Avoid unplanned outages
An assessment shows whether a repair is needed now, can wait for the next planned shutdown, or is not required at all.
Engineering consultancy · Corporate training · Custom engineering software
Keep equipment in service with confidence
API 579-1/ASME FFS-1 is the recognised fitness-for-service standard for pressure equipment across the process and energy industries. When an inspection reports a flaw, we evaluate whether the component can continue to operate safely, estimate its remaining life and recommend the next inspection, using code methods and 3D fracture mechanics simulation.
CRACK GROWTH ANALYSIS · HOW IT IS PREPAREDPY-FFS
Where API 579 fitness-for-service is usedTypical equipment we assess in each industry
- RefiningReactors, fractionation columns, heat exchangers, process piping
- Petrochemical · chemicalCrackers, reformers, pressure vessels, process piping
- Fertiliser · ammoniaAmmonia spheres, converters, urea reactors, synthesis loops
- Oil and gas · onshore and offshoreSeparators, scrubbers, slug catchers, flowlines, topside equipment
- Pipelines · gas processing · LNGTransmission pipelines, girth welds, cryogenic storage
- Power generationBoiler drums, headers, steam piping, deaerators
- Storage terminalsAtmospheric and refrigerated tanks, spheres, bullets
- Pulp and paperDigesters, recovery boilers, dryers and pressure vessels
What we offer
Three ways we work with you
Engineering consultancy for your equipment, training for your engineers, and calculation software built around your products and procedures.
01
Engineering consultancy
Fitness-for-service and fracture mechanics assessments to API 579-1/ASME FFS-1, crack growth analysis, remaining life and 3D fracture mechanics simulation.
Consultancy services → 02Corporate training
Courses for engineers and inspectors on fitness-for-service, fracture mechanics and crack growth, at your site or online, with worked examples from real assessments.
Training programmes → 03Custom engineering software
Calculation tools developed for your products, standards and procedures: verified against benchmarks, documented and handed over with training.
Software development →Why fitness-for-service
An inspection finding is the start of an engineering decision
Design codes set rules for new equipment. Equipment in service has a known history and a measurable condition, and its remaining strength can be calculated. Fitness-for-service (API 579-1/ASME FFS-1) provides a recognised procedure to turn an inspection finding into a quantified decision.
Support ageing assets
Vessels, spheres and pipelines built decades ago remain essential to refining, chemicals and power. Life extension is supported by documented engineering evidence.
Make the most of modern NDE
Phased-array and TOFD ultrasonics size flaws accurately. Fracture mechanics assessment turns those sizes into acceptance decisions.
Run, repair, replace or monitor
The outcome is an operating envelope: allowable pressure and temperature, remaining life under cycling, and the next inspection date.
Engineering consultancy · API 579-1/ASME FFS-1
Fitness-for-service assessment to API 579-1/ASME FFS-1
From a Level 1 screening of a single inspection finding to a full 3D elastic-plastic analysis, with the other API 579 damage mechanisms covered when they are found together.
Fracture mechanics assessment
Failure assessment diagram for surface, embedded and through-wall flaws.
- Plates, shells, nozzles, bolts, weld toes
- Primary, secondary and residual stress
- Flaw characterisation and recategorisation
- Limiting flaw size
3D fracture mechanics
Finite element models with the flaw inserted, for geometries and loads outside handbook solutions.
- K and J along the crack front
- Mixed-mode and thermal loading
- Crack growth simulation and crack arrest
- Component-specific FAD (Method C)
Crack growth analysis
Fatigue and environmentally assisted growth under real operating histories.
- Constant and variable-amplitude loading
- Vibration-driven growth
- Remaining life with margin
- Inspection interval
Toughness and residual stress
Material and weld inputs that govern most assessments.
- Charpy to fracture toughness
- Ductile tearing (J-R curves)
- Weld residual stress profiles
- Weld simulation where needed
Other in-service damage
Damage mechanisms that are often found alongside a flaw.
- Brittle fracture (minimum temperature)
- General and local metal loss, pitting
- Hydrogen blisters and HIC
- Dents, gouges and creep
Inspection planning
From a single answer to a risk-informed plan.
- Sensitivity and partial safety factors
- Probability of failure over time
- Inspection timing and method
- Repair or replacement planning
3D fracture mechanics
Crack growth simulation in real components
Many flaws are found at locations where standard solutions do not apply: pump volutes, gear roots, turbine blades, casings and bolt holes. We insert the flaw into the finite element model of the actual component and simulate its growth, step by step, under the real loading.
- Stress intensity factors KI, KII, KIII and the J-integral along the whole crack front
- Crack path predicted by the mixed-mode growth direction
- Growth under cyclic and vibration loading to the critical size
- Crack arrest prediction when K falls below the threshold
Stress intensity along the crack front
The governing point depends on the flaw shape
a/c = 0.2a/c = 0.5a/c = 1.0
- Stress and modal analysisOperating loads, residual stress and natural frequencies of the component.
- Flaw insertionFlaw placed at the critical location with a refined crack-front mesh.
- Fracture parametersK and J at every crack-front node for each load case.
- Growth simulationCrack front advanced in increments along the predicted path.
- Life and arrestCycles to critical size, or the point where growth stops.
Project · pressure vessel
3D crack growth in a multilayer pressure vessel
A multilayer pressure vessel shell is assessed for crack growth. The vessel, its layers, heads and saddle supports are modelled in 3D; an axial surface crack is inserted in the shell and grown step by step, with the mesh refined around the crack front at each step. The stress field shows the concentration at the two crack tips as the crack opens along the shell.
- Steps
- 3D model · flaw insertion · growth simulation · stress field
- Tools
- ANSYS 3D crack growth
- Result
- Crack path along the shell and growth to the critical length
Project · offshore structure
3D crack growth at a tubular joint of an offshore jacket
Wave loading cycles the brace-to-chord joints of a jacket. A 3D model of the T-joint is built and meshed, an initial flaw is inserted at the hot spot of the weld intersection, and the crack front is advanced step by step. The stress intensity factors along the growth and the crack length against load cycles give the remaining life.
- Steps
- 3D model · flaw insertion · growth simulation
- Tools
- ANSYS 3D crack growth
- Result
- KI, KII, KIII along the growth and cycles to the critical length
Project · pump
Crack growth analysis of a pump casing
Failure of a pump casing evaluated using fracture mechanics. The crack initiated at the tongue region and propagated along the casing volute; the 3D simulation reproduced the observed path.
- Sector
- Hydropower
- Tools
- FRANC3D with ANSYS
- Result
- Crack path and growth life along the volute
Validation · gears
Crack growth simulation of a spur gear tooth
Crack paths in a spur gear predicted for two rim backup ratios. A thick rim (mb = 3.3) gives tooth fracture; a thin rim (mb = 0.3) gives rim fracture. The simulation captures both.
- Tools
- ANSYS 3D crack growth
- Result
- Crack path and propagation life against crack length
Project · gas turbine
Crack growth simulation of a turbine blade under vibration
Modal analysis identifies the excited modes and the vibratory stress. Flaws are inserted at the critical locations of the blade and grown under that stress to give the number of cycles to the critical length.
- Steps
- Modal analysis · flaw insertion · growth under vibration
- Result
- Crack path and cycles to critical length
Project · gas turbine casing
Crack arrest prediction at an eccentric pin hole
A crack at an eccentric pin hole of a gas turbine casing is grown through the stress field of the casing. The stress intensity rises, peaks and then falls below the threshold, which shows where the crack arrests.
- Result
- Stress intensity along the path and the arrest length
KI mode IKII mode II
Reference cracked models
Standard cracked geometries from public test standards and the API 579 solution library, used to verify our models before they are applied to a project.
C(T) specimenASTM E399 / E647
SE(B) specimenASTM E1820
M(T) panelThrough-wall flaw
Surface flawAPI 579 KPSCE
Flaw at a holeAPI 579 KPHT / KPHS
Nozzle corner flawAPI 579 KNCC
Case studies
Assessments across industries
Typical assignments by industry, and published benchmark problems used to verify the calculations.
Pressure vessels · Crack growth analysis
Vessel seam flaw
A 2.5 mm deep surface flaw at the longitudinal seam of a pressure vessel. Each pressure cycle extends the flaw; depth and length grow together and every step is checked on the Level 2 FAD.
- 27,600cycles to the limiting flaw size
- 0.10 → 0.61a/t at the deepest point
- Level 2FAD check at every step
Illustrative case: vessel of the published API 579-2/ASME PTB-14 example; flaw size and pressure chosen for illustration.
Case videos · select a category
- Pressure vesselsCrack growth analysisVessel seam flaw
A 2.5 mm deep surface flaw at the longitudinal seam of a pressure vessel. Each pressure cycle extends the flaw; depth and length grow together and every step is checked on the Level 2 FAD.
- 27,600cycles to the limiting flaw size
- 0.10 → 0.61a/t at the deepest point
- Level 2FAD check at every step
Illustrative case: vessel of the published API 579-2/ASME PTB-14 example; flaw size and pressure chosen for illustration.
- Refining · petrochemicalCrack growth analysisReactor nozzle corner crack
A quarter-circular crack at the inside corner of a nozzle, driven by pressure and thermal stress. The corner-crack solution follows the front around the corner until the solution limit.
- 80,300cycles to a/tn = 0.5
- 4 → 15 mmcorner crack radius
- Cornerstress through the nozzle corner
Illustrative case computed with PY-FFS; dimensions, loads and material data chosen for illustration.
- Oil and gas · pipelinesCrack growth analysisPipeline girth weld
A circumferential flaw at an as-welded girth weld. Bending cycles from a free span grow the flaw while pressure and weld residual stress stay in the FAD check.
- 1.54 millionbending cycles to a/t = 0.8
- 3 → 7.6 mmflaw depth
- As-weldedresidual stress in Kr
Illustrative case computed with PY-FFS; dimensions, loads and material data chosen for illustration.
- Storage terminalsFracture mechanics assessmentTank shell minimum temperature
A weld flaw in a tank shell. Toughness from the ASME Section XI curve rises with temperature; the FAD point enters the acceptable region at the minimum safe metal temperature.
- ≈ 10 °Cminimum safe metal temperature
- 40 → 84Kmat, MPa√m from −40 to 40 °C
- Level 2FAD with residual stress
Illustrative case computed with PY-FFS; dimensions, loads and material data chosen for illustration.
- Fertiliser · chemicalsCrack growth analysisAmmonia sphere weld
A surface flaw at a weld of a pressurised sphere. An environment factor on the growth rate represents the service; the flaw is tracked through the wall.
- 122,000cycles to a/t = 0.8
- 3 → 32 mmflaw depth
- 10 ×environment factor on da/dN
Illustrative case computed with PY-FFS; dimensions, loads and material data chosen for illustration.
- PowerCrack growth analysisSteam header attachment weld
A flaw at the toe of an attachment fillet weld under thermal cycles. This video covers the fatigue part; creep damage is assessed separately to API 579 Part 10.
- 232,000cycles to the FAD limit
- 4 → 9.3 mmflaw depth at the weld toe
- Part 9 + 10fatigue here, creep separately
Illustrative case computed with PY-FFS: fatigue part only; creep damage is assessed separately (API 579 Part 10).
- Rotating equipmentCrack growth analysisStud bolt thread root
A straight-front crack at the thread root of a Ø50 mm stud under axial load and bending. The crack grows across the section until the FAD limit.
- 3.5 millioncycles to the FAD limit
- 2 → 24 mmcrack depth
- a/D 0.48at the limit
Illustrative case computed with PY-FFS; dimensions, loads and material data chosen for illustration.
- Offshore structures3D fracture mechanicsJacket tubular joint
A 3D model of a brace-to-chord T-joint with an initial flaw at the hot spot of the weld intersection. The crack front is advanced step by step and the stress intensity factors are extracted at each step.
- Mode Igoverns; modes II and III stay small
- 0.2 → 1.1 mmcrack length tracked
- 19 stepscrack front advanced in the 3D model
Finite element crack growth simulation by Pythagoras Engineering (ANSYS).
- Rotating equipment · gears3D fracture mechanicsSpur gear tooth and rim
A crack inserted at the tooth root of a spur gear is grown in the 3D model for two rim thicknesses. A thick rim gives tooth fracture, a thin rim gives rim fracture.
- Tooth fracturethick rim, backup ratio 3.3
- Rim fracturethin rim, backup ratio 0.3
- Lifestress intensity and cycles along each crack path
Finite element crack growth simulation by Pythagoras Engineering (ANSYS).
- Pressure vessels3D fracture mechanicsMultilayer vessel shell
An axial crack is inserted in the 3D model of the shell and grown step by step; the stress field shows the concentration at the two crack tips.
- Multilayershell layers, heads and supports in 3D
- Two tipsstress concentrates at both crack tips
- Step by stepmesh refined around the front at each step
Finite element crack growth simulation by Pythagoras Engineering (ANSYS).
Crack growth analysis at a reactor nozzle
Thermal and pressure cycles at a nozzle corner. A 3D crack model provides the driving force around the corner; growth sets the inspection interval to the next turnaround.
Fracture mechanics assessment of a pipeline girth weld
Pressure, bending from spans and settlement, and as-welded residual stress act together. The weld residual stress profile and toughness determine whether a repair is required.
Brittle fracture assessment of a tank shell
Old shell plate, low metal temperature and a weld flaw. Toughness from Charpy data, the Master Curve and constraint set the minimum safe temperature.
Fracture mechanics assessment of an ammonia sphere
Environment-assisted cracking at welds of a pressurised sphere. We assess the flaws found and the growth rate to support continued operation.
Creep and crack growth analysis of a steam header
Creep and fatigue at a branch weld. Remaining life combines creep damage with crack growth between outages.
Crack growth analysis of shafts and bolts
Cracks at shoulders, keyways and threads under bending and torsion. Round-bar and bolt solutions or a 3D model give the safe running period.
Illustrative case types. Project case studies are published with the permission of the equipment owner.
Results for published example problems of API 579-2/ASME PTB-14, computed with our in-house software. The values agree with the published results; small differences come from rounding in the published hand calculations.
Level 2 · FAD
Fracture mechanics assessment (FAD)
Failure lineCrack growth pathAssessment point
Crack growth · remaining life
Crack growth analysis and remaining life
Crack depth a
Level 1 · Figure 9.13
Level 1 screening
Curve A base metalCurve B weld, PWHTCurve C as-welded
Toughness · Master Curve
Fracture toughness from Charpy data
9.10D fit · 71.19.10A 5 °C · 61.19.10B 25 °C · 54.99.10C 65 °C · 42.0
Corporate training
Training for engineers and inspectors
Practical courses built from real assessments. Each course mixes the theory with worked examples, so participants can apply the methods to their own equipment. Delivered at your site or online, and tailored to your plant and procedures.
Fitness-for-service to API 579-1/ASME FFS-1
The assessment levels, the damage mechanisms and the data each part needs, with worked examples from the API 579-2/ASME PTB-14 example problems.
Fracture mechanics for engineers
Stress intensity, J-integral, the failure assessment diagram, toughness and residual stress, explained for practising engineers.
Crack growth analysis and remaining life
Fatigue and environment-assisted crack growth, load spectra, remaining life and setting inspection intervals.
Brittle fracture and material toughness
From Charpy energy to fracture toughness, the Master Curve and minimum safe temperature.
3D fracture mechanics with finite elements
Crack insertion, crack-front meshing, K and J extraction and crack growth simulation, with hands-on exercises.
In-house programme for your team
A course built around your equipment, codes and inspection findings, from a half-day briefing to a full workshop.
Course content and duration are adapted to each group. Use the enquiry form and choose "Training or workshop".
White papers
Technical papers from our project work
Short, practical papers based on assessments and simulations we have carried out, written for plant engineers and inspectors. Request a copy and we will email it to you.
Crack growth analysis of a pump casing: from the tongue to the volute
How a crack that started at the tongue of a pump casing was reproduced with a 3D model, and what the growth life meant for the repair decision.
Request the paper →Tooth fracture or rim fracture? 3D crack paths in spur gears
The effect of the rim backup ratio on the crack path: when a thin rim turns tooth fracture into rim fracture.
Request the paper →3D crack growth at a tubular joint of an offshore jacket
Building the 3D model of a brace-to-chord joint, inserting the flaw at the hot spot and growing it under wave loading.
Request the paper →Crack growth in a multilayer pressure vessel shell
An axial crack grown through the 3D model of a multilayer vessel, and the stress field at the two crack tips.
Request the paper →Crack arrest at an eccentric pin hole of a gas turbine casing
Why the stress intensity rises, peaks and falls below the threshold, and how that predicts where the crack stops.
Request the paper →Receive new papers
Ask to be added to the distribution list. New papers from our project work are added here as they are released.
Join the listCustom engineering software
Calculation software built for your products
We develop engineering calculation software around your own products, standards and procedures: design and rating calculations, assessment tools for your equipment, and tools that turn test or field data into decisions. Each tool is verified against benchmarks or your test data, documented and handed over with training.
- RequirementsYour product range, codes, inputs and the outputs your engineers need.
- DevelopmentDesktop, Excel or Python tools with clear inputs, checks and reports.
- VerificationResults checked against hand calculations, published benchmarks or your test data.
- HandoverDocumentation, user training and support as your requirements change.
Our own in-house software · an example of what we build
PY-FFS
Our in-house software for fracture mechanics assessment to API 579-1/ASME FFS-1 Part 9, from Level 1 screening to Level 3, with crack growth analysis and remaining life. Every release is verified against the published API 579-2/ASME PTB-14 example problems.
21flaw families
50Annex 9B / 9C solutions
3assessment levels
How it makes the calculations easier
- Levels 1, 2 and 3 in one workflow
- The code solution chosen from a drop-down
- Inputs checked against the solution limits
- SI and US customary units, switchable
- Crack growth and remaining life computed automatically
- Every step traced to the API 579 equation
- Plots and Excel / PDF reports
- Worked examples built in for training
Why work with us
Specialist capability, delivered clearly
We combine full-fledged in-house software with advanced simulation and code expertise, so each assessment uses the method that fits the problem.
01
Full-fledged in-house software
A complete fitness-for-service software covering 21 flaw families and three assessment levels, verified against published benchmarks.
02
High-end technical expertise
Fracture mechanics, 3D crack growth simulation, finite element analysis and the API 579 / ASME codes, in one team.
03
Validated methods
Simulation checked against experiments and code examples before it is applied to your equipment.
04
Clear, traceable reports
Results your inspection team and third-party reviewers can follow, with every assumption stated.
How we work
From finding to decision in five steps
The same route for a single flaw or a plant-wide campaign.
- Review the dataInspection results, drawings, materials, operating and design history.
- Choose the levelScreening first; detailed and 3D analysis where it adds value.
- AnalyseStresses, toughness, FAD and crack growth, with uncertainties stated.
- DecideRun, repair, replace or monitor, with remaining life and operating limits.
- Plan inspectionWhat to inspect, where, how and when.
About us
Pythagoras Engineering Consultancy & Services
We are an engineering consultancy dedicated to fitness-for-service and fracture mechanics, offering consultancy, corporate training and custom engineering software. We help operators of pressure equipment and rotating machinery keep damaged components in safe service, with assessments that are transparent, traceable to the codes and supported by our in-house software.
Our work ranges from screening a single inspection finding to 3D crack growth simulations and life-extension studies for refining, petrochemical, oil and gas, power, hydro, fertiliser and storage facilities.
API 579-1 / ASME FFS-1ASME Section VIII3D fracture mechanicsCrack growth analysisLife extensionCorporate trainingCustom engineering software
Contact us
Consultancy projects, corporate training and custom software. For a project, tell us about the inspection finding and the operating conditions; we reply with the assessment route, the data we need and a time estimate. Drawings and reports can follow by email.
- Office
- Inspire Workplace, #134 & 135, Karthik Nagar, LRDE Layout, Doddanekundi Post, Bangalore – 560037, India
- Phone
- +91 70422 43776