Modeling of mechanical damage detection in CFRPs via electrical resistance

Carbon fiber reinforced polymer composites (CFRPs) are inherently multifunctional materials that, in addition to their primary function as a structural material, allow for the sensing and monitoring of in situ damage nucleation and evolution by the measurement of the material electrical resistance. Here an analytic model is developed for the transverse (perpendicular to the fibers) electrical resistance of pristine and damaged unidirectional composites, complementing earlier work on the longitudinal resistance. The ratio of transverse to longitudinal resistance for undamaged materials provides a direct measure of the internal density of fiber-fiber electrical contacts, a key material parameter in linking to the response of damaged materials. Under uniaxial loading with evolving fiber breakage, the normalized transverse resistance versus strain is predicted to have exactly the same form as that for the longitudinal resistance. Numerical studies show this agreement for uniform fiber-fiber contact distributions but, for random contact distributions, the longitudinal resistance is larger than predicted while the transverse resistance is smaller; these differences are shown to arise as a result of the statistically-preferential breaking of longer fiber segments. Analysis of multiple numerical simulations shows that variations in the electrical resistance are not directly correlated with variations in the stress-strain response. Thus, statistical methods are required to relate resistance to strain or damage. The Weibull modulus of the resistance change increases with increasing applied strain, with values exceeding 10 and 20 for the transverse and longitudinal resistance, respectively, demonstrating increasing reliability at higher damage levels and good correlation of average resistance change to applied strain. The present study shows that both longitudinal and transverse resistance changes are sensitive to damage in a predictable manner and can be used together to improve the reliability of damage assessment during loading of CFRPs. (c) 2006 Elsevier Ltd. All rights reserved.