Predicting the extent of resin infiltration in pin-assisted pultrusion
The infusion of a polymeric resin into a fibrous network is the determining step in many processes for the manufacturing of composites (e.g., pultrusion and resin transfer). Poor resin infusion, however, is at the heart of most quality-control problems in manufactured composite components and the source of in-service failure. During pin-assisted pultrusion, a porous roving is pulled through a molding die and over an array of solid pins that are located inside a pool of resin. The objective of this process is to spread the fibers on the pin surfaces and force an adequate amount of resin into the roving, to ensure complete saturation.
Besides the mechanical action of the pin for spreading the fibers, the saturation process is facilitated by the formation of a small wedge-shaped region filled with resin, which forms between the pin surface and the roving (see Figure 1). Lubrication theory mandates a pressure rise occurs within this region, and this pressure forces the resin to infiltrate into the fibrous roving. This has been demonstrated clearly in previous studies that have also highlighted the influence of processing and material parameters.1–3
In our work,4,5 we have conducted a large number of simulations for various combinations of material (i.e., with different substrate permeability, K, and resin viscosity, μ) and process parameters. Such process parameters include the pin radius (R), roving speed (V), gap size (δ), and saturated porous zone thickness (Lo). We have thus developed an extensive database in which the infiltration depth (hf) is expressed as a function of these parameters. The dimensionless group that we propose can collapse all the parametric data into a master curve and thus be used for the formulation of a simple explicit expression of hf. Our reasoning for this dimensionless group can be summarized as follows: the fluid entering the wedge (at flow rate Qin) will either be pushed into the roving (at rate Qp) or will exit the wedge through the gap (δ) at rate Qd. Although Qin is the result of drag flow, which is resisted by the pressure developing in the wedge,4 the ratio Qd/Qp is important. This is because it defines the limits inside which most of the resin infiltrates the web (i.e., a ‘good’ process) or is ‘wasted’ by exiting the wedge through the gap. If we assume an average pressure (2).
It is evident from our results that for Λ< 0.1, the infiltration depth during pin-assisted pultrusion reaches a plateau of maximum efficiency. For Λ> 0.1, however, the efficiency of the resin infiltration decreases exponentially with Λ. Overall, the data in Figure 2 can be described by the power law hf=hf, max[1+mΛn]−1, where hf, max is the maximum infiltration depth (8.21×10−4±0.0005m), and m and n are constants (equal to 0.879 ± 0.011 and 1.2± 0.1, respectively).
The results shown in Figure 2 and the resultant power-law relationship offer a means for analyzing actual pultrusion data and for optimizing operations. By replacing the average pressure (which is difficult to measure) with the tensioning force (T), through
We have reported parametric analyses based on this model,5 and our results are in line with experimental evidence. For example, the extent of infiltration is predicted to increase with N and contact time, and to decrease with increasing V and μ. An example comparison between our model data and experimental data2 is shown in Figure 3. Any direct comparison between model and experimental data sets, however, is hampered by lack of reliable data for K and δ. In addition, the extent of resin infiltration is usually determined indirectly in experiments by measuring a mechanical property of the pultruded tape or strip. We therefore regard any agreement between our model data and experimental results as semi-quantitative at best. Better material characterization is therefore required.
In summary, we have conducted a comprehensive numerical study of pin-assisted pultrusion, based on which we have proposed a simple explicit model that can be used to estimate the resin infiltration depth as a function of measurable parameters. In our work so far, the roving has been treated as non-deformable. In our current work, therefore, we are examining the effect of roving deformability. As a way to guide future theoretical work, we also wish to investigate the relationship between resin infiltration and the dimensionless group (Π) in actual pultrusion lines.
- P. J. Bates and J. M. Charrier, Effect of process parameters on melt impregnation of glass roving, J. Thermoplast. Compos. Mater. 12, pp. 276-296, 1999.
- P. J. Bates and X. P. Zou, Polymer melt impregnation of glass roving, Int'l Polym. Process. 17, pp. 376-386, 2002.
- R. J. Gaymans and E. Wevers, Impregnation of a glass fibre roving with a polypropylene melt in a pin assisted
process, Compos. Part A: Appl. Sci. Manufact. 29, pp. 663-670, 1998.
- N. D. Polychronopoulos and T. D. Papathanasiou, Pin-assisted resin infiltration of porous substrates, Compos. Part A: Appl. Sci. Manufact. 71, pp. 126-135, 2015.
- N. D. Polychronopoulos and T. D. Papathanasiou, A novel model for resin infiltration in pin-assisted pultrusion, Polym. Compos., 2015. First published online: 19 November. doi:10.1002/pc.23860