Micromechanical finite element modeling of tensile failure in unidirectional composites
Date
2022
Authors
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Publisher
University of Delaware
Abstract
In a unidirectional composite under axial tensile loading, damage initiates in the form of fiber breaks. The breaking of a fiber is a locally dynamic process which leads to stress concentrations in the matrix and neighboring fibers and debonding of the interface that can propagate at high speed over long distances. The brittle fiber fracture within the composite results in release of stored strain energy as a compressive stress wave that propagates along the length of the broken fiber at speeds approaching the axial wave-speed in the fiber (6 km/s). This wave induces an axial tensile wave with a dynamic tensile stress concentration in adjacent fibers that diminishes with distance. These stress concentrations lead to additional fiber breaks in the neighboring fibers leading to the formation of break clusters. The composite fails catastrophically when a critical cluster size is reached. ☐ To study the dynamics of a single fiber break within a composite and the associated stress wave propagation and interfacial debond growth a micromechanical Finite Element (FE) modeling framework is developed. In the case of higher strength fibers breaks, unstable debond growth is predicted where the debond grows unbounded and the traveling stress waves will be arrested only when it reaches a boundary of the composite or encounters another break in the same fiber. A stability criterion to define this threshold fiber break strength is derived based on an energy balance between the release of fiber elastic energy and energy absorption associated with interfacial debonding. This dynamic debond growth can explain the axial splitting seen during the failure of these composites in tension experiments. The prevalent approach in literature of modeling the fiber break as a static process (starts off with a pre-broken fiber) to determine Stress Concentration Factors (SCFs) cannot capture this failure mode. Based on the ratio of shear yield strength of the matrix and mode II peak traction of the interface cohesive law (Rshear), two distinct regimes of damage exist – only matrix yielding occurs when this ratio is less than 1 while both interfacial debonding and matrix yielding occur when it is greater than 1. ☐ Tensile strength distribution of S-Glass fibers at small gage lengths on the order of the ineffective length is an essential input for both analytical and FEA models of composite tensile strength. This historically has been done by extrapolating Weibull strength distributions measured at large gage lengths to smaller length scales (100 - 300 um). As will be shown in this thesis, this method leads to a significant over-estimation of fiber strengths at the shorter gage lengths, and consequently leads to an over-prediction of the composite strength. Filament tensile tests (gage lengths > 4mm) and a continuously-monitored Single Fiber Fragmentation Test (SFFT, gage length = 544um) were performed on fiber specimens from the same spool to quantify the inaccuracy in the Weibull extrapolation down to shorter gage lengths. A Bimodal Weibull equation has been fit to the combined data from the 2 experiments. While this Bimodal distribution predicts the experimental data well across the entire range of gage lengths tested, from 500um-30 mm, it still does not guarantee the accuracy of the extrapolation down to 100-300um length-scales. More importantly, it does not provide any information about the spatial distribution of defects on the fiber. ☐ In the context of the dynamic stress concentrations and the evolution of break clusters, measuring the size and spacing of surface defects in the Glass fibers is critical. There is no existing test method in the literature to quantify the size and spatial distribution of defects on a fiber surface. In this work, a novel continuous fiber bending test method is developed to measure the size and spatial distribution of critical surface defects in S-glass fibers. The results of this experiment are used to map the critical defects on the tension surface of a glass fiber. A methodology is developed to map additional defects around the circumference of the fiber, while maintaining the size and spatial distribution obtained from the bending tests. The results indicate that extrapolating the Weibull distribution (be it bimodal or unimodal) to gage lengths less than 200 µm leads to serious errors in fiber strength prediction. This is occurring because the defects are not uniformly distributed along the entire gage length of the fiber, as assumed in Weibull theory. ☐ The FE modeling methodology is extended to a 3D model with a hexagonal packing of parallel fibers. In addition to being a more realistic representation of the composite micro-structure, the 3D FE model also enables to model the residual stresses that develop within the micro-structure during the cool down phase of composite cure or post-cure. The mismatch in CTE and Poisson’s ratios of the fiber and the matrix leads to the accumulation of radial compressive residual stresses across the fiber-matrix interface, which in turn leads to frictional dissipation in the debond region of the interface. A map of the SCF values on the surface (along the axial as well as circumferential directions) of the fibers which are neighboring the fiber break is generated using the results from the 3D FE model simulations. In addition to mapping of critical defects, this mapping of dynamic SCFs is an important input for composite strength models. A chain-of-bundles model is used to illustrate the reduction in the error as 1) the Weibull extrapolation is replaced with a direct mapping of defects, and 2) when the additional breaks caused by the propagation of dynamic SCFs are accounted for. Not accounting for these factors leads to a significant over-prediction of composite properties (by ~ 80%) compared to experimental values reported in literature. Using a modified chain-of-bundles model that explicitly accounts for these two effects leads to strength predictions, which are within 4% of the experimental results.
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Keywords
Composites, Glass fiber, Interface, Polymer matrix, Tensile failure, Finite element modeling