Progressive damage modelling of CFRP laminates using a semi-discrete approach in FEM

Abstract

Qualifying weight-efficient Carbon Fibre Reinforced Polymer (CFRP) structures economically depends on being able to predict by simulation, and so reduce the physical testing needed to demonstrate, the point at which a laminate fails rather than merely how stiffly it responds. Establishing that point is hard because the strength of a notched laminate is governed by three damage mechanisms, cracking of the matrix in the plies, separation of the plies at their interfaces, and rupture of the load-bearing fibres, that develop together and in a sequence that itself decides the failure load. The OHT coupon concentrates these mechanisms and their interaction into one reproducible geometry, and is adopted throughout this work as the benchmark against which the modelling is judged.

The framework examined against this benchmark is a semi-discrete one, positioned deliberately between the two established families of failure model. Instead of smearing every crack over the element it occupies, as continuum damage mechanics (CDM) does, or inserting each crack as an explicit discontinuity, as fully discrete methods do, it confines matrix cracking to thin, fibre-aligned strips of ordinary continuum elements while leaving the material between the strips free to be meshed coarsely; delamination, the one mode the plies cannot themselves carry, is added discretely with cohesive elements at every interface. To measure what this construction actually contributes, three models were built from a single automated Python–Abaqus generator and made to differ only in the feature under study: a plain CDM laminate (Model A), the same laminate with cohesive interfaces added (Model B), and the full semi-discrete model carrying both cohesive interfaces and matrix-split strips (Model C). All three draw their constitutive response from a single user material subroutine, which holds the intralaminar ply law and the interlaminar traction–separation law behind a per-material switch and is supported by a dedicated characteristic-length routine (VUCHARLEN), extended here to the distorted hexahedral and prismatic elements that the fibre-aligned split mesh unavoidably produces. The study is carried out on two IM7–8552 layups, a CP and a QI, loaded in open-hole tension.

Before the three models could be compared, every numerical setting not itself under study was fixed by a dedicated study: the cohesive penalty stiffness was raised until the interface was elastically indistinguishable from a tied bond, the quasi-static approximation was confirmed by holding the kinetic energy to a small fraction of the internal energy for every reported run, and the neglected out-of-plane matrix mode was verified to remain well below activation. The most significant, and least anticipated, outcome of this verification concerns mesh objectivity. Because the matrix-split strips give the matrix crack a discrete, localised representation, they reintroduce the process-zone resolution requirement familiar from cohesive-zone modelling, one that the crack-band correction alone does not satisfy and that, unlike for cohesive elements, cannot be relaxed by lowering a strength, because the strip carries a genuine material property. Refining only the region around the hole therefore leaves Model C unconverged; objectivity is recovered only once the resolution requirement is met everywhere the strips are free to propagate, which for the present geometry means essentially the whole plate. The discrete fidelity the method delivers is thus bought at the price of a stricter, and less local, mesh demand than a smeared model imposes.

Against the experimental data, Model C predicts the failure load within one experimental standard deviation for the QI laminate (1.5–2% under the mean) and within two for the CP laminate (3–4% over it), in both cases at or within the specimen-to-specimen scatter of the tests. Models A and B both over-predict the measured mean for both laminates. The ablation shows why: the decisive feature is the matrix-split decomposition. By keeping matrix damage within thin strips rather than spreading it across the whole ply, Model C avoids the excessive matrix degradation that otherwise relieves the stress concentration at the hole and lets the 0° fibres survive to an inflated far-field stress. The same feature reproduces the location, orientation and, crucially, the discrete, multi-line character of the matrix cracking, which the single available X-ray CT reference (for the QI laminate) shows across all three ply orientations, whereas Model B renders it only as a smeared patch of the right position but the wrong character. The cohesive interface, by contrast, adds little to the failure load under the in-plane-dominated loading considered here; its value lies in damage-mode completeness, being the only feature by which delamination can be represented at all, and the interlaminar patterns are matched only qualitatively, with neither cohesive model a consistently closer match to the scans.

These outcomes are obtained at a cost that confirms the method’s intended position between the continuum and discrete families. The mesh requirement identified above, resolving the process zone over essentially the whole plate, does make Model C more demanding than a locally refined smeared model, but not by enough to change its cost class: it completes in roughly one hour for the CP laminate and at most about nine hours for the most demanding QI case on standard cluster hardware. Although the fibre-aligned split mesh forces very small elements, the mass scaling used to compensate for them keeps this runtime close to that of the far simpler Model B and in the same cost class as a plain CDM analysis, rather than approaching that of a discrete method. For the two carbon/epoxy layups studied, the semi-discrete framework therefore reproduces the load–displacement response and failure load of room-temperature OHT specimens realistically and at tractable cost, together with the discrete character of the matrix damage for the QI laminate against which CT data are available. As qualified below, however, the QI failure load is matched more convincingly than the QI failure mode.

The conclusion is positive but bounded. It rests on two layups of a single material system, one experimental campaign, and a single CT reference available only for the QI laminate. Objectivity of the full model is conditional on the process-zone resolution requirement noted above. The split-to-bulk ratio that sets the width of the matrix-split strips is not yet shown to converge to a limit as it is narrowed, so it must be treated as a potential free parameter of the model rather than a settled discretisation choice; and the reduced cohesive strength used to resolve the interface process zone is implicated in a spurious QI delamination that overrides the split-to-bulk ordering the notch-blunting mechanism predicts, so that the close QI failure-load agreement is reached alongside an interlaminar damage development that is likely premature and a delamination-dominated failure mode, where the literature expects fibre pull-out for this layup. Recalibrating that strength, establishing convergence of the split-to-bulk ratio, improving the mesh generation, and extending the framework to further layups, materials and loadings, and eventually to temperature-dependent and cryogenic behaviour, are the principal directions left for future work.