چكيده به لاتين
Most of the engineering materials used in industries are heterogeneous which are typically loaded under various conditions. Since the mechanical behaviors of inhomogeneous materials in macro- scale are related to the microstructure and micro-scale behavior, it is important to develop a model to correlate between the micro-mechanical and macro- mechanical behaviors of the nonhomogeneous materials. In this regard, homogenization models are developed and employed to correlate the micromechanical properties to the mechanical properties at macro-scale. The objective of this research work is to develop a self-consistence homogenization model to predict the effective elastic and non-linear visco-plastic behaviors of an inhomogeneous polycrystal.
Reviewing different homogenization models reported in the literature, in this study, a self-consistent mean field model was considered as a key for broadcasting the specific properties for inhomogeneous materials such as polycrystals. This method is based on continuum mechanics and constitutive equations in which for the numerical calculation of these equations, incremental collocation method was applied by development of a Fortran program. In elastic part, anisotropic localized behavior for copper polycrystal with 2000 random and 938 real orientations in a representive volume element was considered and isotropic specific behavior was evaluated.
Furthermore, elastic and thermoelastic behaviors of virtual dual-phase material under different boundary conditions were calculated by the developed Fortran program and compared the computed results with those obtained by analytical solutions which an excellent agreement was obtained. Also, from the comparison of the anisotropic elastic behavior of copper and α-brass, it has been observed that the more anisotropic intensity cause the occurrence of early-slip systems. In addition, the developed model has been able to analyze the non-linear viscoplastic behavior in cyclic loading and also to predict the dissipation energy because of the hysteresis loop. It has been shown that the dissipation energy has a direct relationship with stress and hardening parameters and indirect relationship with frequency. From computed results, it has been also confirmed that the variations of dissipation energy with stress follows a second-order equation of stress which is in conformity with experimental results. By studying the viscoplastic behavior in different stresses and frequencies, it has been shown that anisotropy causes to lower dissipation energy.
Keywords: Homogenization, Self-consistent, Constitutive equations, Polycrystal, Cyclic loading
