Fracture Toughness Calculator
A 2 mm edge crack under 300 MPa produces a stress intensity of 26.6336 MPa·√m, so a material with K_Ic = 50 MPa·√m survives with margin.
1.0 for a central crack in a wide plate, 1.12 for an edge crack.
26.6335594399124 MPa·√m
Full answer, then cut to fewer decimals (not rounded):
- 26.6335594399124 MPa·√m
- 26.633559439912 MPa·√m
- 26.63355943991 MPa·√m
- 26.6335594399 MPa·√m
- 26.633559439 MPa·√m
- 26.63355943 MPa·√m
- 26.6335594 MPa·√m
- 26.633559 MPa·√m
- 26.63355 MPa·√m
- 26.6335 MPa·√m
- 26.633 MPa·√m
- 26.63 MPa·√m
- 26.6 MPa·√m
Step-by-step solution
- K = Yσ√(πa) = 1.12 × 300 × √(π × 0.002)
- K = 26.63355944 MPa·√m (fracture if K ≥ K_Ic)
Fracture Toughness Formula
K_I = Y σ √(πa)
fracture when K_I ≥ K_Ic; a edge crack length or half an internal crack
Worked Example
A 2 mm edge crack (Y = 1.12) under 300 MPa:
- K = Yσ√(πa) = 1.12 × 300 × √(π × 0.002)
- K = 26.63355944 MPa·√m (fracture if K ≥ K_Ic)
GATE tip
Griffith: σ_f = √(2Eγ_s/πa). Irwin’s K_Ic replaces 2γ_s with the energy release rate G_c, so K_Ic = √(EG_c) in plane stress.
More Mechanical Behaviour Calculators
-
Paris Law Calculator
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
Example: A crack growing from 1 mm to 10 mm under a 150 MPa stress range, C = 10⁻¹¹, m = 3, Y = 1.12: Cycles to grow the crack N_f = 163791.
-
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
What is plane-strain fracture toughness?
K_Ic, the critical stress intensity measured in thick specimens where the crack tip is constrained: a material property in MPa·√m.
How tough are common materials?
Glass about 0.7, alumina 3–5, aluminium alloys 20–45, steels 50–200 MPa·√m.
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). Fracture Toughness Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/fracture-toughness-calculator/
IEEE
Scientific Converters, "Fracture Toughness Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/fracture-toughness-calculator/