Fragmentation model for the tensile response of unidirectional composites based on the critical number of fiber breaks and the correction of the fiber-matrix interfacial strength.

Juan David Vanegas-Jaramillo,Iván David Patiño-Arcila

doi:10.1590/1679-78255326

Juan David Vanegas-Jaramillo, Iván David Patiño-Arcila

Open Access

https://doi.org/10.1590/1679-78255326

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Abstract

Abstract A fragmentation model based on global load sharing (GLS) theory is developed to obtain stress-strain curves that describe the mechanical behavior of unidirectional composites. The model is named CNB+τ* because it is based on the Critical Number of Breaks model (CNB) and on the correction of the fiber matrix interfacial strength, τ*. Model allows both obtaining the ultimate tensile strength of CFRP and GFRP composites, and correcting the σ vs e curve to match its peak point with the predicted strength, which is more accurate than the one obtained by previous GLS-based models. Our model is used to classify the mechanical response of the material according to the energetic contributions of two phenomena up to the failure: intact fibers (IF) and fragmentation (FM). Additionally, the influence of fiber content, Vf, on the tensile strength, σU, failure strain, eU, and total strain energy, UT, is analyzed by means of novel mechanical-performance maps obtained by the model. The maps show a dissimilar behavior of σU, eU and UT with Vf between GFRP and CFRP composites. The low influence of Vf on the percent energetic contributions of IF and FM zones, as well as the larger energetic contribution of the FM zone, are common conclusions that can be addressed for both kinds of composites.

Highlights

Most of the analytical models used to predict the mechanical behavior of unidirectional composite materials consider the stochastic representation of the occurrence of fiber breakings
The CCCCCC + ττ∗ model developed in the present work is used to predict the stress-strain behavior of the material 1 shown in that table, which corresponds to carbon fibers T700SC reinforced with an epoxy matrix
This happens because the Critical Number of Breaks model (CNB)+τ* is essentially a fitting model that ‘contracts’ the original σ vs. ε curve predicted by the Neumeister equation, taking into account the ultimate tensile strength obtained by CNB and modifying, recursively, the fiber-matrix interfacial strength, τ*

Summary

Introduction

Most of the analytical models used to predict the mechanical behavior of unidirectional composite materials consider the stochastic representation of the occurrence of fiber breakings. Curtin was the first to develop a law of fragmentation from an expansion of Taylor series that allow approximating the Weibull function, obtaining analytical solutions for the curve σ vs ε (Curtin 1991a, 1991b). This model was later extended by Neumeister to roughly explain the superposition of the zones of influence adjacent to the fiber breaks (Neumeister 1993a, 1993b).

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