Modeling and analysis of interphase damage in carbon nanotube reinforced materials and structures
Final Report Abstract
The main goals of the project were elaboration of a new approach to modeling and homogenization of random Carbon NanoTube reinforced materials (CNTRMs) and to demonstrate the effectiveness of that approach in its application to analysis of stress/strain fields in composite structural elements. In the proposed model Carbon NanoTubes (CNTs) are assumed to be dispersed within the matrix material in a prescribed random manner. Microstructure of the material is described by probability functions specifying volume fraction of CNTs, their orientations, dimensions and other relevant parameters. From mechanics viewpoint, CNTs were modeled as hollow cylindrical nanoinhomogeneities of finite length, with a graphene layer considered as a Gurtin-Murdoch (GM) material surface. The CNT/matrix interphases can be described using the spring layer model. Mathematically, the homogenization problem was solved by Energy Equivalent Inhomogeneity (EEI) approach in conjunction with the Method of Conditional Moments (MCM). The basic idea of the EEI is to replace the inhomogeneity and the surrounding its interphase by a single equivalent inhomogeneity, combining properties of both, which is then perfectly boned to the matrix. EEI was developed and verified for spherical inhomogeneities with GM and spring layer models of interphases and then it was extended for the case of cylindrical inhomogeneity of finite length with GM and spring layer interphases. That makes it possible to model the CNT as a high-stiffness surface described by GM model and then the CNT/matrix interphase described by spring layer model was introduced using the concept of energy equivalence hierarchically one more time. This leads to the final solid equivalent cylinder combining properties of the CNT and of its interphase. The MCM was used in evaluation of the governing equations to extract closed-form expressions for effective elastic moduli (size-dependent) of CNTRMs. Several specific materials were analyzed, their effective properties determined and comparisons with the existing theoretical and experimental results were made. As an illustration, the proposed model was used in the FEM analysis to predict the behavior of composite structures whose geometry and loading are relevant to applications. A plate with a central circular hole subjected to an in-pane loading was investigated. It was demonstrated how variations of spatial distribution of CNTs change the structural behavior and how it may be beneficial in optimal design of those structures. The main goal of the extension project was to develop a method of evaluating the overall nonlinear behavior of CNTRMs associated with damage of matrix/inhomogeneity interphases. In the model the interphases was represented by layers of springs whose stiffness parameters change as a result of damage associated with gradually increasing loading. Consequently, due to local degradation of the interphase, variation of these parameters over the inhomogeneity surface becomes progressively non-uniform. This, in turn, causes the effective properties of the composite to become increasingly anisotropic even in the case of spherical inhomogeneities. To describe the effects of interphase damage on the overall properties of the composite three ideas were utilized. One is the MCM, a statistical homogenization technique developed in the past and extended in the project to analyze the effective properties of random composites with orthotropic components. The second idea was the notion of EEI, developed in the first project for linear problems with interphases and extended for the case of surface-varying interphase. The most important and novel was the third idea concerning the statistical interphase damage model. In the proposed approach local microdamage of interphases is modeled by an increasing fraction of randomly distributed destructed springs in the spring layers surrounding the inhomogeneities of the composite. The model assumes that the local interphase micro-strength at the points located on the surface of different inhomogeneities and specified by the same spherical coordinates is described by one-point Weibull distribution function. In view of the strong nonlinearity of the problem, an incremental/iterative scheme was used in practical evaluation of effective properties. Interphase damage model was evaluated for composites with randomly distributed spherical inhomogeneities under interphase damage. These results could be used for investigation of interphase damage in CNTRM with randomly distributed and randomly oriented CNTs in approximate manner.
Publications
- 2016. Effective properties of short-fiber composites with Gurtin-Murdoch model of interphase. Int. J. Solids Struct., 97-98, 75-88
Nazarenko L, Stolarski H, Altenbach H
(See online at https://doi.org/10.1016/j.ijsolstr.2016.07.041) - 2016. Energy-based definition of equivalent inhomogeneity for various interphase models and analysis of effective properties of particulate composites. Comp. Part B., 94, 82–94
Nazarenko L, Stolarski H
(See online at https://doi.org/10.1016/j.compositesb.2016.03.015) - 2017. A model of cylindrical inhomogeneity with spring layer interphase and its application to analysis of short-fiber composites. Comp. Struct. 160, 635-652
Nazarenko L, Stolarski H, Altenbach H
(See online at https://doi.org/10.1016/j.compstruct.2016.10.024) - 2017. Thermo-elastic properties of random particulate nano-materials for various models of interphase. Int. J. Mech. Sci., 126, 130-141
Nazarenko L, Stolarski H, Altenbach H
(See online at https://doi.org/10.1016/j.ijmecsci.2017.03.021) - 2018. Effective properties of particulate composites with surface-varying interphases. Comp. Part B., 149, 268–284
Nazarenko L, Stolarski H, Altenbach H
(See online at https://doi.org/10.1016/j.compositesb.2018.05.002) - 2018. Effective thermo-elastic properties of random composites with orthotropic components and aligned ellipsoidal inhomogeneities. Int. J. Solids Struct., 136-137, 220-240
Nazarenko L, Stolarski H, Altenbach H
(See online at https://doi.org/10.1016/j.ijsolstr.2017.12.016) - 2018. On Modeling and Analysis of Effective Properties of Carbon Nanotubes Reinforced Materials. Comp. Struct., 189, 718-727
Nazarenko L, Stolarski H, Altenbach H
(See online at https://doi.org/10.1016/j.compstruct.2018.01.027) - 2018. Thermo-elastic properties of random composites with unidirectional anisotropic short-fibers and interphases. Eur. J. Mech. / A Solids, 70, 249-266
Nazarenko L, Stolarski H, Altenbach H
(See online at https://doi.org/10.1016/j.euromechsol.2018.01.002) - 2019. A statistical interphase damage model of random particulate composites. Int. J. Plasticity, 116, 118-142
Nazarenko L, Stolarski H, Altenbach H
(See online at https://doi.org/10.1016/j.ijplas.2018.12.011) - 2019. On modeling of carbon nanotubes reinforced materials and on influence of carbon nanotubes spatial distribution on mechanical behavior of structural elements. Int. J. Engin. Sci., 143, 1-13
Nazarenko L, Chirkov AYu, Stolarski H, Altenbach H
(See online at https://doi.org/10.1016/j.ijengsci.2019.06.008)
