Volume fraction optimization for minimizing thermal stress in Ni–Al2O3 functionally graded materials

Abstract Functionally graded heat-resisting material, in which the volume fraction of constituents varies continuously and functionally, is investigated for high-temperature engineering applications. In this advanced material, the thermomechanical behavior of FGMs is strongly influenced by the spatial distribution of the volume fraction. So, the determination of volume fraction distribution becomes a crucial part in the FGM design, for a given specification and loading condition. This paper is concerned with the volume fraction optimization for minimizing steady-state thermal stresses in Ni–Al 2 O 3 heat-resisting FGM composites. Interior penalty-function method and golden section method are employed as optimization techniques, together with finite difference method for the sensitivity analysis and an appropriate material-property estimate for calculating thermomechanical properties of the graded layer. The introduced optimization method, through the numerical experiments, is found to provide optimal volume fraction distributions that minimize thermal stresses significantly, as well as the rapid and stable convergence.

[1]  J. Tinsley Oden,et al.  Functionally graded material: A parametric study on thermal-stress characteristics using the Crank-Nicolson-Galerkin scheme , 2000 .

[2]  Viggo Tvergaard,et al.  MICROMECHANICAL MODELS FOR GRADED COMPOSITE MATERIALS , 1997 .

[3]  V. F. Poterasu,et al.  Design of thermoelastic materials using direct sensitivity and optimization methods. Reduction of thermal stresses in functionally gradient materials , 1993 .

[4]  Richard Schapery.  Thermal Expansion Coefficients of Composite Materials Based on Energy Principles , 1968 .

[5]  Garret N. Vanderplaats,et al.  Numerical Optimization Techniques for Engineering Design: With Applications , 1984 .

[6]  Jin-Rae Cho,et al.  Averaging and finite-element discretization approaches in the numerical analysis of functionally graded materials , 2001 .

[7]  Subra Suresh,et al.  Elastoplastic analysis of thermal cycling: layered materials with compositional gradients , 1995 .

[8]  N. Noda,et al.  Steady Thermal Stresses in a Plate of Functionally Gradient Material , 1991 .

[9]  H. Tsukamoto,et al.  Mean-field micromechanics model and its application to the analysis of thermomechanical behaviour of composite materials , 1991 .

[10]  Ryuusuke Kawamura,et al.  Optimization of material composition of nonhomogeneous hollow sphere for thermal stress relaxation making use of neural network , 1999 .

[11]  Mica Grujicic,et al.  Determination of effective elastic properties of functionally graded materials using Voronoi cell finite element method , 1998 .

[12]  Robert J. Asaro,et al.  A micromechanical study of residual stresses in functionally graded materials , 1997 .

[13]  Imao Tamura,et al.  Tensile deformation of two-ductile-phase alloys: Flow curves of α-γ FeCrNi alloys , 1976 .

[14]  K. S. Ravichandran,et al.  Thermal residual stresses in a functionally graded material system , 1995 .