ABSTRACTMULTISCALE MODELING OF COMPOSITE LAMINATES WITH FREE EDGE EFFECTSByChristopher R. CaterComposite materials are complex structures comprised of several length scales. In composite laminates, the mechanical and thermal property mismatch between plies of varying orientations results in stress gradients at the free edges of the composites. These free edge stresses can cause initial micro-cracking during manufacture, and are a significant driver of delamination failure. While the phenomenon of free edge stresses have been studied extensively at the lamina level, less attention has been focused on the influence of the microstructure on initial cracking and development of progressive damage as a consequence of free edge stresses. This work aimed at revisiting the laminate free edge problem by developing a multiscale approach to investigate the effect of the interlaminar microstructure on free edge cracking. First, a semi-concurrent multiscale modelling approach was developed within the commercial finite element software ABAQUS. An energetically consistent method for implementing free edge boundary conditions within a Computational Homogenization scheme was proposed to allow for micro-scale free edge analysis. The multiscale approach was demonstrated in 2D tests cases for randomly spaced representative volume elements of unidirectional lamina under tensile loading. Second, a 3D multiscale analysis of a [25N/-25N/90N]S composite laminate, known for its vulnerability to free edge cracking, was performed using a two-scale approach: the meso-scale model captured the lamina stacking sequence and laminate loading conditions (mechanical and thermal) and the micro-scale model predicted the local matrix level stresses at the free edge. A one-way coupling between the meso- and micro-scales was enforced through a strain based localization rule, mapping meso-scale strains into displacement boundary conditions onto the micro-scale finite element model. The multiscale analysis procedure was used to investigate the local interlaminar microstructure. The results found that a matrix rich interlaminar interface exhibited the highest free edge stresses in the matrix constituent during thermal cooldown. The results from these investigations assisted in understanding the tendency for pre-cracks during manufacture to occur at ply boundaries at the free edge and the preferential orientation to the ply interfaces. Additionally, analysis of various 90/90 ply interfaces in the thicker N=3 laminate found that the free edge stresses were far more sensitive to the local interlaminar microstructure than the meso-scale stress/strain free edge gradients. The multiscale analysis helped explain the relative insensitivity of free edge pre-cracks to progressive damage during extensional loading observed in experiments. Lastly, the multiscale analysis was extended to the interface between the -25 and 90 degree plies in the [25N/-25N/90N]S laminate. A micro-model representing the dissimilar ply interface was developed, and the homogenized properties through linear perturbation steps were used to update the meso-scale analysis to model the interlaminar region as a unique material. The analysis of micro-scale free edge stresses found that significant matrix stresses only occurred at the fiber/matrix boundary at the 90 degree fibers. The highest stresses were located near the matrix rich interface for both thermal and mechanical loading conditions. The highest matrix stresses in the case of extensional loading of the laminate, however, were found at the interior of the micro-model dissimilar ply micro-model within the -25 degree fibers.
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