Transverse Failure of Unidirectional Composites: Sensitivity to Interfacial Properties
345
before becoming positive during the failure events. It should also be noted that
the sensitivity with respect to δ c3 is substantially smaller than the sensitivity with
respect to δ c2 .
Due to the complexity of the large 406-fiber microstructure and of the stress field
in the 90 ◦ ply, the failure of the fiber/matrix interfaces is a complex function of the
applied strain, rendering a precise determination of the onset of transverse cracking
difficult when only inspecting the stress-strain response or deformed geometry.
However, the evolution of the sensitivities of the transverse stress with respect to
the cohesive parameters provides a clear insight on the correlation between applied
strain and the onset of transverse cracking.
7 Conclusion
A computational framework has been presented for the modeling of transverse
cracking in realistic virtual microstructures of 90 ◦ composite plies reconstructed
directly from optical images. The underlying numerical method relies on a discontinuous, multi-interface extension of an interface-enriched generalized finite
element method, which allows for the simulation of fiber/matrix debonding in composite layers with high fiber volume fractions. This computational model has been
validated against strain measurements of the onset of transverse cracking performed
on a [0/90/0] T carbon/glass-epoxy laminate. Also included in the computational
framework is the analytic extraction of the sensitivity of the macroscopic transverse
stress with respect to the parameters that define the cohesive failure law. By monitoring the evolution of these sensitivities, the onset and propagation of transverse
cracks can be assessed. It should be noted, however, that in the present study, all
fiber/matrix interfaces are assumed to have the same cohesive properties. The next
steps include relaxing that assumption and deriving individual interface property
sensitivities, i.e., extracting how sensitive the transverse stress is to the critical
stress of individual fibers. With these individual sensitivities, one could study the
sensitivity to the parameters that define the distributions of the interface properties,
e.g., the sensitivity to the average and standard deviation of the interface strength.
Appendix: Sensitivity to Critical Displacement Jumps
For completeness, a summary of the sensitivity formulation with respect to the
critical displacement jumps δ c1 , δ c2 , and δ c3 is included hereafter, starting from
Equation (18) in Sect. 4.
For linearly elastic volumetric elements, again there is no explicit dependence of
the internal force contribution on δ ci and no displacement discontinuity. Therefore,
Equation (18) simply becomes
345
before becoming positive during the failure events. It should also be noted that
the sensitivity with respect to δ c3 is substantially smaller than the sensitivity with
respect to δ c2 .
Due to the complexity of the large 406-fiber microstructure and of the stress field
in the 90 ◦ ply, the failure of the fiber/matrix interfaces is a complex function of the
applied strain, rendering a precise determination of the onset of transverse cracking
difficult when only inspecting the stress-strain response or deformed geometry.
However, the evolution of the sensitivities of the transverse stress with respect to
the cohesive parameters provides a clear insight on the correlation between applied
strain and the onset of transverse cracking.
7 Conclusion
A computational framework has been presented for the modeling of transverse
cracking in realistic virtual microstructures of 90 ◦ composite plies reconstructed
directly from optical images. The underlying numerical method relies on a discontinuous, multi-interface extension of an interface-enriched generalized finite
element method, which allows for the simulation of fiber/matrix debonding in composite layers with high fiber volume fractions. This computational model has been
validated against strain measurements of the onset of transverse cracking performed
on a [0/90/0] T carbon/glass-epoxy laminate. Also included in the computational
framework is the analytic extraction of the sensitivity of the macroscopic transverse
stress with respect to the parameters that define the cohesive failure law. By monitoring the evolution of these sensitivities, the onset and propagation of transverse
cracks can be assessed. It should be noted, however, that in the present study, all
fiber/matrix interfaces are assumed to have the same cohesive properties. The next
steps include relaxing that assumption and deriving individual interface property
sensitivities, i.e., extracting how sensitive the transverse stress is to the critical
stress of individual fibers. With these individual sensitivities, one could study the
sensitivity to the parameters that define the distributions of the interface properties,
e.g., the sensitivity to the average and standard deviation of the interface strength.
Appendix: Sensitivity to Critical Displacement Jumps
For completeness, a summary of the sensitivity formulation with respect to the
critical displacement jumps δ c1 , δ c2 , and δ c3 is included hereafter, starting from
Equation (18) in Sect. 4.
For linearly elastic volumetric elements, again there is no explicit dependence of
the internal force contribution on δ ci and no displacement discontinuity. Therefore,
Equation (18) simply becomes