Multiscale Modeling of Epoxies and Epoxy-Based Composites
281
changes in density or specific volume, Fig. 6a demonstrates that the average FV
radius can also be used to calculate T g in CG-MD simulations [64].
Figure 6b also shows the effect of the average FV hole volume, degree of crosslinking, and length of prepolymers on the predicted T g . The average volume of
FV holes, χ, decreases with the increase in the degree of cross-linking and an
increase of prepolymer length. For smaller average volumes of FV holes, the T g
becomes higher, which indicates a low mobility of the polymer chains and a more
stable molecular structure. An analytical predictive model was also developed from
CG-MD simulations, and the model was shown to be able to predict T g based
only on the initial FV distribution that is calculated from simulations or measured
experimentally [64].
3.5 Elastic Modulus
Two approaches are commonly used to calculate the elastic modulus from
molecular-scale simulations [40]. In the first approach, molecular mechanics (MM),
which is a static method, is used to predict the elastic tensor of epoxies [40, 42]. In
this approach, the predicted elastic tensor is usually non-symmetric, and non-zero
off-diagonal components are common due to the fact that the simulated system
has relatively small dimensions to be considered a perfect isotropic material. This
method was employed by Wu and Xu [40] to predict the bulk, elastic, and shear
modulus of DGEBA/IPD epoxies, which were 15% higher than experimental
predictions. This discrepancy is systematically observed between MM simulations
and experiments. It is attributed to the ideally constructed epoxy structure and the
chosen force field in the MM simulations. In the second approach, the epoxy moduli
in different directions can be predicted from MD simulations. As summarized in
Table 3, the elastic modulus of DGEBF systems as predicted from MD simulations
is in the range of 2.258–3.2 GPa, and that of DGEBA systems is in the range of
1.10–8.5 GPa, which are in reasonable agreement with experimental measurements
that are in the range of 2.34–3.1 GPa [5, 86].
It should be noted that there are conflicting reports in literature on the effect of
the high strain rate imposed in MD simulations on the predicted elastic modulus
[28, 31, 45, 83]. Moller et al. showed a log-linear dependence of the elastic modulus
and yield strength on strain rate in an MD simulation of DGEBA [45]. Odegard
et al. also showed that the elastic properties are over predicted in MD simulations
due to the high strain rate discrepancy between simulation and experiments [28].
On the contrary, Li and Strachan indicate that in various thermoset systems, the
elastic modulus is insensitive to strain rate, while the yield strength was strongly
affected by it [83]. They argue that this is mainly due to the short relaxation time
required for solid materials to relax in a small deformation region. Because of such
conflicting reports on the effects of strain rate on the elastic response of epoxies,
further research is needed on this topic. Nevertheless, the effect of strain rate usually
plays a more important role in large deformation of epoxies [97].
281
changes in density or specific volume, Fig. 6a demonstrates that the average FV
radius can also be used to calculate T g in CG-MD simulations [64].
Figure 6b also shows the effect of the average FV hole volume, degree of crosslinking, and length of prepolymers on the predicted T g . The average volume of
FV holes, χ, decreases with the increase in the degree of cross-linking and an
increase of prepolymer length. For smaller average volumes of FV holes, the T g
becomes higher, which indicates a low mobility of the polymer chains and a more
stable molecular structure. An analytical predictive model was also developed from
CG-MD simulations, and the model was shown to be able to predict T g based
only on the initial FV distribution that is calculated from simulations or measured
experimentally [64].
3.5 Elastic Modulus
Two approaches are commonly used to calculate the elastic modulus from
molecular-scale simulations [40]. In the first approach, molecular mechanics (MM),
which is a static method, is used to predict the elastic tensor of epoxies [40, 42]. In
this approach, the predicted elastic tensor is usually non-symmetric, and non-zero
off-diagonal components are common due to the fact that the simulated system
has relatively small dimensions to be considered a perfect isotropic material. This
method was employed by Wu and Xu [40] to predict the bulk, elastic, and shear
modulus of DGEBA/IPD epoxies, which were 15% higher than experimental
predictions. This discrepancy is systematically observed between MM simulations
and experiments. It is attributed to the ideally constructed epoxy structure and the
chosen force field in the MM simulations. In the second approach, the epoxy moduli
in different directions can be predicted from MD simulations. As summarized in
Table 3, the elastic modulus of DGEBF systems as predicted from MD simulations
is in the range of 2.258–3.2 GPa, and that of DGEBA systems is in the range of
1.10–8.5 GPa, which are in reasonable agreement with experimental measurements
that are in the range of 2.34–3.1 GPa [5, 86].
It should be noted that there are conflicting reports in literature on the effect of
the high strain rate imposed in MD simulations on the predicted elastic modulus
[28, 31, 45, 83]. Moller et al. showed a log-linear dependence of the elastic modulus
and yield strength on strain rate in an MD simulation of DGEBA [45]. Odegard
et al. also showed that the elastic properties are over predicted in MD simulations
due to the high strain rate discrepancy between simulation and experiments [28].
On the contrary, Li and Strachan indicate that in various thermoset systems, the
elastic modulus is insensitive to strain rate, while the yield strength was strongly
affected by it [83]. They argue that this is mainly due to the short relaxation time
required for solid materials to relax in a small deformation region. Because of such
conflicting reports on the effects of strain rate on the elastic response of epoxies,
further research is needed on this topic. Nevertheless, the effect of strain rate usually
plays a more important role in large deformation of epoxies [97].