A graph-theoretical, statistics-driven model for the tensile strength of natural fibre composites: Closed-form network strength with a percolation-controlled reinforcement transition

Micromechanical models in common use for short natural fibre composites (NFCs), such as the rule of mixtures, the Kelly–Tyson relation and the Halpin–Tsai equations, represent reinforcement primarily through averaged quantities such as fibre volume fraction. None of these models explicitly describes the topology of the load-bearing fibre network, nor do they account for the substantial property scatter characteristic of plant fibres. We propose an analytical strength model that treats the composite as a weighted graph whose vertices are fibre junctions and whose edges are load-bearing fibre segments. Each edge capacity is represented as a random variable governed by fibre length, orientation, interface quality and flaw-controlled (Weibull) strength. Under load control and a perfectly brittle edge response, the network capacity is bounded by the graph minimum cut, and this bound motivates the closed-form mean-field strength law, 𝜎 𝑐 = 𝜎 𝑚 ⁢ ( 1 − 𝑉 𝑓 ) + 𝑘 ⁢ 𝑉 𝑓 ⁡ ⟨ ̃ 𝑤 ⟩ ⁢ ( 𝑉 𝑓 ) ⁢ ˆ 𝛷 ⁡ ( 𝑉 𝑓 ) ⁢ 𝜂 𝑑 , in which the percolation order parameter ˆ 𝛷 = [ 𝑧 ⁡ ( 𝑉 𝑓 ) − 𝑧 𝑐 ] 𝛽 + provides a built-in brittle-to-reinforced transition. Fibre-strength variability enters the edge capacity through the Weibull mean strength 𝜎 0 ⁢ 𝛤 ⁢ ( 1 + 1 / 𝑚 ) , while the characteristic graph-edge length is treated self-consistently as the inter-contact segment length ̄ ℓ 𝑠 = ̄ 𝐿 / ( 1 + 𝑧 ) . As fibre loading increases, network connectivity therefore rises while the effective load-bearing segments shorten, progressively shifting the reinforcement mechanism towards the pull-out regime. The resulting closed form recovers the Kelly–Tyson relation and the rule of mixtures under appropriate limiting conditions. Calibrated against published tensile data for random short sisal/polyester composites, the self-consistent model reproduces the reinforcing branch with 𝑅 2 = 0 . 8 7 , compared with 0.76 for the whole-fibre treatment and 0.44 for a fixed-exponent variant. Because only three calibration points are available, the two fitted constants cannot be independently identified; accordingly, 𝛽 is reported as a phenomenological shape descriptor rather than an experimentally measured critical exponent. The resulting framework provides a closed-form, connectivity-aware link between fibre-network topology, stochastic fibre strength, interfacial load transfer and macroscopic composite strength that is absent from established volume-fraction-based NFC models.