Characterization of viscoelastic bending stiffness of uncured carbon-epoxy prepreg slit tape

Highlights

• Viscoelastic behavior of uncured tows determined experimentally in relevant temperature range.

• Measurements show tow obeys time temperature superposition principle (TTSP)

• WLF and Arrhenius models are excellent fits to data.

• TTSP for WLF model provide results over 9 decades of time.

• Data shows tow is elastic during wrinkle formation in AFP manufacturing of thermoset composite components.

Abstract

In support of computational modeling of tow placement at elevated temperature, the creep response of IM7/8552 uncured prepreg slit tape material during 3-point bend loading at different temperatures is measured using an RSA III dynamic mechanical analyzer. Short term creep experiments were conducted for a duration of 1000 s at ten different temperatures ranging from −5°C (below T_g of 0 °C) to 40 °C, with the latter being the nominal processing temperature for the tow. Results show that the tow material obeys the time-temperature superposition principle (TTSP) in the temperature range selected for the creep experiments. Using the TTSP, creep compliance master curve spanning more than eight logarithmic decades is obtained for the nominal processing temperature of 40 °C. The time–temperature shift factor is observed to follow closely the William-Landel-Ferry (WLF) model, with the WLF parameters obtained by least square fitting of the experimentally determined shift factors utilizing closed form shifting algorithm (CFS). The WLF model for the material is used to extend the master curve to a range of temperatures above glass transition temperature (T_g) of the material. The creep compliance data is further employed to obtain the retardation spectra of the material using an algorithm based on the work of a co-author and applied recently to a different material system by the authors. Details for extraction of the retardation spectra from the creep compliance results are provided. Results from these studies demonstrate that the creep compliance reconstructed from the retardation spectra accurately represent the experimental results while providing baseline data to quantify the importance of viscoelastic behavior in wrinkle formation during advanced manufacturing of aerospace components.

Introduction

Recent advances in rapid manufacturing of composite components, such as automated tape layup and automated fiber placement (AFP), have resolved many of the difficulties in manufacturing of high-quality composite material parts at higher production rates. These have led the commercial aircraft industry to begin replacing conventional aluminum aircraft structural components with advanced composite materials. For example, the Boeing 787 has more than 50% by weight manufactured using advanced composites [1], resulting in a 20% reduction in weight compared to conventional aluminum airframes.

Of particular interest in this study is the AFP process. This lay-up process consists of a computer controlled system to heat, apply pressure, place and adhere bands of tows (8 to 32 bands) having widths ranging from 3 mm to 12 mm (0.125 in to 0.5 in) to the underlying composite along predefined paths [2]. The AFP process has the ability to orient fibers within each lamina along optimal paths that can result in favorable stress distributions and improved performance of a laminate for specific applications [3], [4] without addition of material, with further weight reduction possible. Furthermore, analysis of variable angle tow composites [5], [6] has shown that buckling resistance can be significantly improved by optimizing the tow path. Conversely, if path curvature increases beyond a critical value, previous studies have shown that various defects can occur in the tows [7], including wrinkling of the tow on the compression side, splitting of tows due to in-plane shear and in-plane buckling. Out-of-plane wrinkling is the most commonly observed defect when performing AFP along curved path with tight radii [7]. In a recent study, Liang et al. [8] identified the out-of-plane bending stiffness of the prepreg tow as a critical factor influencing the size and number of wrinkles. To more efficiently define the AFP manufacturing process for minimal wrinkling, accurate prediction of wrinkle formation during the placement process is needed. A recently successful tow placement simulation methodology [9] employed the finite element (FE) method with continuum material parameters. The simulations require measurement of an “effective” bending stiffness of the tow material for the range of temperatures relevant to the AFP process. In the remainder of the introduction, a review of previous research regarding FE modeling and experimental characterization of effective tow bending stiffness is discussed.

Modeling of bending of prepreg material has been a focus of many studies related to thermoforming processes. Conventional plate theory assuming zero through-thickness shear deformation is observed to over-predict the bending stiffness of the prepreg, especially at higher temperatures¹ [8], [10]. For a prepreg fabric with a weak matrix material (uncured thermoset tow or thermoplastic prepreg near matrix melting temperature), significant though-thickness shear may be present during bending. In order to account for the significant difference in the in-plane tensile modulus and out of plane bending modulus, a common method adopted by many investigators is to decouple bending and membrane behavior in the FE formulation. For example, Dörr et al. [11] modelled the bending response of thermoplastic prepreg using conventional shell elements with decoupled bending and membrane behavior. The bending moment and membrane forces are calculated independently using the curvature tensor and membrane strains, respectively. Authors have also included viscoelastic effects in the bending response using Maxwell and Kelvin-Voigt models in an effort to improve predictions. In a related paper, Soulat et al. [12] used standard shell finite elements in thermoforming simulation of unidirectional thermoplastics tows. The authors included an additional degree of freedom to model thickness changes during consolidation of the prepreg. The primary focus of their FE model was porosity reduction predictions during reconsolidation. In both models, the effect of intra-ply shear during bending is ignored.

An alternate approach to FE modeling of bending of prepreg is employed in [9] where the geometric thickness of the tow is adjusted so that a single modulus in the fiber direction (E₁) can be used to predict both the bending and membrane tensile stiffness. This approach allows use of continuum shell element finite element formulations in AFP simulations for predicting wrinkles. In our recent finite element modeling of the AFP process and tow wrinkle formation [9], the authors used a reduced tow thickness with shell elements to model tow response, confirming that the model predictions of wrinkle shape and frequency are consistent with experimental observations and measurements.

Previous work characterizing bending stiffness, such as employed in ASTM D1388 cantilever beam tests and Kawbata bending tests [13], were primarily focused on the response of woven textile fabrics. Liang et al. [8] measured the bending stiffness of thermoplastic prepreg material using a cantilever beam bending experiment performed at temperatures relevant for their thermoforming process. The bending moment curvature relation was obtained by measuring deformation of the prepreg sample using images of the side edge at each temperature. The authors have shown that bending stiffness influences the size of wrinkle formation during a thermoforming process. Alshahrani [10] employed a vertical cantilever beam test method to characterize the bending stiffness of out-of-autoclave woven prepreg. To model bending behavior, the authors used Euler-Bernoulli beam theory assumptions. The vertical cantilever test has the advantage of removing the effect of gravity load on the bending response. Short-term stress relaxation experiments (300 s) using the cantilever test method were used to quantify viscoelastic response. The bending experiment relaxation modulus was fitted with a three parameter Prony series to obtain the viscoelastic parameters.² However, the model fit to the moment–curvature relation for small values of curvature was shown to be inaccurate, possibly due to large error in the measurement of the small specimen curvature. In addition, the authors also observed that prediction of specimen response at higher temperature using time–temperature superposition did not agree with independent experimental measurements (see footnote 2).

In another study, bending stiffness measurements for unidirectional thermoset prepregs were obtained in Wang [15] et al. by performing a bucking experiment. The authors identified three distinct responses, such as elastic buckling for small deformation of the prepreg, a transition region and plastic buckling associated with large deformation, fiber slipping and intra-lamina shear deformation. It was assumed that elastic buckling response can be modelled using simple beam bending theory whereas in the transition and plastic buckling regions, the response is much more complex. A comprehensive review on different types of bending tests performed for characterizing bending behavior of uncured slit tape and woven fabrics is given in [10].

Though the cantilever beam test method is commonly used for characterizing the bending behavior of woven fabric and prepreg material, drawbacks of the cantilever bending experiment identified in various studies are (a) difficulty in measuring accurate moment–curvature data near the clamped edge (data corresponding to small curvatures), (b) viscoelastic or rate effects are difficult to quantify due to imprecise load/displacement measurements and (c) requirements for accurate temperature control using a custom-built testing frame.

An alternative, a widely accepted approach for characterizing the bending behavior and viscoelastic properties of polymeric materials over a broad range of temperatures is to employ a Dynamic Mechanical Analyzer (DMA). Interestingly, there are relative few authors who have published DMA-based data for characterizing the viscoelastic bending stiffness of uncured thermoset prepreg. Erland et al. [16] modified simple beam theory to include the effect of intra-ply shear by allowing plane sections of the beam to be non-orthogonal to the neutral plane. The resulting equation for bending deflection has an additional term that is a function of beam length. In their studies, the authors found that the oscillatory intra-ply shear modulus is a strong function of temperature. However, viscoelastic effects were not obtained by the authors. Dodwell et al. [17] employed a simplified one-dimensional analytical model for predicting out-of-plane wrinkling during compaction of multilayer plies over an external radius in a thermoforming process. For predicting wrinkling behavior of uncured AS4/8552 prepreg, the authors performed DMA experiments to determine the bending stiffness of a prepreg. Margossian et al. [18] used DMA experiments to quantify the bending stiffness of a thermoplastic prepreg laminate in the molten state. The bending stiffness was calculated for constant strain rates using Euler-Bernoulli beam assumptions for small deformation of the beam. The time–temperature dependent viscoelastic parameters normally calculated from standard viscoelastic experiments such as creep, relaxation or oscillatory tests were not reported in their work. In a related study, Ropers et al. [19] determined the viscoelastic properties of a thermoplastic prepreg using DMA at different frequencies and temperature ranges. Time temperature superposition was used to obtain the master curve for frequencies ranging from 10⁻⁹ sec⁻¹ to 10¹¹ sec⁻¹. The authors also compared results from a finite element simulation based on a 20-term Prony series model fit to the experimental data (the method used to obtain the Prony series terms was not reported). Their simulation predictions deviated substantially from the experimental measurements with increasing temperature.

Since most published literature for viscoelastic characterization is for fiber-reinforced woven or unidirectional composites with thermoplastic matrix material, research focused on characterizing the viscoelastic behavior of uncured thermoset tow materials continues to be of long-term interest. This is especially relevant in advanced manufacturing applications. For example, AFP processing occurs at speeds up to 2 m/s in aerospace applications, resulting in highly transient thermomechanical conditions in each tow. In such cases, characterization of the linear viscoelastic response of tows is important to quantify the significance of time-dependent effects in wrinkle formation and for robust FE modeling of the AFP process. In the enclosed study, the authors have employed a Dynamic Mechanical Analyzer and performed tow bending experiments over a range of temperatures relevant to AFP processes to determine both the creep compliance and the retardation spectra for an uncured thermoset prepreg material (IM7/8552-1) that is used in manufacturing of composite parts in aero-structures. Since it was shown in our previous study [9] that tow deformation during the early stages of wrinkle formation is small, the work of Liang et al. [8] is relevant. As shown in their previous experimental studies, a linear relationship between the bending moment and curvature of the tow exists for small curvatures.³ Thus, for relatively thin thermoset tows undergoing small deformations, the bending deflection can be approximated using Euler-Bernoulli beam theory to determine the viscoelastic bending stiffness of uncured thermoset tow material. The linear moment–curvature relationship is written M = EI κ, where κ is the curvature and EI is the bending stiffness. Using the linear moment–curvature relationship in our studies, the authors performed short-term creep experiments for eight different temperatures in the range −5°C to 40 °C. Time-temperature superposition is employed to obtain a master curve extending over nine logarithmic decades. Section 2 presents the experimental setup and materials used for bending stiffness characterization. Consistent with observed tow processing conditions, linear viscoelastic theory is used to model the material response and is briefly explained in Section 3. Experimental results are presented in Sections 4. Section 5 provides a Discussion of the results and their relevance in assessing the importance of viscoelasticity in wrinkle formation. Conclusions are given in Section 6. Acknowledgements and References are provided after the Conclusions.