Fracture Mechanics

Irradiation raises yield strength and lowers fracture toughness, so the assessment point of a cracked plate drifts toward the failure assessment line year by year. This post assesses the FITNET training example 'Plate under neutronic irradiation' with the BS 7910 Clause 7 fracture assessment calculator: 12 assessment points are compared one by one with the source, and the most critical point (year 20, 350 MPa) has a reserve factor on load of 1.19 against about 1.2 read from the source chart. All inputs, calculation steps and comparison tables are included.

How a material's yielding behaviour changes the failure assessment line (FAL) in a BS 7910 fracture assessment. What yielding is, how continuous and discontinuous yielding (the Lüders plateau) differ, which materials fall into each group, how to make a safe assumption when you are not sure, and how Option 1 (swap the equations) and Option 2 (one equation, with a Lüders-strain step added to the reference strain) each handle the two cases. With original stress-strain and failure-assessment-line figures, the code equations, and a live online calculator.

A walkthrough of the three assessment options of the BS 7910:2019 Clause 7 Failure Assessment Diagram (FAD): Option 1 (yield/tensile strength only), Option 2 (true stress-true strain curve), and Option 3 (elastic-plastic J-integral). The code equations and their physical reading, how the three failure assessment lines step up in data need, accuracy and conservatism, when to choose which, and the low-strain-hardening exception — with an original comparison figure and a live online calculator.

A guide to BS 7910:2019 Annex P: it explains the physical meaning of the reference stress σ_ref and the reference-stress method, the equivalence of σ_ref and the limit load P_L, how it gives the FAD horizontal axis L_r, the general framework and net-section degradation, the plastic cut-off L_r,max and flow stress, and the calculation steps — with original diagrams and a live worked example.

A guide to BS 7910:2019 Annex M: starting from crack-tip stress singularity, it explains the physical meaning of the stress intensity factor K_I, the general Annex M framework and its correction factors, the semi-elliptical surface-crack solution and evaluation points, the weld-toe magnification factor Mk, and the full calculation steps — with original diagrams and a live worked example.

When two plates or shells to be welded together are 'not aligned' (axial misalignment or angular distortion), the load path of a tensile load is forced to bend, adding a layer of local bending stress σs at the weld. BS 7910:2019 Annex D is a look-up handbook: it gives a formula for each of 10 standardized misalignment configurations (7 butt-joint types + 3 cruciform types), letting you compute σs directly from the geometry, or convert it to a stress magnification factor km to feed into the Annex M stress intensity factor and the Clause 7 fracture assessment. This article gives the physics, then a figure and algorithm for each type.

FITNET's SSTP10 worked example — a welded stainless-steel wide plate with a through-thickness crack failing by ductile tearing. This post works out the assessment point in mechCalc's BS 7910 Clause 7 fracture assessment calculator (the calculator does not do a ductile tearing analysis, so K_mat is converted point by point and entered directly), shows where it lands on the Failure Assessment Diagram, and compares it point by point with FITNET: the horizontal coordinate L_r is close to the literature (0.511 vs 0.51), while the vertical coordinate K_r cannot be compared directly because the source includes an unquantified welding residual stress.

Across the four A533B welded-plate problems, the residual stress intensity factor K_I^S≈46 MPa·m^0.5 has always been entered directly into the FAD — but where does that number actually come from? This post uses the BS 7910 Annex M.4.2 calculator in mechCalc (finite-plate surface flaw, polynomial stress) to integrate the measured welding residual stress polynomial profile into the SIF at the deepest point of the crack, yielding 44.84 MPa·m^0.5 — only 2.5% off the 46 reported by FITNET.

The finale of the four problems on the A533B-1 welded plate: same temperature and regime as Problem 3 (HLAW) — −30 ℃, high load ratio — but with post-weld heat treatment (PWHT). This article works through HLHT to show the double dividend of PWHT — it both relaxes the residual field (K_I^S 46→5) and restores toughness by an order of magnitude (K_mat 62→321) — and how this drives K_r down from 3.94 to 0.60; plus a thought-provoking twist: even with smaller residuals and higher toughness, HLHT fails at a slightly lower load than HLAW.

Third of four problems on the welded A533B-1 plate: the HLAW specimen — as-welded, warmed to −30 ℃, with the load raised into the high load-ratio (large-plasticity) regime. We run it in mechCalc's BS 7910 Clause 7 fracture assessment calculator to see how the assessment calls plastic collapse once L_r=1.80 exceeds the cut-off value L_r,max, and why the relative weight of residual stress is diluted by plasticity at high L_r so that fracture toughness becomes the governing factor.