Abstract
An in-plane elasto-plastic material model and a hygroexpansivity-shrinkage model for paper and board are introduced in this paper. The input parameters for both models are fiber orientation anisotropy and dry solids content. These two models, based on experimental results, could be used in an analytical approach to estimate, for example, plastic strain and shrinkage in simple one-dimensional cases, but for studies of the combined and more complicated effects of hygro-elasto-plastic behavior, a numerical finite element model was constructed. The finite element approach also offered possibilities for studying different structural variations of an orthotropic sheet as well as buckling behavior and internal stress situations under local strain differences. A few examples are presented of the effect of the anisotropy and moisture streaks under stretching and drying conditions on strain differences and buckling. The internal stresses were studied through a case in which the drying of different layers occurred at different stages. Both the anisotropy and moisture streaks were capable of rendering the buckling of the sample visible. The permanency of these defects highly depends on several process stages and tension conditions of the sheet, as demonstrated in this paper. The application possibilities of the hygro-elasto-plastic model are diverse, including investigation into several phenomena and defects appearing in drying, converting and printing process conditions.
Highlights
Paper and board have elasto-visco-plastic properties, exhibiting such rheological behaviors as delayed strain recovery, stress relaxation and creep (Skowronski and Robertson, 1986; Rance, 1956; Steenberg, 1947; Gates and Kenworthy, 1963; Lyne and Gallay, 1954)
The use of the anisotropy index instead of that of traditional fiber orientation anisotropy simplified the handling of different in-plane directions in the case of the anisotropic sheet and, for instance, the determination of Hill’s yield surface for the finite element approach is straightforward
The elasto-plastic model and hygroexpansivity-shrinkage model based on experimental results can be solved analytically and separately in one dimension, but the full potential of these models is achieved through the numerical solution of a continuum mechanical model
Summary
Paper and board have elasto-visco-plastic properties, exhibiting such rheological behaviors as delayed strain recovery, stress relaxation and creep (Skowronski and Robertson, 1986; Rance, 1956; Steenberg, 1947; Gates and Kenworthy, 1963; Lyne and Gallay, 1954). An in-plane elasto-plastic material model and a hygroexpansivity-shrinkage model that are functions of the dry solids content and fiber orientation anisotropy index are introduced. In this paper, the dry solids content dependent hygroexpansivity, over the entire range from wet to dry, has been introduced These two models, the elasto-plastic material model and the hygroexpansivity-shrinkage model, were exploited when numerical solutions were obtained with the finite element method. Analytical one-dimensional solutions were used to estimate plastic and hygroscopic strains in simple cases and the results were compared with numerical simulations
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