Finite element analysis of initial imperfection effects on kinking failure of unidirectional glass fiber-reinforced polymer composites
Introduction
The kinking failure of unidirectional glass fiber-reinforced polymer (GFRP) composites is primarily caused by disproportional fiber microbuckling, as for instance experimentally observed in Ref. [1], to which this paper refers to. Finite element (FE) analysis can increase the understanding of such complex failure mechanisms since the individual composite components (fibers, resin and interfaces) can be modeled and their deformation on the micro-scale can be obtained, something that cannot be easily observed during experiments.
For the prediction of compressive failure mechanisms, i.e. kinking or delamination, FE models have been proposed in the literature on the macro-scale (multilayer models) and micro-scale (micromechanical models). Multilayer approaches [2], [3], [4], [5], [6], [7], [8], [9] model each lamina of the laminate as a separate layer consisting of specific categories of elements, such as shell [2], brick [3], [4] solid [5] or truss elements [8]. Individual fibers, resin, interfaces, and initial imperfections, such as initial fiber waviness or resin/interface defects caused by voids for example, existing in each lamina, are normally not modeled separately. Additional layers to take into account the interface material with a user-defined strength were however implemented for the simulation of delamination failures, e.g. in [6]. Element failure detection was based on a user-defined failure criterion, and when failure occurred the stiffness of the failed elements was reduced to a certain extent, e.g. 10% of the original value [3]. The models were then updated by assuming the deteriorated element properties, and an iterative process was followed until the compressive failure of the whole laminate occurred [6]. These models have been applied for the prediction of the compressive failure of various composites, such as notched multidirectional carbon fiber-reinforced epoxy laminated panels [2], carbon fiber-reinforced composite laminates with an open hole in the center [3], and laminates without any initial artificially drilled holes or cracks [6], [7]. The success of the multilayer models mainly laid in the prediction of the failure load, initial slopes on the load-displacement curve, and the failure area. The mechanisms behind the compressive failure, such as the disproportional fiber deformation, or the failure modes affected by the initial imperfections, were beyond the prediction capacity of these models.
Micromechanical models were established based on the assumption that the global behavior of a composite specimen can be simulated by a representative volume element (RVE), comprising in this case a fraction of the fibers and resin surrounding these fibers. According to the micromechanical models, deformation and failure of the volume element are representative of the deformation and failure of the entire composite [10], [11], [12], [13], [14], [15], [16], [17], [18]. For unidirectional fiber composites, periodic boundary conditions can be applied [11] assuming that all fibers throughout the specimen volume deform proportionally to the fibers of the representative volume element. Different numbers of fibers were used for the definition of the RVEs in different models, as few as two to four single fibers [11], [12], and up to as many as 40 e.g. [13]. The micromechanical models were established in either two dimensions [11], [14] or three dimensions [12], [13]. 2-D models with periodic boundary conditions could only be used for the prediction of the failure of specimens demonstrating uniform fiber deformation across the cross section, such as buckling failure. 3-D model predictions can theoretically predict the failure of materials showing non-uniform deformation [16]. However, the prediction, limited by the scale of the RVE, could provide an assessment of the global failure propagation path across the entire width/height of the composite concerned [13]. Moreover, experimental validation of the micromechanical model predictions is lacking in several works in the literature [13], [17], [18].
The above-mentioned literature review shows that both multilayer and micromechanical models comprise inherent drawbacks due to their basic assumptions. The multilayer models are not capable of considering initial imperfections, including initial fiber waviness and defects and therefore cannot predict the failure modes related to these imperfections. The micromechanical models, due to the limited size of the RVE, cannot predict the failure propagation on a macroscopic scale. New FE models are thus presented in this work for simulation of the kinking failure of glass fiber-reinforced polymer composites. The new models were established in such a way that they incorporate both the simplicity of the multilayer models and the precision of the micromechanical models. Initial imperfections, including fiber waviness and initial defects (e.g. voids) are implemented in the models. The numerically estimated failure mode, peak load, fiber microbuckling development and strain fields are compared to the experimental results obtained in Ref. [1]. The effect of initial imperfections on the kinking failure formation is thoroughly investigated.
Section snippets
Experimental results summary
Prismatic non-slender specimens with nominal dimensions of 12.7 × 12.7 × 50 mm3 according to ASTM D695-10 [19] were cut from a fully cured GFRP unidirectional laminate and subjected to axial compression [1]. The quasi-static experiments were performed at different temperatures at a displacement rate of 0.5 mm/min. The specimen displacements were recorded by monitoring the movement of the machine loading head and by a digital image correlation (DIC) system. At a temperature of 90 °C (still below
Load-displacement curves
The load-displacement curves obtained by the FE models are shown in Fig. 3. A linear increase of the load with displacement up to the peak load was observed in all the four models. The initial stiffness was only slightly changed by adding either one or two groups of defects (F1, F2A and F2B) when compared to the results of F0. The difference between the peak loads calculated by the FE models with initial defects (F1, F2A and F2B) was negligible, while the peak load calculated by model F0 showed
Comparison of FE models and experimental results
A comparison between the experimental and numerical load-displacement curves is shown in Fig. 3. The experimental displacements were obtained by calculating the difference between the displacements at the top and bottom of the specimen, measured by DIC. As can be seen, the initial slope of the load-displacement curves obtained from the four FE models corroborated well the experimentally derived one. The peak loads predicted by the three models with initial defects (F1, F2A and F2B) were
Conclusions
Finite element models were developed to investigate the kinking failure mode of non-slender unidirectional glass fiber-reinforced polymer specimens, subjected to axial compression at an elevated temperature of 90 °C. The models included initial imperfections such as fiber bundle waviness and defects in the resin or the resin/fiber interfaces. The peak load, fiber microbuckling amplitudes and kink band formation and propagation were numerically obtained and compared to experimental results. The
Acknowledgement
The authors would like to thank the Swiss National Science Foundation for funding this project (Grant No. 200021_129613).
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