Theory

Key Differences — Speed, Medium & Energy Loss

The animations show how the two waves look. Three practical consequences follow from the speed hierarchy: refraction angles at every material interface are fixed by speed ratios (Snell's law); water-path timing in immersion rigs must account for the ~4× speed jump between water and steel; and depth-sizing accuracy is bounded directly by how well the wave speed in the test piece is known.

Types of Elastic Waves

In a solid, atoms are linked by elastic bonds. A disturbance can move through that lattice in several ways, classified by how the particles move relative to the wave direction. Each isometric sample below is a small block of material with particles tracking their true 3-D motion as the wave passes through it, left to right.

📈 Snell's Law & Mode Conversion

When an ultrasonic wave strikes a planar interface at oblique incidence, it simultaneously produces a refracted P-wave and a mode-converted S-wave in the second medium. Both obey Snell's law independently, each governed by its own wave speed:

Because c_L2 ≠ c_S2, the two transmitted beams diverge in direction. In steel (c_L = 5900 m/s, c_S = 3200 m/s) the refracted P bends nearly twice as far from the normal as the mode-converted S.

Immersion UT at θ_i = 20° — between the two critical angles for water–steel. The refracted P-wave undergoes total internal reflection, so only the mode-converted S (≈ 48°) propagates into the steel.

Critical Angles

As θ_i increases, two thresholds mark where a transmitted wave reaches 90° (grazes the interface) and undergoes total internal reflection (TIR):

• First critical angle (θ_c1): sin(θ_c1) = c_L1 / c_L2. The refracted P-wave undergoes TIR; for θ_i > θ_c1, only the mode-converted S transmits into the solid.
• Second critical angle (θ_c2): sin(θ_c2) = c_L1 / c_S2. The mode-converted S also undergoes TIR; for θ_i > θ_c2, both waves are totally reflected and Rayleigh surface waves can be generated along the interface.

Angle-beam probes are designed to operate with the wedge angle strictly between θ_c1 and θ_c2, ensuring a single-mode (pure shear) beam enters the test piece.

What Is Ultrasound?

Ultrasound is sound with a frequency above the upper limit of human hearing — roughly 20 kHz. It obeys exactly the same wave physics as the audible sound covered in Section 1; only the frequency changes. Because higher frequency means shorter wavelength (λ = c / f), ultrasound can resolve much finer detail than audible sound — which is exactly why it is useful for imaging and flaw detection rather than just hearing.

Fundamental Principle of Ultrasonic NDT

In pulse-echo UT, a transducer fires a short burst of ultrasound into the part and listens for returning echoes. The time it takes each echo to arrive directly encodes depth — flaws appear as early echoes, the back wall gives total thickness. Everything flows from d = c × t / 2.

Scanning Methods — A-scan

The A-scan (Amplitude scan) is the most fundamental display in ultrasonic testing. It shows amplitude vs. time for a single transducer position — essentially what the transducer "hears" after it fires a pulse.

The time axis is converted to depth using d = c × t / 2 (round-trip). Three key features appear:

• Initial pulse (IP): The transmitted burst — appears at t = 0.
• Defect echo: A reflection from an internal flaw — appears at a time proportional to the flaw's depth.
• Back-wall echo (BW): Reflection from the far surface — appears at a time proportional to the total thickness.

A-scans can be displayed as RF (raw bipolar), full rectified (both halves folded positive), or envelope (smooth amplitude via Hilbert transform). Most field instruments default to rectified RF.

Scanning Methods — C-scan

A C-scan (Plan view scan) produces a top-down 2D map of the part. The transducer is raster-scanned in X–Y, and at each position a single scalar value extracted from the A-scan within a user-defined depth gate is recorded as one pixel. The result is a spatially registered image of the internal structure projected onto the scan plane.

Depth Gating — How One Pixel Is Formed

The gate is a time window set on the A-scan. Only echoes arriving within the gate contribute to the C-scan pixel. This depth selectivity is the key distinction from a simple reflectivity map: placing the gate at a specific depth range lets the operator image one layer at a time while suppressing reflectors above and below it.

Two distinct C-scan modes extract different information from the gated A-scan:

• Amplitude C-scan: Records the peak (or integrated) rectified amplitude within the gate. A delamination or void produces a strong reflection appearing as a high-amplitude region. Amplitude drop relative to a reference block enables sizing by the −6 dB or −14 dB method.
• Time-of-flight (TOF) C-scan: Records the arrival time of the first echo exceeding a threshold within the gate. Converted to depth via \(d = ct/2\), this produces a continuous thickness or contour map. TOF C-scans are standard for corrosion mapping and thickness verification on curved geometry.

Scan Resolution and Lateral Resolution Limits

C-scan image fidelity is governed by two independent factors. The scan step (Δx, Δy) is the mechanical indexing pitch — analogous to pixel pitch in digital imaging. Nyquist-equivalent spatial sampling requires Δx ≤ d_spot/2, where \(d_\text{spot} \approx 1.02\,\lambda F/D\) is the −6 dB focal spot diameter. Undersampling misses flaws smaller than the step pitch even if the beam could resolve them.

The beam lateral resolution is the hard physical limit: two adjacent reflectors separated by less than d_spot cannot be distinguished regardless of step size. In the far field of an unfocused transducer, lateral resolution degrades linearly with depth, making focused immersion setups necessary for thin-section or high-resolution work.

NDE Example — Immersion C-scan of an L-PBF Ti-6Al-4V Coupon

Laser powder-bed fusion (L-PBF) parts contain sub-surface porosity and lack-of-fusion voids whose spatial distribution governs fatigue life. A representative immersion C-scan protocol for a 10 × 10 × 5 mm coupon:

Voids appear as amplitude drops in through-transmission or amplitude peaks in pulse-echo. Through-transmission eliminates the front-wall dead zone but discards all depth information; pulse-echo retains TOF depth at the cost of a near-surface blind region equal to approximately one pulse length (∼λ/2 per cycle in the burst).

🔴 Attenuation — Detailed

Total attenuation in a polycrystalline metal has two physically distinct contributions: absorption (thermoelastic and viscous energy conversion to heat) and scattering (energy redirected by grain boundaries, pores, and inclusions). Their frequency scalings differ, so the dominant mechanism — and the optimal inspection frequency — depends on grain size relative to wavelength.

where d is mean grain diameter, f is frequency, and α_R, α_S are material constants. The active regime is determined by the dimensionless parameter kd = 2πfd/c:

Three Scattering Regimes

Regime Summary

NDE Example: Austenitic Stainless Steel Welds

Austenitic SS weld metal solidifies as columnar dendritic grains, with effective grain diameters of 50–500 µm and strong crystallographic texture. At a typical 5 MHz inspection frequency in steel (c_L ≈ 5 900 m/s, λ ≈ 1.2 mm), a 200 µm grain gives kd ≈ 0.7 — squarely in the stochastic regime. The consequence is severe coherent grain noise (often called backwall grass) that can mask crack tip signals. The standard engineering response is to drop to 1–2 MHz, accepting lower axial resolution, to push kd back into the Rayleigh regime and recover signal-to-noise. The trade-off is quantified by the figure of merit:

FOM is approximately constant within the stochastic regime and is used as a material characterisation parameter for phased-array inspection qualification. For fine-grained carbon steel (d ~ 20 µm), FOM ≈ 0.005–0.02 dB/(mm·MHz²); for coarse austenitic weld metal it can reach 0.1–0.5 — an order-of-magnitude degradation in inspectability.

🔋 Phased Arrays & Advanced Imaging

A phased array transducer replaces a single piezoelectric element with a linear (or matrix) array of small elements — typically 16 to 128 — each fired with an independently programmed time delay. By controlling those delays, a single probe can steer the beam to any angle, focus at any depth, and reconstruct a full cross-sectional image without moving the probe. This is electronic scanning rather than mechanical scanning.

Delay-Law Beam Steering

For a linear array with element pitch p (centre-to-centre spacing), the delay applied to the n-th element to steer the beam to angle θ is:

Element 1 fires first; each successive element fires later by an increment p sinθ /c. The wavefronts from all elements constructively interfere along the chosen steering direction, forming a coherent beam at angle θ. Applying a parabolic delay profile on top of the steering ramp simultaneously focuses the beam at depth F:

Ten-element array with staggered transmit delays (blue bars, proportional to τ_n) steering a focused beam to 30°. Purple dashed rays represent the full S-scan sector swept electronically without moving the probe.

Sectorial Scan (S-scan)

In an S-scan, the delay law is updated in real time to sweep the beam through a preset angular range — typically 40° to 70° for shear-wave weld inspection — while simultaneously adjusting the focus depth at each angle. Each angular position yields one A-scan; stacking them produces a cross-sectional image where steering angle maps to lateral position and time-of-flight to depth. A single probe placed beside the weld delivers the full volumetric image that conventional UT would require three separate angle-wedge setups to achieve.

Full Matrix Capture & Total Focusing Method (FMC/TFM)

FMC is an acquisition mode in which every transmit–receive pair is recorded independently: element 1 transmits while all N elements receive; then element 2 transmits; and so on. For an N-element array, FMC yields N² A-scans. TFM then reconstructs an image by coherent delay-and-sum over every pixel (x, z):

Because each pixel is reconstructed with its own exact delay law, TFM achieves diffraction-limited focusing uniformly across the image — not only at the single depth a conventional focused probe can target. The N² summation also suppresses incoherent grain noise by approximately √N² = N relative to a coherent flaw signal, improving SNR by ~20 log₁₀(N) dB; for N = 64 that is 36 dB. The computational cost is substantial — a 64-element, 10 MHz array over a 50×50 mm image at 0.1 mm pixel pitch requires O(10⁹) multiply-accumulate operations per frame, typically handled by GPU or FPGA.

NDE Example — Inspection of Metal Additive Manufactured Parts

Laser powder-bed fusion (LPBF) components present a demanding inspection scenario: sub-millimetre lack-of-fusion (LOF) voids and keyhole pores (10–200 µm diameter), columnar grain texture aligned with the build direction, and near-net-shape surfaces. Conventional pulse-echo at 5–10 MHz detects pores > ~0.5 mm in diameter reasonably well, but planar LOF defects oriented parallel to the build layers — the highest-risk flaw type in fatigue-critical components — return amplitudes well below a standard DAC curve because their specular reflection is directed away from the transducer.

Multi-mode TFM (LL, LT, TT propagation paths) addresses both limitations. Longitudinal– Longitudinal (LL) mode at near-normal incidence minimises mode-conversion noise from the textured grains; Longitudinal–Transverse (LT) and TT modes illuminate LOF faces at oblique incidence, returning an amplitude that is far less sensitive to defect tilt angle. For an LPBF IN718 coupon (c_L ≈ 5 700 m/s, α ≈ 0.3 dB/mm at 10 MHz), a 64-element, 10 MHz, 0.6 mm-pitch immersion array achieves a focal spot d_spot = 1.02λF/D ≈ 0.35 mm at 15 mm depth — resolving individual 250 µm LOF defects invisible to conventional single-element UT. Qualification per ASTM E2700 and ASME Code Case 2541 requires demonstrating detection of 0.8 mm FBH equivalents at T/4, T/2, and 3T/4 across the inspection volume.

⚡ Pulser-Receiver & the Signal Chain

Every UT system revolves around a pulser-receiver: the instrument that fires the transducer and amplifies the returning echoes. Understanding its settings is essential for optimising sensitivity, resolution, and noise rejection.

Pulser Settings

Receiver Settings

Rectification Modes — Animated

The raw A-scan is a bipolar RF voltage. Rectification converts it for easier visual interpretation:

🔧 Application — Weld Inspection

Weld inspection is the dominant contact UT application, and the one that most directly motivates the beam physics covered earlier. A complete weld examination follows a two-stage procedure mandated by AWS D1.1 and ASME Section V: first a straight-beam lamination check of the base metal, then an angle-beam volume scan of the weld itself.

Stage 1 — Straight-Beam Lamination Scan

A 0° longitudinal probe scans the base metal on both sides of the weld — specifically the heat-affected zone (HAZ), the region where thermal cycling has altered the grain structure. The goal is to detect pre-existing laminations or delaminations in the plate stock. An undetected lamination lying parallel to the surface will shadow the angle beam in Stage 2, creating a false "clean" weld — the most dangerous miss in contact UT.

Stage 2 — Angle-Beam Weld Volume Scan

Refracted shear waves (typically 45°, 60°, or 70°) are directed through the weld cross-section using a wedge probe. Because the weld cap blocks direct access, the beam must travel an oblique V-path. The probe is indexed to place the beam at the root (first leg — direct downward path) and at the crown interior (second leg — beam reflected off the backwall), then progressively shifted to sweep the full volume.

The half-skip distance — the surface distance from probe exit to where the beam completes one V-path and returns to the top surface — is:

where T is wall thickness and θ is the refraction angle in the material. For a 20 mm wall at 45°: S½ = 40 mm; at 70°: S½ = 110 mm. The large change in index distance is why 70° is preferred for thin plate and 45° for thick sections — the probe simply cannot be placed close enough to the weld for a 70° beam to reach the root in thick material without standing on the weld cap.

Cross-section view. Blue = 45° SV-wave, first leg sweeping the root region. Purple dashed = second (reflected) leg sweeping the weld interior and cap. Stage 1 straight-beam probe (left) pre-clears the HAZ for laminations before the angle scan.

Worked NDE Example — Pipeline Girth Weld

Consider inspection of an API 5L X65 pipeline girth weld: wall thickness T = 20 mm, V-groove butt joint, material c_S = 3250 m/s. Per ASME B31.3 / API 1104, two refraction angles are required for full volumetric coverage.

For a 45° shear-wave probe: S½ = 2 × 20 × tan(45°) = 40 mm. Place the probe so its index point is 40 mm from the weld centreline — the beam then completes one V-path and illuminates the weld cap interior on the far side. Shift the probe to index point + 20 mm (i.e. S¼ = T × tanθ) and the first leg terminates at the root — the most fracture-critical location.

A 70° probe gives S½ = 2 × 20 × tan(70°) ≈ 110 mm. This covers the weld sidewalls and upper-bead region that the 45° beam illuminates at an unfavorable angle. The combination — 45° for root/cap, 70° for sidewalls — satisfies the ASME requirement that every volume element be interrogated from at least two directions. Sensitivity is set by calibrating on a 1.5 mm side-drilled hole (SDH) at T/4, T/2, and 3T/4 depths in the reference block.

Common Weld Defects Detectable by UT

Angle Beam Geometry

For a shear wave refracted at angle θ_R in a plate of wall thickness T, the depth and surface distance from the probe entry point to any point at beam path length ℓ are:

The half-skip distance S_½ = T tanθ_R is the surface distance at which the beam terminates at the backwall — the critical stand-off for root inspection. After one reflection the beam returns to the scanning surface at the full-skip distance 2S_½ = 2T tanθ_R. The four canonical probe positions and the weld zones they illuminate are:

45° SV-wave V-path in a plate of thickness T. Coloured markers show the four standard probe stand-off positions used for full weld-volume coverage.