Composite Materials Research Progress

An Experimental and Analytical Study of Unidirectional Carbon Fiber… 147
Numerical Simulation of Tensile Failure Process of Layered
Composites
The tensile failure of fiber reinforced composite material involves a complicated damage
accumulation process resulting from random fiber breakage, stress transfer form broken to
intact fiber, and interface debonding between the fiber and matrix. It is difficult to analyze
such a complicated probabilistic failure phenomenon precisely by means of analytical
methods. The Monte Carlo simulation technique coupled with a stress analysis method is one
of the most effective tools for understanding the tensile failure process [23-27]. In past
Monte Carlo simulations, a micro-composite unit with a coarse mesh and a few fibers of short
length was always used as the numerical model. In practice, structural composites usually
contain large quantities of fibers, when such micro-composite unit is applied to simulate the
failure process of practical composites, it may result in a lack of statistical effects and
magnification of boundary effects, causing errors in calculations of the stress concentration.
Yuan et al. [28] presented a two-dimensional large-fine numerical micro-composite model
with fine mesh, sufficient fibers and adequate length instead of the aforementioned model and
developed a new Monte Carlo simulation method to study the tensile failure process of
unidirectional composites. Based on the new model and method, the average statistical
evolution of the composites deformation and failure, caused by the accumulation of the
random breakages of large quantities of fibers, matrices and interfaces, is successfully
simulated. By taking account of the inertial effect, strain-rate effect of components and the
softening effect caused by the thermo-mechanical coupling in the simulation model, the
tensile stress–strain curves of unidirectional fiber reinforced resin matrix composites CFRP
and GFRP at different high strain-rates were successfully predicted, which agree well with the
experimental results [29-31].
All above Monte Carlo simulations were coupled with the classical shear-lag model. It is
assumed that the fibers bear the whole axial load and the matrix only carries the shear stress.
Ochiai et al. [32, 33] proposed a modified shear-lag model, which takes the axial load born by
the matrix into account, to study the stress concentration in the elastic and elastic-plastic
matrix caused by single fiber breakage. In the present study, Monte Carlo numerical
constitutive model according to Ochiai's modified shear-lag model with fine mesh, sufficient
fibers and adequate length was established to study the failure process of unidirectional
layered composites, to predict the mechanical behavior of these composites with the prepreg
epoxy matrix and to study the relationship between the interface and composite strengths.
Model of Composites
Figure 20 shows the large-fine numerical model of unidirectional composite that consists of n
fibers and n+1 matrices. Each fiber or matrix, at the length of L, is composed of m elements
of length Δx=L/m in the longitudinal direction. The cross-section of the fiber and the matrix
are simplified as rectangle, considering that the simplified fiber has the same sheared area as
that of the actual one, we have