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Qwestrum Engineering360 · Aerospace & Aeronautical · Aircraft Structures

Fatigue and Fracture

Fatigue and fracture methods predict crack initiation and growth under repeated aircraft load cycles.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • Endurance limit exists for ferrous alloys; aluminium has no true endurance limit
  • KI=YσπaK_{I} = Y \sigma \sqrt{\pi} a (stress intensity factor, crack length a)
  • K_IC: fracture toughness — fast fracture when K_I reaches K_IC

Topic details

Introduction

Exams combine S-N life checks with Paris-law crack growth and damage-tolerance interpretation for aluminum airframes.

Key relations & formulas

S−Ncurve:Nf=CS−mS-N curve: N_{f} = C S^-m
(empirical fatigue life, Paris region separate)
ΔK=Kmax−Kmin\Delta K = K_{max} - K_{min}
(stress intensity range)
dadN=C(ΔK)n\frac{da}{dN} = C (\Delta K)^n
(Paris law crack growth)

Notation and sign conventions

Relation 1 —
S−Ncurve:Nf=CS−mS-N curve: N_{f} = C S^-m
S−Ncurve:Nf=CS−mS-N curve: N_{f} = C S^-m
(empirical fatigue life, Paris region separate)
Write this relation with symbols exactly as in Megson Aircraft Structures — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
ΔK=Kmax−Kmin\Delta K = K_{max} - K_{min}
ΔK=Kmax−Kmin\Delta K = K_{max} - K_{min}
(stress intensity range)
Write this relation with symbols exactly as in Megson Aircraft Structures — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
dadN=C\frac{da}{dN} = C
dadN=C(ΔK)n\frac{da}{dN} = C (\Delta K)^n
(Paris law crack growth)
Write this relation with symbols exactly as in Megson Aircraft Structures — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

Safe-life design limits cycles before crack risk, while damage tolerance assumes detectable cracks and tracks growth under service loads. Fracture toughness sets allowable crack size at critical stress.

Assumptions and validity limits

State assumptions explicitly before using any relation for fatigue and fracture — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Aircraft Structures viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Aircraft Structures papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to fatigue and fracture.
4. Use equation 1:
S−Ncurve:Nf=CS−mS-N curve: N_{f} = C S^-m
.
5. Use equation 2:
ΔK=Kmax−Kmin\Delta K = K_{max} - K_{min}
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Fatigue and Fracture appears in airframe design and certification. In Indian aerospace curricula this topic is tested because it connects theory to thin-walled and composite structures.
GATE and semester exams often combine fatigue and fracture with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use fatigue and fracture?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Common mistakes include mixing MPa*sqrt(m) units for K and using Paris law outside its valid Delta K region.

Quick revision checklist

Before attempting fatigue and fracture problems, confirm you can:
1. Endurance limit exists for ferrous alloys; aluminium has no true endurance limit
2.
KI=YσπaK_{I} = Y \sigma \sqrt{\pi} a
(stress intensity factor, crack length a)
3. K_IC: fracture toughness — fast fracture when K_I reaches K_IC
Revise the solved examples in Megson Aircraft Structures — Standard reference and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Crack growth rate using Paris law

Problem

For C = 2 x 10^-11, n = 3, and Delta K = 20 MPa*sqrt(m), find da/dN.

Solution

da/dN = C(Delta K)^n = 2 x 10^-11 x 20^3 = 1.6 x 10^-7 m/cycle.

Conceptual check — Fatigue and Fracture

Problem

In a Aircraft Structures semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of fatigue and fracture." What should a complete answer include?

Exams & GATE

Megson Ch. 14 — Palmgren-Miner cumulative damage Σ(n_i/N_i) = 1.

📖 Standard books (India)

  • Megson Aircraft Structures — Standard reference

    Read: Syllabus unit

    Referenced in Indian B.Tech syllabus

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