On the origin of start-up effects in ply-ply friction for UD fiber-reinforced thermoplastics in melt

Rens Pierik. Faculty of Engineering Technology, Chair of Production Technology, University of Twente, Enschede, The Netherlands ThermoPlastic composites Research Center (TRPC), Enschede, The Netherlands. Corresponding author: Rens Pierik. E-mail address: e.r.pierik@utwente.nl Wouter Grouve. Faculty of Engineering Technology, Chair of Production Technology, University of Twente, Enschede, The Netherlands Sebastiaan Wijskamp. ThermoPlastic composites Research Center (TRPC), Enschede, The Netherlands Remko Akkerman. Faculty of Engineering Technology, Chair of Production Technology, University of Twente, Enschede, The Netherlands ThermoPlastic composites Research Center (TRPC), Enschede, The Netherlands


Intr Introduction oduction
Hot press forming is an attractive processing technology for thermoplastic composites due to the short processing cycles, which allows for cost-effective manufacturing of complex parts with continuous fiber reinforcements [1]. Preconsolidated blanks are heated above melt temperature and subsequently shaped to their desired form by closing carefully designed tooling. The tooling temperature is controlled to regulate the cooling rate and a pressure is applied to obtain a properly consolidated part [2]. The final part quality depends on the tool design and the processing parameters. Engineers rely on dedicated process simulation software to ease tool and process design to enable firsttime-right manufacturing.
Currently, most press-formed parts are relatively simple and are based on woven fabric reinforced blanks with a uniform thickness. However, the industry is moving towards unidirectional (UD) ply-based components with thickness variations and more complex geometries [3]. This shift comes with new challenges, as forming trials on UD plybased laminates showed the occurrence of defects, like fiber wrinkling, that were not present with woven fabrics [4]. More importantly, some of these defects, especially those on a small scale, cannot be predicted with the current simulation approach. Hence, more advanced process simulations tools are needed to enable defect-free-manufacturing Process simulation for press forming requires a careful mathematical description of the governing deformation mechanisms, most notably intra-ply shear, inter-ply slip and bending [2]. None of these mechanisms is negligible or dominant, as the formability is said to be a result of a 'delicate balance' between them [4]. Improvement of the predictive quality therefore requires, among others, more advanced constitutive modelling of each of the deformation mechanisms. The current study focuses in particular on the inter-ply slip mechanism. Ply-ply slip is essential in curved parts, as the relative movement of subsequent ply layers releases compressive stresses in an inner radius bend and consequently prevents fiber buckling [5,6]. Current simulation approaches often use a steady-state slip coefficient to describe ply-ply friction, neglecting any transient (start-up) effects. However, the initial transient response might be the key to improve the predictive quality.
Especially if one considers that the relative displacement of adjacent plies in the forming process is typically small [2,7]. Hence, the direct objective is to characterize and describe the full nonlinear ply-ply slippage response considerably more accurately for the use in forming simulation software with improved predictive capability for forming defect generation. As a first step, this study focuses on the identification of the underlying governing mechanisms, which will form the basis for future constitutive models.  Figure 1a and generally consists of an overshoot, followed by a decay leading towards a steady-state or long-time value [2]. Although the transient response, including an overshoot, has been recognized a long time ago [e.g. 5,8], a clear view on the origin is still lacking to the best of authors' knowledge. Therefore, two possible explanations for the overshoot will be discussed briefly using the numbered boxes in the schematic ply-ply cross-section shown in Fig. 1b. per percolation (Bo colation (Box 3) will be adr x 3) will be adressed in the discussion. essed in the discussion.
The first explanation is that the shear stress overshoot is caused by nonlinear viscoelasticity (NLVE) [6]. The transient behavior seen in polymer melts is due to the entangled structure formed by the macromolecules [1,9]. At low shear rates within the linear VE region, the shear stress monotonically increases leading towards a steady-state value.
However, at higher deformation rates, the chain diffusion process is not able to accommodate to the deformation fast enough and the junctions act as permanent bonds leading to a rubber-like response. The shear stress increases On the origin of start-up effects in ply-ply friction for UD fiber-reinforced thermopla...

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until the chains slip in these junctions, which partly destroys the temporary network of entangled polymer chains (schematically shown in Box 1 in Fig. 1b) [9]. This 'catastrophic realignment' is accompanied by a decrease in the shear stress [1], giving rise to an overshoot.
Alternatively, Sachs [2] proposed a slip relaxation effect as a second explanation for the overshoot in a study on tool-ply friction of UD C/PEEK. Hatzikiriakos and co-workers [10-12] discussed a slip relaxation effect in their studies on wall slip in polymer melts. Two wall slip mechanisms are generally accepted, namely desorption of macromolecules at the wall, or fiber in the present case as shown in Box 2a, or disentangling of adsorbed chains from the bulk (Box 2b) [10, 13,14]. The relaxation of chains next to the wall differs from those in the bulk, which could result in delayed slip [10].
Hence, a slip relaxation effect might become active, explaining the overshoot observed as a gradual rise in wall slip.
Ply-ply friction experiments have been performed to test the viability of these hypotheses. The materials and methods will be discussed next, followed by a presentation of the results and a discussion.

Mat Materials and t erials and testing set-up esting set-up
The material under investigation consists of carbon fibers with a poly(ether-ether-ketone) (PEEK) matrix in the form of unidirectional tape known as Toray Cetex® TC1200, manufactured by Toray Advanced Composites. According to the manufacturer, the melting and processing temperature equal 343°C and 385°C respectively. The viscosity of the matrix material, Victrex PEEK 150P, was measured using a plate-plate rheometer.
Ply-ply friction tests were performed on a benchmarked friction tester schematically shown in Fig. 2a [2]. A specimen consists of two outer plies and a middle ply with all fibers aligned in the longitudinal direction, as visualized in Fig. 2b.
The specimen was mounted in a universal testing machine. The velocity of the upper clamp can be controlled resulting in a relative movement between the middle ply and the outer plies. The resulting pull force, Fp, was measured using a 1 kN loadcell, which was used to calculate the shear stress: with A the area of the heated pressure plates (50x50 mm 2 ). A normal force can be applied on the plates, which was measured using three loadcells. The pressurized area remained constant by using an additional overlap of 15 mm as shown in Fig. 2a. The ply-ply friction response of UD C/PEEK is shown in Figure 3a for different rates. Several measurements at 25 mm/ min, plotted in gray, indicate a fair repeatability of the measurements. The response at low rate follows a monotonic stress growth, whereas higher rates cause a shear stress overshoot, τp, leading towards a long-time shear stress, τ∞.
Stress relaxation occurs when the test is stopped. Normalized relaxation curves are shown in Fig. 3b, which are corrected for the residual stress after full relaxation, around 2 kPa for each experiment, and plotted on logarithmic scale with time to emphasize the difference in relaxation rate with sliding velocity. The second friction response in the interrupted velocity experiments, in which the sliding velocity was restarted after different rest times, is shown in Fig. 3c. The overshoot is almost fully recovered after more than 30 s, whereas a small overshoot is already visible after 1.2 s.
On the origin of start-up effects in ply-ply friction for UD fiber-reinforced thermopla...

Shear str Shear stress o ess ov vershoot ershoot
A closer look at the stress build up is shown in Fig. 4a. The monotonic shear stress increase at low velocities changes into a curve exhibiting an overshoot, which reduces in width and increases in magnitude with sliding velocity. The ratio of τp and τ∞ is plotted in Fig. 4b and indicates that the overshoot starts to occur at velocities higher than 0.1 mm/s (or 6 mm/min). The ratio rapidly increases up to almost a factor of three.

Long-time shear str Long-time shear stress ess
The long-time shear stress, τ∞, is evaluated as the mean in the steady region, as indicated in Figure 1a. A relation between τ∞ and the matrix material's viscosity is expected if a thin resin-rich layer is present at the slip interface.
The viscosity of PEEK 150P, as measured by plate-plate rheometry, is plotted in Fig. 5a for 380  with η0 the zero shear rate viscosity, τ * the critical shear stress at the onset of shear thinning and n the Power Law Index, was used to fit the viscosity with shear rate, γ, on 385 °C by means of interpolation. Equation 2 can be rewritten as, with V the sliding velocity and h the film thickness to compare the viscosity and friction data in terms of shear stress. A straightforward relation between τc and τ∞ could not be drawn using a constant film thickness, as visualized in Fig. 5b.
However, a correction can be applied to τ∞ by subtracting the residual stress after full relaxation, τy, possibly attributed to fiber-fiber contact. The result is shown in Fig. 5c together with τc using a film thickness of 2.5 µm. , which is compar hich is compared with τ ed with τ∞ ∞ fr from the friction om the friction t tests b ests by using se y using sev ver eral film thicknesses (b) and corr al film thicknesses (b) and correct ected τ ed τ∞ ∞ f for the r or the residual str esidual stress aft ess after full r er full relax elaxation, τ ation, τc c, sho , shown with wn with the Cr the Cross model fit using a film thickness of 2.5 µm (c). oss model fit using a film thickness of 2.5 µm (c).

Discussion Discussion
The experimental observations will be used to evaluate the hypotheses, namely nonlinear viscoelasticity (NLVE) and a slip relaxation effect giving rise to wall slip, to shed light on the mechanism responsible for the shear stress overshoot.
Nonlinear viscoelasticity complies with several experimental observations. The monotonic stress increase at low rates, while an overshoot appears at higher rates that shifts towards shorter times with a more narrow and larger peak ( Fig. 4a), shows a striking similarity with NLVE [9]. The relaxation curves, shown in Fig. 3b, are straight lines at low rate resembling linear VE, whereas the relaxation rate increases at higher velocities. The higher relaxation rate could be due to the new structure formed by the oriented chains with less entanglements [1,9]. All curves tend to become parallel with time, as the original structure recovers during relaxation. Lastly, the interrupted velocity experiments, as illustrated in Fig. 3c, showed that the recovery time for the overshoot is a bit longer than the time required for relaxation, which can be expected since many segmental motions of the macromolecule are required to recover the On the origin of start-up effects in ply-ply friction for UD fiber-reinforced thermopla...
The above suggests NLVE as the mechanism causing the transient friction response. However, the shear strain unit at the overshoot peak conflicts with the notion of Schweizer [17], who stated that this value should be around 2 at the first emergence of an overshoot based on experiments at different laboratories on several polymer systems. When looking at the C/PEEK data, the shear strain at the overshoot exceeds 250 when using a film thickness of 3 µm. Further, a straightforward relation between τ∞ and the matrix material's viscosity could not be established (Fig. 5b), which would be expected in case of NLVE.
A gradual increase of wall slip, or a slip relaxation effect, was also mentioned in section 2, for which the long-time shear stress with velocity as plotted in Fig. 5c is useful. The correction on τ∞ by the residual stress after full relaxation, τy, can be interpreted as a yield stress according to the findings of Murtagh [8] on stress-controlled experiments with UD C/PEEK, possibly due to fiber-fiber contact [1]. As an alternative or addition to the discussed hypotheses, τ∞ could be influenced by an increasing film thickness with rate, as suggested in Fig. 5b. The film thickness increase could be due to resin percolation towards the slip interface, possibly encouraged by reordering of the fibers due to the pull force, which could cause the observed transient response (see Box 3 of Fig. 1b). However, the concept of wall slip better explains the small width of the overshoot with time at high rates, showing signs of failure (Fig. 4a). A wider overshoot would be expected at higher rates in case of an increasing thickness, as more resin needs to percolate.

Conclusions Conclusions
Ply-ply friction tests were performed on unidirectional C/PEEK tape to investigate the nature of the transient response, which exhibits a shear stress overshoot. Hypotheses for this overshoot were outlined, namely nonlinear viscoelasticity (NLVE) and a slip relaxation effect giving rise to wall slip. NLVE seems to comply with most of the experimental observations, but the long-time values do not correspond well with the matrix viscosity. This deviation can be solved for the full velocity range by means of a changing film thickness or at low velocities by introducing a yield stress. However, the overshoot shows signs of failure at higher rates rather than a smooth transition from peak towards steady-state, which would be expected in case of film thickness increase by resin percolation. Furthermore, the flow curve corrected for the yield stress matches with the concept of wall slip. Although wall slip seems to be related to the viscoelasticity of the matrix material, more effort is required to further investigate the relation between the slip relaxation effect and the apparent NLVE characteristics of the friction response. The improved understanding will form the basis for more advanced constitutive ply-ply friction models, leading to improved simulation accuracy, in turn facilitating defect-freemanufacturing using hot press forming. well as the support funding from the Province of Overijssel for improving the regional knowledge position within the Technology Base Twente initiative. Further, the authors would like to thank Marten van der Werff for carrying out the rheometer measurements.