Study of Ultra High Temperature Fracture of Functionally Graded Material by Neural Network

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Composite material has a complicated microscopic material constituent, where the material inhomogeneity generates a high stress concentration at the interface. Nonlinear phenomena, therefore, such as plastic flow, delamination, cracking, damage, etc. might occur in the micromechanical area. When the volume fraction of the inclusions is high, the interaction between the inclusions promotes the phenomena, which would reflect to the macromechanical performance of the composite. In this research, the objective is set to the thorough investigation of the micromechanical phenomenon, upon which the most reliable constitutive mode is developed over the nonlinear loading range of composite materials including a functionally graded material (FGM). The effort of this work is focused on the three subjects : a mesomechanics analysis by a finite element method and neural network generalization ; application of homogenization method to the meso-domain of the composite, and a theoretical development o … More f the constitutive law by using equivalent inclusion method.(1) A neural network procedure was developed to computationally build a constitutive law for nonlinear composite materials. A particle dispersed composite pattern was modeled by the finite element method, generating discrete nonlinear tensile data with a temperature and a volume fraction as parameters. The data were fed to the neural network to optimize the network parameters for the thermo-mechanical constitutive behavior of the composite. Although this method requires the preparation of the instructive data, it provides a fast process for nonlinear composites even for the varying volume fraction such as in the FGM.An application was made to the fracture evaluation of the thermally shocked FGM plate with an edge crack that dynamically propagates in the graded medium. The procedure uses fuzzy inference technique at the intermediate grade to average the neuro-deduced material characteristics of the ceramics base and the metal base.(2) The homogenization method is most suited to computationally describe the constitutive tensor for arbitrary composite patterns. In the present, the development of the constitutive law was attempted for the particle dispersed composite where the matrix locally undergoes a plastic deformation or a damage, which is caused by the stress interaction between particles. An advatage of this method is in that the micromechanical phenomena can be monitored as well as the macromechanical characteristic is obtained. However, the computational process takes too much time, especially for the nonlinear problem, for practical use.(3) The reason for the development of the above two method is to circumvent the difficulty of totally theoretical development of the constitutive model for the nonlinear composite. However, an attempt was made to build a constitutive model for a composite with ellipsoidal inclusions. The most of the existing models use Mori-Tanaka's mean field theory, but the applicability of the model is limited to a narrow band of the material rigidity ratio of the matrix and the inclusion, and to the low volume fraction. On the other hand, the present model is valid and has a good accuracy over the entire range of the rigidity ratio and the volume fraction. Also the developed model was expanded to the elastoplastic regime by using a stochastic approach to the distributed plastictiy. The model was applied to a thermal shock fracture problem of the functionally graded material. Another application was made to the phase transforming problem, and showed the significance of the mixing law in the constitutive modeling for the shape memory alloy and the plasticity induced phase transformation phenomena. Less