Abstract
A mathematical model has been developed to describe the structural geometry of three-dimensional textile preforms made by the two-step braiding process. These structures consist of parallel yarns, interconnected with braiding yarns, that lie in complex spatial orientations. The model predicts structural features such as fibre orientation, fibre volume fraction, and interyarn voids from the key process variables of braiding pattern, advance rate, and yarn geometry. The limiting geometry was computed by establishing the point at which yarns jam against each other. Using this factor makes it possible to identify the complete range of allowable geometric arrangements for this type of preform. Experiments of several bare and impregnated samples confirmed the theoretical predictions and demonstrated that very high fibre loadings (above 75% fibre volume fraction) could be achieved. The modelling technique used a “unit cell” approach, which can be applied to many other types of preform for advanced composites.
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Abbreviations
- k :
-
fibre packing fraction (fibre-to-yarn area ratio)
- N r :
-
number of rings in idealized yarn with open packing
- N f :
-
number of filaments in yarn
- f a :
-
aspect ratio of axial yarns (as defined in Equation 3)
- f b :
-
aspect ratio of braiders (thickness to width)
- f :
-
aspect ratio of braid completed (thickness to width)
- γ:
-
angle of braider yarns to braid surface (in end projection)
- S :
-
yarn dimension (m)
- t :
-
braid thickness (m)
- w :
-
braid width (m)
- m :
-
number of axial columns
- n :
-
number of axial layers
- α:
-
angle of braider yarn to axial yarn (braider yarn orientation)
- h :
-
pitch length for two braiding steps (m)
- λ :
-
yarn linear density (kg m−1)
- ρ:
-
fibre density (kg m−3)
- L b :
-
length of braider in a unit cell (m), P1 to P2 in Fig. 6
- L p :
-
projected length ofL b (m)
- V :
-
volume of yarn or void component in a unit cell (m3)
- v f :
-
fibre volume fraction — all fibres to total volume
- v b :
-
braider volume fraction — braider fibres to total fibres
- v v :
-
void volume fraction — interyarn voids to total volume
- o:
-
refers to theoretical open packing
- c:
-
refers to theoretical close packing
- a:
-
refers to axial yarns
- b:
-
refers to braiders
- m, n:
-
refer to axial yarns on braid face (see Fig. 5)
- t:
-
refers to total unit cell
- j:
-
refers to jamming point
References
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Du, GW., Chou‡, TW. & Popper, P. Analysis of three-dimensional textile preforms for multidirectional reinforcement of composites. J Mater Sci 26, 3438–3448 (1991). https://doi.org/10.1007/BF00557129
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DOI: https://doi.org/10.1007/BF00557129