The importance of accounting for large deformation in continuum damage models in predicting matrix failure of composites

The work presented in this paper investigates the ability of continuum damage models to accurately predict matrix failure and ply splitting. Two continuum damage model approaches are implemented that use different stress–strain measures. The first approach is based on small-strain increments and the Cauchy stress, while the second approach account for large deformation kinematics through the use of the Green–Lagrange strain and the 2nd Piola–Kirchhoff stress. The investigation consists of numerical benchmarks at three different levels: (1) single element; (2) unidirectional single ply open-hole specimen and (3) open-hole composite laminate coupon. Finally, the numerically predicted failure modes are compared to experimental failure modes at the coupon level. It is shown that it is important to account for large deformation kinematics in the constitutive model, especially when predicting matrix splitting failure modes. It is also shown that continuum damage models that do not account for large deformation kinematics can easily be adapted to ensure that the damage modes and failure strength are predicted accurately

Experimental and numerical evaluation of conduction welded thermoplastic composite joints

The capability of joining two thermoplastic composite parts by welding is a key technology to reduce the weight and cost of assembled parts and enables high volume manufacturing of future aeronautical structures made of thermoplastic composite materials. However, there is not much experimental understanding of the mechanisms involving welded joint failure, and the computational tools available for the simulation of thermoset composites have not yet been completely assessed for thermoplastic materials. In this work, a numerical and experimental evaluation is performed to investigate the strength and failure behavior of conduction welded thermoplastic composite joints. A welded single lap shear joint is designed, manufactured, tested and analyzed proposing two distinct modeling approaches. A simplified modeling strategy which only accounts for damage at the weld is compared to a high-fidelity model which can take into account the physical failure mechanisms at the lamina level. The high-fidelity modeling methodology is able to predict the experimental failure mode of the investigated welded joints with high accuracy and is used to gain new insights into the key-variables that influence the strength of thermoplastic welded joints. It is also found that the joint strength is highly influenced by the failure mechanisms not only of the welded interface but also of the surrounding plies

Characterization and analysis of the interlaminar behavior of thermoplastic composites considering fiber bridging and R-curve effects

Thermoplastic composites can enable the development of new manufacturing techniques to make the aviation industry more sustainable while at the same time greatly benefit cost-efficient and high-volume production. One of the thermoplastic composite materials that can enable this transition is AS4D/PEKK-FC. In this work, the interlaminar properties of AS4D/PEKK-FC thermoplastic composite are characterized and analyzed by means of Mode I, II and Mixed Mode I/II at 50:50 tests, while considering fiber bridging and R-curve effects. In order to achieve stable crack propagation the test configurations are adjusted to account for the large fracture process zone ahead of the crack tip and an appropriate data reduction method is selected. The experimental data is reduced using an inverse methodology to extract cohesive laws based on only the load–displacement curves. Additionally, the use of this methodology provides new insights into the validity of two different mode II tests and the influence of fiber bridging on the mixed-mode interlaminar behavior. The interlaminar damage mechanisms are investigated by means of scanning electron microscopy. The resulting cohesive laws are implemented in commercial finite element software in tabular form, without the need for user-subroutines. All experimental test configurations are analyzed using a single material card and it is shown that fiber bridging and R-curve effects are well captured

Skin-stringer separation in post-buckling of butt-joint stiffened thermoplastic composite panels

Two aeronautical thermoplastic composite stiffened panels are analysed and tested to investigate the buckling behaviour, the skin-stringer separation and the final failure mode. The panels are made of fast crystallising polyetherketoneketone carbon composite, have three stringers with an angled cap on one side, and are joined to the skin by a short-fibre reinforced butt-joint. The panels contain an initial damage in the middle skin-stringer interface representing barely visible impact damage. Finite element analysis using the virtual crack closure technique are conducted before the test to predict the structural behaviour. During the tests, the deformation of the panels is measured by digital image correlation, the damage propagation is recorded by GoPro cameras and the final failure is captured by high speed cameras. The panels show an initial three half-wave buckling shape in each bay, with damage propagation starting shortly after buckling. A combination of relatively stable and unstable damage propagation is observed until final failure, when the middle stringer separates completely and the panels fail in an unstable manner. The test results are compared to the numerical prediction, which shows great agreement for both the buckling and failure behaviour

Leximals, the Lexicore and the Average Lexicographic Value

The lexicographic vectors of a balanced game, called here leximals, are used to define a new solution concept, the lexicore, on the cone of balanced games. Properties of the lexicore and its relation with the core on some classes of games are studied. It is shown that on cones of balanced games where the core is additive, the leximals, the lexicore and the Average Lexicographic (AL-)value are additive, too. Further, it turns out that the leximals satisfy a consistency property with respect to a reduced game `a la Davis and Maschler, which implies an average consistency property of the AL-value. Explicit formulas for the AL-value on the class of k-convex games and on the class of balanced almost convex games are provided.