Accurate modelling of instabilities caused by multi-site interface-crack onset and propagation in composites using the sequentially linear analysis and Abaqus

Even well-established non-linear FEM codes may present convergence issues when solving highly unstable problems, e.g. fracture mechanics problems, especially in the presence of a pronounced snap-back behaviour. In composites, at lamina level, the debonds occurring between the fibres and matrix, lead to multiple-crack configurations. Each individual debond growth is an unstable process. Then, when multiple debonds occur the problem becomes highly unstable. Moreover, experimental evidence shows that a sequence of multiple debonds originates a macro-crack that extends over the whole lamina thickness. In this article a new Python based numerical tool implementing a Sequentially Linear Analysis (SLA) procedure, which is able to call the FEM software Abaqus, is described and tested. The Linear Elastic Brittle Interface Model (LEBIM) is also included in Abaqus by means of a UMAT subroutine. Numerical results for a representative 100-fibre model show that the tool is able to adequately model simultaneous onset and propagation of multiple debonds resulting in a completely unstable process composed by a series of instability events. Eventually, these numerical results together with some previous experimental results for transverse failure loads for unidirectional carbon fibre-epoxy matrix plies allow us to estimate the tensile strength and critical fracture energy of the fibre-matrix interface by a simple inverse analysis.