Page 230 - Fiber Fracture

STRENGTH AND FRACTURE OF METALLIC FILAMENTS 215

slope. His samples, however, had elongations at rupture that varied with the number of
grains in the cross-section from 40 to 80%. The observed effect might therefore at least
partially stem from strain hardening.

Fatigue of Polycrystalline Wires

Wires are often applied because of their almost unlimited flexibility. Nevertheless
repeated bending as well as all other cyclic solicitations fatigue the material. Indeed,
fatigue fracture belongs to the most common types of material failure in wires. Many
investigators use rod or thick wire-shaped samples to study fundamental aspects of
fatigue. Here we will look at micro-wires that are used in electronics for flexible cables
or for electrical connections in microelectronics. Almost all modem electronic devices
contain several centimeters of interconnections that are made with such bond wires; in
vehicles and aircraft these interconnections are subject to fatigue by vibrations. Also
from a scientific point of view these micro-wires are interesting objects permitting to
study the effect of their high surface to volume ratio on the mechanical properties.
Crystalline and amorphous high-strength metallic filaments are promising fibers for
reinforcement in composite materials and their fatigue behavior is of technological
importance. No attempt is made to review the huge literature on wire ropes where the
failure often results from interactions between wires.
Fatigue of micro-wires and thin foils is usually measured in uniaxial tension-tension
tests, using load cells with resolutions in the mg range. Clearly tension-compression
tests would be more elegant and easier to interpret, but even with gauge lengths of 1
mm, a 25 mm thick wire is 40 times longer than thick and inevitably buckles when
compressed. In the tension-tension loading mode wires are subject to a non-vanishing
mean stress which even at room temperature induces the sample to creep and results in
a complementary stress relaxation. According to whether the sample is tested in strain-
or stress-controlled tests this elongation demands a continuous readjustment to keep the
strain or stress amplitude constant. In addition, with gauge lengths of few millimeters
the strain measurement is not easy. In view of the small forces and sizes it is practically
impossible to fix an extensometer directly on the gauge length. Even though it is known
to result in a poor precision, strain is therefore often inferred from the grip displacement.
Description of experimental setups can be found in Hofbeck et al. (1986), Hausmann
(1 987), Kim and Weil (I 987), Kronert and Raith (1989), Judelewicz (1 993), Judelewicz
et al. (1994) and Read (1998b). Sometimes much simpler bending tests can be used to
establish the fatigue life curves (S-N curves). Geminov and Kopyev (1979) enclose the
wire in a curved groove and rotated it around its axis. The total strain is calculated from
the curvature of the groove that imposes the bending of the wire but since yielding takes
place only at the surface and strain hardening is nonhomogeneous almost nothing can
be said about the stress dependence of fatigue. Hagiwara et al. (1985) bend the wire by
drawing it over a roll. Similar techniques are used by Doi et al. (1981) and Tanaka et al.
(1980). Unfortunately, direct comparisons of these bending tests for micro-wires with
tension-tension tests are not available. Since in most of these tests the sample surface
is in gliding or rolling contact with another object crack initiation and thus fatigue life
might be modified.