Quantitative damage detection in CFRP composites: coupled mechanical and electrical models

Electrical resistance in carbon-fiber reinforced polymers has been shown experimentally to be a sensitive measure of internal damage. To quantify the dependence of electrical resistance on mechanical fiber damage at the micromechanical level, a numerical electrical resistor network model has been developed. The electrical model is coupled to the fiber damage through a numerical mechanical model, which here is a shear-lag model; the latter informs the electrical model of the locations of broken fibers and the stresses on unbroken sections of fiber. The electrical model accounts for both the longitudinal fiber electrical conductivity and the occasional fiber–fiber contacts that permit electrical coupling of touching fibers. An earlier analytic model based on the global load sharing (GLS) theory is tested against the numerical simulations. Good agreement is found for voltage leads that contact the ends of all fibers in the composite and when the “electrical ineffective length” in the GLS model is related to the density of fiber contacts fc in the numerical model by the relationship View the MathML source where L is the sample gauge length. Voltage leads that contact only surface fibers lead to a resistance behavior that cannot be predicted by the analytic model; this demonstrates the spatial sensitivity of the electrical response to damage and the need for simulation models to correlate local electrical response to local damage. Sensitivity of the electrical response to the voltage lead geometry suggests that the coupled numerical model can be used to design electrode arrays to optimize spatial damage detection inside composite structures.