence for design flaw size) Calibration: per Code Case procedure; T-scan block specific to weld configuration Acceptance: linear defects > 3 mm reportable; assessed per ASME Section XI acceptance

AWS D1.1 Structural Welding Code — PAUT: Annex Q: PAUT acceptance criteria for prequalified welds Calibration: SDH 1.6 mm diameter reference; sensitivity set to 80% FSH Acceptance: indicative discontinuities exceeding acceptance criteria → reject/repair

ASME Section V Article 4 (UT) and Code Case 2235 (TOFD for sizing): Combined PAUT + TOFD often used: PAUT for detection; TOFD for accurate through-wall sizing

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Standards and References

Standard	Scope
ASME Code Case 2541	PAUT for weld inspection
ASME Section V Article 4	Ultrasonic examination
AWS D1.1 Annex Q	PAUT for structural welds
EN 12668-1	Ultrasonic equipment characterization
ASTM E2700	Standard practice for contact PAUT
ISO 13588	PAUT for weld examination

Output

Provide: application (weld type: butt/T/nozzle; material: steel/SS/Ti; thickness t [mm]; geometry: flat/curved; code: ASME/AWS), probe selection (N elements; pitch p [mm] ≤ λ/(1+sin(θ_max)) to avoid grating lobes; frequency f [MHz]; aperture A = N×p [mm]; near-field N₀ [mm]; coupling: contact/immersion/phased-contact-wedge), scan type (E-scan/S-scan/FMC+TFM; for weld: S-scan from 40–70° in 1° steps; E-scan coverage if needed), focal laws (delay t_i [ns] for beam angle θ and focus F; verification: beam simulation software; focal spot size [mm]), calibration (reference reflector: SDH Ø[mm] at depths [mm]; TCG applied; sensitivity at −6 dB reference amplitude; calibration block drawing per code), coverage (sound paths from all scanning positions; wedge choice; coverage map confirming full weld volume examined; dead zone near surface [mm] compensated by TOFD?), sizing (method: 6dB drop / tip echo diffraction / TFM; accuracy ±[mm]; minimum detectable flaw size [mm]), acceptance criteria (code: ASME CC2541 or AWS D1.1 Annex Q; reportable indications size; reject/accept assessment), and applicable standard (ASME CC2541; AWS D1.1 Annex Q; ASTM E2700).