Statistical Equivalence of Intra- and Interlaminar Mode I Fracture Toughness in IM7/8552: Weibull B-Basis and Bootstrap Uncertainty

Abstract

The intralaminar and interlaminar mode I initiation fracture toughness of unidirectional IM7/8552 carbon/epoxy composites were re-evaluated using only the published experimental data. Classical statistics, two-parameter Weibull analysis (location fixed at zero), non-parametric kernel density estimation (KDE), bootstrap resampling (10,000 replications), and bootstrap-based uncertainty quantification were applied to the fatigue-precracked (FPC) initiation values (n = 12) and the corresponding R-curves. The pooled FPC mean initiation toughness was 0.1982 kJ/m2 (COV = 8.50%). Weibull fitting yielded a shape parameter β = 12.33 and scale η = 0.2058 kJ/m2, providing a B-basis value of 0.1715 kJ/m2 (90% reliability) and an A-basis value of 0.1417 kJ/m2 (99% reliability). The Kolmogorov–Smirnov test confirmed statistical equivalence between intralaminar and interlaminar groups (p > 0.05), validating the use of a single initiation toughness for both crack planes when sharp fatigue-precracked starter cracks are employed. Intralaminar R-curves exhibited significantly steeper propagation, rising to approximately 0.385 kJ/m2 at Δa = 30 mm due to extensive fiber bridging, whereas interlaminar R-curves reached a near-plateau after 12–15 mm. Bootstrap 95% confidence bands quantified the higher uncertainty associated with the intralaminar R-curve. Teflon-insert data produced artificially high initiation values and unstable growth, confirming that only fatigue-precracked results are suitable for design allowables. This study demonstrates that a single, statistically robust initiation toughness (B-basis = 0.1715 kJ/m2) can be used interchangeably for intra- and interlaminar cracking in progressive-damage models and preliminary design analysis of IM7/8552 structures. The open-source statistical workflow (KDE + bootstrap) developed here is transferable to other small-sample composite datasets, though the numerical B-basis value (0.1715 kJ/m2) is specific to IM7/8552 and should not be generalized without validation.