Fracture, Fatigue, Creep & Failure Analysis

Why things break — and how to prevent it. Learn ductile vs brittle fracture and fracture surfaces, stress concentrations, linear-elastic fracture mechanics (stress intensity factor K, fracture toughness K_IC, critical crack size, leak-before-break), fatigue (S–N curves, endurance limit, mean-stress effects, Paris-law crack growth, beach marks), creep (stages, Larson–Miller parameter), wear, and the failure analysis methodology (evidence, fractography, metallography, root cause) — with Python for critical crack size, Paris-law fatigue life and creep rupture life.

Most engineering failures are not simple overloads: they grow from cracks by fatigue, corrosion or creep over time until the remaining section suddenly fractures. Famous disasters (Comet airliners, Liberty ships, Aloha Airlines 243, Silver Bridge) shaped modern fracture mechanics and inspection practice.

Materials engineers design against these mechanisms and investigate failures to find root causes and prevent recurrence.

An analogy

A crack in a metal is like a tear in a sheet of paper: a small tear barely weakens it, but pull hard enough and the tear races across. Fracture toughness tells you how big a tear the material can tolerate at a given stress.

Ductile vs brittle fracture

Ductile fracture: significant plastic deformation, necking, cup-and-cone surfaces with dimples (microvoid coalescence) — gives warning. Brittle fracture: little deformation, flat faceted surfaces (cleavage) or intergranular fracture, chevron marks pointing to the origin — sudden. BCC steels become brittle at low temperature; hydrogen, temper embrittlement and sensitisation also cause brittle behaviour.

Fracture mechanics

Real parts contain flaws. K combines stress, crack size and geometry; fracture occurs when K ≥ K_IC. High-strength materials often have lower toughness — so allowable crack sizes shrink. Design options: lower stress, tougher material, or reliable inspection to find cracks smaller than a_c (NDT: ultrasonic, radiography, eddy current, dye penetrant, magnetic particle). Leak-before-break: a pressure vessel crack should leak through the wall before becoming unstable.

Fatigue

Failure under repeated loading below yield:

Creep, wear and failure analysis

Creep: time-dependent deformation above ~0.4 T_m — primary, secondary (steady) and tertiary stages ending in rupture; resisted by high melting point, precipitates, single crystals and coatings (superalloys, 9Cr steels). Wear: adhesive, abrasive, erosive, fretting. Failure analysis method: collect background and service history, preserve evidence, visual and macro examination, NDT, fractography (stereo microscope, SEM), metallography, hardness and chemistry checks, mechanical tests, stress analysis, root-cause determination (e.g. 5 Whys, fishbone) and corrective actions.

Formulas

Worked example: Stress intensity

Given: σ = 200 MPa, centre crack 2a = 10 mm, Y = 1

Find: K.

Answer: 25.1 MPa√m

Worked example: Allowable stress

Given: K_IC 40, detectable crack 3 mm, Y 1.12

Find: σ_max.

Answer: 368 MPa

Worked example: Goodman

Given: S_e 250, S_ut 600, σ_m 200

Find: Allowable σ_a.

Answer: 167 MPa

Critical crack, fatigue life and creep rupture

import math
# Fracture mechanics: critical crack size, and fatigue life with the Paris law
K_IC, sigma, Y = 50.0, 300.0, 1.12            # MPa*sqrt(m), MPa, edge-crack factor
a_c = (1 / math.pi) * (K_IC / (Y * sigma)) ** 2
print(f"critical crack length {a_c*1000:.2f} mm")
C, m = 1e-11, 3.0                              # Paris law da/dN = C (dK)^m, dK in MPa*sqrt(m)
ds, a0 = 150.0, 0.5e-3                         # stress range, initial crack
N, a, da = 0, a0, 1e-6
while a < a_c:
    dK = Y * ds * math.sqrt(math.pi * a)
    N += da / (C * dK ** m)
    a += da
print(f"cycles to grow from {a0*1000:.1f} mm to critical: {N:.3e}")
# Creep: Larson-Miller parameter for a turbine alloy
LMP = (800 + 273) * (20 + math.log10(10000)) / 1000
print(f"LMP at 800 C for 10 000 h = {LMP:.1f} (x1000)")
T_new = 850 + 273
print(f"same LMP at 850 C -> rupture life {10**(LMP*1000/T_new - 20):.0f} h")
# critical crack length 7.05 mm
# cycles to grow from 0.5 mm to critical: 2.487e+05
# LMP at 800 C for 10 000 h = 25.8 (x1000)
# same LMP at 850 C -> rupture life 854 h

At 300 MPa this steel tolerates a 7 mm edge crack before fast fracture. A 0.5 mm flaw grows to that size in about 250 000 cycles of 150 MPa — inspection intervals are set to find cracks well before then (damage-tolerant design). For creep, running a turbine alloy just 50 °C hotter cuts rupture life from 10 000 h to ~850 h, which is why turbine temperature is controlled so carefully.

Common mistakes

Applications

Key takeaways

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