# Mechanics of microdamage development and stiffness degradation in fiber composites

Sammanfattning: Damage in composites reduces its performance and durability and thus its usefulness. The common subject in all papers presented in the licentiate thesis is distributed microdamage, and the materials of interest are a Hemp/Lignin natural composite and glass/carbon fiber reinforced plastics composites. The focus is on how the damage affects the performance in terms of creep strain and stiffness. In Paper A a nonlinear viscoelastic viscoplastic model of a Hemp/Lignin composite is generalized by including stiffness reduction, and thus the degree of microdamage, in the composite (when loaded in the axial direction). Schapery's model is used to model the nonlinear viscoelasticity whereas the viscoplastic strain is described by a nonlinear function presented by Zapas and Crissman. In order to include stiffness reduction due to damage, Schapery's model is modified by incorporating a maximum strain-state dependent function reflecting the elastic modulus reduction with increasing strain measured in tensile tests. The model successfully describes the main features for the investigated material and shows good accuracy within the considered stress range. In Paper B the stiffness reduction of a unidirectional (UD) composite containing fiber breaks with partial interface debonding is analyzed. The analysis is performed by studying how the average crack opening displacement (COD) depends on fiber and matrix properties, fiber content and debond length. The COD is normalized with respect to the size of the fiber crack and to the far field stress in the fiber. In contrast to other performed analysis an analytical relationship is developed which links the entire stiffness matrix of the damaged UD composite with the COD and the crack sliding displacement (CSD). However, the CSD is excluded from the analysis since it is found by parametric inspection that it does not affect the longitudinal stiffness. Some trends regarding the COD dependence on the different properties can be extracted from available approximate analytical stress transfer models. To obtain more reliable results, in the current analysis these dependences are extracted from extensive FEM based parametric analysis performed on a model consisting of three concentric cylinders: a) broken fiber; b) matrix cylinder around it; c) large effective composite cylinder surrounding them. This model is used since it is more adequate than unit cell models considering only fiber and matrix. The cracks, which are only in the fibers, are distributed in such a way that they are non-interactive. It is shown that the parameters that affect the COD the most are the ratio of the longitudinal fiber modulus and matrix modulus, the fiber content and the debond length. These relationships are described by simple fitting functions which excellently fit the numerical results. These simple functions are merged into one relationship describing the COD's dependence on the relevant parameters. Simulations performed for carbon and glass fiber polymer composites show that the relative longitudinal stiffness reduction in the carbon fiber composite is slightly larger than in the glass fiber composite. This trend holds for all considered debond lengths and is related to higher longitudinal fiber and matrix modulus ratio in the carbon fiber composite leading to larger crack openings and larger stress perturbation zones. It is shown that the stiffness reduction depends on the debond length. In Paper C the analysis performed in Paper B is continued by studying how the COD is affected when the cracks are interactive. It is shown that the effect on the COD in the glass fiber composite is negligible. However, the effect on the COD in the carbon fiber composite is significant. This difference is related to higher longitudinal fiber and matrix modulus ratio for the carbon fiber composite. In Paper D the same model is used to analyse the strain energy release rate related to the debond crack growth along the fiber. The energy release rate is calculated using the virtual crack closure technique applied to displacement and stress field in the vicinity of the debond crack tip calculated using refined FE model. It is shown that the energy release rate is larger for very short debonds. It reduces to a constant value indicating a stable debond crack growth after its initiation. It is shown that the strain energy release rate in the plateau region also can be calculated using a simple analytical model based on the self-similar crack growth assumption. When the stress state perturbations related to debonds at both fiber ends start to interact, the energy release rate decreases. In a future work the obtained relationships for the energy release rate will be incorporated in a microdamage evolution model describing the statistics of fiber breaks and debond growth in fatigue loading conditions.

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