  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.
