Plasticity and Energy Dissipation in Metals
Henry A Padilla II, University of Illinois at Urbana/Champaign, Department of Mechanical and
Industrial Engineering Department, MC-244, 1206 W Green Street, Urbana IL 61801
INTRODUCTION
The research presented here adds a new dimension to findings over the last twenty years regarding the high
strain rate energy dissipation properties of crystalline metals. For most metals it is expected that nearly all of the
available plastic work during deformation dissipated as heat. Experimentalists have found this to be true for
aluminum, copper, steel, and various other alloys. There is conflicting evidence, however, whether there are some
metals which do not dissipate most of this available energy, specifically titanium and hafnium. These two
materials are both h.c.p. in their crystal structure and it has been suggested that perhaps the formation and
presence of deformation twins plays a role in the storage of some fraction of the plastic work energy. In this work
we measure the mechanical response and heat dissipation during high rate compression of oxygen free high
conductivity copper and α−zirconium. The copper represents an f.c.c. material which traditionally has been found
to dissipate nearly all of its energy as heat, while zirconium bears many similarities to titanium and hafnium in
both its crystal packing structure and deformation mechanisms. We complement the mechanical and thermal data
with microstructural evidence of different deformation mechanisms in the two types of materials and seek to better
understand the thermomechanical coupling between strength, microstructure and thermal behavior.
EXPERIMENTAL PROCEDURES
Cylindrical specimens of OFHC copper and zirconium were deformed at high strain rates in a split-Hopkinson
pressure bar, while simultaneously gathering surface temperature data using a linear array of HgCdTe
photodetectors. Sample geometries were 4x8mm (length x diameter) for Cu and 3x5mm for Zr. Lateral surfaces
were turned on a lathe, roughened with 320 grit silicon carbide paper and coated with a layer of black permanent
marker ink to raise the emissivity closer to that of a black body. Static calibrations of both materials were carried
out for each element of the detector array that was used. Samples were then prepared for both TEM microscopy
and Electron Backscattered Diffraction (EBSD) SEM.
RESULTS
The mechanical response of copper and zirconium is shown in Figure 1(a). The low yield strength and high
hardening behavior of the copper is typical of an annealed starting microstructure. The yield and flow stress of
zirconium is significantly higher than the copper. Figure 1(b) shows the results of the dissipation calculation for the
copper and zirconium samples of Figure 1(a), plotted as the fraction of energy dissipated, β, against true strain.
Copper clearly dissipates nearly all of the energy of deformation, while zirconium dissipates roughly 55%.
Figure 2(a) is a TEM micrograph which shows evidence of dislocation slip in Cu by the cell structure which has
formed. It can be concluded that forest dislocation cutting is the dominant mechanism in annealed OFHC copper,
which supports a dissipation measure of nearly 100%. Figure 2(b) is a TEM image of a deformation
microstructure in zirconium deformed at 1200 /s to 6% strain. The presence of both dislocations and deformation
twins implies a more complicated interplay between mechanisms. The bracket indicates two twin boundaries,
while arrows point out a dislocation pileup which has penetrated through one twin boundary into the twin interior.
One feature of this image which is important to note is the presence of long, wavy contrast changes, commonly
referred to as bend contours. They are caused by distortion of the crystal lattice. Zirconium TEM samples are
roughly 3 mm in diameter and 150 µm thick. The warping in such thin foils of the material is almost always
present and is presumably due to residual stress. The orientation image map (OIM) shown in Figure 2(c) is
constructed from EBSD data from a zirconium sample deformed at 1800 /s to 20% strain. The color of each pixel
corresponds to a specific crystallographic direction which is oriented out of the plane of the image. The legend
allows regions with similar or different crystallographic texture to be identified. The (010) and (120) directions both
lie at a right angle to the (001) direction in the h.c.p. unit cell. Deformation twins are ubiquitous in this
microstructure and can be seen to have the lenticular shape commonly found in zirconium.
(a)
(b)
Figure 1. (a) Stress vs. Strain response of copper and zirconium at high strain rates. (b) Fraction of
dissipated energy (as heat) vs. Strain for the same two samples in (a).
(a)
(b)
(c)
Figure 2. (a) TEM of high strain rate deformed copper and (b) zirconium. Twin boundaries are noted by the
bracket, while the dislocation pileup is pointed out by the arrows. (c) EBSD orientation map of a high
strain rate deformed zirconium sample.
CONCLUSIONS
It is well established that there is a strong dependence of the strength and hardening response of polycrystalline
metals on the microstructure evolution. These experiments explore the possible role that structure evolution may
also play in the thermomechanical coupling of these materials. The energy dissipation of OFHC copper is found to
have the expected trend of 100% dissipation, while that of zirconium is markedly different. The two materials differ
not only in their mechanical response at high strain rates, but also in the operative deformation mechanisms. The
possibility that zirconium may store significant amounts of energy in the microstructure is supported by a measure
of the heat dissipation, the overwhelming presence of a distinctly different deformation mechanism, as well as
qualitative observations of the behavior of thin films during TEM sample preparation. Further investigation into
these findings is warranted given the unique nature of the results.