Liquid Penetrant Inspection

Liquid Penetrant Inspection (manufacturing-quality/ndt/liquid-penetrant-inspection)

Use when the task is executing liquid penetrant inspection (PT) on a part: computing the capillary pressure and rise that pull the penetrant into a surface-breaking crack, applying the Washburn equation to estimate how deep the penetrant reaches during the dwell time, sizing the dwell time for a crack of given width and depth, and sizing indications from the bleed-out of excess penetrant under the developer.

Domain quick reference

• Capillary pressure: P = 2 * gamma * cos(theta) / r, with gamma the surface tension in N/m, theta the contact angle in degrees, and r the effective capillary radius in meters. This pressure difference drives the penetrant into the crack; a tighter crack gives a higher driving pressure, which is why penetrant finds tight fatigue cracks.
• Capillary rise: h = 2 * gamma * cos(theta) / (rho * g * r), the height at which the hydrostatic head balances the capillary pressure in a vertical crack. Water in a 0.5 mm tube rises about 5.9 cm.
• Washburn penetration: L = sqrt(r * gamma * cos(theta) * t / (2 * eta)), with eta the penetrant viscosity in Pa.s and t the dwell time in seconds. Depth grows as the square root of time, so doubling the dwell time multiplies the penetration by sqrt(2), about 1.41.
• Dwell time sizing: t = 2 * eta * L^2 / (r * gamma * cos(theta)), the inverse of the Washburn equation. Dwell time scales with the square of the depth and inversely with the capillary radius, so a crack twice as deep needs four times the dwell and a crack with half the radius needs twice the dwell.
• Penetration rate: dL/dt = r * gamma * cos(theta) / (4 * eta * L). The front slows as it advances, so most penetration happens early in the dwell time.
• Crack width to radius: a slit crack of opening width w behaves as a capillary of radius r = w / 2.
• Bleed-out: the developer draws excess penetrant out of the flaw, so the visible indication is wider than the actual opening. Tight cracks typically bleed out 3 to 5 times their opening width, and the bleed-out ratio (indication width over flaw width) converts a measured indication to an implied flaw size.
• Developer coverage: developer mass = area * areal density, with dry developer typically applied at 0.1 to 0.2 kg/m2 of part surface.
• Contrast: contrast ratio = abs(bg - ind) / max(bg, ind), near 1 for a bright fluorescent indication on a dark background or a dark dye indication on a white developer background, near 0 when the indication is indistinguishable from the background.
• Acceptance: indications are compared with reference standards and the engineering specification, recorded, and dispositioned under special-process control by NAS 410 qualified personnel. The penetrant process (penetrant, dwell time, developer, removal method) must match the qualified procedure for the sensitivity level required.

Workflow

1. Establish the penetrant system: surface tension gamma in N/m, viscosity eta in Pa.s, and contact angle theta in degrees (below 90 degrees, the wetting condition for capillary pull).
2. Convert the crack opening width to an effective capillary radius with crack_radius_from_width (radius = width / 2).
3. Compute the capillary pressure with capillary_pressure to confirm the penetrant can enter the crack, and the capillary rise with capillary_rise_height where the crack is vertical.
4. Size the dwell time with dwell_time_for_depth for the crack depth, radius, and penetrant properties, then confirm the penetration with washburn_penetration_depth over that dwell time and with penetration_rate at the target depth.
5. After development, measure the indication width and convert it to an implied flaw width with bleed_out_ratio and bleed_out_width; check the contrast ratio with contrast_ratio to confirm the indication is visible above the background.
6. Compare the indication with the acceptance criteria in the engineering specification, record the results, and disposition the part.

Pitfalls

• Using a non-wetting penetrant: a contact angle at or above 90 degrees gives zero or negative capillary pull and the penetrant never enters the crack; the wetting condition theta below 90 degrees is enforced by the math.
• Forgetting the sqrt scaling of the Washburn equation: doubling the dwell time does not double the penetration, it multiplies it by sqrt(2), so a shallow indication after a short dwell needs a much longer dwell, not a marginally longer one.
• Treating dwell time as linear in depth: dwell scales with depth squared, so a 2 mm crack needs four times the dwell of a 1 mm crack at the same radius.
• Sizing the flaw as the indication width: the bleed-out makes the indication 3 to 5 times wider than the opening; dividing by the bleed-out factor recovers the implied flaw size.
• Ignoring viscosity: a thick penetrant at a cold temperature takes far longer to fill the same crack, since dwell time scales linearly with viscosity.
• Skipping the developer step in the math: the indication only appears after the developer draws the penetrant back out; the bleed-out width, not the penetration depth, is what the inspector sizes.
• Reading a low-contrast smear as an indication: a contrast ratio near 0 means the mark is indistinguishable from the background and is background bleed, not a flaw.
• Skipping procedure qualification: PT results are dispositioned under special-process control with NAS 410 qualified personnel, and the penetrant materials, dwell time, and developer must match the qualified procedure for the required sensitivity level.

Behavior contract (gate 3)

The inspection math is exercised by the gate 3 contract test: scripts/test_liquid_penetrant_inspection.py against scripts/liquid_penetrant_inspection_logic.py (stdlib unittest, offline). Run: python3 scripts/test_liquid_penetrant_inspection.py

Compliance

• Standards referenced, not reproduced: AS9100 clause 8.5.1.3 frames NDT as a special process requiring controlled procedures and qualified personnel, and NAS 410 sets the qualification and certification requirements for the NDT personnel who execute liquid penetrant inspection; the capillary, Washburn, and bleed-out calculations above are common PT methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.