Buckle-driven delamination models for laminate strength prediction and damage tolerant design

Minimum-mass optimisation for high-rate manufacture of damage tolerant and unbuckled composite components

“…A two-dimensional analytical model was previously derived [10] for determining strains required to propagate elliptical delaminations with known dimensions, arising at a specified ply interface, via the opening mode shown in Figure 1c). This methodology was compared against a more-comprehensive model comprising other modes of delamination propagation in [13], alongside nonlinear finite element analysis and experimental tests. Although the simplified model [10] was found to be conservative, it adequately predicted relative trends in the damage tolerance of different stacking sequences, and as such, its use in design applications was considered justified by its relatively low computational cost.…”

“…The two-dimensional propagation model outlined in Section 2, derived in [10], and subjected to a detailed comparative study in [13] has previously been validated against experimentally-obtained propagation strains in a range of laminates with artificial circular Polytetrafluoroethylene (PTFE) delaminations [10,13]. Readers are referred to [8,10,13] for full details of these experimental results. Here, in order to justify the use of the plate model for laminate optimisation considering Compression After Impact (CAI), the results of Eq.…”

“…Results from these two cases are shown in columns a) and b) of Table 1 respectively. Analytical propagation strains are determined for each assumed morphology for two limiting cases of the Strain Energy Release Rate, specifically, GC = G1C and GC = G1IC, as used in [13]. The experimental propagation strains in Table 1 are taken from the strain data in Figure 6 of [53], which shows that failure of the Control and 90° outer laminates occurred suddenly at the propagation strain.…”

“…A similar method was recently developed by Köllner et al using a Rayleigh Ritz formulation for sub-laminate buckling around an elliptical boundary combined with a mixed-mode criterion [12]. These two approaches were recently compared alongside nonlinear finite element analysis and experimental tests in [13], to verify the suitability of the simplifying assumptions associated with the Mode I-based criterion of [10] for design, and to ensure these assumptions are conservative in comparison to a mixed-mode criterion. A key consideration when modelling panels containing delaminations is the dependence of compressive behaviour upon delamination size and through-thickness location, as investigated in [14].…”

“…In this paper, the compression after impact model from [10,13] and Compatibility Index from [27] are expanded upon to develop two novel optimisation constraints for damage tolerance and formability respectively.…”