General mean-field theory to predict stress-compression behaviour of lightweight fibrous materials

We have postulated a new theory to describe the stress-strain behaviour of low-density random fibre networks under compression [1]. Predictions of the theory were verified with experiments on more than a hundred different bio-based fibre materials with varied density and raw materials. In parallel to mechanical testing, high-speed imaging and acoustic emission measurements revealed key mechanisms and domains in which the theory was applicable.
Material compression causes axial stress in fibres in addition to their bending. By assuming that fibre segments longer than a0s(e) (a0 is the mean segment length) undergo a buckling failure at strain e, the compressive stress σ becomes [1]
σ(e)=σ1/[s(e)]2, with s satisfying [s(e)+1]exp[−s(e)]=e.
The theory was applied to fibre materials produced with laboratory foam forming process, which uses aqueous foam as transfer medium to deposit fibres into a connected structure. The achieved low density (20−100 kg/m3) of the dried material allowed for individual fibres to bend without contacting the neighbouring fibres. The used raw materials in our experiments were chemical, mechanical and regenerated cellulose fibres of varied dimensions.
The above simple mean-field theory described the experimental stress-strain behaviour surprisingly well at moderate, from 10% to 50%, compression levels. Moreover, high-speed imaging during compression showed abrupt local dislocations, interpreted as buckling failures of heterogeneous fibres under axial stress. In cyclic measurements, we observed significant acoustic emission only when the compressive strain exceeded the previous strains. This suggested a failure source other than fibre bending. Beyond c.a. 50% compression, the number of acoustic events grew rapidly suggesting a crossover to collective phenomena. At the same time, the compression-stress behaviour began to deviate from the mean-field prediction.
REFERENCES
[1] J. A. Ketoja, S. Paunonen, P. Jetsu, E. Pääkkönen, Compression strength mechanisms of low-density fibrous materials. Materials, Vol. 12, 384, 2019.