One of the most counterintuitive repair techniques in structural engineering is also one of the oldest: to stop a fatigue crack from growing, you drill a hole at its tip. Adding material loss to an already cracked structure seems like exactly the wrong prescription — yet stop drilling is a well-established, theoretically grounded, and widely practiced method for crack arrest in metal structures. And one of history’s most famous cracks offers a cautionary lesson in what happens when the technique is applied incorrectly — or not at all.
The Liberty Bell: America’s Most Famous Fatigue Failure
The Liberty Bell, cast in 1752 by the Whitechapel Bell Foundry in London and recast twice in Philadelphia after initial cracking, cracked again sometime in the early nineteenth century — most likely around 1846, though accounts vary. The crack propagated over many years of cyclic ringing, driven by the alternating tensile and compressive stresses induced by each stroke of the clapper against the bell wall.
In a well-intentioned attempt to arrest the crack, workers drilled and filed the crack edges to widen the gap and relieve contact stress between the two faces. The goal was to prevent the crack faces from rubbing together under vibration — a form of fretting that accelerates crack growth. This intervention is documented but is not a proper stop-drill repair: no circular hole was drilled at the crack tip to blunt the stress concentration. The crack continued to propagate until the bell could no longer ring, and it was silenced permanently in 1846.
Today the Liberty Bell displays a crack roughly 24.5 inches long and approximately 0.5 inches wide at its widest point. It is one of the most recognizable fracture mechanics case studies in American history — a monument to both the significance of fatigue and the consequences of an incomplete repair.
[Image: The Liberty Bell crack, Philadelphia. The wide, irregular crack profile reflects both fatigue propagation and the historical widening intervention. Photo credit: public domain / National Park Service.]
Fracture Mechanics Basis for Stop Drilling
To understand why stop drilling works, we begin with linear elastic fracture mechanics (LEFM) and the stress intensity factor \( K \).
For a through crack of half-length \( a \) in an infinite plate under remote tensile stress \( \sigma \), the Mode I stress intensity factor is:
\[ K_I = \sigma \sqrt{\pi a} \cdot F(a/W) \]
where \( F(a/W) \) is a geometry correction factor (finite width, edge effects, etc.). The stress field ahead of the crack tip has the well-known singularity:
\[ \sigma_{yy}(r, 0) = \frac{K_I}{\sqrt{2\pi r}} \]
As \( r \to 0 \), the stress approaches infinity — a mathematical singularity that physically corresponds to a very high but finite stress in the plastic zone ahead of the crack tip. Each load cycle drives the crack forward by an increment governed by the Paris Law:
\[ \frac{da}{dN} = C \left( \Delta K \right)^m \]
where \( \Delta K = K_{max} – K_{min} \) is the stress intensity range, and \( C \) and \( m \) are material constants. For aluminum alloys, \( m \) is typically in the range 3–4; for steels, 2.5–4. The crack grows fastest where \( \Delta K \) is largest — at the crack tip.
What the Stop Hole Does
When a circular hole of radius \( r_0 \) is drilled at the crack tip, several beneficial effects occur simultaneously:
- Eliminates the singularity. The mathematical stress singularity \( \propto 1/\sqrt{r} \) exists only at a sharp crack tip. A circular hole has no such singularity. The maximum stress at the hole edge is governed by the stress concentration factor \( K_t \), which for a circular hole in an infinite plate under uniaxial tension is exactly 3.0 — large, but finite and bounded.
- Redistributes the stress field. The stress intensity factor \( K_I \) is identically zero for a hole with no crack emanating from it. The crack no longer “sees” a singular tip; the geometry has been fundamentally changed.
- Introduces compressive residual stress. Cold expansion of the stop hole (discussed below) induces a compressive residual hoop stress in the material surrounding the hole. This opposes the applied tensile stress, reducing the effective \( \Delta K \) and significantly extending the crack reinitiation life.
- Removes the damaged material. The plastic damage zone at the crack tip — containing microvoids, dislocations, and microcracking — is physically removed by the drilling operation.
The net result is a dramatic reduction in crack driving force. For a properly drilled and cold-expanded stop hole, fatigue life extension factors of 3–10× are commonly reported in the literature.
Stress Concentration at the Stop Hole
The stop hole is not stress-free — it introduces its own concentration. For a circular hole of radius \( r_0 \) in a plate under biaxial stress \( \sigma_x \), \( \sigma_y \), the hoop stress at the hole edge is:
\[ \sigma_{\theta\theta}(\theta) = (\sigma_x + \sigma_y) – 2(\sigma_x – \sigma_y)\cos 2\theta \]
Under uniaxial loading \( \sigma_x = \sigma \), \( \sigma_y = 0 \), the maximum hoop stress at \( \theta = 90° \) is \( 3\sigma \) — the classical \( K_t = 3 \) result. This means a new fatigue crack can initiate at the stop hole edge if the applied stress is high enough and cyclic loading continues.
This is why stop drilling is a temporary arrest measure, not a permanent repair. In most structural applications, a proper permanent repair follows: the stop hole is cold-expanded (using a split sleeve mandrel) to introduce beneficial compressive residual stress, and in many cases a fastener is installed to carry load across the repaired region and reduce the net section stress at the hole.
Cold Expansion of Stop Holes
Cold expansion (Cx) is a controlled plastic deformation process developed by Fatigue Technology Inc. (FTI) and standardized in AFRL/MIL practice. A split sleeve mandrel slightly larger than the hole diameter is pulled through the hole, plastically deforming the surrounding material. Upon mandrel removal, springback of the elastic far-field creates a compressive residual hoop stress in an annular zone around the hole of approximately:
\[ \sigma_{res}(r) \approx -\sigma_y \left[ 1 – \left(\frac{r_p}{r}\right)^2 \right], \quad r_p \le r \le r_{elastic} \]
where \( r_p \) is the plastic zone radius and \( r_{elastic} \) is the elastic-plastic boundary. The compressive zone extends to approximately 1.5–2.0 hole radii from the edge. The beneficial effect on crack reinitiation life can be dramatic: NASA and USAF studies on 2024-T3 aluminum have shown fatigue life improvements of 3–5× for simple stop holes, and 10–20× for cold-expanded stop holes under representative flight spectrum loading.
Proper Procedure for Stop Drilling
The effectiveness of stop drilling depends critically on execution. The following procedure is representative of aerospace and bridge maintenance practice:
- Locate the crack tip precisely. Dye penetrant inspection (PT), magnetic particle inspection (MT), or eddy current (EC) methods are used. The crack tip is often ahead of the visible surface indication — the actual tip may be 1–3 mm beyond the visible end of the crack. Drilling short of the true tip leaves the singularity intact and provides no benefit.
- Select the stop hole diameter. Larger holes provide greater stress redistribution but reduce net section. Typical diameters are 3–6 mm for thin sheet structures and up to 12–19 mm for heavy bridge plates. The hole should fully encompass the crack tip damage zone.
- Drill perpendicular to the plate surface. Angled entry creates an elliptical hole cross-section with a higher effective \( K_t \).
- Ream to final size and deburr. Drill-induced surface roughness and burrs are stress concentrators. The hole edge should be smooth and the surface finish should meet the applicable specification (typically Ra ≤ 1.6 μm for aerospace, Ra ≤ 3.2 μm for bridge applications).
- Cold-expand if required. For primary structure and long-term repairs, cold expansion using a split sleeve mandrel per AFRL TO 1-1A-9 or FTI SPF/LPF process is performed.
- Install a fastener if required. In many airframe repairs, a high-interference fit fastener (Hi-Lok, NAS1351, or equivalent) is installed in the stop hole to carry shear load across the repair region and introduce additional compressive stress via bearing.
- Document and re-inspect. The repair is logged and the structure is placed on an accelerated inspection interval to detect reinitiation.
Applications in Practice
Aviation
Stop drilling has been used in airframe repair since World War II. The technique appears in FAA Advisory Circular AC 43.13-1B (Acceptable Methods, Techniques, and Practices — Aircraft Inspection and Repair) and numerous manufacturer structural repair manuals (SRMs). Common applications include fuselage skin cracks at window corners (high stress concentration due to the cutout geometry), wing lower surface fatigue cracks from bending-induced tensile stress, and pressure bulkhead cracks.
The classic stress concentrator in airliner fuselages is the window corner, where the hoop and longitudinal pressure stresses combine with the cutout \( K_t \). The de Havilland Comet disasters of 1954 were caused by fatigue crack initiation at square window corners (effectively \( K_t \approx 6–7 \) for the early square geometry) propagating under pressurization cycling. The Comet investigation directly drove the modern understanding of pressure cabin fatigue and damage tolerance design.
Steel Bridges
The American Association of State Highway and Transportation Officials (AASHTO) bridge inspection and repair guidelines endorse stop drilling for fatigue cracks in steel bridge girders. Weld toe cracks, which initiate at the high-stress concentration at the weld termination, are a common application. The FHWA Bridge Inspector’s Reference Manual and NCHRP Report 721 both address stop drilling in the context of fatigue crack retrofit.
Bridge stop holes are typically larger than aerospace equivalents — 19–25 mm (3/4″ to 1″) diameter is common — because the plate thickness is much greater and the goal is to reduce the through-thickness stress intensity across the full thickness. High-strength bolts (ASTM A325 or A490) are frequently installed to clamp the crack faces and introduce beneficial friction on the crack plane.
Ships and Offshore Structures
Fatigue cracking in ship hull plate and offshore platform tubular joints is a persistent maintenance challenge. Stop drilling combined with weld repair (gouging out the cracked zone and rewelding) is standard practice in classification society guidance (DNV-GL, Lloyd’s, ABS). The marine environment introduces the additional complexity of corrosion fatigue, where crack growth rates can be 3–10× higher in seawater than in air for the same \( \Delta K \), making prompt crack arrest especially important.
Paris Law Perspective on Arrest
The Paris Law provides quantitative insight into why crack tip blunting is so effective. Consider a crack of half-length \( a = 20 \) mm in a steel plate under \( \Delta\sigma = 100 \) MPa. The stress intensity range is:
\[ \Delta K = \Delta\sigma \sqrt{\pi a} = 100 \sqrt{\pi \times 0.020} \approx 25.1 \; \text{MPa}\sqrt{\text{m}} \]
With Paris constants \( C = 6.9 \times 10^{-12} \) (m/cycle per (MPa√m)^m) and \( m = 3 \) for structural steel:
\[ \frac{da}{dN} = 6.9 \times 10^{-12} \times (25.1)^3 \approx 1.09 \times 10^{-7} \; \text{m/cycle} \]
That is approximately 0.11 mm per 1000 cycles — a rate that produces visible macroscopic crack growth within tens of thousands of cycles. After stop drilling, \( K_I = 0 \) at the hole (no crack tip singularity), and crack reinitiation life under the same loading is governed by the high-cycle fatigue behavior of the material at \( K_t = 3 \), a very different and far longer process.
What Stop Drilling Cannot Do
Stop drilling is not a substitute for understanding the root cause of cracking. If the crack initiated due to:
- Excessive applied stress (overload, underdesign, or load path change)
- Corrosion fatigue (pitting acting as crack initiation sites)
- Fretting fatigue at joints
- Thermal fatigue from cycling temperature gradients
…then the stop hole will eventually spawn a new crack unless the driving mechanism is addressed. In the Liberty Bell case, the cyclic clapper impact was the driving load — and the bell continued to ring after the attempted repair, ensuring continued crack propagation until the crack became so extensive that ringing produced audible buzzing rather than a clear tone.
The lesson is as valid today as it was in 1846: crack arrest without load reduction or design modification is temporary. Damage tolerance analysis — tracking the crack reinitiation and growth life from the stop hole under the expected load spectrum — is required to determine the inspection interval and the point at which permanent structural repair or replacement is necessary.
Summary
Stop drilling is a simple, elegant application of linear elastic fracture mechanics: eliminate the crack tip singularity by replacing the sharp tip with a smooth circular boundary, redistribute the stress field, and optionally introduce beneficial compressive residual stress by cold expansion. The technique has been used for nearly a century in aviation, bridges, ships, and heavy machinery.
The Liberty Bell stands as a permanent reminder that understanding the mechanics is only part of the problem. Correct execution — drilling far enough, reaching the true crack tip, cold-expanding for long-term benefit, and addressing the underlying load — is what separates a successful arrest from a prolonged failure.
The bell still hangs in Philadelphia, its crack a testament to the difficulty of fatigue repair and the enduring importance of fracture mechanics in structural engineering.
References
- Anderson, T. L., Fracture Mechanics: Fundamentals and Applications, 4th ed., CRC Press, 2017.
- FAA Advisory Circular AC 43.13-1B, Acceptable Methods, Techniques, and Practices — Aircraft Inspection and Repair, FAA, 1998.
- Fatigue Technology Inc. (FTI), Cold Expansion of Fastener Holes, SPF/LPF Process Specification, 2020.
- FHWA, Fatigue and Fracture Reliability Assessment of Steel Bridges, FHWA-SA-97-007, 1997.
- Paris, P. C. and Erdogan, F., “A Critical Analysis of Crack Propagation Laws,” Journal of Basic Engineering, Vol. 85, pp. 528–534, 1963.
- Rooke, D. P. and Cartwright, D. J., Compendium of Stress Intensity Factors, HMSO, London, 1976.
- Suresh, S., Fatigue of Materials, 2nd ed., Cambridge University Press, 1998.
- NCHRP Report 721, Fatigue Evaluation of Steel Bridges, Transportation Research Board, 2012.
- Witmer, M., “The Liberty Bell Crack,” American Heritage of Invention and Technology, Vol. 9, No. 3, 1994.
Tom Irvine is the founder of VibrationData, an IACET-accredited continuing education platform specializing in structural dynamics, shock, vibration, and acoustics. Course catalog and free ebooks are available at vibrationdata.com.