A Practical User Guide
A Practical User Guide
Version 5.9.4 · McFadden CAE · www.mcfaddencae.com
The Unified Fracture Mechanics Tool is a professional and educational application for analyzing cracks in engineering structures. It brings the full damage‑tolerance workflow — from a static stress‑intensity check to variable‑amplitude fatigue life, elastic‑plastic fracture, and the time‑dependent cracking that governs glass and corroding metals — into a single, verified, tabbed interface. Every calculation engine is checked against closed‑form solutions (76 of 76 tests passing).
📄 Illustrated PDF: a fully illustrated version of this guide — with a screenshot of every tab — is available to download. [https://www.dropbox.com/scl/fi/jdh5jqfthd2hzjmdybqhg/UnifiedFractureTool_User_Manual_v5.9.4.pdf?rlkey=xyc15qhnzzdkftimr90jk0c0g&st=dbseo4rs&dl=0 ]
What the tool does
Linear elastic fracture mechanics (LEFM) — stress intensity K, geometry factors, critical crack size, safety margins, and plane stress/strain determination.
Fatigue crack growth — five da/dN models (Paris, Forman, Walker, NASGRO, Exponential) with propagation life and inspection‑interval calculation.
Variable‑amplitude loading — repeating stress histories of tension + bending ranges, run to failure.
Crack‑tip stress fields — 2D contours, crack‑plane cross‑sections, and interactive 3D views for surface and corner cracks.
Elastic‑plastic fracture (EPFM) — J‑integral, CTOD, HRR fields, and a small‑scale‑yielding validity check that tells you when LEFM applies.
Materials library — 103 cited materials across 14 categories with search, sort, comparison, and an Ashby chart. Every stored property, including Poisson's ratio, density, the environmental SCCG constants, and the hardening exponent, is viewable in one place.
Subcritical crack growth (SCCG) — time‑dependent static fatigue and stress‑corrosion cracking for glass, ceramics, and metals, using a trilinear v–K model (Region I / plateau / Region III) with selectable environments and 10 measured metal‑SCC systems.
Learning Center — 17 lessons, each with a "Try It Live" button that runs the analysis it teaches.
Tools (appearance) — change the theme, colors, and fonts across the whole program, with font‑safe window scaling so nothing is ever clipped.
Who it's for — and a word on scope
Practicing engineers use it for preliminary damage‑tolerance assessments, material screening, and inspection planning. Educators and students use it as a hands‑on companion to a fracture‑mechanics course — every calculation is transparent, verified against textbook solutions, and reproducible.
Important: this tool uses closed‑form (handbook) solutions, not finite‑element analysis. Its results are excellent for screening, teaching, and preliminary design, but library values are typical/representative — not design allowables. Certified analysis requires MMPDS, the NASGRO database, or your own ASTM E399/E647/E1681 test data.
Getting started
The tool ships as a single self‑contained Windows executable. There is nothing to install and no dependencies to manage.
Requirements — 64‑bit Windows. No Python, no packages, no administrator rights.
Launch — copy UnifiedFractureTool.exe to a folder and double‑click it. The first launch takes a few seconds while the application unpacks itself; later launches are quicker.
Portable — it runs from any folder, a network share, or a USB drive, and writes nothing outside the application.
Confirm your build: the window title bar and Help ▸ About show the build string (e.g. "v5.9.4 — verified 2026‑07‑18, 76/76 checks"). Quote that string in any support request.
The ten tabs at a glance
You define the problem once on the Setup tab; every analysis tab reads from that shared definition. The Tools tab is independent — it controls the program's appearance.
Setup — geometry, loading, and material (the shared problem definition).
LEFM Results — K, geometry factor, critical crack size, margins, plane condition.
Fatigue — constant‑amplitude propagation and inspection intervals.
Stress History — variable‑amplitude (repeating spectrum) life.
Stress Fields — crack‑tip contour, cross‑section, and 3D stress views.
J‑Integral / EPFM — J, CTOD, HRR fields, and the SSY validity check.
Materials Library — 103 cited materials: search, sort, compare, full properties.
Subcritical Growth — time‑dependent SCCG for glass, ceramics, and metals, with environments.
Learning — 17 lessons with live demonstrations.
Tools — theme, colors, and fonts across the whole program.
Core concepts common to every tab
Units
The tool works in one consistent unit system: lengths (a, c, W, B) in mm; stresses in MPa; modulus E in MPa (the library stores GPa and converts on load); stress intensity K in MPa√m (1 ksi√in = 1.0989 MPa√m); Paris C in m/cycle on a MPa√m basis; J‑integral in kJ/m² (numerically = N/mm); CTOD in µm; SCCG velocity in m/s; SCCG time in seconds (also shown in hours, days, years).
The most common mistake: hand calculations must put crack size in meters inside √(πa) to get MPa√m. The tool does this internally, but if you cross‑check by hand, don't forget it — a factor‑of‑1000 length error becomes a factor‑of‑√1000 ≈ 32 error in K.
Geometry — the seven crack configurations
Each configuration uses a verified handbook stress‑intensity solution, selected on the Setup tab. A live, to‑scale schematic redraws as you type so you can confirm the geometry before running anything.
Through Crack (Center, 2a) — inputs a, W; limit 2a < W.
Through Crack (Double edge, 2a) — inputs a, W; limit a < W/2.
Edge Crack (Single edge, a) — inputs a, W; limit a < W.
Through Crack (Circular hole, 2a) — inputs a, W, hole radius R; limit 2(R+a) < W.
Elliptical Surface Crack (a × 2c) — inputs a, c, W, B; limit a < B.
Semi‑Circular Surface Crack (a = c) — inputs a, W, B; limit a < B.
Quarter‑Circular Corner Crack (a = c) — inputs a, W, B; limit a < B.
Selecting a material
Choose a Category then a Material; the tool auto‑fills K_IC, σ_y, E, ν, and the Paris constants — all editable. Selecting a material also loads its description. Use the Materials Library tab to browse or compare the full library and to see every stored property, including the environmental SCCG constants. Save your own edited properties with Materials ▸ Save Current as Custom Material.
Plane stress vs plane strain
The Plane condition dropdown offers Auto, Plane Stress, or Plane Strain. In Auto, the tool applies the ASTM E399 thickness criterion: if B ≥ 2.5 (K_IC / σ_y)² the section is plane strain, otherwise plane stress. This choice affects the plastic‑zone size (a factor of 3), the effective modulus E′ used in the J‑integral, and the CTOD constraint factor.
Saving, sharing, and appearance
File ▸ Save / Load Session — stores every input and the stress‑history table as a JSON file.
File ▸ Export Report — writes a text report spanning LEFM, fatigue, stress history, and EPFM results.
Materials ▸ Save Current as Custom Material — persists edited properties to a portable JSON file.
Appearance — theme, colors, and fonts are controlled from the Tools tab and apply across every tab; your choice can be saved as the default. When you enlarge the font, the window re‑scales and dense panels gain a scrollbar automatically, so nothing is clipped.
Tab‑by‑tab guide
Tab 1 — Setup
Define the problem here once. Pick a crack type; the schematic and the relevant fields update immediately. Enter the crack size and geometry (width, thickness, and where applicable half‑length or hole radius), then the applied stress and a plane condition (Auto is recommended). Finally choose a material category and material, editing any auto‑filled property if you have better data. Read the schematic as a sanity check: the crack is drawn in red, any hole as a white circle, and blue arrows show the applied stress. If the crack looks wrong relative to the plate, your inputs are inconsistent.
Tab 2 — LEFM Results
The fundamental linear‑elastic assessment. Click Calculate LEFM Results to compute the current stress intensity K = Y·σ·√(πa), the geometry factor Y, the critical crack size a_crit (found by root‑finding K_I(a) = K_IC), and the safety margins. The K‑margin (how much more stress) and the a‑margin (how much more crack) differ because K ∝ √a. The plot shows K rising as the crack grows: the dashed line is K_IC, the dotted line is a_crit, and the dot is your current crack. When the dot sits well below K_IC, the part is stable under static load; fatigue and subcritical growth then walk it rightward over time.
Two failure modes: the tool distinguishes "critical stress intensity exceeded" (K_I reached K_IC) from "dimensions exceeded" (the crack consumed the section first). Very tough materials at low stress often fail by the latter.
Tab 3 — Fatigue (Constant Amplitude)
Propagates a crack under constant‑amplitude cyclic loading and computes life to failure plus a damage‑tolerance inspection interval. Set the R ratio (σ_min/σ_max), the frequency (used to convert cycles to time), and the max‑cycle cap, then choose a growth model:
Paris Law — Region II only; quick estimates and teaching the baseline.
Forman — Region III plus some R‑dependence; use when life is dominated by the approach to K_IC.
Modified Forman (Walker) — R‑ratio scaling; use for significant mean‑stress effects.
NASGRO — threshold + Region III + closure; the industry standard and most complete.
Exponential Acceleration — a sharpened Region III for empirical fits to accelerating data.
NASGRO applies Newman's crack‑closure function, so it correctly predicts longer life than plain Paris at the same C and m — comparing models on the same case is a revealing exercise. For the inspection interval, enter your smallest reliably detectable crack size and a safety factor; the tool integrates from detectable size to half the critical size and divides by the safety factor, explaining any case where no interval exists rather than returning a misleading number.
Tab 4 — Stress History (Variable Amplitude)
Real structures see spectra, not single cycles. Build a repeating history from one or more ranges (cycles, tensile max/min, bending max/min) with Add Range, cap the number of history repeats, and run. Results report N_fail (total cycles to failure), X_hist (how many times the full history repeated), and the cause of failure. Bending on surface cracks is scaled by the Newman‑Raju deepest‑point factor, so a deep crack correctly feels less of the bending field. The history is saved and loaded with sessions.
Limitation: ranges are applied block‑by‑block with no load‑interaction model — no overload retardation, no underload acceleration. Results are typically conservative when overloads dominate, but not guaranteed so.
Tab 5 — Stress Fields
Visualizes the crack‑tip stress field with three views and six field components, plus an optional plastic‑zone overlay and automatic validity warnings. The views are In‑plane 2D (every geometry), Crack‑plane cross‑section (surface and corner cracks, showing the elliptical front and how K varies along it), and a rotatable 3D view. The components are von Mises (the yielding driver), σ_x, σ_y (the opening stress), τ_xy (shear), and the two principal stresses.
Why τ_xy looks "asymmetric": for a Mode‑I crack the shear field is antisymmetric — equal magnitude, opposite sign, mirrored across each symmetry plane. That is correct physics; the magnitude |τ_xy| is perfectly symmetric, and τ_xy is exactly zero on the crack plane ahead of the tips. When K_I ≥ K_IC or the plastic zone exceeds the crack size, a red warning appears and the elastic field is for reference only — move to the EPFM tab.
Tab 6 — J‑Integral / EPFM
When small‑scale yielding is violated, linear‑elastic K is no longer valid and elastic‑plastic parameters take over. This tab reports the J‑integral (elastically J = K²/E′, in kJ/m²), the CTOD (δ = J/(m_c·σ_y), in µm), the Irwin plastic‑zone radius with the correct plane‑stress or plane‑strain factor, and — crucially — an SSY validity verdict that compares the plastic zone to the smallest structural dimension and states whether LEFM is valid, marginal, or invalid. The HRR field (controlled by the Ramberg‑Osgood hardening exponent n) is overlaid on the elastic K/√(2πr) singularity on log‑log axes; they cross near the plastic‑zone boundary, HRR governing inside and LEFM outside.
Read the verdict first: before trusting any LEFM life number from Tabs 2–4, glance at the SSY verdict here. If it reads "SSY NOT VALID," lean conservative or move to a full EPFM analysis.
Tab 7 — Materials Library
The library holds 103 materials across 14 categories, every entry carrying a source citation. Search by live text match, filter by category, and sort by any column (click again to reverse — sort by K_IC to find damage‑tolerant candidates fast). The table columns are Material, Category, σ_y, K_IC, E, ν, ρ, ΔK_th, Paris C, and Paris m — so Poisson's ratio and density are visible at a glance.
Selecting a material shows the complete parameter set in one place: σ_y, K_IC, E, ν, ρ, ΔK_th and the Paris constants; two derived quantities (the ASTM E399 minimum thickness for plane strain and the transition crack size (K_IC/σ_y)²/π); the EPFM Ramberg‑Osgood hardening exponent; and, for materials that carry measured environmental data, the SCCG constants — the exponent n, the threshold K_ISCC, and the Region‑II plateau velocity — followed by the source citation. Select 2–6 materials and click Compare Selected for a side‑by‑side property table, an Ashby K_IC‑versus‑σ_y chart, a da/dN overlay, and every citation.
Category counts: Steel 24, Aluminum 15, Display Glass 10, Metal SCC 10, Plastics 9, Titanium 7, Nickel 5, Tool Steel 5, Ceramics & Glass 8, Composites 3, and Cast Iron / Copper / Magnesium 2 each. Values are typical/representative from cited public sources (ASM Handbook Vols. 19 and 13A, Anderson, MMPDS‑consistent typicals, NASGRO/Carpinteri constants, Barsom & Rolfe class laws, Wiederhorn/Speidel SCG data, vendor datasheets) — for education and screening, not design allowables.
Tab 8 — Subcritical Crack Growth
Subcritical crack growth is slow, stable crack extension at K_I below K_IC, driven by an aggressive environment. It governs the service life of glass, ceramics, and metals under sustained load — and it is a function of time, not load cycles.
A trilinear v–K law. Growth follows the Charles‑Wiederhorn power law v = da/dt = A·K_Iⁿ in Region I, then a near‑constant Region‑II plateau, then a steep Region‑III rise toward K_IC. Below the threshold K_ISCC (the static‑fatigue limit) there is no growth. The exponent n is steep (12–20 for soda‑lime glass, up to ≈38 for fused silica), and because lifetime scales as σ⁻ⁿ, a small stress increase collapses life dramatically. Glass and ceramics are usually Region‑I dominated; metals are usually plateau‑dominated — just above K_ISCC the crack jumps onto a near‑constant velocity.
Environments. An Environment dropdown scales the kinetics — Water, Humid Air (50% RH), Dry Air, and Vacuum. Water accelerates growth; dry air and vacuum nearly stop it. This is the design lever that explains why the same part survives indefinitely in one setting and cracks in months in another.
Metal stress‑corrosion cracking. The Metal SCC category supplies 10 measured material‑environment systems across the four classic mechanisms: anodic dissolution (7075‑T651 / 7075‑T7351 / 2024‑T351 in NaCl, Cu‑30Zn brass in ammonia; K_ISCC ≈ 7–20), hydrogen embrittlement (AISI 4340 and 300M in seawater/water; ≈12–15), chloride SCC (304 SS in boiling MgCl₂, Ti‑6Al‑4V in NaCl vs methanol; ≈7–45), and high‑temperature water (Inconel 600 PWSCC; ≈10). Loading their parameters switches the model to Trilinear automatically and marks them as measured.
Loading modes: Sustained stress (classic static fatigue), Constant strain rate (the dynamic‑fatigue experiment used to measure n), and Repeated load blocks (a stress‑time block applied over and over, carrying the crack across cycles). Workflow: select a glass, ceramic, or Metal‑SCC material on Setup; on this tab click Load SCCG params from current material; then choose an environment and loading mode, enter the stress and a time or cycle cap, and Run.
The design levers. Try a soda‑lime edge flaw at 35, 30, then 25 MPa — time‑to‑failure explodes as stress drops, which is why a glass part that survives installation can still fail months later under constant load. For metals, switch a peak‑aged alloy (7075‑T651, K_ISCC ≈ 7) to its resistant temper (7075‑T7351, K_ISCC ≈ 20): the same crack may now fall below threshold and never grow.
Tab 9 — Learning Center
A built‑in course of 17 lessons across six categories, each written for this tool. Its signature feature is the "Try It Live" button, which configures the tool and runs the very analysis the lesson describes. Filter by category and difficulty, select a topic to read it, and click Try It Live to load and run the example; the status bar suggests a follow‑up experiment. The curriculum covers Foundations (why strength isn't enough, the K factor, critical crack size and margins, plane stress vs strain, reading stress fields including τ_xy antisymmetry), Fatigue & Life (Paris law, thresholds/Stage III/NASGRO, variable amplitude, inspection intervals), Advanced EPFM (plastic zones and small‑scale yielding, J‑integral/CTOD/HRR), Glass & Ceramics (why glass breaks, static fatigue/SCCG), Materials (strength vs toughness, and stress‑corrosion cracking of metals), and Behind the Scenes (how the tool is verified, assumptions and limitations).
Tab 10 — Tools (Appearance)
The Tools tab changes the theme, colors, and fonts used across the whole program; nothing here affects a calculation. Pick a theme preset (Light, Dark, Slate, Sepia, or High Contrast) to fill in all the colors at once, choose the underlying widget theme, or set individual colors for the accent, window background, panel background, text, and entry/list background. Choose a font family (from installed fonts) and size (8–16), then Apply, Reset to defaults, or Save as default. A live preview shows the result as you go.
Font‑safe scaling: every time you apply a font or theme, the window re‑flows and grows to fit its content (capped to the screen), and a minimum size is set. Dense control columns gain a vertical scrollbar only when their content is taller than the visible area, so a larger font never hides a button, and plot interiors stay light in every theme so curves and labels remain legible. "Save as default" persists your choice for the next launch; on first run the native appearance is left untouched.
Assumptions & limitations
Honest tools state their boundaries. Read this before using the tool for any critical decision.
Mechanics — Mode I only (no mixed‑mode or crack‑kinking); K solutions are handbook closed forms (uniform remote stress, a single crack, no residual stress, no multiple‑crack interaction); the hole‑crack factor under‑predicts K for very short cracks (verify against Bowie/Tada); surface/corner cracks use the deepest‑point Newman‑Raju solution with fixed a/c during growth; stress‑field plots are for insight, not for extracting design stresses.
Fatigue — variable amplitude is block‑by‑block with no load‑interaction models; da/dN constants are R=0‑basis typicals unless you change them, and NASGRO closure uses standard defaults (α = 2.0, S_max/σ₀ = 0.3), all user‑overridable.
EPFM & SCCG — J is the elastic J (= G), with no fully‑plastic J or J‑R tearing; SCCG uses a trilinear v–K model with an environment scaling factor, and K_ISCC and plateau velocities depend strongly on temper, orientation (short‑transverse worst), temperature, and chemistry — the built‑in values are screening data; obtain ASTM E1681 K_ISCC data for design.
Data — library values are typical/representative for education and screening only; design allowables come from MMPDS, the NASGRO database, or your own ASTM testing. For glasses and ceramics, σ_y is a characteristic strength, not a yield stress; density is displayed for reference and is not used in any calculation.
When in doubt: the SSY check (Tab 6) tells you when LEFM is out of bounds, and the verification suite tells you the code matches theory. Neither can tell you whether the model matches your hardware — that judgment stays the engineer's.
Verification
Every calculation engine is checked against closed‑form solutions — the current suite is 76 tests, all passing, in v5.9.4, and the build you run is stamped in Help ▸ About. Coverage spans K solutions (infinite‑plate, secant width correction, edge factor, Newman‑Raju), critical crack size, Paris life against the closed‑form integral, the NASGRO closure decomposition, stress‑history bookkeeping, Kirsch and Williams field solutions, EPFM unit checks, materials‑library integrity, and the subcritical‑growth engine (the analytic static‑fatigue lifetime, the σ⁻ⁿ exponent, the trilinear plateau and Region‑III rise, environment scaling, and all 10 metal‑SCC systems). A separate headless GUI smoke test exercises every tab, growth model, field type, Learning‑Center demonstration, and the Tools‑tab theming and font‑safe scaling.
Key equations
Stress intensity: K = Y·σ·√(πa), where Y is the geometry factor.
Critical crack (infinite plate): a_crit = (1/π)(K_IC/(Yσ))²; finite width is solved by root‑finding.
E399 thickness (plane strain): B ≥ 2.5(K_IC/σ_y)².
Irwin plastic zone: r_p = (1/kπ)(K/σ_y)², with k = 1 (plane stress) or 3 (plane strain).
Paris law: da/dN = C·ΔKᵐ (Region II).
J‑integral (elastic): J = K²/E′, where E′ = E (plane stress) or E/(1−ν²) (plane strain).
CTOD: δ = J/(m_c·σ_y), with m_c = 1 or 2.
HRR field: σ ~ σ_y[EJ/(ασ_y²·I_n·r)]^(1/(n+1)).
SCCG velocity (Region I): v = A·K_Iⁿ (Charles‑Wiederhorn).
SCCG threshold: K_ISCC = r·K_IC (static‑fatigue limit).
Trilinear cap: v = min(A·K_Iⁿ, v_II), rising steeply near K_IC.
Static‑fatigue life: t_f ∝ σ⁻ⁿ (steep stress sensitivity).
Weibull failure: P_f = 1 − exp[−(σ/σ₀)ᵐ] (glass/ceramic strength).
Unit conversions
ksi√in → MPa√m: multiply by 1.0989.
MPa√m → ksi√in: multiply by 0.9102.
Paris C (in/cyc, ksi√in) → SI (m/cyc, MPa√m): multiply by 0.0254 / 1.0989ᵐ.
J: MPa·m → kJ/m²: multiply by 1000.
ksi → MPa: multiply by 6.895.
GPa → MPa: multiply by 1000.
Troubleshooting
The window opens without the version banner — you're running an old executable; replace it with the current UnifiedFractureTool.exe (Help ▸ About should read v5.9.4).
First launch is slow — normal; the self‑contained exe unpacks on first run.
K_I = 0 or blank results — the crack exceeds the geometry limit (check the Setup schematic).
Stress history reports "no failure" — loads are below ΔK_th, or raise the Max history repeats cap.
SCCG reports no growth / infinite life — K_I is below K_ISCC; increase stress or crack size, or check the environment.
Fonts look too large / controls hard to reach — adjust the size on the Tools tab; the window re‑scales and dense panels scroll automatically. Reset to defaults restores the light theme.
Windows SmartScreen prompts on first run — expected for a new unsigned exe; choose "More info ▸ Run anyway" if you trust the source.
Unified Fracture Mechanics Tool v5.9.4 · Joseph P. McFadden Sr. · www.mcfaddencae.com. Library values are representative screening data for education and preliminary analysis — not certified design allowables.
