// multi-utility computation suite · offline · instant · precise
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sci.ceramic-Weibull-failure Calculator
Calculates probability of ceramic fracture from Weibull statistics: P_f = 1 − exp(−(σ/σ₀)^m × V/V₀), accounting for volume scaling. Weibull modulus m: m = 5–10 for ceramics (high scatter); m = 20–50 for metals; m → ∞ for deterministic failure — larger specimens have higher probability of containing critical flaws.
Inputs
Sigma Mpa
Internal force per unit area (Pa or MPa). Must stay below yield strength in service.
Sigma0 Mpa
Reference formula or conversion factor shown for context.
M Modulus
Reference formula or conversion factor shown for context.
V Mm3
Three-dimensional space occupied (m³ or L). 1 m³ = 1,000 L.
Results
probability of failure Pf
Reference formula or conversion factor shown for context.
survival probability Ps
Reference formula or conversion factor shown for context.
median fracture stress σ₅₀ (MPa)
Internal force per unit area (Pa or MPa). Must stay below yield strength in service. Beyond yield: permanent deformation. Beyond tensile strength: fracture.
size effect factor (vs 1000 mm³ ref)
A dimensionless multiplier applied in the calculation.
Pf = 1 − exp(−(σ/σ₀)^m)
Reference formula or conversion factor shown for context.
m interpretation
Qualitative summary of what the computed numbers mean in practical terms.