Paris Law Fatigue Crack Growth Calculator
Use this calculator to estimate fatigue crack growth rate and cycle life from Paris law inputs. Enter a stress range, geometry factor, crack lengths, and material constants. The tool returns ΔK, da/dN, integrated cycles, and charts for engineering review.
Formula Used
Paris law models stable fatigue crack growth in the mid-range propagation region. The main relation is:
da/dN = C(ΔK)m
where:
- da/dN = crack growth per load cycle
- C = material constant
- m = material exponent
- ΔK = stress intensity factor range
The stress intensity range is estimated with:
ΔK = Y · Δσ · √(πa)
For constant amplitude loading and constant geometry factor, the cycle count from ai to af is integrated from:
N = ∫ da / [C(YΔσ√(πa))m]
Closed-form solution for m ≠ 2:
N = [af1-m/2 - ai1-m/2] / [C(YΔσ√π)m(1 - m/2)]
Special case for m = 2:
N = ln(af/ai) / [C(YΔσ√π)2]
This calculator assumes a simplified constant-amplitude loading condition. Use validated fracture mechanics inputs for design-critical work.
How to Use This Calculator
- Enter the stress range Δσ for the repeated load case.
- Provide the geometry factor Y for the chosen crack geometry.
- Enter the current crack length for direct ΔK and da/dN output.
- Enter initial and final crack lengths for life estimation.
- Enter material constants C and m from fatigue crack growth data.
- Select the displayed rate unit and preferred plotting density.
- Click the calculation button to show the result below the header.
- Review the exported CSV, PDF summary, and Plotly charts.
Example Data Table
| Case | Δσ (MPa) | Y | a (mm) | C | m | ΔK (MPa√m) | da/dN (m/cycle) |
|---|---|---|---|---|---|---|---|
| Steel Sample A | 120 | 1.12 | 5.0 | 1.0E-12 | 3.2 | 16.772 | 8.224E-09 |
| Steel Sample B | 95 | 1.05 | 3.0 | 6.5E-13 | 3.0 | 9.655 | 5.840E-10 |
| Alloy Sample C | 140 | 1.20 | 7.5 | 2.2E-12 | 3.5 | 25.760 | 1.891E-07 |
Frequently Asked Questions
1. What does Paris law calculate?
Paris law estimates fatigue crack growth rate under cyclic loading. It relates crack extension per cycle to the stress intensity range through material constants C and m.
2. What is ΔK in this calculator?
ΔK is the stress intensity factor range. This tool estimates it using geometry factor, stress range, and crack length, which strongly affect crack propagation speed.
3. Why are C and m important?
C and m describe how a specific material responds to fatigue crack growth. Higher values can produce much faster crack propagation for the same loading condition.
4. Can I use this for any crack geometry?
You can use it for simplified cases when your geometry factor Y is known. Complex structures still need validated fracture mechanics models and engineering judgment.
5. What units should I use?
Use consistent units for stress, crack length, and Paris constants. This page calculates internally with meters for crack length and MPa-based stress intensity output.
6. Does this include threshold or fracture toughness limits?
No. This version focuses on the Paris regime only. Threshold behavior at low ΔK and final instability near fracture toughness are not modeled here.
7. How is fatigue life estimated?
The tool integrates the Paris law equation from the initial crack length to the final crack length. That gives the estimated number of loading cycles.
8. When should I avoid relying only on this calculator?
Avoid using it alone for safety-critical decisions, variable amplitude loading, residual stress effects, or mixed-mode cracks. Detailed analysis may require laboratory data and specialist review.