ISSN 1070-4272, Russian Journal of Applied Chemistry, 2014, Vol. 87, No. 4, pp. 500−508. © Pleiades Publishing, Ltd., 2014.
Original Russian Text © A.S. Ermilov, E.M. Nurullaev, 2014, published in Zhurnal Prikladnoi Khimii, 2014, Vol. 87, No. 4, pp. 509−518.
AND POLYMERIC MATERIALS
Numerical Simulation and Derivation of an Equation
for Calculation of the Mechanical Fracture Energy
of Elastomer Filled with Multifractional Silica
A. S. Ermilov and E. M. Nurullaev
Perm National Research Polytechnic University, Komsomol’skii pr. 29, Perm, 614990 Russia
Received March 19, 2014
Abstract—Numerical simulation of the fracture of a three-dimensional cross-linked elastomer ﬁ lled with solid
particles enabled deriving an equation that relates the structure of a composite material and energy of its mechanical
fracture in uniaxial stretching. It was shown that the resulting equation can be used to select the optimal asphalt
pavement composition with high service life.
Polymer composites based on three-dimensional
cross-linked elastomeric matrix ﬁ lled with solid parti-
cles are widely used in parts and units of various designs
automobile, aircraft, and ship building. Abrasive materi-
als containing corundum (aluminum oxide) allow high-
quality grinding in mechanical engineering. Elastomers
ﬁ lled with quartz (silicon dioxide) are used in the build-
ing industry including coverage of buildings and ﬂ oor-
ing in sports facilities. Mechanical characteristics of
these polymer composite materials signiﬁ cantly affect
the service life of certain construction parts and units.
Therewith molecular structure of the polymer backbone,
a type and degree of its plasticization, a degree of efﬁ -
cient bulk ﬁ lling depending on the shape and fractional
composition of dispersed ﬁ ller particles as well as the
physico-chemical interaction at a elastomer–ﬁ ller inter-
face are the most important structural parameters .
Bond strength (adhesion) of polymer binder and
surface of ﬁ ller particles is of particular importance for
providing increased service life under a dynamic vibra-
tional load such as a in contact of an automobile wheel
with the asphalt pavement. For example, in the case of
uniaxial tension of composite samples with reduced
adhesion of the components their delamination can oc-
cur that results in an internal fracture of the material.
This contributes to the early fracture of the sample as a
whole, which is manifested by corresponding changes
in a type of tension diagram until an appearance of cone-
shaped curves .
An effect of the formation of a vacuolar cavity be-
tween the ﬁ ller particles and 3D cross-linked polymer
matrix on the form of a stress-strain diagram of the sam-
ple was investigated by Sato and Furukawa, who devel-
oped a molecular theory of elastomer reinforcement by
ﬁ ller based on the concept of the internal deformation
[3, 4]. However, their solution of the problem was of
a discrete character (case 1: a 100% adhesion and case 2:
zero adhesion), and the corresponding model (the ﬁ ller
spherical particle of a diameter d was included in the
composite sphere of a diameter D and d/D =
φ is a volume fraction of the ﬁ ller) did not allowed tak-
ing into account the kinetics of accumulation of delami-
nated particles upon the composite deformation.
On the phenomenological basis using dilatometry
of sample volume (ΔV/V
) at uniaxial tension Farris
justiﬁ ed and proposed a formula, which quantitatively
takes into account the formation of vacuoles between
spherical particles and the polymer matrix of composite
describing a dependence of stress σ on strain ε and the
initial viscoelastic modulus E: