Geometric Modeling of Transverse Cracking of Composites
351
The proposed geometric model consists of three components, which are
described in the next three sections. Firstly (Sect. 2), realistic virtual specimens
are constructed based on spatial statistics of the actual composite system. Secondly
(Sect. 3), estimates of the stress concentration associated with a pair of adjacent
fibers on the distance between them and their relative orientation with respect to
the loading direction are used to identify potential points of failure initiation. Lastly
(Sect. 4), an iterative process is adopted to determine the location of successive
cracks, taking into account the shielding associated with previously introduced
transverse cracks. Section 5 summarizes the results of a convergence and calibration
analysis of the proposed model. In Sect. 6, we apply the geometric model to a
statistical investigation of the impact of some of the microstructural parameters on
the predicted transverse cracking response.
2 Problem Description
Multiple statistical metrics can be extracted from the optical images of the composite microstructure similar to that shown in Fig. 1. Two of these statistical
measures are presented in Fig. 2: the distribution of fiber diameter (top figure) and
the distribution of the projected nearest-neighbor distance (NND) (bottom figure),
defined as the NND projected onto the direction of the transverse loading. The latter
parameter is used in the next section in the estimation of the stress concentration
factor that drives the crack initiation process. Due to the high fiber volume fraction
of the composite laminate of interest, the measured NND for the system of interest
is approximately 0.3 μm [3]. For reference, the diameter for a typical carbon fiber
is approximately 7.5 μm.
In the experiments, the monitoring of transverse cracking process is achieved
using two distinct methods. As shown in Fig. 3, optical images augmented by
a fluorescent dye show that the failure process takes place primarily along the
fiber/matrix interfaces. Another, more global approach based on acoustic emission
is illustrated in Fig. 4, which also presents the transverse constitutive response
dominated by the stiff, linear response of the 0 ◦ plies. Video observations of the
failure process show that the transverse cracks initiate inside the 90 ◦ ply, propagate
dynamically across the transverse layer, and are arrested by the adjacent 0 ◦ plies,
as illustrated in Fig. 4 (top). More details on the experimental aspects of the project
can be found in [2].
Once the virtual model of the laminate, built in this work directly from optical
images, is defined in terms of the number, diameter, and placement of the fibers
in the transverse ply, the problem description is completed by specifying the
interfacial strength distribution. It should be noted here that virtual models of the
microstructure can also be built numerically using a variety of statistical metrics,
such as the fiber diameter and NND distributions or the one- and two-point
correlation functions, combined with an optimization scheme aimed at matching the
numerically computed and experimentally measured values of these distributions.
351
The proposed geometric model consists of three components, which are
described in the next three sections. Firstly (Sect. 2), realistic virtual specimens
are constructed based on spatial statistics of the actual composite system. Secondly
(Sect. 3), estimates of the stress concentration associated with a pair of adjacent
fibers on the distance between them and their relative orientation with respect to
the loading direction are used to identify potential points of failure initiation. Lastly
(Sect. 4), an iterative process is adopted to determine the location of successive
cracks, taking into account the shielding associated with previously introduced
transverse cracks. Section 5 summarizes the results of a convergence and calibration
analysis of the proposed model. In Sect. 6, we apply the geometric model to a
statistical investigation of the impact of some of the microstructural parameters on
the predicted transverse cracking response.
2 Problem Description
Multiple statistical metrics can be extracted from the optical images of the composite microstructure similar to that shown in Fig. 1. Two of these statistical
measures are presented in Fig. 2: the distribution of fiber diameter (top figure) and
the distribution of the projected nearest-neighbor distance (NND) (bottom figure),
defined as the NND projected onto the direction of the transverse loading. The latter
parameter is used in the next section in the estimation of the stress concentration
factor that drives the crack initiation process. Due to the high fiber volume fraction
of the composite laminate of interest, the measured NND for the system of interest
is approximately 0.3 μm [3]. For reference, the diameter for a typical carbon fiber
is approximately 7.5 μm.
In the experiments, the monitoring of transverse cracking process is achieved
using two distinct methods. As shown in Fig. 3, optical images augmented by
a fluorescent dye show that the failure process takes place primarily along the
fiber/matrix interfaces. Another, more global approach based on acoustic emission
is illustrated in Fig. 4, which also presents the transverse constitutive response
dominated by the stiff, linear response of the 0 ◦ plies. Video observations of the
failure process show that the transverse cracks initiate inside the 90 ◦ ply, propagate
dynamically across the transverse layer, and are arrested by the adjacent 0 ◦ plies,
as illustrated in Fig. 4 (top). More details on the experimental aspects of the project
can be found in [2].
Once the virtual model of the laminate, built in this work directly from optical
images, is defined in terms of the number, diameter, and placement of the fibers
in the transverse ply, the problem description is completed by specifying the
interfacial strength distribution. It should be noted here that virtual models of the
microstructure can also be built numerically using a variety of statistical metrics,
such as the fiber diameter and NND distributions or the one- and two-point
correlation functions, combined with an optimization scheme aimed at matching the
numerically computed and experimentally measured values of these distributions.