Dr. Crakk's Arcanum of Fatigue & Damage Tolerance

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★ WELCOME TO THE MOST RADICAL FATIGUE SITE ON THE INTERNET ★ PARIS AIR SHOW 1997 UPDATE COMING SOON ★ K_IC FOR TITANIUM ADDED TO DATA TABLE ★ NEW SECTION: VARIABLE AMPLITUDE LOADING ★ FRACTOGRAPHY GALLERY UNDER CONSTRUCTION ★ SIGNING MY GUESTBOOK MAKES YOU COOLER ★

✦ NET SECTION YIELDING IS REAL ✦ FLOW STRESS = (σ_ys + σ_UTS)/2 ✦ FAILURE ASSESSMENT DIAGRAMS SAVE STRUCTURES ✦ da/dN = C(ΔK)^m ✦ WÖHLER WAS RIGHT ✦ LOG-LOG PLOTS 4 LIFE ✦ INSPECT DON'T NEGLECT ✦

☢️ SECTIONS ON CORROSION FATIGUE AND FRETTING STILL UNDER CONSTRUCTION! ☢️

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★★★ READ THIS BEFORE YOU DO ANYTHING ELSE ON THIS SITE ★★★

YO, LISTEN UP!! This website is a TOTALLY FREE, FOR-FUN, EDUCATIONAL RESOURCE thrown together by one dude with a modem, a copy of Broek's textbook, and way too much Mountain Dew. It is NOT a substitute for professional engineering advice. Like, at ALL.

THE INFORMATION ON THIS SITE MAY BE:

⚡ Completely wrong. The kind of wrong that makes your professor weep.
⚡ Dangerously out of date. Engineering standards change!!
⚡ Misapplied. Your application is NOT the same as the generic case!!
⚡ Oversimplified to the point of uselessness for any real engineering decision.
⚡ Based on my misreading of textbooks at 2am while listening to Prodigy on Winamp.
⚡ Full of typos, sign errors, and unit conversion mistakes I haven't noticed yet.

DO NOT USE THIS WEBSITE TO DESIGN, ANALYSE, CERTIFY, INSPECT, APPROVE, OR MAKE ANY DECISION WHATSOEVER about any structure, machine, aircraft, pressure vessel, bridge, nuclear facility, or anything else that matters even slightly.

If you need real fatigue or damage tolerance analysis, hire a licensed Professional Engineer (PE) or Chartered Engineer (CEng). Consult the relevant codes (FAR 25, MIL-SPEC, ASME, BS 7910, API 579) — not this website!!

THE OWNER, AUTHOR, WEBMASTER, AND ANY ASSOCIATED PARTIES OF THIS WEBSITE ("DR. CRAKK," HIS CAT, HIS ISP, NETSCAPE COMMUNICATIONS CORP., AND THE INTERNET IN GENERAL) PROVIDE ALL CONTENT ON AN "AS IS," "AS WRONG AS IT WANTS TO BE," AND "PROBABLY INCORRECT" BASIS, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED.

IN NO EVENT SHALL DR. CRAKK BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, CONSEQUENTIAL, OR CATASTROPHIC DAMAGES (INCLUDING BUT NOT LIMITED TO: STRUCTURAL COLLAPSE; FAST FRACTURE; CORROSION; DELAMINATION; CRACK COALESCENCE; OR BUSINESS INTERRUPTION) HOWEVER CAUSED, EVEN IF DR. CRAKK HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

BY SCROLLING PAST THIS DISCLAIMER YOU ACKNOWLEDGE THAT: (A) YOU ARE NOT GOING TO DO ANYTHING RECKLESS WITH THIS INFORMATION; (B) YOU UNDERSTAND THIS IS AN ENTHUSIAST WEBPAGE AND NOT A PROFESSIONAL ENGINEERING RESOURCE; AND (C) DR. CRAKK OWES YOU NOTHING. NOT EVEN AN APOLOGY.

✅ OK I UNDERSTAND AND I PROMISE NOT TO SUE DR. CRAKK ✅

GEAR!!

RUBIK!!

💥 CRACKS HAPPEN 💥

FOR SCIENCE!!

MORE GEAR!!

🔥 What Is Metal Fatigue?? 🔥

Metal fatigue is what happens when you bend a paperclip back and forth until it SNAPS!! But imagine that on an AIRPLANE WING or a BRIDGE or a NUCLEAR REACTOR!!!

Under cyclic loading — stresses that go up and down — tiny microscopic cracks nucleate at stress concentrations like notches, holes, inclusions, or surface defects. These cracks PROPAGATE, one tiny increment per load cycle, until the remaining cross-section can no longer carry the load and CATASTROPHIC FRACTURE occurs!!

The sneaky thing about fatigue?? Stresses can be WAY BELOW the material's yield strength!! Component looks totally fine, then — BOOM — total failure. No warning. Just SUDDEN FAILURE

Stage I — Crack Initiation: Persistent slip bands form, micro-cracks nucleate. Can take 90% of total fatigue life!!
Stage II — Crack Propagation: Crack grows stably, leaving beach marks & striations. This is where Paris Law RULES!!
Stage III — Final Fracture: Remaining ligament fails rapidly. Fast fracture. Game over.

THE KRAZY KAT ENGINEER
ALWAYS CHECKS FOR FATIGUE

⚡ PARIS LAW ⚡ 🦄 S-N CURVES 🦄 🔥 FRACTURE TOUGHNESS 🔥 ★ DAMAGE TOLERANCE ★ ☢️ NDE METHODS ☢️

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MYSTERIOUS!!

CRACKS ARE BAD!!

SPIRAL OF DOOM!!

KRAZY KAT ENGINEER

⚙️

📐 Paris Law: The Most Radical Equation!! 📐

In 1963, Paul Paris and Fazil Erdogan published the most famous equation in all of fracture mechanics:

da/dN = crack growth rate (m/cycle)
ΔK = stress intensity factor range = K_max − K_min (MPa√m)
C and m = material constants. Steels m≈3, Al≈3–4, Ti≈4–5.

DOUBLE ΔK → growth rate goes up by 2^m. For m=3 that's 8× increase!!! EXPONENTIAL DOOM!!

PRO TIP Log-log axes → straight line. Slope = m. Intercept = log C.

MONITORING CRACK GROWTH
FROM THE OBSERVATORY!!

Region I correctly dives to −∞ at threshold!!

✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦

📊 S-N Curves — The OG Fatigue Data!! 📊 CLASSIC!

August Wöhler figured this out in the 1860s testing railroad axles. LEGEND!!

Endurance limit (Fe steels only!!): Below ~10⁷ cycles some steels show a horizontal asymptote — stress below this = infinite life!! Magic!!
No endurance limit for aluminium: Al alloys just keep getting tired.
Mean stress effects: Goodman, Gerber, Soderberg corrections.
Surface finish MATTERS: Polished > machined > hot-rolled > as-cast.

WÖHLER PROBABLY

BEAUTIFUL S-N CURVE

✈️ Damage Tolerance Philosophy ✈️ AEROSPACE!!

Damage Tolerance says: "We KNOW cracks will be there. We're going to design for it ANYWAY."

Replaced the older safe-life approach after the Comet accidents (1954) and Aloha Airlines Flight 243 (1988). FAA mandates damage tolerant design under FAR 25.571.

Assume initial flaw size from NDE limits (~1.27mm visual)
Calculate cycles to critical size (K = K_Ic → fast fracture)
Set inspection intervals at ⅓–½ of that life
Find and fix cracks before they go CRITICAL!!
Provide redundancy — multiple load paths

LOVE CRACKS!!

COMPLEX!!

K < K_Ic
= SAFE 🦄

K ≥ K_Ic
= BOOM 💥

SPIN AND GRIN!!

🦄 🦄 🦄 🦄 🦄 🦄 🦄 🦄 🦄 🦄 🦄 🦄 🦄 🦄 🦄

📏 Stress Intensity, Critical Crack Size & Net Section Yielding!! 📏

Y = geometry factor; σ = stress (MPa); a = crack half-length (m)
Mode I Opening (most common!!), Mode II Sliding, Mode III Tearing

Critical crack size (wide plate through crack):

a_c = (1/π)(K_Ic / σ·Y)²

This is your FUSE!! Detect it before it gets there!!

STRESS CONCENTRATION
IS NOT YOUR FRIEND!!

⚡ But Wait — Net Section Yielding Ruins Everything!! ⚡

LEFM's dirty secret: it only works when the plastic zone is small compared to the remaining net section. When the net section yields entirely, LEFM breaks down spectacularly!!

Net section stress:

σ_net = P / (B · (W − a))

When σ_net ≥ σ_ys → net section yielding → K is meaningless!! ASTM E399 demands:

B, (W−a) ≥ 2.5 (K_Ic / σ_ys)²

Violate this and your "K_Ic" is actually K_Q — belongs in the bin!!

FLOW STRESS:

σ_f = (σ_ys + σ_UTS) / 2

Net section collapse: Codes use σ_f because materials strain-harden — real collapse is higher than simple yield predicts.
Residual strength: Short fat cracks in tough materials fail by net section flow, not K_Ic. The FAD handles both.
Large-scale yielding (Lr→1.0): LEFM invalid — need EPFM: J-integral or CTOD!!
Constraint: Plane stress (thin) vs plane strain (thick) — huge toughness difference!!

FAD: Kr vs Lr — stay inside the curve or else!!

★ NET SECTION YIELDING IS REAL ★ σ_f = (σ_ys + σ_UTS)/2 ★ ASTM E399 OR BUST ★ FAD: BS 7910 / API 579 ★ K_max < K_Ic ★ CHECK YOUR PLASTIC ZONE SIZE ★

💾 Material Properties Data Table 💾

Last updated: November 14, 1997 | Data from MIL-HDBK-5 and ASM Handbook Vol. 19

Material	K_Ic (MPa√m)	σ_UTS (MPa)	Fatigue limit	Paris m	Uses
Al 2024-T3	34–44	483	~138 MPa	3.2–3.6	Fuselage skin, lower wing
Al 7075-T6	24–30	572	~159 MPa	3.4–4.0	Upper wing, spar caps
Ti-6Al-4V	55–115	950	~620 MPa	4.0–5.0	Engine discs, fasteners
4340 Steel (HT)	50–65	1860	~620 MPa	2.8–3.4	Landing gear, shafts
316L SS	150–200	515	~195 MPa	3.0–3.5	Medical implants, nuclear
Inconel 718	60–100	1240	~550 MPa	3.5–4.5	Turbine blades, discs

* Approximate — always consult your material spec!! See disclaimer above!!

ENIGMATIC!!

BEAUTIFUL LIKE
A CLEAN S-N CURVE

🦄

OBSERVING CRACKS!!

CRACK SPIRAL!!

🔔 Famous Structural Failures Hall Of Shame 🔔

🦄

STUFF BROKE SPECTACULARLY

🦄

✈️ De Havilland Comet (1954)

First commercial jetliner. Square windows!! Fatigue cracks grew from window corners (Kt ~3). Two aircraft broke up in flight. Led to complete redesign of airframe structures and the birth of damage-tolerant design.

✈️ Aloha Airlines Flt 243 (1988)

B737 with 89,000+ cycles. Multiple Site Damage (MSD) in lap joint. 18 feet of fuselage roof peeled off at 24,000 ft. Led to worldwide aging aircraft programs.

🚂 Versailles Rail Disaster (1842)

Wöhler started his fatigue research BECAUSE of this!! Locomotive axle failed. 55+ passengers lost. Rotating bending on a press-fitted axle. Still happens if engineers skip their homework!!

🏗️ Alexander L. Kielland (1980)

North Sea oil platform. Fatigue crack at a hydrophone mount hole (bad weld toe) propagated through a main brace. Platform capsized in 17 minutes. 123 people lost. All from one little crack.

⚠️ THIS IS WHY WE DO FATIGUE ANALYSIS, PEOPLE ⚠️

🔍 Non-Destructive Evaluation — How We Find Cracks!! 🔍

Better NDE = smaller assumed flaw = longer inspection intervals!! It sets your initial flaw size assumption.

Method	Detectable Size	Depth	Good for	Limitations
Visual (VT)	~1.27mm	Surface	Quick checks	Misses subsurface!!
Dye Penetrant (PT)	~0.5mm	Surface	Any nonporous material	Must be clean & accessible
Magnetic Particle (MT)	~0.25mm	Near-surface	Ferromagnetic only	No Al or Ti!!
Eddy Current (ET)	~0.5–1mm	~6mm	Conductive materials	Conductivity changes signal
Ultrasonic (UT)	~1–2mm	Full thickness	Bulk material, welds	Needs good coupling
X-Ray (RT)	~2% thickness	Full thickness	Complex geometry	Misses tight fatigue cracks!!

SPINNING!!

SCIENCE!!

🦄
MAGICAL
ENGINEERING

KRAZY KAT!!

LOVE LEFM!!

SPIRAL!!

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🦄MOST EXTREME FATIGUE DATA

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🔗 Links & Resources — The Best On The Web!! 🔗

📚 TEXTBOOKS (ACTUALLY GOOD):

Broek — "Elementary Engineering Fracture Mechanics"
Anderson — "Fracture Mechanics: Fundamentals & Applications"
Suresh — "Fatigue of Materials"
MIL-HDBK-5 — Material Properties Bible
BS 7910 / API 579 — FAD fitness-for-service

🌐 COOL LINKS:

FAA Damage Tolerance Regs (FAR 25)
ASTM E647 (da/dN testing)
ASTM E399 (K_Ic testing)
AFGROW — crack growth software (FREE!)
NASGRO — NASA crack growth software

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Dr. Crakk's Arcanum Of Fatigue & Damage Tolerance

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DR. CRAKK'S ARCANUM OF FATIGUE & DAMAGE TOLERANCE