A micromechanical study of residual stresses in functionally graded materials

A physically based computational micromechanics model is developed to study random and discrete microstructures in functionally graded materials (FGMs). The influences of discrete microstructure on residual stress distributions at grain size level are examined with respect to material gradient and FGM volume percentage (within a ceramic-FGM-metal three-layer structure). Both thermoelastic and thermoplastic deformation are considered, and the plastic behavior of metal grains is modeled at the single crystal level using crystal plasticity theory. The results are compared with those obtained using a continuous model which does not consider the microstructural randomness and discreteness. In an averaged sense both the micromechanics model and the continuous model give practically the same macroscopic stresses; whereas the discrete micromechanics model predicts fairly high residual stress concentrations at the grain size level (i.e., higher than 700 MPa in 5-6 vol% FGM grains) with only a 300 degrees C temperature drop in a Ni-Al2O3 FGM system. Statistical analysis shows that the residual stress concentrations are insensitive to material gradient and FGM volume percentage. The need to consider microstructural details in FGM microstructures is evident. The results obtained provide some insights for improving the reliability of FGMs against fracture and delamination. (C) 1997 Acta Metallurgica Inc.