Springback Angle of a C/PPS Laminate with a Textile Reinforcement
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The residual stresses arising in fiberreinforced laminates during their curing in closed molds lead to changes in the composites after their removal from the molds and cooling. One of these dimensional changes of angle sections is called springback. The article compares the springback angles computed by a model representating the weave geometry (for plain and satin weaves) and by a model with straight fibers with values measured after the manufacturing process. A comparison between the thermoelastic characteristics of composites computed by both the models also presented.
Keywords
springback thermoplastic matrix carbon fiber reinforcement woven compositesIntroduction
The use of hitech thermoplastic matrices (e.g., PEKK, PEEK, or PPS) in carbonfiberreinforced composites constantly grows, especially in the aircraft industry. In addition, thermoplastic materials show significant advantages during their fabrication and allow the application of an optimized metal processing technology (stamping). However, the high temperature at which a thermoplastic composite must be processed suggests an increased significance of thermally induced stresses and distortions in a finished product. This is why the prediction of its dimensional changes (e.g., the springback) is necessary to make the final part more precise.
Tool angles have to be modified to eliminate this problem. The tool design is based on either the rules of thumb, on the past experience, or on the trialanderror approach. For angular parts, the compensation is normally between 1 and 3°. The most common problem encountered is the fact that the springback may vary with layup, material, cure temperature, etc. Therefore, what worked once will not necessarily work next time.
1. Representation of Weave Geometry

the mass of fabric M, g/m^{2},

the number of threads n, 1/cm,

fabric thickness h, mm,

the warp and weft materials and their geometry, and

weave type.

the total thickness of the element is the sum of fabric and matrix thicknesses;

the weave of fabric is tight;

the fibers are prismatic, and their curvature is regular (sinusoidal);

fibers in the cross section of the element are distributed equally;

the matrix and fibers are linearly elastic, the matrix is isotropic, and the fibers are transversely isotropic;

the temperature is the same throughout the volume of the element, and residual stresses are absent;

no other constituents or defects exist in the composite along with the fibers and matrix.
But the compliances are found from the wellknown transformation relations [4, 5]. These properties are used to calculate the effective thermoelastic characteristic by using the classical lamination theory (CLT) and equations for the throughthickness characteristics of composite plates of the given layup (see [4] or [5] for details).
2. Micromechanics of Straight Fibers
3. Springback Phenomenon
4. Comparison of Models
To compare the springback angles computed by both models, we used a C/PPS composite material (manufactured by Letov Letecká Výroba, s.r.o.) reinforced with a 5H satin weave, with a fiber volume content V _{ f } = 49%, mass M = 285 g/m^{2}, fabric, Toray T300J 3K fibers, and thread number n _{ x } = n _{ y } = 70 bundles per 10 cm for the warp and weft threads. The thickness of the fabric was 0.3 mm. The thermoelastic characteristics of the fibers and matrix were as follows: E _{ fL } = 230 GPa, E _{ fT } = 15 GPa, ν _{ f } = 0.3, G _{ f12}, = 50 GPa, G _{ f23} = 27 GPa^{*}, α _{ fL } = −3.8·10–7 °C^{−1}, α _{ fT } = 12.5·10^{−6} °C^{–1*}, Φ _{ f } = 0, E _{ m } = 3800 MPa, ν _{ m }= 0.36, α _{ m } = 5.2·10^{−5} °C^{–1}, and Φ _{ m } = 2.015%; the data with asterisks are estimated according to [3]; ΔT = 160°C and Δc = 0.
5. Conclusions
A springback analysis of curved C/PPS composite parts with textile reinforcement has been performed. An analytical model with straight fibers was used and compared with a model with undulated fibers, which can be found in woven textile composites. The thermoelastic characteristics of various layered composites in relation to the fiber undulation angle were constructed.
It the case of a satinweave fabric 0.3 mm thick, the maximum difference between the thermoelastic characteristics computed by the models with straight and undulated fibers was 4% (for the moduli E _{ x } and G _{ xy }). With a plainweave fabric, the maximum difference would be greater — 12% (again for E _{ x } and G _{ xy }). For the given composite parts, for all the layups considered (for straight fibers and plain and satin weaves), the computed values fit into the range limited by the standard deviation.
The analytical model presented can also be used for hybrid fabrics.
Notes
Acknowledgements. This work was supported by the Ministry of Industry and Trade of the Czech Republic number FRTI1/463 and by the Grant Agency of the Czech Technical University in Prague, grant No. SGS12/176/OHK2/3T/12.
References
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