Per-phase spatial correlated damage models of UD fibre reinforced composites using mean-field homogenisation; applications to notched laminate failure and yarn failure of plain woven composites

Abstract

A micro-mechanical model for fibre bundle failure is formulated following a phase-field approach and is embedded in a semi-analytical homogenisation scheme. In particular mesh-independence and consistency of energy release rate for fibre bundles embedded in a matrix phase are ensured for fibre dominated failure. Besides, the matrix cracking and fibre-matrix interface debonding are modelled through the evolution of the matrix damage variable framed in an implicit non-local form. Considering the material parameters of both fibre and epoxy matrix phases identified from manufacturer data sheets, it is shown that the failure strength of a ply loaded along the longitudinal

An incremental‐secant mean‐field homogenization model enhanced with a non‐associated pressure‐dependent plasticity model

“…In this work, we consider the damage of the matrix phase only since we are interested in accounting for the effect of the pressure‐dependent yield surface on the homogenization scheme. The formulation can be extended to account for fiber failure by considering a scalar damage variable in the inclusion phase in order to capture the composite response 78 . As shown by Wu et al, 82 the system of equations composed by Equation (67) and (68) can be solved by combining a weak finite element form with Newton–Raphson linearization technique.…”

“…In order to recover this size objectivity, a new reference quantity, such as the energy release rate, must be used as a target in order to correctly define the failure stage of the material 68,84 . We note that because of the use of a nonlocal damage evolution law, MFH is energy consistent during localization since the characteristic length can be evaluated to recover the right amount of dissipated energy during failure 78 . Nevertheless the MFH response during localization cannot be compared to the direct finite element response since the latter depends on the size of the volume element.…”

“…As previously mentioned, the Periodic Boundary Conditions are suitable for all cases while remaining out of the localization onset, but once this onset is reached, the PBC suitability can be degraded in the case of shear loading, as multiple shear bands appear. After this localization onset a loss of size objectivity appears for direct numerical simulation and the results cannot be compared with the MFH which does not suffer from this drawback since the energy dissipation, within a multiscale framework, is governed by the nonlocal characteristic length 78 . Figure 16 shows a detailed comparison of the phases average stress between the full‐field simulation and the MFH prediction.…”

“…A nonlocal length of 80 $$$ \mu $$$m is used in the multiscale simulation. This nonlocal value, as well as the post failure onset damage parameters could be calibrated68 in order to recover the measured experimental energy release rate $$$ {G}_c $$$ following the approach set in Reference 78, but this is beyond the objective of the work.…”

“…Regarding the structure of this article, Section 2 starts by presenting a recall of MFH incremental‐secant generalities. When considering homogenization of composite materials through a MFH scheme, scalar damage variables can be considered in each phase in order to capture the composite response 78 . In this article, we consider the damage of the matrix phase only since we are interested in accounting for the effect of the pressure‐dependent yield surface on the homogenization scheme.…”