Fracture Mechanics

In a BS 7910 fracture assessment most attention goes to flaw size, stress and toughness — but one thing hidden in the material is easy to miss: when this steel yields, does it pass smoothly into plasticity, or does it “catch, then let go” first? This small metallurgical detail grows a cliff in the failure assessment line near $L_r=1$ — get it wrong and you badly overestimate the safety margin. This article explains what yielding is, how continuous and discontinuous yielding differ, and how Option 1 and Option 2 each handle them. ...

In a BS 7910 fracture assessment, the horizontal axis $L_r$, the vertical axis $K_r$, and the failure assessment line (FAL) that separates “safe” from “unsafe” — how the assessment point is computed and how the verdict is read — are covered thoroughly in the BS 7910 Fracture Assessment — A Concise Guide . This article covers one thing only: Clause 7 gives three ways to draw that FAL curve (Option 1 / 2 / 3). They step up in the material data they need, in computational accuracy and in conservatism; understanding their differences is a key step to doing a fracture assessment “correctly and economically”. ...

A fracture assessment watches two things at once — how close to brittle fracture, and how close to plastic collapse. Annex M (the stress intensity factor) covers the first and gives the vertical axis $K_r$ of the Failure Assessment Diagram (FAD); this guide’s reference stress $\sigma_{ref}$ (Annex P) covers the second and gives the horizontal axis $L_r$. Together they complete the Clause 7 fracture assessment . Prologue: the horizontal axis measures “how close to plastic collapse” A cracked structure can fail along two paths: brittle fracture, where the crack-tip driving force exceeds the toughness, and plastic collapse, where the cracked section as a whole yields and loses its capacity. The first is measured by $K_I$ (vertical axis); the second relies on the reference stress $\sigma_{ref}$ (horizontal axis). ...

The first step of a fracture assessment is to compute the stress intensity factor $K_I$ at the crack tip. This guide explains what $K_I$ is and how BS 7910 Annex M computes it — from the general master formula and its correction factors to the common semi-elliptical surface-crack solution and the weld-toe correction. It feeds the vertical axis $K_r$ of the Failure Assessment Diagram (FAD), and together with Annex P (reference stress) for the horizontal axis $L_r$ completes the Clause 7 fracture assessment . ...

In a fitness-for-service (FFS) assessment of a welded pressure-bearing structure, there is a class of stress that comes neither from external load nor from a residual field, but from imperfect fabrication and fit-up — the weld joint is “not aligned”. BS 7910:2019 Annex D handles exactly this: when two plates or shells to be welded together have axial misalignment or angular distortion, the load path of a tensile load is forced to bend, and a layer of local bending stress $\sigma_s$ appears at the weld. ...

This is the second worked example in the [[FITNET|FITNET]] FAD example collection (§13.2.6, SSTP10). Its focus differs from the [[bs7910-a533b-residual-stress-fad|first A533B example]]: this time it is a welded stainless-steel wide plate with a through-thickness crack, assessed for ductile tearing (the crack grows stably as the load rises) on the FAD. We follow the [[bs7910-a533b-residual-kis-annexm|usual routine]] — run it in mechCalc’s BS 7910 Clause 7 fracture assessment calculator, read the chart, and cross-check point by point against the FITNET literature. ...

In the FAD assessment of the [[bs7910-a533b-residual-stress-fad|four A533B welded-plate problems]], the residual stress intensity factor for the as-welded case, $K_I^S \approx 46\ \mathrm{MPa\cdot m^{0.5}}$, has always been entered directly: FITNET obtained it by integrating the measured residual stress profile, and we simply fed that ready-made number into the vertical coordinate $K_r$. A natural follow-up question: how does that 46 actually emerge from a residual stress curve, and can mechCalc compute it on its own? ...

This is the finale of the four problems on the A533B-1 welded plate. It is the counterpart to Problem 3, [[bs7910-a533b-hlaw-fad-walkthrough|HLAW]], and it pushes the power of PWHT in this test series into its most visible form. The shared background and method for all four problems are covered in the overview, [[bs7910-a533b-residual-stress-fad|Where does residual stress push the assessment point?]]. What this problem asks HLHT = High-$L_r$ + Heat-Treated: PWHT applied, assessment temperature −30 ℃, high load ratio. It shares the temperature and regime of HLAW, and the difference is still that one thing — post-weld heat treatment. But at −30 ℃, PWHT delivers a double dividend: ...

This is the third of four problems on the welded A533B-1 plate. The first two both sat in the low load-ratio brittle-fracture regime and compared residual stress; this one shifts the battlefield — to the high load-ratio, large-plasticity regime. For the shared background and method behind all four problems, see the overview post [[bs7910-a533b-residual-stress-fad|Where does residual stress push the assessment point?]]. What this problem asks HLAW = High-$L_r$ + as-Welded: as-welded condition, assessment temperature raised to −30 ℃, load increased into the high load-ratio regime. The warmer temperature lifts the fracture toughness somewhat off the lower shelf ($K_{mat}=62\ \mathrm{MPa\cdot m^{0.5}}$), while the load is raised to a failure load of 5.10 MN. The residual stress stays the as-welded value ($K_I^S=46$). ...

This is the second of the four problems on the A533B-1 welded plate, and the companion to Problem 1 [[bs7910-a533b-llaw-fad-walkthrough|LLAW]]. The two problems were designed for a single-variable comparison: The shared background and method for all four problems are in the overview [[bs7910-a533b-residual-stress-fad|Where do residual stresses push the assessment point?]]. What this problem asks LLHT = Low-$L_r$ + Heat-Treated: post-weld heat treatment (PWHT) applied, assessment temperature −120 ℃, low load ratio. It is at the same temperature as LLAW, in the same region, and uses the same set of measured residual-stress profiles — the only variable is PWHT. The heat treatment relaxes the welding residual stress by at least an order of magnitude, so the residual $K_I^S$ drops from 46 in the as-welded state to 5 MPa·m$^{0.5}$. The load capacity rises accordingly, from LLAW’s 1.27 MN to 2.19 MN (about 1.7×). ...