Recycled Blend Property Budget

How to read this sheet

Tenacity is interpolated on the elongation-limited model rather than the rule of mixtures: fibres of different breaking elongation do not break together, so at the strain where the first fibre fails the survivors are carrying only the stress they hold at that strain. Stress is taken as proportional to strain up to break, which is the standard simplification behind this model and the assumption most worth knowing - a fibre with a markedly non-linear curve will not follow it. The consequence that surprises people is that a blend can be weaker than every fibre in it, which the rule of mixtures cannot produce at any ratio; it is reported as its own flag because a mill that has landed there is usually about to add more of the strong fibre and make it worse. Everything reported is a fibre-level figure and not a yarn figure: twist, drafting, fibre length, migration and spinning system all sit between this number and the yarn that comes off the frame, and they all cost more of it. Treat the blend tenacity as a ceiling that the fibres permit rather than a prediction of yarn strength, and set the specification floor accordingly. Recycled content that reaches the yarn is the fed share less its own process waste, which is higher for a shorter and more variable recycled stream; the feed needed to support a claim is the inverse of that arithmetic and is the number to write into the purchase contract rather than the number on the label. Shares are normalised, so a blend entered as 55 and 45 and a blend entered as 11 and 9 are the same blend. The maximum recycled share the specification permits is found by scanning rather than solved, because the model is piecewise and its governing strain changes partway; internal ratios inside the recycled and virgin groups are held, so it answers how much more of the same recycled fibre can be carried and not what a different fibre would allow.