Issue 33

C. Gao et alii, Frattura ed Integrità Strutturale, 33 (2015) 471-484; DOI: 10.3221/IGF-ESIS.33.52 472 their full strengthening potential. However, agglomeration and imperfect interfacial load transfer of CNTs still often exist in these composites. To facilitate the applications of CNT-reinforced metal matrix nanocomposites, it is essential to develop a reliable micromechanical constitutive model that can be used to describe and predict their mechanical properties. Some modeling efforts have been made to describe the mechanical properties of the CNT-reinforced nanocomposites. Courtney [13] established a classic model for short-fiber-reinforced plastic-matrix composites by introducing the effect of the aspect ratio into the basic role-of-mixture model, which can be applicable to CNT-reinforced nanocomposites. Based on the generalized shear-lag model [14] for metal matrix composites with reinforcement in cylindrical forms, Kim et al. [11] proposed a strength model to describe a two-stage yielding process in the experimental stress–strain curves of the CNT/Cu nanocomposites, and also observed elongated CNT clusters in the microstructure of the composite. Barai and Weng [15] developed a two-scale micromechanical model to make a pioneering analysis of the effect of CNT agglomeration and interface condition on the strength of CNT-reinforced MMNCs. Obviously, it is inevitable that a lot of CNT agglomerations in metallic matrix materials will appear because of easy entanglement of CNTs, especially for those with the high aspect ratio, as observed in [16-18]. Although there are also some other models proposed for CNT-reinforced polymers matrix nanocomposites [1, 3, 19, 20], a model with consideration of clustering phenomenon is still lacking. To describe the flow stress and estimate the plastic strength of CNT-reinforced metal matrix composites, a new micromechanical constitutive model, with consideration of the effect of CNT clusters and the influence of CNT misorientation angle, will be proposed in this paper. In the "Modelling of CNT-reinforced MMNCs" section, the cluster effect is introduced into the new model by using the statistically average equivalent length and diameter of CNTs, and the misorientation angle effect is reflected by a definition of an effective load transfer coefficient. In the next section, the model parameters are determined for the CNT/Al nanocomposite by a nonlinear multi-variable global optimization method, i.e., generic algorithm. In the "Results and discussion" section, the new model is experimentally validated, and some important predictions of the model are given and discussed. M ODELLING OF CNT- REINFORCED MMNC S acroscopically, the CNT reinforced metal matrix nanocomposite is deformed homogeneously, in which the metal matrix is plastic and the CNT fiber is elastic. The MMNCs derive their plasticity from the good plastic behavior of the metallic matrix materials. The flow stress of CNT-reinforced MMNCs during the elastoplastic deformation process can be generally expressed below with the classical rule of mixtures as widely used for two-phase composites [20]:   1 c f f f m         (1) where c  the flow stress of nanocomposites is, f  is the stress of CNTs at composite failure, m  is the flow stress of the pure matrix material. f v denotes the volume fraction of CNTs. For MMNCs reinforced with discontinuous CNTs, the applied load transfers from the matrix to CNTs along the CNT– matrix interface by the way of shear stress, and interfacial bonding significantly affects the strength of the composite. In order to load high-strength fibers to their maximum strength, the metallic matrix will flow plastically in response to the high shear stress developed. Plastic deformation of a matrix implies that the shear stress at the interface will never go above the matrix shear yield strength. In such a case, the following equation can be derived on a perfect bonding interface based on the equilibrium of forces [13]: 2 4 2 fm i y D lD      (2) where i y  is the shear yield strength of the interface and  fm is the maximum stress in CNTs, l and D are the average length and diameter of primary CNTs, respectively. It can be seen that the maximum stress in CNTs varies with the length of CNTs. If a carbon nanotube is sufficiently long, it should be possible to load the CNT to its breaking stress, fm fb    , by means of load transfer through the metallic matrix flowing plastically around it. That is to say, there exists a critical M