Numerical analysis of size effects on open-hole tensile composite laminates
Introduction
Composite materials possess considerable advantages over traditional metallic materials on both weight and mechanical properties. Recently, composite materials are replacing more and more traditional metallic materials in industrial applications. However, optimal design with composite materials is often not achieved due to uncertainties in failure prediction. Despite decades of research, accurate failure prediction of composite materials remains a challenging topic. In many cases, the high count of matrix cracks and of the failure modes, as well as their interactions, poses great challenges for both numerical models and material constitutive laws.
It is observed that the strength of composites is dependent on specimen size. This size effect has been studied previously by many researchers and comprehensive reviews of early studies can be found in [1], [2], [3]. It is generally established that the strength decreases with increasing specimen size. Recently, Green et al. [4] have performed a series of detailed experiments on open-holed quasi-isotropic ([45m/90m/−45m/0m]ns) carbon-epoxy composites. Three different scaling methods were applied in the experiment, namely in-plane-scaling (Fig. 1), sublaminate-scaling (m = 1, n = 1, 2, 4, 8) and ply-scaling (m = 1, 2, 4, 8, n = 1). Three distinctive failure modes namely brittle failure, pull-out, and delamination (Fig. 2) exist for specimens of different sizes and lay-ups. The failure mode of the sublaminate-scaled specimens is either pull-out or brittle and the load-drop is caused by fibre-breaking in 0 plies. Ply-scaled specimens however all fail in delamination mode and the load-drop is caused by delamination at the −45m/0m interface prior to fibre-breaking of the 0 plies. The experiment recorded mainly four sets of size effect data, i.e. the in-plane size effect and thickness size effect of both sublaminate-scaled specimens and ply-scaled specimens.
Numerical studies of size effects of open-hole composites have been performed by Camanho et al. [6], Hallett et al. [7], Abisset et al. [8] and van der Meer et al. [9] using four different methods. Camanho et al. [6] used an energy-regularized Continuum Damage Mechanics (CDM) model to predict material local behaviour. The stress–strain relationship of each element was regularized such that the total energy dissipation upon failure equals the fracture toughness of the material. Shell elements formulated based on Classical Lamination Theory (CLT) were used in the model. Only the in-plane size effect of brittlely-failed sublaminate-scaled specimens was studied and good results were obtained. Hallett et al.’s model [7] included cohesive elements inserted between plies to model delamination and also at certain potential crack paths in plies to model matrix cracking. A global criterion based on Weibull’s statistical model was used to determine fibre failure of the entire structure. The model gave good predictions on the interaction between matrix cracks and delamination which shows that cohesive elements are versatile for matrix crack modelling if positioned correctly. Abisset et al. [8] used a brittle model for fibre breaking and a CDM model for matrix cracking and delamination. The coupling between matrix crack and delamination is accounted for in the material constitutive law for the interface cohesive elements. The in-plane size effect of both the sublaminate-scaled and the ply-scaled specimens, as well as the thickness size effect of the ply-scaled specimens, were studied. The thickness size effect of the sublaminate-scaled specimens was not investigated. van der Meer et al. [9] used a phantom-node method to explicitly represent matrix cracks in plies and a smeared crack model for fibre failure modelling. Good predictions were obtained for the in-plane size effect of both the sublaminate-scaled and the ply-scaled specimens and for the thickness size effect of the ply-scaled specimens. The thickness size effect of the sublaminate-scaled specimens was not successfully predicted.
From the above review it is seen that for deterministic failure theories, i.e. theories without considering statistical variations of material properties, the prediction of the thickness size effect of the sublaminate-scaled specimens remains a challenge.
This paper presents a numerical study of the size effects on open-hole tensile composite laminates recorded in the experiment by Green et al. [4]. Section 2 will present the failure theories used in this work. A discussion about the choice between deterministic theories and statistical theories will be given in Section 2.1. The thickness dependence of translaminar fracture toughness will be for the first time included in the numerical modelling of composites (Section 2.2). Different numerical methods will be tested for mesh convergence and a mesh-independent numerical method will be selected in Section 3. The sublaminate-scaling thickness size effect will be studied and the importance of including the thickness dependence of translaminar fracture toughness in the failure modelling of composites discussed in Section 4.1. The ply-scaling thickness size effect will be studied in Section 4.2. The in-plane size effect of the sublaminate-scaled specimens will be studied in Section 4.3 and that of the ply-scaled specimens in Section 4.4.
Section snippets
Fibre failure
Carbon fibres normally show brittle behaviour and their strength usually decreases with increasing fibre length due to the Weakest Link Theory. This size effect of fibre strength can be characterised by a Weibull statistical distribution [10]. The fibre–matrix composite however is not exactly brittle. Fibre–matrix debonding and friction result in a high fracture energy and therefore a more gradual propagation of fracture [11], [12]. In the presence of stress concentrations caused by notches and
Mesh refinement study of numerical methods
In this section, three different numerical methods are examined for accuracy and convergence on one selected test case of hole diameter d = 3.175 mm and lay-up [−45/90/45/0]s for four different in-plane meshes (Fig. 5). All material properties used are summarised in Table 1.
Sublaminate-scaling thickness size effect
CSLI models with the same mesh as Mesh 2 were created for the two thicker sublaminate-scaled specimens, as shown in Table 2. It can be seen that for specimens of the same in-plane scales, strength decreases while sublaminates are blocked and the rate of decrease slows down as the number of sublaminates increases. Simulation results correctly predict these two phenomena and they are in good agreement with the experimental values. The failure modes of the two thicker sublaminate-scaled specimens
Conclusion
This work presents a numerical study of the size effects observed on open-hole composite laminates. On the numerical side, it is shown that models without considering delamination give mesh-dependent and over-estimated strength predictions and therefore are not suitable for the failure modelling of composite laminates. The CSLI model, where the matrix cracking is modelled by smeared crack elements and delamination is modelled by cohesive elements, gives accurate and mesh-independent predictions
Acknowledgements
The first author gratefully acknowledges the research scholarship from National University of Singapore and would like to thank Dr. M. Ridha and Dr. X.S. Sun for helpful and useful discussions on the topics of this paper.
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