Weibull Statistical Analysis of Fibre Strength
topic
Weibull statistical analysis of single-fibre tensile strength data characterises the brittle fracture behaviour of high-performance fibres (glass, carbon, ceramic, aramid) where failure initiates from the largest surface flaw present in the gauge length — a fundamentally different failure mechanism from ductile fibres (polyester, nylon) better described by normal or log-normal distributions. Two-parameter Weibull distribution: F(σ) = 1 − exp[−(σ/σ₀)^m] where F = cumulative failure probability, σ = applied stress, σ₀ = characteristic strength (63.2% failure probability), m = Weibull modulus (shape parameter indicating scatter — m > 10 = low scatter, high reliability; m 5–10 = moderate; m < 3 = high scatter, inconsistent quality). Estimation methods: linear regression on Weibull probability plot (ln(−ln(1−F)) versus ln σ, slope = m, intercept = −m·ln σ₀) or maximum likelihood estimation (MLE, ISO 20501, more statistically efficient for m estimation). Gauge length scaling (Weibull weakest-link theory): σ₀(L₂) = σ₀(L₁) × (L₁/L₂)^(1/m) — characteristic strength decreases with longer gauge length as larger volume samples more potential flaw sizes; critical for comparing literature data from different gauge lengths. Carbon fibre T300: m = 6–10, σ₀ = 3,800–4,500 MPa at 25 mm gauge; E-glass: m = 3–6, σ₀ = 1,500–2,500 MPa at 20 mm gauge — glass lower m indicates higher strength scatter requiring higher design safety factors in composite structures. Composite reliability (Monte Carlo simulation using Weibull parameters): 10⁶ fibre failures simulated → probability of composite failure at operating stress calculated for NASA AIAA aerospace safety targets (<10⁻⁶ failure probability per flight hour).
Role
Weibull statistical analysis of fibre strength data is the analytical bridge between single-fibre tensile testing and composite structural reliability assessment — with Weibull modulus m and characteristic strength σ₀ parameters directly entering the probabilistic design calculations that determine safety factors, minimum laminate thickness, and proof test pressures for aerospace pressure vessels, aircraft primary structure, and Type IV hydrogen storage cylinders.