Small diameter fiber braid with central core member

A cord, comprising:

• a tubular braided sheath comprising:
• strands having an outer surface, an inner surface, and a central hollow portion defined by the inner surface and having a volume;
• and
• a core within the central hollow portion of the tubular braided sheath;
• wherein:
• the strands each have a tensile strength of about 8 cN/dtex or more;
• when the cord is in a relaxed state, the tubular braided sheath has a substantially cylindrical shape having an outer diameter of from about 20 μm to about 5 mm and a volume of the central hollow portion, wherein the core does not completely fill the volume of the central hollow portion of the tubular braided sheath in the relaxed state;
• and
• when the cord is in a longitudinal tensioned state, the tubular braided sheath elongates under longitudinal tension such that a volume of at least a part of the central hollow portion of the tubular braided sheath in the longitudinal tensioned state is less than the volume in the relaxed state;
• in the longitudinal tensioned state, the inner surface of the tubular braided sheath contacts and cinches a surface of the core such that slippage between the core and the tubular braided sheath is reduced;
• and
• the core comprises one or more filaments selected from the group consisting of a liquid crystalline polyester filament, an aramid filament, co-polymer aramid filament, a polyether ether ketone filament, a poly(phenylene benzobisoxazole) filament, a polypropylene filament, a polyethylene terephthalate filament, a polyamide filament, a polyhydroquinone diimidazopyridine filament, and combinations thereof
• wherein the core occupies greater than about 95% of the volume of the central hollow portion of the tubular braided sheath in the relaxed state,
• wherein a braid angle of the tubular braided sheath is from about 5° to about 85° in the relaxed state and the braid angle is decreased in the longitudinal tensioned state, and
• wherein, when in the relaxed state, a relationship between the sheath and core components of the cord conforms to the equation (I):
• c/10≤p/t≤(1.2·c)
• wherein c is a strand count of the tubular braided sheath, p is a pick count per meter in the sheath, and t is a twist level of the core in turns per meter.