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Title: Modelling delamination in fibre-reinforced composites via stress gradient elasticity
Author: Gaite, Oliver Anthony Lawrence
ISNI:       0000 0004 9357 1047
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2020
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Continuous fibre-reinforced polymer (CFRP) composites are susceptible to damage by delamination. Simulation of delamination initiation and propagation are valuable mitigation strategies in designing and lifing CFRP assets. Linear elastic fracture mechanics (LEFM) predicts infinite stresses at the tips of sharp, discrete delaminations. In order to determine whether a delamination front will advance, finite element method (FEM) approaches utilise non-linear decohesion elements that consume energy equivalent to the material fracture toughness. Nonlocal field theory predicts a non-zero finite stress at the delamination front, with a maximum stress occuring some distance ahead of the crack. Nonlocal stress fields therefore offer the prospect of a linear maximum stress fracture criterion. Since nonlocal elasticity is predicated on the concept of non-finite range forces, the theory predicts that the stresses at the crack tip will be redistributed over some proximate region that must include part of the crack wake. Nonlocal FEM implementations require that these crack wake tractions are artifically imposed (as they do not result from FEM approximations that otherwise rely on LEFM). If the necessary redistribution of stress concentrations ahead of the crack is explicitly imposed on the free edges of the crack in its wake, continuous stress and strain fields are recovered. Moreover the work performed by the imposed crack wake tractions is equivalent to the interlaminar fracture toughness of the material such that stress and energetic fracture criteria are unified. To the best of the author’s knowledge use of the imposed crack wake tractions is novel in a finite element context. The material constitutive equations are written in a nonlocal form and incorporated into a finite element method solver by a procedure that produces a global stiffness matrix containing banded terms accounting for the cross-bracing inherent in nonlocal fields. The solution to the crack wake traction distribution is imposed by modelling the tractions as discrete springs and augmenting the global stiffness matrix with these stiffness terms. Nonlocal mode I and mode II delamination propagation has been explored and compared to benchmark analyses obtain from local elasticity using the virtual crack closure technique (VCCT). The behaviour of the present implementation of nonlocal FEM is observed to differ with respect to each of these crack opening modes. In the case of the mode I delamination, the stress response is underpredicted by 8.6%. In the case of the mode II delamination, the stress response is overestimated by 2.4%. In a static mixed-mode analysis, the present implementation of nonlocal elasticity does not produce behaviour consistent with the mixed-mode fracture toughness.
Supervisor: Pinho, Silvestre Sponsor: EPSRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral