The mode-I dynamic fracture energy and failure mechanisms of glass fiber-reinforced polymer composites are investigated with an embedded cell model of the single-edge-notched-tension (SENT) geometry. Under an applied dynamic loading, a crack may propagate in the embedded microstructure, accompanied by the development of a fracture process zone in which fiber/matrix debonding, matrix cracking and ductile matrix tearing are observed. Reaching a maximum nominal strain rate of 250/s, a series of SENT tests are performed for different loading velocities and specimen sizes while the dynamic energy release rate is evaluated using the dynamic version of the J-integral. The influence and interaction of loading rate, time-dependent material nonlinearity, structural inertia and matrix ligament bridging on the fracture toughness and failure mechanisms of composites are evaluated. It is found that with the given material parameters and studied loading rate range, the failure type is brittle with many microcracks but limited plasticity in the fracture process zone and a trend of increasing brittleness for larger strain rates is observed. The inertia effect is evident for larger strain rates but it is not dominating. An R-curve in the average sense is found to be strain-rate independent before the fracture process zone is fully developed and afterwards a velocity–toughness mechanism is dictating the crack growth.

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The application of fiber-reinforced polymer (FRP) composites is gaining increasing popu-larity in impact-resistant devices, automotives, biomedical devices and aircraft structures due to their high strength-to-weight ratios and their potential for impact energy absorption. Impact-induced high loading rates can result in significant changes of mechanical properties (e.g., elastic modulus and strength) before strain softening occurs and failure characteristics inside the strain localization zone (e.g., failure mechanisms and fracture energy) for fiber-reinforced polymer composites. In general, these phenomena are called the strain rate effects. The underlying mechanisms of the observed rate-dependent deformation and failure of composites take place among multiple length and time scales. The contributing mechanisms can be roughly classified as: the viscosity of composite constituents (polymer, fiber and interfaces), the rate-dependency of the fracture mechanisms, the inertia effects, the thermomechanical dissipation and the characteristic fracture time. Numerical models, including the viscosity type of constitutive models, rate-dependent cohesive zone models, enriched equation of motion and thermomechanical numerical models, are useful for a better understanding of these contributing factors of strain rate effects of FRP composites.

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With a classical notched configuration, the damage process in the transverse plane of fiber-reinforced polymer composites are studied by a direct numerical simulation model (DNS). However, to avoid high computational costs the region in which the fiber/matrix microstructure is explicitly modeled must remain small. Therefore, away from the notch tip, a homogenized model is needed to capture the far-field mechanical response without damage but with possibly rate-dependent nonlinearity. In this contribution, with a representative volume element (RVE), a step-by-step numerical homogenization procedure is introduced to calibrate a homogenized viscoelastic-viscoplastic (VE-VP) model with the same formulation as the VE-VP model used for describing the polymer behavior in the RVE model. The calibrated VE-VP model is used in a homogenized FEM model to describe the composite material response and compared against the RVE model. It is found that: (1) the homogenized model captures the viscoelastic deformation, the rate-dependent yielding, stress relaxation and unloading behavior of the polymer composite well, although the assumptions of a single plastic Poisson's ratio and pure isotropic hardening are oversimplifications of the composite behavior; (2) the novel step-by-step numerical homogenization procedure provides an efficient and accurate way for obtaining material parameters of a VE-VP model.

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Fiber reinforced polymer composites are increasingly used in impactresistant devices, automotives, and aircraft structures due to their high strengthtoweight ratios and their potential for impact energy absorption. Dynamic impact loading causes complex deformation and failure phenomena in composite laminates. Moreover, the high loading rates in impact scenarios give rise to a significant change in mechanical properties (e.g. elastic modulus, strength, fracture energy) and failure characteristics (e.g. failure mechanisms, energy dissipation) of polymer composites. In other words, both mechanical deformation and failure are strainrate dependent. The contributing mechanisms can be roughly classified as viscous material behavior, changes in failure mechanism, inertia effects and thermome chanical effects. These effects involve multiple length and time scales. In experiments it is difficult to isolate single mechanisms contributing to the overall ratedependency. Therefore, it is difficult to quantify the contribution of each mechanism at different scales. The aim of this thesis is to establish a multiscale numerical framework in which three of the contributing mechanisms, i.e. the viscous material behavior, changes in fracture mechanisms and inertia effects, can be investigated at different scales. The research in this thesis is divided into four parts, one related to the macroscale, where the composite material is treated as homogeneous, and three on exploring possibilities to include microscale information, taking into account the microstructure of fibers and matrix. @en

An asymptotic homogenization model considering wave dispersion in composites is investigated. In this approach, the effect of the microstructure through heterogeneity-induced wave dispersion is characterised by an acceleration gradient term scaled by a “dispersion tensor”. This dispersion tensor is computed within a statistically equivalent representative volume element (RVE). One-dimensional and two-dimensional elastic wave propagation problems are studied. It is found that the dispersive multiscale model shows a considerable improvement over the non-dispersive model in capturing the dynamic response of heterogeneous materials. To test the existence of an RVE for a realistic microstructure for unidirectional fiber-reinforced composites, a statistics study is performed to calculate the homogenized properties with increasing microstructure size. It is found that the convergence of the dispersion tensor is sensitive to the spatial distribution pattern. A calibration study on a composite microstructure with realistic spatial distribution shows that convergence is found although only with a relatively large micromodel.@en

The mode-I interlaminar fracture toughness of composite laminates under different loading rates can be measured by the double cantilever beam (DCB) test. It is observed from the DCB test of a unidirectional PEEK/carbon composite laminate that as the loading rate increases from quasi-static to dynamic range: (1) delamination crack growth exhibits a transition from stable to unstable (“stick/slip”) and back to a stable type; (2) the interlaminar fracture toughness is not constant as the loading rate increases. In this paper, two numerical approaches are used to reproduce the experimental observations: a cohesive zone model (CZM) and the interfacial thick level set (ITLS) model. CZM simulations with rate-independent and rate-dependent cohesive laws are carried out. A new version of the ITLS is introduced with a phenomenological relation between crack speed and energy release rate. The simulation results of the CZM and the ITLS model are compared with the real DCB test data to evaluate the capability of these two types of models. It is found that the used CZM can reproduce rate-dependence of the fracture energy, but not the stick/slip behavior. The ITLS can capture the stick/slip behavior, but needs different parameter sets for different loading rates.

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In this paper, the thick-level-set method is used to model stable and unstable (stick/slip) crack propagation in the dynamic double cantilever beam (DCB) test for unidirectional composite laminates. The thick-level-set method uses a predefined damage profile to describe the fracture process zone and allows for accurate evaluation of the global energy release rate. A phenomenological model is introduced to calculate the crack speed as a function of the energy release rate. The potential capability of the proposed approach is demonstrated by simulating a series of dynamic DCB tests under variable test rates.@en