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Paris-Erdogan Fatigue Crack Growth Calculator

Linear Elastic Fracture Mechanics (LEFM) recognizes that engineering structures contain microscopic flaws or manufacturing defects.

Initial flaw size detected by NDT inspection (e.g. 2 mm = 0.002 m).

Critical crack size based on fracture toughness K_IC (e.g. 25 mm = 0.025 m).

Cyclic tensile stress range: σmax - σmin.

Material empirical Paris coefficient (typically 1×10⁻¹¹ to 5×10⁻¹¹ for structural steels).

Paris law power exponent (typically ~3.0 for steel, ~3.5 to 4.0 for aluminum).

Stress intensity boundary correction factor (1.12 for surface edge crack, 1.0 for center crack).

Calculated Result
2.053e+5 cycles

Fatigue Crack Propagation Life (N)

Initial Stress Intensity (ΔKi)

9.77 MPa·√m

Final Stress Intensity (ΔKf)

34.53 MPa·√m

Crack Growth Span

2.0 mm → 25.0 mm

Calculation Breakdown

  1. Paris Law Formulationda/dN = C · (ΔK)ᵐ = C · [Y · Δσ · √(π·a)]ᵐ
  2. Defect Integration SolutionN = ∫ da / [C·(ΔK)ᵐ] = 2.053e+5 load cycles

What Is the Paris-Erdogan Fatigue Crack Growth Calculator?

P.C. Paris, M.P. Gomez, and W.E. Anderson proposed in 1961 that cyclic crack extension rate da/dN scales with the stress intensity factor range ΔK.

It represents Stage II stable fatigue crack propagation on a log(da/dN) vs log(ΔK) plot.

How Does the Paris-Erdogan Fatigue Crack Growth Calculator Work?

Stress concentrates at the sharp crack tip, driving incremental microscopic crack advance with every tensile load cycle.

Integrating the differential equation from initial flaw size ai to critical failure size af yields total inspection-to-failure cycles.

Paris-Erdogan Fatigue Crack Growth Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\frac{da}{dN} = C (\Delta K)^m, \quad \Delta K = Y \Delta\sigma \sqrt{\pi a}, \quad N = \int_{a_i}^{a_f} \frac{da}{C (Y \Delta\sigma \sqrt{\pi a})^m}

Paris-Erdogan power-law for stable fatigue crack propagation.

How to Use the Paris-Erdogan Fatigue Crack Growth Calculator

  1. Input initial and critical crack depths, stress range, Paris constants C and m, and geometry factor Y.
  2. Review total fatigue cycles N and initial/final stress intensity factor ranges.

Step-by-Step Example Calculation

Pressure Vessel Weld Toe Crack

Input Values:

initialCrackSizeMeters:0.003
finalCrackSizeMeters:0.02
cyclicStressRangeMPa:120
parisConstantC:1.2e-11
parisExponentM:3
geometryFactorY:1.12
Worked Steps: Predicts ~68,000 pressurization cycles before critical crack size is reached.

Understanding Your Result

Enables "damage tolerance" design: establishing mandatory non-destructive testing (NDT) inspection intervals before cracks reach critical size.

Factors That Affect the Result

  • Corrosive environments (corrosion fatigue) dramatically increase crack growth rates by multiples.

When Should You Use This Calculator?

  • Aircraft fuselage inspection intervals, offshore welded tubular joint fatigue, pipeline flaw assessments (API 579 / BS 7910).

Assumptions & Limitations

  • Linear elastic fracture mechanics assumption requiring small-scale yielding at the crack tip.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard ASTM E647 measurement of fatigue crack growth rates.

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