Nonlinear effects of material wrinkles on the stiffness of thin polymer films

There is currently considerable interest in precision space structures employing thin polymer films operating at low stress levels. Achieving high surface accuracies in such structures requires a fundamental understanding of the material load-deformation behavior. Most polymers are linear and obey Hooke’s law. However, folding or crushing a thin film structure, as required for packaging, causes material yielding in the local vicinity of creases and the formation of permanent wrinkles. The nonlinear effects of these wrinkles on the in-plane stiffness characteristics of thin films are investigated in this paper. Results from biaxial tensile tests performed on wrinkled 1.0 mil Kapton@ HN are presented. From this data, effective isotropic Hooke’s law material properties (Young’s modulus, Poisson’s ratio and shear modulus) are calculated. Extensional and shear moduli were found to be initially reduced and an initially negative Poisson’s ratio was observed. At higher stresses, wrinkles pulled out and the material behavior approached that of the base material before wrinkling. Introduction There is currently considerable interest in precision space structures employing thin polymer films operating at low stress levels. Achieving high surface accuracies in such structures requires a fundamental understanding of the material constitutive behavior. Most polymers are linear and obey Hooke’s law. However, folding or crushing a thin film structure, as required for packaging, will cause material yielding in the local vicinity of creases and the formation of permanent material wrinkles. These wrinkles cause extreme nonlinearities in the constitutive behavior of thin films at the low level of stress required for many space applications. The nonlinear effects of wrinkles on the in-plane stiffness characteristics of thin films are investigated in this paper. * Ph. D. Candidate “. ’ Professor, Center for Aerospace Structures, Fellow AIAA Copyright 01999 by Murphey. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. 1227 General deformation mechanisms are identified through analysis of the surface geometry of wrinkled thin films. General stiffness effects are illustrated through an analysis of the extensional behavior of a sinusoidal beam. Due to their similar profiles, the behavior of a sinusoidal beam lends considerable insight into the stiffness effects of wrinkles on thin films. While wrinkled thin films no longer follow Hooke’s law, the model serves as a useful reference relative to which their behavior can be described. A methodology for determining effective isotropic Hooke’s law material properties (Young’s moduli, Poisson’s ratios and shear moduli) in wrinkled thin films is described. The constitutive behavior of a wrinkled thin film is first characterized through general biaxial tensile tests conducted on 1 .O mil Kapton” I-IN. From this data, numerical experiments are performed to calculate the effective material properties as functions of uniaxial and equibiaxial stress. Terminolow and Assumptions Material wrinkles are permanent out-of-plane deformations resulting from imperfections in manufacturing processes or from yielding of the material when it is folded in a tight radius. Material wrinkles remain after loads are removed. In contrast, structural wrinkles are caused by buckling of thin films under compressive stresses. Structural wrinkles disappear when loads are removed. Figures 1 and 2 show examples of material wrinkles and structural wrinkles, respectively. Figure 1 also illustrates two classes of material wrinkles: random and sysfematic. Random wrinkles result from uniformly crushing a thin film to varying degrees. They are assumed to be homogeneous and directionally independent at scales much larger than a single wrinkle. While these assumptions may not be true for actual structures, they provide a workable first look at the constitutive effects of wrinkles on thin films. Systematic material wrinkles are those generated by folding or otherwise creasing a thin film in a specific, repeating pattern. Although systematic wrinkle patterns may exist that result in constitutive behaviors similar to random wrinkles, they are generally different. The directional dependence of systematic wrinkles causes their behavior to be orthotropic while random patterns are isotropic. Wrinkled thin Iilm deformations can be either plastic or elastic, depending on the loads to be applied and on the stress history since -wrinkling. Consider a thin film sample that is crushed into a small ball to induce random wrinkles as sho.wn in figure 3a. This state may correspond to a thin film structure that is packaged for transportation. As shown in figure 3b, the film does not expand to any resemblance of a flat surface when compressive loads are removed. Rather, it retains a shape closer to that of the compressed ball. This behavior is a result of yielding and the associated plastic deformations that have occurred in the crushing process. In this ball-like state, the material will behave elastically as long as only very small loads are applied. However, application of larger loads (figure 3c) will cause further plastic deformations in the vicinity of creases and permanently decrease wrinkle amplitudes. After being pulled out with a higher stress, the material will no longer return to the ball like shape when loads are removed. A plastic response is observed. With adequate loads, enough wrinkles are removed and a sample can be considered flat in a global sense (figure 3d). In this ‘flat’ state, loads up to the maximum applied stress will result in only elastic deformations. The material will follow the elastic response curve. Two constitutive behavior problems become apparent with the deployment and operation of thin ftlm structures such as the Next Generation Space Telescope (NGST) Sunshield. There is Iirst the plasticity problem of characterizing the load-deformation behavior of a structure as it is stretched out from a packaged shape (figure 4a) to its operational shape (figure 4b). This initial expansion involves mainly plastic deformations. There also exists the problem of characterizing the constitutive behavior of a wrinkled thin film after it has been stretched out to its linal, flat operating state. In this state, small loads, such as those from vibrations, result in only elastic deformations. This paper focuses on the behavior of relatively flat randomly wrinkled thin films loaded such that they behave elastically. The base, unwrinkled thin film material is assumed to be linear and isotropic. AIAA 99-1341 Deformation Mechanisms A developable surface is one that can be formed from a flat plane through purely inextensional deformations. The surface formed by a wrinkled thin film is such a surface. It is initially formed from and can be returned to a flat plane through only bending of the material. Figure 5 shows a highly wrinkled thin film under low (a) and high (b) equibiaxial stress. While several large wrinkles are visible in the low stress sample, in the high stress sample, the majority of wrinkles have been removed and the material is relatively flat. With application of the higher stress, the sample stretched by 0.01 in/in. Only 6% of this can be accounted for by mid-plane stretching due to the base material stiffness. Bending is the dominant deformation mechanism of wrinkled thin films at low stresses. At higher stresses, wrinkles are pulled out and deformations are governed by the propertics of the base material. A unique result of the geometry of a wrinkle and the inextensional deformations associated with it is an initially negative Poisson’s ratio. In conlrast to typical engineering materials, w/rinkled thin ftlms expand in both, the axial and transverse directions when subjected to only an axial stress. Two similar mechanisms, bubble expansion and off-axis wrinkle expansion, cause this behavior. The high degree of randomness in magnitude and spacing of wrinkles allows a thin film to reprcscnt a doubly curved or bubbled surface at scales larger than that of a single wrinkle. Such a surface has the property that expanding it in one direction causes it to also expand in all other directions. A linear finite element analysis was performed to demonstrate this coupling mechanism and is shown in ligure 6a. A doubly curved plate, representing a wrinkled thin film was modeled. A stress applied in only the axial direction caused signiIicant positive strains to occur in the transvcrsc direction as well. A second mechanism causing a negative Poisson’s ratio is expansion of off-axis wrinkles, illustrated in ligure 6b. A uniaxial stress will not only pull out wrinkles that run perpendicular to the stress direction, it will also pull out other wrinkles, as long as they arc not exactly parallel to the load. When an off-axis wrinkle is stretched, it will expand primarily perpendicular to the wrinkle direction and thus have positive strain components in the load direction as well as the transverse direction. Behavior of a Sinusoidal Beam While in the previous section the general deformation mechanisms of a wrinkled thin film wcrc