A Cohesive-Zone-Modified Point-Stress Criterion for Notched Polymer Composites: Derivation, Calibration, and Validation

Abstract

The point-stress criterion (PSC) offers a practical approach for predicting the notched strength of polymer composites, but its reliance on an empirically fitted characteristic length d0 limits its predictive generality. This study presents a physics-based modification of the Srivastava-style PSC, where d0 is derived directly from the fracture process zone (FPZ) length obtained from cohesive zone modeling, eliminating the need for geometry-dependent empirical fitting of d0 while requiring only a single calibration of constants C and k using a reference geometry. These constants remain fixed for all subsequent predictions across different hole sizes and specimen widths. A unified computational framework implementing constant and linear traction-separation laws is developed within a MATLAB environment. The optimal FPZ length is determined from the stationary point of the R-curve (dσN/dl=0), subject to a critical crack opening displacement cutoff. The framework is validated against comprehensive experimental data for a Glass/Epoxy laminate (σu=351.4 MPa) across a wide range of hole radii (0.3-20 mm) and specimen widths (10, 20, 40 mm). Results demonstrate that the constant cohesive law significantly outperforms the linear law, achieving an overall prediction accuracy of 84.7% (15.3% mean error) with an optimal FPZ length lopt=2.3 mm. The linear law yields slightly lower accuracy (82.9%, lopt=3.0 mm), while the exponential law is unsuitable for this quasi-brittle system. The proposed framework successfully captures size effects and finite-width dependence without empirical fitting of d0. By linking the characteristic length directly to cohesive zone mechanics, this work provides a robust, physically consistent, and predictive extension of the PSC for engineering design of notched polymer composite structures.