"HOTCFGM-1D" denotes a collection of four computer programs, plus the underlying theory, for calculating thermomechanical and inertial effects in axisymmetric cylindrical multiphase-composite-material objects that are functionally graded along their radial coordinates. The theory and programs are valid for the special case in which a thin cylindrical structural component is subject to macroscopically axisymmetric thermal and thermomechanical and inertial loads applied uniformly along its cylindrical axes.

The term "functionally graded" characterizes a class of materials, the microstructures of which are spatially graded to achieve specific thermal and/or mechanical properties. In the case of a multiphase composite material, functional grading can be effected by use of spatially variable spacing between individual fibers or other inclusions (see figure) and/or by use of inclusions of different properties, sizes, and shapes.

In the Geometric Model of HOTCFGM-1D, reinforcing phases are uniformly distributed in the axial and circumferential directions but arbitrarily distributed (for functional grading) in the radial direction. In this example, the reinforcing phases are axial fibers; in other examples, they could be circumferential fibers or discontinuous inclusions.

The "1D" in "HOTCFGM-1D" refers to the fact that the theory is a quasi-one-dimensional version of a more-general higher-order theory, currently under development. The one-dimensionality is a consequence of the shapes of objects and symmetry of loading conditions described above. One aspect of this one-dimensionality is that the overall deformation of an object is characterized by a constant average axial stress and strain.

The one-dimensional higher-order theory was developed for use in the analysis, optimization, and design of axisymmetric cylindrical components of aircraft engines (e.g., combustor linings, rotor disks, and heat shields). The theory will enable designers to use functional grading to enhance the performances (e.g., deformation characteristics, resistances to thermal fatigue, and service lives) of such components. In the theory, coupling between microstructural and macrostructural effects in cylindrical bodies of revolution is explicitly taken into account for the sake of accuracy; in contrast, functionally graded objects cannot be analyzed accurately by following the older standard micromechanics approach based on the concept of representative volume-element mathematical models coupled with macrostructural-analysis models in a noninteractive manner.

The quasi-one-dimensional version of the theory includes representations of inertial body forces to account for effects of rotation. The theory also accounts for externally applied loads and radial temperature gradients. Applied loads and other boundary conditions can be in the form of temperatures imposed on the inner and outer surfaces, radial pressures, and/or radial displacements. The theory and computer programs can readily be modified by incorporation of constitutive theories of inelastic responses and of damage in constituent materials under nonisothermal conditions. At present, the computer programs include subprograms that implement the classical incremental theory of plasticity and the generalized viscoplasticity with potential structure (GVIPS) unified viscoplasticity theory. Three of the computer programs, called "fgmp.tube.f," "fgmp.homog.tube.f," and "fgm.gvips.tube.f," are research-oriented codes for investigating the effects of (1) functional gradings and (2) properties of multiphase reinforcements upon the temperature, stress, and inelastic strain field in thin shells subjected to axisymmetric thermomechanical and inertial loads. The user specifies the radial distribution of reinforcing material. The thermoelastic and inelastic properties of the individual phases can vary with temperature. The elastic phases can be isotropic; alternatively, they can be transversely isotropic with radial, circumferential, or longitudinal axes of symmetry. The inelastic phases can be modeled either by classical plasticity theory in fgmp.tube.f or GVIPS unified viscoplasticity theory in fgm.gvips.tube.f. A homogenization capability within fgmp.homog.tube.f admits the inclusion of heterogeneous phases.

The fourth computer program, called "fgmp.tube.opt.f," combines a major analysis module from fgmp.tube.f with a commercial optimization code called "DOT." The total optimization software package enables the user to identify radial distributions of reinforcing phases that minimize or maximize objective functions defined by the user; examples of such functions include internal moments or plastic strains.

This work was done by Marek-Jerzy Pindera of the University of Virginia and Jacob Aboudi of Tel-Aviv University for Lewis Research Center. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com under the Physical Sciences category. Inquiries concerning rights for the commercial use of this invention should be addressed to

NASA Lewis Research Center, Commercial Technology Office, Attn:Tech Brief Patent Status, Mail Stop 7-3, 21000 Brookpark Road, Cleveland, Ohio 44135.

Refer to LEW-16753.

NASA Tech Briefs Magazine

This article first appeared in the April, 1999 issue of NASA Tech Briefs Magazine.

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