Dynamic Crease Relaxation Kinetics in Water-Coated Solid Bleached Sulfate Board
Water-coated SBS board requires wider female creasing channels to offset aqueous polymer springback and prevent high-speed folder-gluer carton failures.
Time Constant
Relaxation Rate
The characteristic duration required for an elastic or viscoelastic paper system to dissipate a fixed fraction of applied mechanical stress under constant strain defines the time constant. In paperboard physics, this metric corresponds to the ratio of material viscosity to elasticity, typically derived from Maxwell or Burgers rheological models representing the cellulose network. When a cartonboard flap is folded to a fixed angle, the internal stress peaks instantaneously and subsequently decays as fibres and binder networks relax internally.
The time constant marks the interval required for the decaying stress to fall to approximately thirty-six point eight percent of its initial value, representing the reciprocal of Euler’s number. This parameter provides packaging line designers with a mathematical baseline for the rate of molecular relaxation across scoring lines and folded edges. It excludes instantaneous elastic recovery, capturing exclusively the time-dependent viscous flow of the paperboard structure.
Viscoelastic Dissipation Mechanics
Under constant mechanical displacement, cellulose chains slide along adjacent microfibrils, redistributing localized stress concentrations through microscopic rearrangements. This internal creep response depends directly on sheet moisture content, ambient temperature, and the chemical composition of the papermaking furnish. Elevated moisture plasticizes the amorphous regions of cellulose and hemicellulose, lowering the material viscosity and shortening the time constant significantly.
Bleached chemical softwood fibres provide a rigid framework that resists rapid viscous relaxation, yielding a longer constant than recycled multi-ply paperboards containing fragmented fibres and residual starches. Creased folding boxboard panels exhibit multi-phase relaxation, requiring multiple time constants to describe the rapid dissipation within the compressed creasing groove alongside the slower relaxation occurring within the tensile outer liner.
Line Timing Optimization
Automated packaging equipment utilizes known relaxation rates to establish mandatory dwell times on flap-sealing stations and folding guides. In high-speed cartoning machines, folder belts must maintain hold-down contact on folded flaps for a duration that accounts for the material time constant, allowing internal stresses to decay before releasing the panels. If the machine releases the folding compression too rapidly, residual elastic stress overcomes the curing hot-melt adhesive bond, springing the flap open and jamming the exit conveyor.
Packaging engineers calculate maximum machine line speeds by aligning flap compression dwells with the measured relaxation rate of the specified board grade. Determining these constants through dynamic mechanical analysis ensures packaging lines minimize carton spring-back and maintain square package shapes during transit and palletizing.