Every structure contains discontinuities. Castings have porosity, forgings have laps, welds have inclusions and lack of fusion, and machined parts have tool marks. Most of them never matter. Fracture mechanics exists to say which ones do, by tying three quantities together: the size of the flaw, the stress acting on it, and the material's resistance to a crack running from it. Fix any two and the third follows, which is why the framework is so useful when a dispute turns on whether a part was defective or simply overloaded.
The quantity that links the three
The stress intensity factor describes the severity of the stress field at a crack tip. It rises with the applied stress, with the square root of the flaw size, and with a geometry term reflecting the shape of the flaw and the part around it.
Fracture occurs when that quantity reaches the material's toughness. Below it the crack does not run; at it, propagation becomes self-sustaining and effectively instantaneous. The practical consequence is that a flaw is not large or small in the abstract, only relative to a stress and a toughness.
Fix two, solve for the third
Run forward with a known flaw and a known stress and the answer is whether the part was near its limit. Run it the other way, holding toughness and stress fixed, and it yields a critical flaw size: how big a discontinuity had to be before the part could not carry its load.
Solving for stress is often the most informative. Given the flaw found on the fracture surface and a measured toughness, the calculation returns the stress required to break the part, which can be compared against the loads the service record supports.
Where the toughness value comes from
ASTM E399 covers plane-strain fracture toughness, and imposes size and validity requirements so the measured value reflects a constrained, thickness-independent property rather than the specimen's geometry. Where a material is too tough or too thin to satisfy them, the test does not produce a valid result.
ASTM E1820 covers elastic-plastic behaviour through the J-integral and crack-tip opening displacement, which is the appropriate route for tougher structural steels. Which standard was used is a real distinction, and using a literature value in place of a tested one is a routine point of challenge.
Where the applied stress comes from
The nominal stress from the design load is only part of it. Residual stress from welding, forming or heat treatment adds to the applied stress at the crack tip, and near a weld it can approach yield magnitude without appearing in any calculation the designer performed.
Local geometry multiplies what remains. A fillet radius, a keyway, a thread root or a section change raises stress well above nominal, so the value that matters is the stress at the flaw, not the stress on the drawing.
Where the flaw size comes from
The most reliable source is the fracture surface itself. An initiating discontinuity can usually be located and measured directly, and its character established by metallography and by ASTM E340 macroetching, which reveals flow lines, segregation and weld fusion boundaries.
Inspection records supply the alternative. Radiography, ultrasonics or magnetic particle results from manufacture or an in-service examination give a size at a known date, and the difference between that and the size at failure is itself informative.
What a fitness-for-service assessment answers
API 579-1/ASME FFS-1 is the standard framework for assessing equipment containing a known flaw. It is structured in tiers, from a conservative screening assessment through more detailed analysis that requires better inputs and produces a less conservative answer.
What it returns is an engineering judgement about whether a component with a defined flaw is acceptable for continued service under defined conditions. It does not determine cause and does not assign responsibility, and its output should not be presented as though it did.
Defective, or overloaded
The comparison that does the work is between the flaw present and the flaw the part could have tolerated at the stress it actually saw. If sound material would comfortably have carried the load and the discontinuity far exceeded the acceptance criteria, the flaw is doing the explanatory work.
If the calculated critical flaw size at the applied stress is smaller than anything inspection could realistically detect, the position reverses. A part loaded that far beyond its capacity would have failed from an ordinary, acceptable discontinuity, and the loading is the operative variable.
What the assessment assumes about the flaw
Assessment procedures idealise real discontinuities as simple shapes, typically a semi-elliptical surface crack or an embedded elliptical flaw, characterised by depth and length. Irregular volumetric defects such as porosity clusters or laps have to be recharacterised into that idealisation before any calculation runs.
That step is a judgement, conservative by design. It is also where two analysts working from the same fracture surface reach different numbers, so stating the idealisation explicitly is part of doing the work defensibly.
Where these opinions are challenged
Predictably: that toughness was taken from a handbook rather than measured on the material, that the strength inputs came from the certificate rather than from ASTM E8 testing of the actual part, that residual stress was omitted, and that the flaw idealisation flattered the conclusion.
Work that states each input, its source, and the sensitivity of the conclusion to it withstands that scrutiny. A single critical flaw size presented without its assumptions does not.
This article is general technical orientation, not a failure analysis, an engineering opinion, or advice on any specific matter. Determining the cause of a particular incident requires hands-on examination by a credentialed expert.