Chapter 14 FE Modeling of Paperboard Material Using Sandwich Structure Method W. Yang, M.W. Allin, and C.J. Dehenau Abstract Paperboard materials have been widely used in industrial applications, especially in packaging. It is very important and necessary to model the material behaviors of paperboard in order to accelerate product development processes and optimize the product designs. In this paper, the sandwich structure method is applied to describe the mechanical behavior of the paperboard, which is modeled by two shell surfaces and one solid core. The two shell surfaces represent the in-plane (machine direction [MD] and cross direction [CD]) properties while the core represents the out-of-plane (thickness direction [TD]) properties. The anisotropic elastic plastic material and isotropic elastic material models within ABAQUS are employed for the two shell surfaces and core, respectively. The two material models are validated based on the tests. Then the two material models are implemented into a paperboard beverage package to predict the packaging performance under different loading conditions. The quasi-static handle test is also performed to validate the Finite Element Simulation. A good agreement between the FE result and tests is achieved. This method will play important role in packaging products development. Keywords Paperboard • Packaging • Sandwich structure • ABAQUS 14.1 Introduction Paperboard is one of the most commonly used materials in every industry. Paperboard is a paper material which generally consists of several pulp fiber sheets bonded by adhesive materials, and is usually a multilayered structure. Schematic of typical paperboard’s micro and macro-structure are shown in Fig. 14.1 [1], in which three orthogonal directions are depicted for paperboard. MD refers to the machine direction and CD refers to the cross or transverse direction. The machine and cross directions generate the plane of the structure, and ZD refers to the out of plane or thickness direction. The fibers are mainly oriented in the plane and along machine direction. So the paperboard in-plane properties are dominated by the fibers. Paperboard materials generally exhibit complex anisotropic and nonlinear mechanical behavior due to fiber orientation distributions, which is also highly affected by the moisture and temperature, and paperboard also exhibits viscosity and has different properties between compression and tension. So in order to have the practical use of the material model, the material model should be as simple as admitted and the material parameters can be obtained easily by the material testing. There are many material models proposed and developed for paperboard by previous researchers. Some of these material models are developed by the theory of micromechanics and used to predict paperboard mechanical properties based on the properties of fibers and fiber-fiber interfaces. Perkins and Sinha created a based network constitutive model for the inplane properties of paper [2, 3], in which a representative meso-scale element was built for fibrous paper microstructure. The mechanical behavior of the representative element depends on the properties of fiber and fiber interfaces, and the fiber interfaces play a key role in the overall in-plane inelastic behavior of paper. The material models of paperboard were developed based on classic laminate theory by Page and Schulgasser [4, 5], which can be only used to predict elastic behavior. Gunderson used Tsai–Wu quadratic yield condition to model the failure loci they obtained experimentally [6, 7]. Xia developed an anisotropic elastic-plastic constitutive mode for paper and paperboard [1], in which a multi-surface yield function, anisotropic hardening, different mechanical behaviors between tension and compression, and an out of plane nonlinear elastic description were incorporated. But this complex model requires a lot of experimental work to validate it. W. Yang ( ) • M.W. Allin • C.J. Dehenau Senior R&D Engineer, Food & Beverage, MeadWestVaco. 501 S 5th Street Richmond, VA 23219, USA e-mail: wenong.yang@mwv.com © The Society for Experimental Mechanics, Inc. 2015 A. Wicks (ed.), Shock & Vibration, Aircraft/Aerospace, and Energy Harvesting, Volume 9, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-15233-2_14 137
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