Paris Law Calculator
A crack growing from 1 mm to 10 mm under a 150 MPa stress range lasts about 163791 cycles.
163790.535505572
Full answer, then cut to fewer decimals (not rounded):
- 163790.535505572
- 163790.53550557
- 163790.5355055
- 163790.535505
- 163790.53550
- 163790.5355
- 163790.535
- 163790.53
- 163790.5
- Initial ΔK
- 9.416385244 MPa·√m
- Initial growth rate da/dN
- 8.349349758 × 10⁻⁹ m/cycle
Step-by-step solution
- da/dN = C(ΔK)^m with ΔK = YΔσ√(πa)
- N = ∫ da ÷ [C(YΔσ√π)^m a^(m/2)] from a₀ to a_f
- N_f = 163790.5355 cycles
Paris Law Formula
da/dN = C (ΔK)^m, ΔK = YΔσ√(πa)
N = [a_f^(1−m/2) − a₀^(1−m/2)] / [C(YΔσ√π)^m (1 − m/2)] for m ≠ 2
Worked Example
A crack growing from 1 mm to 10 mm under a 150 MPa stress range, C = 10⁻¹¹, m = 3, Y = 1.12:
- da/dN = C(ΔK)^m with ΔK = YΔσ√(πa)
- N = ∫ da ÷ [C(YΔσ√π)^m a^(m/2)] from a₀ to a_f
- N_f = 163790.5355 cycles
Initial growth rate da/dN: 8.349349758 × 10⁻⁹ m/cycle
GATE tip
Use consistent units: if C is given for ΔK in MPa·√m and da/dN in m/cycle, crack lengths must be in metres.
More Mechanical Behaviour Calculators
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Fracture Toughness Calculator
K_I = Y σ √(πa)
fracture when K_I ≥ K_Ic; a edge crack length or half an internal crack
Example: A 2 mm edge crack (Y = 1.12) under 300 MPa: Stress intensity K_I = 26.6336 MPa·√m.
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Larson-Miller Parameter Calculator
LMP = T (C + log₁₀ t_r)
T in kelvin, t_r in hours, C ≈ 20 for many alloys
Example: An alloy that ruptures in 1000 h at 650 °C, raised to 700 °C at the same stress: Rupture time t₂ = 65.8068 h.
-
True Stress-Strain Calculator
σ_T = σ_e(1 + ε_e), ε_T = ln(1 + ε_e)
Hollomon σ_T = Kε_Tⁿ; necking begins at ε_T = n
Example: A tensile test reading 400 MPa at 20 % engineering strain: True stress σ_T = 480 MPa.
Frequently asked questions
Why does the initial crack size matter most?
Growth is slowest when the crack is small, so most of the life is spent near a₀; halving a₀ can extend life far more than raising a_f.
How is the final crack length found?
From the fracture toughness: a_f = (1/π)(K_Ic/(Yσ_max))².
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Paris Law Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/paris-law-calculator/
IEEE
Scientific Converters, "Paris Law Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/paris-law-calculator/