Micro-mechanically based modeling of mechano-sorptive creep in paper

Abstract: The creep of paper is accelerated by moisture content changes. This acceleration is known as mechano-sorptive creep, which is also found in wood and some other materials. Mechano-sorptive creep has been known for several decades but it is still not well understood, and there is no generally accepted model explaining the effect.In this thesis, it is assumed that mechano-sorptive creep is the result of transient redistributions of stresses during moisture content changes in combination with non-linear creep behaviour of the material. The stress redistributions are caused by the anisotropic hygroexpansion of the fibres, which will give a mismatch of hygroexpansive strains at the bonds and hence large stresses each time the moisture content changes. This redistribution will lead to an uneven stress state. If the creep of the material depends non-linearly on stresses this will give an increase in creep rate where the stresses are high, that is larger than the decrease of creep rate where stresses are low, so in average there will be an increase in creep rate. The stress distribution evens out as the stresses relax during creep, and the moisture content has to change again to create a new uneven stress state and maintain the accelerated creep.Two different network models based on this mechanism are developed in this thesis. Numerical simulations show that the models produce results similar to the mechano-sorptive creep found in paper. In the first model it is assumed that creep takes place in the fibre-fibre interfaces at the bonds, in the second the creep of the fibres themselves is accelerated. The second model is further developed. Experiments verify model predictions of the dependence of the amplitude of moisture changes.The second model shows a linear relationship between mechanical load and deformation, although creep of the fibres depends non-linearly on stresses. This linear behaviour is also found in applications. Further analysis shows that the mechanical load can be treated as a small perturbation of the internal stress state caused by moisture content changes. This can be used to develop a linearized model, from which a continuum model can be derived. This leads to a reduction of the necessary number of variables, and a significant increase in speed of calculations. Hence, this linearized continuum model can be used as a constitutive law of paper in problems with complicated geometries, for example a corrugated board box in varying humidity.