Abstract
Paper is a material exhibiting a complex microstructure that is composed of a network of fibres at the micro-level. When subjected to external loading or variations in moisture conditions over different time scales, changes in strain that are non-linear with respect to time are observed at the sheet level (macro-scale). In order to investigate this time-dependent behaviour of paper, a creep power law model is implemented within a finite element approach at the level of single fibres. This rate-dependent model is found to capture experimental results available in literature for single fibres with a good agreement (both quantitatively and qualitatively). Based on the identified model at the level of single fibres, the time-dependent hygro-mechanical response is upscaled towards the network scale. To this end, random model networks of ribbon shaped fibres are generated and their response is simulated. The network-scale response, emerging from the rate-dependent fibre model, demonstrates the ability to predict the response of networks subjected to relaxation at a constant moisture level. The developed numerical model predicts lower values of overall stress response in single fibres as compared to networks. Also, stress relaxation predicted by the rate-dependent model in the cross-direction of the networks is in agreement with the experimental observations by Johanson and Kubát (1967). Therefore, one of the remarkable findings of the present work is that the developed rate-dependent model is robust enough to capture the sheet scale response also qualitatively. Based on the study of these computational results, a better understanding is achieved regarding the influence of mechanical and rate-dependent properties of single fibres on the hygro-expansion of complete fibre networks, and in particular of paper sheets.
Highlights
Paper is a complex material consisting of elongated, ribbon-shaped fibres exhibiting an anisotropic behavior
Our main interest in this contribution is in modelling the time-dependent and creep effects in the irre85 versible hygro-mechanics of paper sheets, and in identifying the fibre and network properties that affect the creep response at the sheet-scale
The time dependent hygro-mechanical responses of a single fibre and of a fibre network were studied under an external loading and under changes in moisture content
Summary
Paper is a complex material consisting of elongated, ribbon-shaped fibres exhibiting an anisotropic behavior. The time-dependent response of sheets of paper was investigated under constant and cyclic humidity conditions (Byrd, 1972; Coffin and Boese, 1997; Panek et al, 2004; Salmen and Olsson, 2014) It was observed by Coffin and Boese (1997) that the creep strain rate in single fibres is significantly higher than in paper 35 sheets; this is further investigated in the present study. Our main interest in this contribution is in modelling the time-dependent and creep effects in the irre versible hygro-mechanics of paper sheets, and in identifying the fibre and network properties that affect the creep response at the sheet-scale. The fibre-scale numerical model is used to obtain the rate-dependent response of fibre networks subjected to constant and cyclic moisture conditions under the presence of tensile loads.
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