Stress and strain field singularities, micro-cracks, and their role in failure initiation at the composite laminate free-edge.

摘要

A state-of-the-art multi-scale analysis was performed to predict failure initiation at the free-edge of an angle-ply laminate using the Strain Invariant Failure Theory (SIFT), and multiple improvements to this analysis methodology were proposed and implemented. Application of this analysis and theory led to the conclusion that point-wise failure criteria which ignore the singular stress and strain fields from a homogenized analysis and the presence of free-edge damage in the form of micro-cracking, may do so at the expense of failure prediction capability.;The main contributions of this work then are made in the study of the laminate free-edge singularity and in the effects of micro-cracking at the composite laminate free-edge. Study of both classical elasticity and finite element solutions of the laminate free-edge stress field based upon the assumption of homogenized lamina properties reveal that the order of the free-edge singularity is sufficiently small such that the domain of dominance of this term away from the laminate free-edge is much smaller than the relevant dimensions of the microstructure. In comparison to a crack-tip field, these free-edge singularities generate stress and strain fields which are half as intense as those at the crack-tip, leading to the conclusion that existing flaws at the free-edge in the form of micro-cracks would be more prone to the initiation of free-edge failure than the existence of a singularity in the free-edge elasticity solutions.;A methodical experiment was performed on a family of [±25°/90°] s laminates made of IM7/8552 carbon/epoxy composite, to both characterize micro-cracks present at the laminate free-edge and to study their behavior under the application of a uniform extensional load. The majority of these micro-cracks were of length on the order of a few fiber diameters, though larger micro-cracks as long as 100 fiber diameters were observed in thicker laminates. A strong correlation between the application of vacuum during cure and the presence of micro-cracks was observed. The majority of micro-cracks were located along ply interfaces, even along the interfaces of plies with identical orientation, further implicating processing methods and conditions in the formation of these micro-cracks and suggesting that a region of interphase is present between composite plies. No micro-cracks of length smaller than approximately 36 fiber diameters (180 µm) grew or interacted with the free-edge delamination or damage at ultimate laminate failure, and the median length of micro-cracks which did grow was approximately 50 fiber diameters (250 µm). While the internal depth of these free-edge cracks was unknown, the results of these experiments then suggests a critical free-edge crack-length in the [±25°/90°]s family of laminates of approximately 50 fiber diameters (250 µm, or 1.5 lamina thicknesses).;A multi-scale analysis of free-edge micro-cracks using traditional displacement based finite element submodeling and XFEM was used to explain the experimental observation that micro-cracks did not grow unless they were of sufficient length. Analysis of the stress-intensity factors along the micro-crack front revealed that penny shaped micro-cracks in the 90° plies of the [±25°/90°] s family of laminates of length two fiber diameters or longer are under mode I dominated loading conditions when oriented parallel or perpendicular to the laminate loading direction. The maximum observed KI along the crack-front of these modeled micro-cracks was no larger than 26% of the ultimate KIC of the matrix material, under the application of a uniform temperature change (ΔT=-150°C) and uniform extension equal to the experimentally measured ultimate failure strain of the laminate. This indicates that insufficient energy is supplied to these small micro-cracks to facilitate crack growth, confirming what was experimentally observed. A method for estimating a critical micro-crack length based upon the results of the fracture mechanics analysis was developed, and predictions for this critical crack length were between 26 and 255 fiber diameters with a nominal prediction of approximately 73 fiber diameters, which agreed quite well with the experimentally observed critical micro-crack length of approximately 50 fiber diameters.;The overall conclusion of this work is that the composite laminate does not appear to be as sensitive to free-edge singular stress-fields or free-edge micro-cracking and damage as the research community has portrayed in the literature. In laminates designed to delaminate, material flaws on the order of the relevant dimensions of the micro-structure appear to have little to no effect on the static strength of a composite laminate.