# Coarse-grained model of the J-integral of carbon nanotube reinforced polymer composites

## TL;DR

This paper introduces a coarse-grained simulation method to predict the J-integral in CNT/polymer composites, enabling fracture analysis without detailed crack tip information at the nanoscale.

## Contribution

It presents a novel approach to calculate the J-integral from load-displacement data, applicable to complex polymer systems at the nanoscale.

## Key findings

- J-integral can be predicted without crack tip info
- CNT content and cross-links significantly affect fracture behavior
- J-integral depends on crack length and RVE size

## Abstract

The J-integral is recognized as a fundamental parameter in fracture mechanics that characterizes the inherent resistance of materials to crack growth. However, the conventional methods to calculate the J-integral, which require knowledge of the exact position of a crack tip and the continuum fields around it, are unable to precisely measure the J-integral of polymer composites at the nanoscale. This work aims to propose an effective calculation method based on coarse-grained (CG) simulations for predicting the J-integral of carbon nanotube (CNT)/polymer composites. In the proposed approach, the J-integral is determined from the load displacement curve of a single specimen. The distinguishing feature of the method is the calculation of J-integral without need of information about the crack tip, which makes it applicable to complex polymer systems. The effects of the CNT weight fraction and covalent cross-links between the polymer matrix and nanotubes, and polymer chains on the fracture behavior of the composites are studied in detail. The dependence of the J-integral on the crack length and the size of representative volume element (RVE) is also explored.

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Source: https://tomesphere.com/paper/1704.01842