PhD thesis,
INTERWIRE CONTACT FORCES AND THE STATIC, HYSTERETIC AND FATIGUE PROPERTIES OF MULTI-LAYER STRUCTURAL STRANDS
(1983)
Abstract
Analytical work backed by experimental studies on a
long, 39mm., 91 wire strand with a nominal breaking load of
1.23MN is reported.
The theory involves a novel treatment of the layers of
wires in a strand as a series of orthotropic sheets. The
kinematics of a layer of helically laid wires have been used
to predict the circumferential forces between wires in a
given layer as a function of the radial movement of the layer.
A non-linear compatability analysis is then used to determine
the radial and circumferential distribution of the "clench"
forces (induced in the helical wires by an axial load) between
the layers of wires in the strand.
With this information, the initial loads on the contact
patches are determined, and hence the compliances for a
perturbation of a given type and size can be found, as can
interwire movements and changes in wire strains. From the
Properties of the sheets of wires, simple transformations
and summation lead to estimates of axial and torsional
tangent stiffnesses of the strand.
Using the above, the full slip histories on the interwire
contact patches (from the micro-slips on the periphery at low
loads, to the onset of gross slip at higher loads and beyond)
are predicted. In addition, the hysteresis in the strand for
axial and also torsional cyclic loading regimes is estimated.
For a given axial mean load, the response of strand to
an applied bending moment is also considered in some detail.
Two cases have been addressed, namely close to a termination
and (rather more simple) remote from the termination. To
do this, the theoretical stiffness formulations describing
the slippage between the various layers in the strand have
been derived in an analytical form which are then used as
an input to the differential equations describing the behaviour
of individual wires. Using a simplified version of these
equations, some light has been cast on an interesting
phenomenon observed in previously reported bending fatigue
experiments, where the first wire to fail was invariably the
one which entered the socket on the bending neutral axis
rather than (as might be expected) the wires in the "extreme
fibre" positions.
The experimental work concentrated on measurements of
wire stress, torsional and axial stiffness and related
hysteresis and is in substantial agreement with the theory.
It is concluded that theoretical predictions of interwire
forces and slippage and their associated energy
dissipation in large strands such as those envisaged as
tension leg members in buoyant platforms are feasible, and
this information is of obvious value as an input to a
fracture mechanics analysis of the fatigue behaviour of the
strand away from its termination.
