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Single Side Stitching, an innovative textile ... - Mechanical Engineering

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FEM-Simulation of the 3D-Braiding Process<br />

Simulation of the braiding process is a difficult application for finite element <strong>an</strong>alysis. The calculation<br />

must permit very large displacements <strong>an</strong>d a highly efficient contact algorithm is essential to<br />

treat the enormous amount of yarn interaction. Some special features are also needed such as <strong>an</strong><br />

element to model the ‘feed-in’ <strong>an</strong>d ‘feed-out’ of yarn from the bobbin as it tr<strong>an</strong>sverses the base<br />

plate. The key features of a braiding FE model are shown in Figure 3. The yarns are represented as<br />

a fine mesh of bar (or membr<strong>an</strong>e) elements with a typical length of 2 mm so that fine details of the<br />

braid may be captured. All nodes at the braid point are moved vertically with a const<strong>an</strong>t ‘take-up’<br />

velocity <strong>an</strong>d each node at the lower end is assigned a velocity time history to describe the motion of<br />

the bobbin it represents. Stationary yarns are similarly modelled except that their lower nodes are<br />

held fixed. The yarns are given typical material properties <strong>an</strong>d the special elements at the base,<br />

which represent the bobbins, are given a force-deflection behaviour that corresponds to the ‘feedout’<br />

<strong>an</strong>d ‘feed-in’ of yarn from the bobbin. Finally, potential contact, with friction, is defined for all<br />

yarns so that this may be identified <strong>an</strong>d treated.<br />

take-up<br />

velocity<br />

bobbin path<br />

braiding point<br />

(110 mm, 220 mm, 700 mm)<br />

stationary thread<br />

braiding thread<br />

220 mm<br />

bobbin element<br />

bar elements<br />

node j+1<br />

node j+2, j+3<br />

horn gear<br />

velocity<br />

node j<br />

bar n+1<br />

bar n<br />

bar n-1<br />

membr<strong>an</strong>e elements<br />

node j+1, j<br />

membr<strong>an</strong>e n+1<br />

membr<strong>an</strong>e n<br />

membr<strong>an</strong>e n-1<br />

Fig.3: Key features for the finite element<br />

modelling of 3D-braiding using bar <strong>an</strong>d<br />

membr<strong>an</strong>e elements<br />

Braiding<br />

needles<br />

Fig.4: Simulation of a rect<strong>an</strong>gular braid using<br />

membr<strong>an</strong>e elements<br />

The simulation result using membr<strong>an</strong>e elements is shown in Figure 4 for a rect<strong>an</strong>gular braid. A generally<br />

good interaction of the yarns is obtained <strong>an</strong>d the contact between the yarns is seen to function<br />

well. These results allow the motion of yarns <strong>an</strong>d their final positions to be studied <strong>an</strong>d other valuable<br />

information, such as the total feed-out of yarn from each bobbin, to be predicted. Variations in<br />

bobbin tensile force, braid take-up velocity <strong>an</strong>d alternative braiding schemes may be easily simulated<br />

<strong>an</strong>d assessed.<br />

Mech<strong>an</strong>ical <strong>an</strong>alysis of braided composites<br />

From the braiding simulation a detailed model of yarn architecture is obtained which could provide<br />

a basis for a mech<strong>an</strong>ical <strong>an</strong>alysis of the <strong>textile</strong> reinforced composite. The approach being investigated<br />

is to extract a representative section of the braid from the virtual model which is then overlaid<br />

with a mesh of solid elements to approximate the matrix resin. These two independent finite element<br />

meshes are modified <strong>an</strong>d coupled via constraint equations.<br />

This level of modelling is at the ‘meso-’ scale which c<strong>an</strong> give a good local prediction of stress <strong>an</strong>d<br />

strain distribution within each constituent material. The model will correctly capture the effects of<br />

the <strong>an</strong>isotropic yarn reinforcement <strong>an</strong>d, furthermore, should provide a sound basis for failure pre-<br />

3

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