Predicting the extent of resin infiltration in pin-assisted pultrusion

8 March 2016
Thanasis D. Papathanasiou and Nickolas D. Polychronopoulos
A simple explicit model is proposed, based on analysis of computational results that show the extent of resin infiltration in a pin-assisted pultrusion process scales with a novel dimensionless group.

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

Schematic illustration of the model geometry. A saturated porous zone (with thickness Lo) moves with speed (V) over a rigid pin of radius, R. The resin infiltration depth (hf) and gap size (δ) are also indicated.

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 (

) in the wedge, Darcy's law dictates that
Furthermore, if we assume simple shear conditions at the zero tangency point, Qd~Vδ. The Qd/Qp ratio therefore defines the dimensionless group,
. By plotting our computational data for hf in terms of Λ we thus reveal a master curve (see Figure 2).

Plot of computational hf data. The master curve expresses the effect of the dimensionless group

on hf. μ: Resin viscosity.
: Average pressure. K: Substrate permeability. hf , max: Maximum resin infiltration depth.

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

(where W is the width of the roving), we can obtain a new dimensionless group, Π=μVWLo2δ/TKR. Since the action of each pin is additive, we can extend this model to a sequential arrangement of an arbitrary number (N) of pins. At the kth pin, the model will be hfk=h0k+hf, max·[1+mΠn]−1, for k=1… N.

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.

Infiltration degree (equal to hf/H, where H is the thickness of the roving) shown as a function of resin contact time (equal to R/V) with the pin. The continuous and dashed lines correspond to predictions for two and seven pins, respectively. The pulling speed range is about 0.034–0.5m/s and R is 2–7mm. In addition, K = 10-9m2, T = 20N, μ=100Pas, and δ=500μm.

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.


Thanasis D. Papathanasiou
University of Thessaly

Thanasis Papathanasiou obtained his PhD from McGill University, Canada, and is a professor of mechanical engineering. His research involves the use of simulations in the area of porous media flow and transport, as applied to composites.

Nickolas D. Polychronopoulos
University of Thessaly

Nickolas Polychronopoulos holds an MSc and PhD in mechanical engineering. His research experience includes the use of computational fluid dynamics for polymer and composites processing, with a particular emphasis on extrusion and pultrusion.


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  2. P. J. Bates and X. P. Zou, Polymer melt impregnation of glass roving, Int'l Polym. Process. 17, pp. 376-386, 2002.

  3. 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.

  4. 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.

  5. 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

DOI:  10.2417/spepro.006343