Page 225 - Fiber Fracture

210 H.U. Kiinzi

are found by Scheucher (1969a,b) on 0.3 mm thick Cu wires. Murphy and Ball (1972)
studied 1.4 mm thick wires and observed n to be between 0.9 and 1.4. Hausmann
(1987) used a sum of two Avrami functions to fit the experimental data on Au wires
and found that the exponents of both terms are smaller than 1. These findings are
clearly not compatible with the original idea of this model. The existence of a master
curve therefore just asserts that the evolution of the yield stress is governed by thermal
activation during annealing treatments.
The fact that the yield stress may not be described by a theory that just takes into
account the evolution of the recrystallized volume may not be astonishing, even though
this may work for other properties. The yield stress depends on various microstructural
details which during annealing result from different microscopic processes with kinetics
of their own. Depending on the annealing temperature, processes with lower activation
energies leading to restoration and processes with higher activation energies leading to
recrystallization run simultaneously or sequentially.
As opposed to the yield stress the elastic constants measure intrinsic crystalline
properties which depend on short-range interatomic forces that remain practically un-
modified during recrystallization. The elastic modulus measured along the wire therefore
depends only on reorientation of the crystal lattice of grains during recrystallization and
might be expected to be more related to the recrystallized volume than the yield stress.
Nevertheless, its evolution during recrystallization cannot be described by a single
master curve.

Recrystallization Kinetics of Young’s Modulus

As mentioned above, the elastic modulus measured along the wire axis depends on
the elastic anisotropy of the metal and the texture. Whenever drawing texture and
recrystallization texture are not identical Young’s modulus may serve as an indicator for
the texture evolution. Figs. 26 and 27 show the elastic modulus as determined from the
sound velocity at room temperature after cumulative pulsed annealing treatments. For
both metals the modulus first decreases, then passes through a minimum and increases
again. The Cu wire used for these measurements was taken from the same spool as the
sample used for the determination of the pole figures (Fig. 8). Unfortunately, modulus
measurements of the decreasing part are missing. Only the initial value of the as-drawn
wire is known. When measurements were resumed 4 months later, during which the
wire restored at room temperature, the elastic modulus was already at its minimum. The
corresponding pole figure (Fig. Sb) indicates that the volume fraction of the (1 11) fiber
texture present in the as-drawn state (Fig. Sa) decreases with a corresponding increase
of the (1 00) texture.
This decrease has been explained by Lee (1995) as being driven by the dominant
residual stress. In drawn wires the dominant residual stresses result from the nonho-
mogeneous plastic deformation and are oriented parallel to the drawing direction. The
energy released at constant plastic strain can be maximized when the minimum elastic
modulus directions are arranged parallel to the principal directions of the residual stress.
Nucleation vf grains with this orientation is therefore favored. The (1 11) fiber texture
that results from the deformation is therefore partly replaced by the (100) fiber texture.