Dynamic stress concentration in a single particle composite
Date
2012-07-06
Authors
Bugarin, Sinisa
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Abstract
The fracture and fatigue properties of particle reinforced matrix composites are greatly
influenced by stress concentration around the reinforcements as the failure of a structural
member often initiates at regions of high stress concentration. Determining stress
concentration has been the focus of number of researchers for quite some time in order
to better understand the failure mechanics of structural members. The first part of the
study investigates the stress concentration around a spheroidal particle that is embedded in a
large elastic matrix and subjected to dynamic loading. Interaction between neighboring
particles is ignored. The results are therefore valid for composites with low volume fractions.
The problem is studied by extending a hybrid technique that was previously developed for
axisymmetric loading. In the hybrid technique, a fictitious spherical boundary enclosing the
particle is drawn. The fictitious boundary divides the entire region into interior and exterior
regions. The interior region is modeled through an assemblage of conventional finite
elements while the exterior region is represented by spherical wave functions. Coupling of
the solutions for the interior and exterior regions is achieved by imposing the continuity of
displacements and tractions along the common boundary B. This leads to a set of linear
equations that enables the displacements and stresses at any point to be determined. It is
found that the stress concentrations within the matrix at the matrix-particle interface are
dependent on the frequency of the dynamic excitation, aspect ratio of the particle and the
material properties of both matrix and a particle. The study reveals that the dynamic stress
concentration can reach much higher values than the static case.
A second part of the study involved investigating the potential of using an interphase layer to
reduce stress concentrations under a dynamic loading in Mg matrix surrounding a SiC
particle. An interphase layer was applied between the particle and the matrix and the contact
between them was assumed to be perfect. Both constant property materials and functionally
graded materials were considered for the interphase. A constant property interphase was
modelled as a single layer while a functionally graded interphase was divided into a number
of sublayers and each sublayer was treated as having constant material properties. Numerical
results reveal that the interphase layer made of a constant property material shows better
stress concentration reduction than that made of functionally graded materials. An interphase
layer with low values of both shear modulus and Poisson's ratio is necessary for a significant
stress concentration reduction. Studies were focused on reducing the concentration that
occurs over a range of frequencies.
The third part of the study investigates the size effects as the particle size reduces to
nanometers. This part of the study was inspired by the current interest in nanomaterials. For
instance, a quantum dot that is embedded in the matrix of a composite could introduce stress
concentrations under dynamic loading. This is studied here by using the surface/interface
theory of elasticity. It is found that the stress concentration values are significantly
dependent on the elastic properties of the surface/interface and the frequency of excitation.