Accelerated relaxation behavior during water desorption in the mechano-sorptive creep of wood: modeling and analysis based on the free volume concept and Kohlausch–Williams–Watts function

Abstract

Abstract The accelerated creep behavior during water desorption of wood was modeled on the Kohlausch–Williams–Watts (KWW) function and free volume concept. Assuming that the water desorption rate dmc/dln t $\text{dmc/dln\,t}$ is involved in the creation of a new free volume, the net creep compliance during desorption J du(t) was obtained as  ln J du ( t ) = β c ln t − β c ( ln τ c 0 + k f   dmc / d ln t ) + ln J c ∞ $\mathrm{ln} {J}_{\text{du}}\left(t\right)={\beta }_{\text{c}} \mathrm{ln} t-{\beta }_{\text{c}}\left(\mathrm{ln} {\tau }_{\text{c}0}+{k}_{\text{f}}\,\text{dmc}/\text{d}\mathrm{ln} t\right)+\mathrm{ln} {J}_{\text{c}\infty }$ where β c, τ c0 and J c∞ are the stretching parameter, characteristic time of the relaxation, and long-time asymptote compliance at a constant moisture content (mc) equal to the initial mc of the accelerated creep, respectively, and k f is the coefficient of the water desorption rate. These parameters were determined by simulation using experimental data and literature results and were found to be reasonable. The simulation results agreed well with the experimental ones. This verifies the validity of the model and its derived equations.