Micro-mechanical finite element analysis of Z-pins under mixed-mode loading

This work was published with the title of “Micro-mechanical finite element analysis of Z-pins under mixed-mode loading” in the journal Composites Part A: Applied Science and Manufacturing, 2015.

Laminated fibre-reinforced plastic (FRP) composites have become very attractive candidate materials for modern engineers when they need to design lightweight structures that possess high stiffness and strength. Two examples are the Airbus A350-XWB and Boeing B787 airframes, which comprise 53% and 50% FRP composites, respectively. One of the main concerns that has to be considered when designing a laminated composite structure is its resistance to disbond between two adjacent plies (delamination), which can cause catastrophic failure of a laminate structure before the fibre strength is reached.

In order to improve the delamination resistance of a FRP laminate, embedding through-thickness reinforcing (TTR) elements in the thickness direction of the laminate has been proved to be an effective approach. The TTR elements may be in the form of continuous fibre tows/yarns in stitching, tufting, 3D weaving and 3D braiding technologies. On the other hand, Z-pinning technology suppresses delamination through discrete small-diameter TTR rods, generally called Z-pins or Z-fibres (Partridge & Cartié 2005, Zhang et al. 2016). This promising TTR technology has been successfully applied in Boeing F18E/F engine inlet ducts and Lockheed Martin Joint strike fighter (JSF) F-35.

Z-pins inhibit or delay delamination through both pull-out (mode I) and shear deformation (mode II). Analysis and prediction on the delamination suppressing behaviour of Z-pins are quite challenging, especially for the full range of mode mixites. This work proposed a high-fidelity finite element modelling strategy that can be used to predict the Z-pin bridging mechanisms under various loading mode mixities. It employs a versatile ply-level mesh to describe the critical microstructural features of a Z-pin reinforced composite laminate, including Z-pin misalignment, fibre waviness and eyelike resin rich region formed around a Z-pin due to accommodating of the TTR element.

A full three-dimensional mesh can then be created by stacking up a number of ply-level meshes in the thickness direction of the laminate following a given stacking sequence. The Z-pin/laminate interface is described by inserted zero-thickness cohesive elements, followed by frictional contact. The cohesive elements are governed by a quadratic stress criterion for failure initiation, and a power law criterion for failure evolution (Harper & Hallett 2008). The friction law used in the modelling approach adds a shear stress term on top of the standard Coulomb friction, considering that the actual geometry of the Z-pin/laminate contact surface in real coupons shows large geometrical irregularities and roughness. Two failure mechanisms existing in a Z-pin are also considered including shear-driven splitting and fibre rupture, which are respectively described by axially inserted zero-thickness cohesive elements and a statistically based Weibull fibre failure criterion. In addition, modelling of post-cure cool down is also integrated in present numerical tool.

The advanced finite element modelling approach has been validated by single pin tests of T300/BMI Z-pins with the diameter of 0.28 mm. These Z-pins were inserted in quasi-isotropic laminate coupons and tested under varying mode mixities of loading applied by a custom designed Arcan jig. Numerical results correlate very well with experimental measurements in terms of traction versus displacement curves and post-mortem observations. This modelling approach can thus been employed to investigate the various factors that affect the Z-pin bridging ability such as the effects of Z-pin/laminate interface bonding, Z-pin/laminate interface friction and Z-pin splitting.

The numerical methodology described here can be extended directly to Z-pinned laminates with arbitrary stacking sequences, loading mode mixities, different pin and laminate materials. It is also capable of providing reliable guidelines that can be used to optimise the Z-pin configuration for a given laminate across the whole mode-mixity range. The modelling strategy is also a good reference for other TTR technologies for composite laminates, especially stitching and tufting.

Acknowledgement

The authors would like to acknowledge Rolls-Royce for the support of this research through the Composites University Technology Centre (UTC) at the University of Bristol, UK.