MAT-22

Paris crack-growth law

da/dN = C (ΔK)^m in the mid-ΔK regime.

Reading speed

FractureParis–Erdogan 1963

Governing equation

\dfrac{\mathrm{d}a}{\mathrm{d}N}=C(\Delta K)^m

where

C: Paris C (mm/cyc, MPa√m) (—)
\Delta K: SIF range (MPa√m)
m: Paris exponent (—)
da/dN: Growth per cycle (mm/cyc)

Lecture brief

Historical brief

Hooke (1678), Hall–Petch grain size, Arrhenius activation and Paris fatigue-crack growth are the spine of materials selection. The sheets relate stress, microstructure and life. This sheet (MAT-22 — Paris crack-growth law) is the form associated with Paris–Erdogan 1963. Working symbols: $C$ , $\Delta K$ , $m$ $\rightarrow$ $da/dN$ . Paris and Erdogan collapsed fatigue-crack data onto a power law of the stress-intensity range, the basis of damage-tolerant design.

Purpose

Purpose: compute

da/dN

from

C

\Delta K

m

in Materials via

\dfrac{\mathrm{d}a}{\mathrm{d}N}=C(\Delta K)^m

da/dN = C (ΔK)^m in the mid-ΔK regime. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

C = 1.000e-8\,\mathrm{—}

\Delta K = 15.000\,\mathrm{MPa√m}

m = 3.000\,\mathrm{—}

, the governing relation

\dfrac{\mathrm{d}a}{\mathrm{d}N}=C(\Delta K)^m

yields

da/dN = 3.375e-5\,\mathrm{mm/cyc}

. A crack, a ΔK arrow, a growth per cycle. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Paris C (mm/cyc, MPa√m) C1e-8 —SIF range \Delta K15 MPa√mParis exponent m3 —

Outputs

Growth per cycle da/dN0.000034 mm/cyc

Reading speed

Watch on YouTube

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Narration of this film

A crack, a ΔK arrow, a growth per cycle.

Paris and Erdogan collapsed fatigue-crack data onto a power law of the stress-intensity range, the basis of damage-tolerant design.

Reading speed

Watch on YouTube