B. Yasara Dharmadasa Ann and H.J. Smead Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, CO 80309 e-mail: [email protected] Matthew W. McCallum Ann and H.J. Smead Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, CO 80309 e-mail: [email protected] Formation of Plastic Creases Seyon Mierunalan in Thin Polyimide Films Department of Civil Engineering, University of Moratuwa, We present a combined experimental and analytical approach to study the formation of Katubedda 10400, Sri Lanka creases in tightly folded Kapton polyimide films. In the experiments, we have developed a e-mail: [email protected] robust procedure to create creases with repeatable residual fold angle by compressing ini- tially bent coupons. We then use it to explore the influence of different control parameters, Sahangi P. Dassanayake such as the force applied, and the time the film is being pressed. The experimental results Department of Civil Engineering, are compared with a simplified one-dimensional elastica model, as well as a high fidelity University of Moratuwa, finite element model; both models take into account the elasto-plastic behavior of the Katubedda 10400, Sri Lanka film. The models are able to predict the force required to create the crease, as well as e-mail: [email protected] the trend in the residual angle of the fold once the force is removed. We non-dimensionalize our results to rationalize the effect of plasticity, and we find robust scalings that extend our Chinthaka H. M. Y. findings to other geometries and material properties. [DOI: 10.1115/1.4046002] Mallikarachchi Keywords: constitutive modeling, material properties, thin-films, plastic creases Department of Civil Engineering, University of Moratuwa, Katubedda 10400, Sri Lanka e-mail: [email protected] Francisco Lopeź Jimeneź 1 Ann and H.J. Smead Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, CO 80303 e-mail: [email protected] 1 Introduction polymer films such as Kapton and Mylar are commonly used for these space applications. Gossamer space structures often make use of thin films and mem- Two different surface disturbances are observed in membranes branes that are tightly compacted and stowed before launch, and and thin films: wrinkles and creases. Figure 1 shows images of then deployed in space. As an early example, in 1960, NASA suc- the IKAROS solar sail demonstrator during stowage and after cessfully launched ECHO, a reflective satellite balloon that inflated being deployed, where both surface irregularities are clearly to a diameter of 100 feet [1]. Inspired by the success of ECHO, the visible [9]. Wrinkles are temporary distortions that occur due to Inflatable Antenna Experiment (IAE) satellite was launched where compressive buckling in thin films, which remain in the elastic inflated tubes formed a rigidized space antenna structure [2]. Thin regime [10,11]. As such, they are a consequence of the loading con- films are also used for solar sails, a novel propulsion concept in ditions and geometry and disappear once those are corrected and the which the thrust is generated from the impulse of solar photons. membrane is under tension [12]. Creases, on the other hand, are per- A milestone in solar sailing is the IKAROS solar sail demonstrator manent features caused by the highly localized plastic deformation project, where JAXA successfully carried out an orbital deployment that takes place when the film is folded to a very tight radius of cur- of a 196 square meters sail [3]. This technology is ideal for low-cost, vature, which is often the case during the packaging of deployable lightweight CubeSats. It is currently implemented in CubeSail and structures. Figure 2 summarizes the process in which a crease is LightSail [4,5] and has been proposed for future missions such as created, and how it alters the mechanical response of a film. the near-Earth asteroid scout [6]. Other uses of thin films in space Under folding force F, the deformation is highly localized in the include the HabEx starshade [7] and the deployable sun-shield for crease region, which results in permanent deformation of the film. the James Webb Space Telescope [8]. Thermally stable metallic Once the force is removed, the permanent curvature in the crease φ results in an equilibrium fold angle 0. Under tensile loading Ftensile, the fold angle varies, but since φ < 180 deg, there is 1Corresponding author. always a shortening of the in-plane film length compared to the pris- Contributed by the Applied Mechanics Division of ASME for publication in tine condition. The pretension due to this shortening, as well as the the JOURNAL OF APPLIED MECHANICS. Manuscript received November 9, 2019; final manuscript received January 12, 2020; published online January 17, 2020. Assoc. increased bending stiffness due to the out-of-plane deformation, has Editor: Yihui Zhang. a significant effect on the natural frequencies of a membrane Journal of Applied Mechanics Copyright © 2020 by ASME MAY 2020, Vol. 87 / 051009-1 (a) (a) (b) (b) (c) (d) (e) Fig. 2 States of the film geometry during the creasing process: (a) initially flat film, (b) film bent under the folding force F, (c) equilibrium fold angle when the force is released, (d) fold angle expanding (φ1 > φ0) and film bending when subjected to tensile load Ftensile, and (e) shortening of the projected film length due to the crease Fig. 1 (a) Stowed and (b) deployed state of IKAROS solar sail [9] (Reprinted with permission of Elsevier Ltd. © 2011) are often assumed to remain flat. In both cases, it is necessary to carefully characterize the mechanical behavior of the crease; in the case in which it can be assumed to be linear [25], it can be structure. This is the proposed explanation for the difference described by the equivalent rotational stiffness (k) and the equilib- φ between simulations and experimental results for the deployment rium angle under no applied loading ( 0). dynamics of IKAROS [13], which can result in problems with atti- The mechanical properties of creases have been explored exper- tude control and tearing or entangling of the film. Out-of-plane dis- imentally in single creases [21,26] and Z-folds [27,28], as well as tortions caused by the creases can also affect the thrust vector at low using a linkage mechanism able to provide pure bending to arbi- membrane tension [14], and tight packaging can destroy the protec- trarily high curvature [29]. The method to create the crease can sig- tive coatings on the film [15]. Hence, understanding and modeling nificantly affect the results, and even for a given method, it is often the crease behavior is crucial for the successful design of thin film difficult to achieve repeatable folds to use in the experiments structures, from space deployable structures to origami-based [17,26,30,31]. Furthermore, films used in space structures often metamaterials. have a thickness in the micrometer range [32], so measuring Several models have been presented to describe the effect of creases in the mechanical properties of films. Murphey [16] calcu- lated the homogenized stress–strain relationship of a randomly creased sheet when the crease amplitudes and wavelengths are mea- (a)(b) sured, without explicitly resolving the deformed film profile. Hossain et al. [17] characterized the non-linear stress–strain rela- tionship of a crease and modeled it in a finite element framework by defining a softer non-linear material strip. To capture the out-of-plane stiffness, Nishizawa et al. [13] proposed to add beam elements with a second moment of area equivalent to that of the creased region; this model was able to capture the natural frequen- cies of the membrane without explicitly accounting for the deformed geometry. The effect of creases on pressurized cylinders has been modeled numerically, taking into account the mechanics of a single crease [18,19]. However, the most common approach to model creases in the solar sail deployment simulations is to ide- alize them as hinges with torque springs, see Fig. 3. This technique accounts for the stiffness of the hinge, as well as for its effect on the Fig. 3 Torque spring idealization of a crease: (a) unstressed film profile [20,21]. A similar approach is used to model the stiff- state and (b) under tensile loading, showing opening of the ness of fold lines in origami [22–24], although in this case, panels crease as well as bending in the film 051009-2 / Vol. 87, MAY 2020 Transactions of the ASME creasing and unfolding forces becomes challenging. Numerical possible rearrangement of their deformed geometry. As such, the simulations have been used to analyze the creasing process for creases created following both approaches, loading and displace- thicknesses and loading conditions that present difficulties for ment control, are different. This is addressed in detail in Sec. 2.2. experimental exploration. These include one-dimensional simpli- The creasing process is imaged with a USB video microscope fied models as well as solid-based numerical simulations accounting (Mighty Scope 5M). for the elasto-plastic nature of the film [33–36]. However, there is a After the hold period tpress, the top platen is raised at a rate of lack of experimental validation of the predictions for the equilib- 100 mm/min, and the scotch tape is cut, allowing the crease to rium angle. Furthermore, the effect of the viscoelasticity of the unfold. The coupons are then suspended from one end such that film is usually neglected, and so, its influence on the process is the crease line is parallel to gravity. This helps to minimize the not well understood. gravity effects and friction with a possible support. As soon as In this study, we combine experiments and analysis to rationalize the coupons are suspended (which takes approximately 30 s after the different factors that contribute in the formation of a crease, and the end of the test), we capture images of the equilibrium fold how they affect the equilibrium fold angle.