MATERIALE PLASTICE 52 No. 1 2015 http:www.revmaterialeplastice.ro 20Influence of Interface Quality on Stress and Strain Distribution [629408]

MATERIALE PLASTICE ♦ 52 ♦ No. 1 ♦ 2015 http://www.revmaterialeplastice.ro 20Influence of Interface Quality on Stress and Strain Distribution
in a Micro Cell of a Composite
MIHAIL BOTAN *, DUMITRU DANILA , CATALIN PIRVU, LORENA DELEANU
“Dunarea de Jos” University of Galati, Faculty of Mechanical Engineering, 111 Domneasca, 800201, Galati, Romania
This paper presents an analysis of a composite cell at a micro level. The authors modeled the interface
between a micro sphere and a polymeric matrix for two cases: an interface characterized by a strong bond
between the two involved bodies and an interface with low friction between the micro sphere and thepolymeric matrix. Even if these models are ideal images of actual composites, the analysis of strain and
stress distributions reveals there is a big difference in the mechanical behaviour of the two micro cells. These
two cases were analyzed considering a perfect elastic behaviour of involved materials. The shape and theintensity of stress distributions are different for the analyzed models. A weak interface makes the matrix to
have restrained zones with high values of von Mises stresses, concentrated on top and bottom of the sphere
(on the loading direction). An actual cell of a similar composite (polymeric matrix and a micro sphere asreinforcement) could not have an „extremist” behaviour as these two here presented, but an intermediate
one, depending on actual properties of the materials and the nature of the interface.
Keywords:
micro cell composite, strain distribution, stress distribution
Fig. 1. The
deterioration
models for the
interface in
polymeric
composites with
hard spherical
particlesThe mechanical properties of composites depend on
their microstructures, i.e. on the content, geometries,distribution and properties of phases and constituents in
the composites [1-3]. As commented by Mishnaevsky [4],
the concept of computational experiments as a basis forthe numerical optimization of materials is formulated.
Many specialists are interested in simulating the
mechanical behaviour of composites as a sensibleinterpretation of the results could formulate reliable recipes
for composites [4-8].
FEM (Finite Element Method) offers the opportunity for
anticipating the material behaviour, especially for
composites [2, 9-12]. When modeling machine elements
made of polymers, the particular behaviour of thesematerials has to be taken into account [13], including
elasto-plastic aspects.
But a reliable model of a composite has to prove by
experimental research in order to be useful for designers.
In order to solve a design for a composite, there are several
steps to be done: designing the model geometry anddefining the restrictions and the load, meshing the bodies,
including the selection of the element type, identifying
nodes and elements, elaborating the equations for themesh elements, establishing the boundary conditions,
solving the problem and the interpretation of the results.
Modeling the unit cell of a composite with spherical
reinforcement
A composite may be modeled at three different levels:
micro, mezo and macro [4]. For instance, the blade of a
wind turbine from [14] is modeled at a macro scale, taking
into account physical and mechanical characteristics asgiven by the suppliers. The optimization of the material
could rely on a model elaborated at micro, mezo or macro
scale, even on a combined scale model that will reducethe time necessary for the experimental stage of the
material or even for the wind turbine.
The model here presented is done for a unit cell of a
composite, at micro level. It is quite difficult to define aunit cell for a composite, taking into account the diversity
of the involved materials, both matrix and addingmaterial(s). Some specialists considered as the unit cell
of a composite a micro volume including all materials
involved in the composite, with their relevant propertiesfor the composite behaviour , at mezo or macro scale.
According to this idea, any volume including a fiber, a bead,
even a cluster typical for the adding materials, could beconsidered a unit cell of the composite. By this analysis,
the authors would like to emphasize the importance of the
interface for the mechanical behaviour of a composite,even at the micro level of its unit cell. The importance of
the interface properties was underlined by Medadd and
Fisa [15], which proposed a model for traction fracture,that has been proved to be applicable to polymeric
composites with glass beads, in a qualitative way. From
figure 1, it may be noticed that the traction fracture of acomposite with micro spheres depends very much on the
interface quality:
a) the resistant interface is not damaged under load and
the break is initially developed in the composite matrix;
b) a partially damaged interface usually depends on the
elasticity modulus, the volume fraction of the addingmaterial without damaged interfaces and the
complementary volume fraction of the adding material
that has a damaged interface (the ratio between thesetwo interface categories being actually hard to be
estimated);
* email: mihai.botan@ugal.ro Paper presented at The 3rd International Polymer Processing Conference – IPPC
2013, 7-8 November, Sibiu, Roma nia

MATERIALE PLASTICE ♦ 52♦ No. 1 ♦ 2015 http://www.revmaterialeplastice.ro 21
Table 1
CHARACTERISTICS OF MATERIALS
INVOLVED IN MICRO CELL DESIGN AND
SIMULATION
a. perfectly bonded interface b. weak interface (very low friction
between the micro sphere and the
matrix)Fig. 2. The resulted mesh for the micro
unit cell
Fig. 3. Von-Mises stress distribution [MPa] (here the micro sphere is transparent)
c) a weak defective interface is easily destroyed when
applying a traction load.
Taking into account models presented in [2, 15], the
authors simulated the behaviour of a unit cell characterized
by continuous interfaces (without detaching the polymer
from micro spheres), but each one with different properties.The unit cell initially has a cubic shape; then the micro cell
was loaded with a uniform pressure of 1 MPa, applied on
the top face of the cub. The cell contains a micro glassbead (having a perfectly spherical shape), the centre of
the sphere being in the center of the cub. It is an ideal
situation. The aim of this simulation is to use the informationfrom this unit cell to build a virtual composite with desired
properties and to analyze in a future work how far the
composite properties could be as compared to those ofthe unit cell. For this purpose, ANSYS 14.4 was used and
the material characteristics are given in table 1.
This paper is a first step in a more complex study and
here the materials are considered perfectly elastic (both
for the sphere and the matrix).
Actually, many composites,
especially those with polymeric matrix, exhibit an elasto-visco-plastic behaviour.
The analyzed model of the composite cell consists of a
cub of 100 μm in side, with a central sphere characterized
by the radius R (here, R = 25 μm). The centres of the cub
and of the sphere are overlapped. The volume left around
the sphere consists of a polymer (here, PBT). Load wasconsidered uniformly distributed on the top side of the cub
as a compression load of p = 1 MPa and it was directly
applied on the cub surface. Two cases are analyzed:
a.the reinforcement is perfectly bonded to the polymeric
matrix; this configuration implies that interface could not
be destroyed and the separation or the slipping betweenthe two bodies are not allowed;
b.the interface allows for slipping between the two
bodies, this slipping being characterized by a frictioncoefficient; the contact between the reinforcement and
the matrix is designed as a friction contact between twosolids. This paper presents only the results for a very low
friction coefficient ( μ = 5 . 10
-6), implying a very weak
adherence between the materials of the model.
The boundary limits are:
– the micro unit cell of the composite is laying on a
perfectly rigid plane solid (y = 0, x ≠ 0, z ≠ 0, the matrix
material accepting lateral displacements on y, in the plane
next to the bearing rigid surface);
– the load is uniformly distributed on the top face of the
cub (a uniform pressure of 1 MPa).
Figure 2 presents the resulted mesh for the micro unit
cell. Finally, the mesh includes 38,621 interacting elements
and 64,365 nodes.
Figures 3 to 10 present comparative results for a uniform
load of 1 MPa, directly applied on the top surface of the
cub.
The shape and the intensity of stress distributions are
different.
A weak interface makes the matrix to have restrained
zones , with high values of von Mises stresses, concentrated
on top and bottom of the sphere (on the loading direction).
figure 4 presents the Von-Mises stress distribution in the
polymeric matrix and in the glass bead. When the interfaceis bonded to the sphere, a stress concentration is noticed
into the reinforcement body, the values of von Mises
stresses into the matrix being lower as compared to thevalues obtained in the micro glass bead. The advantage is
that the matrix is less loaded and its durability could be
longer, implicitly that of the composite.
Figure 3.b presents the distribution of von Mises stresses
for the second case, when the slipping between the matrix
and the reinforcement is allowed. The maximum valuesare higher (3 MPa), but they are concentrated on the loading
direction and the volume affected by this high stress is
smaller as compared to the first case. This high stress
concentration increases the risk of material failure,
especially for the matrix. In actual cases, the matrix begins
to yield around the more rigid body or the matrix is even

MATERIALE PLASTICE ♦ 52 ♦ No. 1 ♦ 2015 http://www.revmaterialeplastice.ro 22
Fig. 4. Von-Mises stress distribution in the
vertical section containing the micro sphere and
the cub centre [MPa]
Fig. 5. Equivalent elastic strain distribution [MPa]
(matrix made of PBT and the sphere is transparent)
Fig. 6. Strain distribution along Ox axis [mm]
(similar to those along Oz axis)
Fig. 7. Strain distribution along Oy axis [mm]detached from the micro-sphere, the entire strength of the
system being damaged.
Figure 5 presents the elastic equivalent strain distribution
for each of the two cases. This characteristic has also highvalues for the second case, meaning a weak interface is
not recommended for a composite.
Figures 6 and 7 present the strain distribution along the
main direction of the reference system, Ox, Oy (that for
Oz being similar to that for Ox). For the first case of the
bonded interface, the polymer has an obvious tendency tocreep near the cub corners (where the material has poor
properties – those of the matrix). The harder micro sphere
does not allow for the material to be deformed near theinterface due to the strongly bonded interface.
For the second case, the polymeric material is deformed
in almost all its volume, due to the weak interface,characterized by a very small friction coefficient ( μ = 5 .
10
-6), but the values of the maximum strains are similar on
x direction. Differences are noticeable on y direction, but
they are very small. Even if the directional strains havedifferent distributions for the two analyzed cases, their
maximum values are close (figs. 6 and 7).
The shear stress distributions reveal greater differences
between the maximum values of the two models. Thus,
the maximum value for τ
xy is much greater (almost 4
times) for the weak interface and the maximum valuesfor τ
yz and τzx are almost double. The conclusion is that a
weak interface generates greater shear stress and actual
polymer materials could yield or be detached from theharder bodies (figs. 9 and 10). Figure 8 presents the elastic
shear strain in xOy plane. For the weak interface, the
maximum values are almost three times greater ascompared to the bonded interface and they are situated
on the load direction, near the rigid body.

MATERIALE PLASTICE ♦ 52♦ No. 1 ♦ 2015 http://www.revmaterialeplastice.ro 23Fig. 10. Shear stress distribution in yOz plane [MPa]
Fig. 8. Shear stress deformation in plane
xOy for the matrix [mm/m] (transparent
glass bead)
Fig. 9. Shear stress distribution in xOy plane [MPa]
Conclusions
The results of these simulations differentiated only by
the interface properties. The properties of the polymericmatrix and those of the reinforcement were kept constant.
The two analyzed models are not easy to be found in
practice, but they represent two extremes, actual casesbeing between them. In order to give examples of actual
behaviour of two different interfaces, Figure 11.a presents
a composite polyamide + glass beads that behaves as acomposite with weak interface [16] (one may see that
the glass beads could rotate into the matrix, the micro
spheres having high mobility within the polymeric matrixof the superficial layers), this composite being nearer the
model with weak interface and figure 11.b presents a
composite with the same glass beads, but the matrix ismade of PBT [17] (one may see fragmented beads and all
beads did not seem to be moved into the matrix, this
material being closer to the model with bonded interface).
The results underline that the mechanical behaviour of
a micro unit cell for a composite is strongly influenced by
the interface quality.References
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Manuscript received: 15.09.2014
Fig. 11. Different interfaces for polymeric composites with glass
beads