VOID COALESCENCE MODEL FOR DUCTILE DAMAGE
D. L. Tonks, A. K. Zurek, and W. R. Thissell
Los Alamos National Laboratory, Los Alamos, NM 87545.
Abstract.
A model for void coalescence for high strain rate ductile damage in metals is presented. The basic
mechanism is void linking through an instability in the intervoid ligament. The formation probability
of void clusters is calculated, as a function of cluster size, imposed stress, and strain. A wave speed
limiting is applied to the cluster size enhancement of cluster growth. Due to lack of space, model
formulas are merely described and not derived..

INTRODUCTION
High strain rate ductile fracture is caused on the
microscopic scale by the nucleation, growth, and
link up of voids. We present a model for small
scale void cluster growth via the coalescence of
initially existing voids, based on earlier work. [1-3].
Void nucleation for cluster growth is not included.
Inertia is not considered. Hence, the model is not
suited for the growth of macroscopically large
cracks. Due to lack of space, formula derivations
are omitted.
The general phenomenology envisioned for
high and lower strain rates is as follows. At high
strain rates, a random initial void configuration
gives rise  to  a  spatially  disordered  damage
morphology, where widely separated voids have
little time to communicate with each other via stress
waves. In other words, when voids coalesce into a
cluster, there is not time for the enhanced stress and
strain fields to form at cluster boundaries. This
retardation inhibits the potential for large damage
clusters to grow faster than the smaller ones. As a
result, the sample breaks when widespread and
uncorrelated damage finally accumulates to the
point where a damage surface forms, breaking the
sample. At lower strain rates, the ductile damage

tends to consist of flat, disk-like clusters or cracks,
whose   growth   does  benefit from    the  size
enhancement of growth mentioned above.      The
sample breaks with little general damage, when the
biggest crack rapidly outstrips its neighbors. It can
do so because there is time for the size enhancement
of stress and strain fields to occur at its periphery.
Consequently, the strain to fracture in the low strain
rate case is significantly less than in the high strain
rate case. [1,3].
Two analytical models have been formulated to
explain the point of fracture. At high strain rates,
the point of fracture is modeled with random
percolation theory [4]. The organized clusters at
low strain rates are modeled by refining a
probabilistic theory for cluster growth [5].
GENERAL PHYSICAL MODELING AND
FORMULAS
The growing voids must coalesce or link up in
order to form a continuous internal surface that
separates the sample. This will occur in dynamic
situations when the intervoid ligament undergoes a
localized mechanical instability that rapidly thins it
out and causes an elastic unloading in the
surroundings [6-8]. Local straining is necessary to
thin out the intervoid ligament once the applied