A graded interphase enhanced phase-field approach for modeling fracture in polymer composites

The superiority of nanosized filler particles in improving the elastic and fracture behavior of polymers, in comparison to microsized inclusions, has been substantiated by several experimental observations. Accurate modeling of crack propagation in such heterogeneous materials, however, involves resolution of complex crack topologies while taking into account the coalescence and branching of multiple cracks. Such complexity renders the traditional sharp crack modeling approaches, such as those based on the idea of partition of unity, to be of limited suitability, especially in 3D, since these involve explicit tracking of the evolving crack surfaces. Consequently, phase-field fracture approaches have come up as an attractive alternative to the traditional sharp crack models, especially when complex crack topologies need to be handled. Furthermore, standard two-phase continuum models, owing to their lack of the necessary length scale, are unable to capture the previously mentioned smaller is stronger size effect. In order to remedy this shortcoming, in context of finite strain hyperelasticity, a graded interphase based enhancement of the standard first-order continuum model was introduced in our previous work. The present contribution extends the idea of graded interphases to the phase-field fracture approach. Herein, an interphase region around filler particles, as observed experimentally, having continuously varying or graded material properties is considered. Fracture behavior of the composite material can be controlled by means of the degree of grading employed in determining the elastic and fracture properties within the interphase region. An optimal combination of the graded interphase parameters yields a tougher macroscopic response, as observed in case of tougher interphases, in comparison to the one obtained with a standard phase-field fracture model, The appropriateness of the introduced technique for modeling a wide spectrum of experimentally observed fracture behaviors, depending upon the degree of adhesion between the filler and the matrix phases, is depicted by means of extensive numerical experimentation.