 Inter-fibre sliding

Inter-fibre sliding is relative tangential motion between contacting material fibres. It is distinct from stretching both strands together: equal axial extension can occur with no relative motion at a contact, while bending can require strands to exchange longitudinal position. For local strand displacements ${\mathbf{u}}_1$ and ${\mathbf{u}}_2$ and a contact tangent $\mathbf{t}$, the contact slip displacement isThe contact and the sign of $\mathbf{t}$ must be specified. Contact friction can oppose changing ${\delta }_s$ even in an unbonded material-fibre bundle.

An original bending geometry makes the required relative travel visible. Consider two nearby reference paths of radii $R$ and $R+h$, turning through the same angle $\theta$, measured in radians. Their arc lengths differ byFor chosen separation $h=0.50\mathrm{mm}$ and turn angle $30^{\circ }=\pi /6$, this mismatch is $0.262\mathrm{mm}$. If the strands remain inextensible while following those paths, material must feed through the ends to accommodate the difference. Fixing both ends of equal-length strands to remain aligned instead imposes additional strain or a change in the assumed geometry.

This explains the importance of a separate neutral axis for each strand in the freely sliding model for bending rigidity of an unbonded fibre bundle. Bonding imposes longitudinal compatibility and can require axial tension in some strands and compression in others. The usual beam model relates the resulting axial strain to position relative to a common neutral axis.^[ref]

A useful mechanical test marks neighbouring strands, bends the assembly while allowing end travel, and measures their relative mark positions. Repeating the bend with constrained ends tests a different loading condition. Record contact loading and bend history: an absence of observed slip at small applied force does not by itself establish a permanent bond.