Calculating Chemical Cross-Link Density Effects on Trapped Shear Modulus
Trapped shear modulus rises linearly with chemical cross-link density while interstitial woven constraint scales effective shear stiffness by factor 1.4 to 2.2.
Affine Network Model
Structural Assumption
Mathematical representations of fiber assemblies describe how individual filaments behave when a bundle is subjected to tensile load. The affine network model assumes that the junction points between crossing flax fibers move in direct proportion to the overall macroscopic strain applied to the wet-spun bundle. Under this framework, the microscopic displacement of each contact node mirrors the external boundary displacement.
Deformation Process
Tensile deformation in yarn or dense parallel roving depends on the friction and layout of individual strands. When a drafting force is applied to the wet-spun flax roving, the affine network model simulates the redistribution of stress among the constituent technical fibers. This calculation helps mills predict the point at which the roving will slip rather than stretch.
It provides a baseline for setting the draft limit on wet-spinning frames, which prevent premature breaking of the strand. Spun yarn quality improves when draft limits are calculated using this method.
Mechanical Prediction
Localized fiber slip occurs when the friction between parallel strands is insufficient to transmit the tension dictated by uniform strain. In wet spinning of high-grade yarn, this model exposes the boundary where homogeneous deformation breaks down and localized draft failure begins. The predictive value diminishes when the liquor concentration varies or when the flax bundles are poorly scutched.