13.6 AWS D1.1 Decibel Rating, Phased Array & Time-of-Flight Diffraction

4. AWS D1.1 Decibel Rating System (Clause 8 / Clause 6)

AWS D1.1 governs structural weldment acceptance using a standardized Decibel Indication Rating System that eliminates subjective operator interpretation.

                      AWS D1.1 INDICATION RATING FORMULATION

                                  d = a - b - c
                                        |
             +--------------------------+--------------------------+
             |                          |                          |
             V                          V                          V
     Indication Level (a)       Reference Level (b)       Attenuation Factor (c)
     Instrument gain (dB)       Instrument gain (dB)      Sound path correction:
     to bring flaw echo         to bring 0.060" SDH       c = 2 · (S - 1.0 in)
     to reference height        in IIW block to           c = 0.08 · (S - 25 mm)
     (e.g., 50% FSH).           reference height.

Mathematical Formulation

$d = a - b - c$

where:

• $a$ = Indication Level (dB): The calibrated instrument gain setting in decibels required to bring the peak reflection from the unknown discontinuity to the reference screen height (typically $50%$ or $40%$ of Full Screen Height, FSH, per WPS).
• $b$ = Reference Level (dB): The calibrated instrument gain setting in decibels required to bring the reflection from the $0.060\text{ in}$ ($1.5\text{ mm}$) side-drilled hole (SDH) in an IIW Type 1 or 2 calibration block to the identical reference screen height at a known calibration sound path.
• $c$ = Attenuation Factor (dB): A mathematical deduction compensating for sound beam scattering and material attenuation as sound path distance increases beyond $1.0\text{ in}$ ($25\text{ mm}$):
  • Inches: $c = 2 \times (S - 1.0)$, where $S$ is the measured sound path length in inches. If $S \le 1.0\text{ in}$, $c = 0\text{ dB}$.
  • Millimeters: $c = 0.08 \times (S - 25)$, where $S$ is the measured sound path length in millimeters. If $S \le 25\text{ mm}$, $c = 0\text{ dB}$.
• $d$ = Indication Rating (dB): The calculated decibel score evaluated against AWS D1.1 Table 8.2 (Statically Loaded Structures) or Table 8.3 (Cyclically Loaded Structures).

Critical Core Principle: The Counter-Intuitive Decibel Scale In the AWS D1.1 rating formulation, a lower or negative $d$ value represents a larger, more severe discontinuity. Proof: A massive crack reflects intense sound energy back to the transducer. The operator requires very little instrument gain ($a$) to push the echo to $50%$ screen height (e.g., $a = 28\text{ dB}$). When subtracted from reference level $b$ (e.g., $b = 40\text{ dB}$), $d = 28 - 40 - c = -12 - c$, yielding a negative number. Conversely, a tiny pinhole pore reflects almost no energy; the operator must crank the instrument gain up to $a = 65\text{ dB}$, yielding a high positive rating ($d = +20\text{ dB}$). Under AWS D1.1, negative and low ratings trigger Class A (Rejectable Flaws).

AWS D1.1 Indication Severity Classification

Calibration Blocks: IIW vs. DSC Blocks

• IIW Block (International Institute of Welding): Universal standard calibration block. Type 1 contains a $4.0\text{ in}$ ($100\text{ mm}$) radius curved surface, a $1.0\text{ in}$ ($25\text{ mm}$) radius cutout, a $0.060\text{ in}$ ($1.5\text{ mm}$) side-drilled hole, and graduated angle scales. Used to verify probe index point, refracted angle, horizontal linearity, and establish reference sensitivity level ($b$).
• DSC Block (Distance and Sensitivity Calibration): Compact, lightweight field block containing $1.0\text{ in}$ ($25\text{ mm}$) and $3.0\text{ in}$ ($75\text{ mm}$) radii and side-drilled holes. Ideal for calibrating angle-beam sound path distance and sensitivity directly on high-elevation structural steel erection sites.

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5. Advanced Ultrasonic Inspection: PAUT & TOFD

Modern welding quality control increasingly mandates advanced digital ultrasonic techniques that replace traditional single-crystal manual UT.

       PHASED ARRAY UT (PAUT)                       TIME-OF-FLIGHT DIFFRACTION (TOFD)
      Electronic Sectorial Scan (S-Scan)              Pitch-Catch Crack Tip Diffraction

          Multi-Element Array Probe                     Transmitter (T)         Receiver (R)
             [||||||||||||||||]                              +-----+               +-----+
            /   |   |    |    \                              |  T  |               |  R  |
           /    |   |    |     \                             +--+--+               +--+--+
          40°   50° 60°  70°   80°                              \ Lateral Wave (Creep) /
                                                                 \____________________/
                                                                  \   Upper Tip      /
                                                                   \   Diffraction  /
                                                                    \      *       /
                                                                     \     | Crack/
                                                                      \    *     /
                                                                       \ Lower  /
                                                                  ======+======+======
                                                                      Backwall Echo

1. Phased Array Ultrasonic Testing (PAUT)

• Hardware Architecture: Rather than a single piezoelectric element, a PAUT probe contains an array of discrete elements (typically 16, 32, 64, or 128 individual crystal strips), each pulsed independently through multichannel electronics.
• Focal Laws: Computer-controlled pulsing introduces precise time delays (nanoseconds) across adjacent elements. Constructive wave interference steers the acoustic beam across a continuum of angles and focuses beam energy at specific depths (Dynamic Depth Focusing, DDF).
• Sectorial Scan (S-Scan): A single stationary PAUT probe sweeps an angular fan of shear waves through the weld cross-section (e.g., sweeping from $40^\circ\text{ to }70^\circ$). This sweeps the entire weld root, sidewall fusion lines, and crown simultaneously without moving the probe forward and backward, capturing instantaneous cross-sectional data.
• Electronic Scan (E-Scan / Linear Scan): Multiplexes groups of elements along the array length at a constant angle, simulating a rastering probe without mechanical movement.

2. Time-of-Flight Diffraction (TOFD)

• Physics of Crack-Tip Diffraction: Traditional UT relies on specular reflection, which requires the acoustic beam to strike a smooth planar flaw perpendicularly. When sound strikes a sharp crack edge, the tip acts as an independent point source, scattering spherical diffracted waves in all directions.
• Probe Configuration: TOFD utilizes an un-coupled pitch-catch arrangement where a dedicated Transmitter (T) and Receiver (R) probe straddle the weld seam on opposite sides.
• Signal Train: The receiver captures four discrete chronological arrivals:
  1. Lateral Wave: Creeps along the plate surface directly between probe tips (earliest arrival).
  2. Upper Tip Diffracted Wave: Emanates from the top apex of the crack.
  3. Lower Tip Diffracted Wave: Emanates from the bottom root of the crack (exhibiting phase inversion relative to upper tip).
  4. Backwall Reflection: Specular reflection bouncing off the bottom plate surface.
• Sub-Millimeter Flaw Height Sizing: By measuring the exact transit time difference between the upper tip ($t_1$) and lower tip ($t_2$), crack vertical depth ($d$) is calculated geometrically: $d = \sqrt{ \left( \frac{c \cdot t}{2} \right)^2 - s^2 }$ where $2s$ is the probe center separation distance (PCS) and $c$ is longitudinal velocity. This enables precise vertical flaw height sizing ($\Delta h = d_2 - d_1$) with accuracy within $\pm 0.5\text{ mm}$, completely independent of signal echo amplitude.
• TOFD Dead Zones: Near-surface dead zones exist directly beneath the plate surface (obscured by the high-amplitude lateral wave pulse), and backwall dead zones exist immediately above the bottom surface (obscured by the massive backwall reflection). Consequently, TOFD is frequently paired with PAUT to achieve $100%$ volumetric coverage.

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6. Worked Numerical Examples

Example 1: Calculating Refracted Angle in Steel via Snell's Law

Problem: A Lucite angle-beam wedge is manufactured with an internal incident angle $\theta_1 = 40.0^\circ$. The longitudinal velocity in the Lucite wedge is $c_{\text{wedge}, L} = 2730\text{ m/s}$, and the transverse shear velocity in carbon steel is $c_{\text{steel}, S} = 3240\text{ m/s}$.

1. Confirm whether the incident angle falls within the operational angle-beam window.
2. Calculate the exact refracted shear wave angle ($\theta_{S2}$) in the steel plate.

Solution:

• Step 1: Check Operational Angle-Beam Window

  • First critical angle: $\theta_{c1} = \arcsin(2730 / 5900) \approx 27.56^\circ$.
  • Second critical angle: $\theta_{c2} = \arcsin(2730 / 3240) \approx 57.42^\circ$.
  • Because $27.56^\circ < 40.0^\circ < 57.42^\circ$, longitudinal waves are completely eliminated, and only pure shear waves propagate into the steel.

• Step 2: Apply Snell's Law for Shear Wave Refraction $\frac{\sin(\theta_1)}{c_{\text{wedge}, L}} = \frac{\sin(\theta_{S2})}{c_{\text{steel}, S}}$ $\sin(\theta_{S2}) = \sin(40.0^\circ) \times \left( \frac{c_{\text{steel}, S}}{c_{\text{wedge}, L}} \right) = 0.64279 \times \left( \frac{3240}{2730} \right) = 0.64279 \times 1.18681 = 0.76287$ $\theta_{S2} = \arcsin(0.76287) \approx 49.7^\circ$

• Engineering Evaluation: The wedge produces a refracted shear wave angle of $49.7^\circ$ in carbon steel.

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Example 2: AWS D1.1 Indication Rating ($d$) Sizing

Problem: An ultrasonic technician inspecting a $50\text{ mm}$ ($2.0\text{ in}$) thick CJP groove weld in an AWS D1.1 statically loaded building frame detects an internal flaw using a $70^\circ$ angle-beam transducer ($2.25\text{ MHz}$). The testing parameters are:

• Indication Level ($a$): $46\text{ dB}$ (gain to bring flaw peak to $50%$ FSH)
• Reference Level ($b$): $40\text{ dB}$ (gain to bring $0.060\text{ in}$ SDH in IIW block to $50%$ FSH)
• Sound Path Distance ($S$): $4.5\text{ inches}$ ($114.3\text{ mm}$)

Calculate the Attenuation Factor ($c$), determine the Indication Rating ($d$), and identify the severity classification assuming the AWS D1.1 Table 8.2 criteria specifies that for this joint thickness, ratings of $+2\text{ dB}$ and lower correspond to Class A (Rejectable).

Solution:

• Step 1: Calculate Attenuation Factor ($c$) $c = 2 \times (S - 1.0) = 2 \times (4.5 - 1.0) = 2 \times 3.5 = 7.0\text{ dB}$

• Step 2: Calculate Indication Rating ($d$) $d = a - b - c = 46\text{ dB} - 40\text{ dB} - 7.0\text{ dB} = 6.0 - 7.0 = -1.0\text{ dB}$

• Step 3: Severity Evaluation

  • Because $d = -1.0\text{ dB}$, which is strictly less than $+2\text{ dB}$, the indication falls into Severity Class A (Large Discontinuity).

• Engineering Disposition: The flaw is rejected. The weld must be excavated, repaired, and re-examined.

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7. Industrial Scenarios & Certified Welding Engineer Exam Pitfalls

Real-World Engineering Failure Scenario

During the erection of a heavy box girder for a railway bridge, ultrasonic examination of a $40\text{ mm}$ thick web-to-flange CJP groove weld was executed without performing preliminary $0^\circ$ straight-beam base metal scanning. The angle-beam inspection showed zero indications, and the weld was stamped as code-compliant. During heavy freight train traffic eight months later, fatigue cracks ruptured through the web. Post-failure metallurgical investigation uncovered a massive internal mid-plane plate lamination spanning $450\text{ mm}$ adjacent to the weld toe. When the original angle-beam shear wave entered the plate, it struck the upper boundary of the lamination and bounced harmlessly into the top flange, completely missing a massive $8\text{ mm}$ incomplete sidewall fusion defect along the root. Had the technician executed the mandatory AWS D1.1 Clause 8 straight-beam screening, the lamination would have been identified immediately, preventing the false-negative stamp.

Common Exam Traps

Exam Trap 1: Decibel Sign Inversion in AWS D1.1 A major trap on the CWEng exam is assuming that a higher $d$ number means a worse flaw (by analogy with optical density or stress). In the AWS D1.1 formula $d = a - b - c$, the lower the decibel rating, the larger and more hazardous the defect. A rating of $-4\text{ dB}$ is far more severe than $+12\text{ dB}$. Candidates who rank flaws in ascending numerical order will fail classification questions.

Exam Trap 2: Sizing Accuracy of Amplitude vs. TOFD When an exam question asks which technique provides superior flaw height sizing accuracy in thick-wall weldments, avoid selecting "manual angle-beam peak amplitude matching" (such as the $6\text{ dB}$ or $20\text{ dB}$ drop methods). Amplitude drop methods are notoriously inaccurate due to beam spreading, flaw roughness, and orientation. Time-of-Flight Diffraction (TOFD) provides the highest sizing precision because it calculates flaw vertical extent from tip diffraction arrival times, completely independent of reflected beam amplitude.

Exam Trap 3: Shear Waves in Liquids Questions frequently ask why couplant is applied between the Lucite wedge and the steel plate rather than inside the transducer assembly, or whether shear waves can propagate through water. Remember that shear waves require resistance to shear strain ($G > 0$). Transverse shear waves cannot propagate through liquids (water, oil, couplant) or gases. The wave propagating through the couplant film is always a longitudinal compression wave; shear mode conversion occurs exclusively upon entering the solid steel matrix.