Abstract
A framework for damage modelling based on the fast Fourier transform (FFT) method is proposed to combine the variational phase-field approach with a cohesive zone model. This combination enables the application of the FFT methodology in composite materials with interfaces. The composite voxel technique with a laminate model is adopted for this purpose. A frictional cohesive zone model is incorporated to describe the fracture behaviour of the interface including frictional sliding. Representative numerical examples demonstrate that the proposed model is able to predict complex fracture behaviour in composite microstructures, such as debonding, frictional sliding of interfaces, crack deviation and coalescence of interface cracking and matrix cracking.
Highlights
Variational phase field modelling is gaining popularity by virtue of its efficiency in predicting complex fracture initiation and propagation, see e.g. [1,2,3,4,5,6,7] among many others
The combination of the cohesive zone (CZ) theory and phase-field fracture models was first proposed by Verhoosel and De Borst [10], by defining an auxiliary field related to the cohesive crack opening
Cohesive zone models describe the relationship between the displacement jump and traction between the two crack faces, whereas the original concept of the composite voxel technique is expressed with strain and stress (Eq 13)
Summary
Variational phase field modelling is gaining popularity by virtue of its efficiency in predicting complex fracture initiation and propagation, see e.g. [1,2,3,4,5,6,7] among many others. A volumetric representation of the interface has been adopted by Sharma et al [42] to regularise the interface within a small vicinity (artificial interface thickness), and this approach has been further extended to multidimensional problems [43] in the context of crystal plasticity Within their anisotropic FFT phase field model, Ma and Sun [41] explicitly defined the grain boundaries with a set of voxels that were assigned an anisotropic tensor to describe the transverse isotropy with respect to the interface normal direction. The present work proposes an FFT based approach coupling a phase-field (PF) fracture model with a frictional cohesive zone (CZ) model, and aims to provide a first proofof-concept investigation that uses the composite voxel technique to solve the coupled problem. We use simple letters (e.g. a ) to represent scalars, under-bar (e.g. a ) for vectors and bold letters (e.g. a ) for second-order matrices
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