Constitutive modeling for isotropic materials

The third and fourth years of a 4-year research program, part of the NASA HOST Program, are described. The program goals were: (1) to develop and validate unified constitutive models for isotropic materials, and (2) to demonstrate their usefulness for structural analysis of hot section components of gas turbine engines. The unified models selected for development and evaluation were those of Bodner-Partom and of Walker. The unified approach for elastic-viscoplastic constitutive equations is a viable method for representing and predicting material response characteristics in the range where strain rate and temperature dependent inelastic deformations are experienced. This conclusion is reached by extensive comparison of model calculations against the experimental results of a test program of two high temperature Ni-base alloys, B1900+Hf and Mar-M247, over a wide temperature range for a variety of deformation and thermal histories including uniaxial, multiaxial, and thermomechanical loading paths. The applicability of the Bodner-Partom and the Walker models for structural applications has been demonstrated by implementing these models into the MARC finite element code and by performing a number of analyses including thermomechanical histories on components of hot sections of gas turbine engines and benchmark notch tensile specimens. The results of the 4-year program have been published in four annual reports. The results of the base program are summarized in this report. The tasks covered include: (1) development of material test procedures, (2) thermal history effects, and (3) verification of the constitutive model for an alternative material

A survey of unified constitutive theories

The state of the art of time temperature dependent elastic viscoplastic constitutive theories which are based on the unified approach werre assessed. This class of constitutive theories is characterized by the use of kinetic equations and internal variables with appropriate evolutionary equations for treating all aspects of inelastic deformation including plasticity, creep, and stress relaxation. More than 10 such unified theories which are shown to satisfy the uniqueness and stability criteria imposed by Drucker's postulate and Ponter's inequalities are identified. The theories are compared for the types of flow law, kinetic equation, evolutionary equation of the internal variables, and treatment of temperature dependence. The similarities and differences of these theories are outlined in terms of mathematical formulations and illustrated by comparisons of theoretical calculations with experimental results which include monotonic stress-strain curves, cyclic hysteresis loops, creep and stress relaxation rates, and thermomechanical loops. Numerical methods used for integrating these stiff time temperature dependent constitutive equations are reviewed

Unified constitutive models for high-temperature structural applications

Unified constitutive models are characterized by the use of a single inelastic strain rate term for treating all aspects of inelastic deformation, including plasticity, creep, and stress relaxation under monotonic or cyclic loading. The structure of this class of constitutive theory pertinent for high temperature structural applications is first outlined and discussed. The effectiveness of the unified approach for representing high temperature deformation of Ni-base alloys is then evaluated by extensive comparison of experimental data and predictions of the Bodner-Partom and the Walker models. The use of the unified approach for hot section structural component analyses is demonstrated by applying the Walker model in finite element analyses of a benchmark notch problem and a turbine blade problem

Constitutive modeling for isotropic materials (HOST)

The results of the first year of work on a program to validate unified constitutive models for isotropic materials utilized in high temperature regions of gas turbine engines and to demonstrate their usefulness in computing stress-strain-time-temperature histories in complex three-dimensional structural components. The unified theories combine all inelastic strain-rate components in a single term avoiding, for example, treating plasticity and creep as separate response phenomena. An extensive review of existing unified theories is given and numerical methods for integrating these stiff time-temperature-dependent constitutive equations are discussed. Two particular models, those developed by Bodner and Partom and by Walker, were selected for more detailed development and evaluation against experimental tensile, creep and cyclic strain tests on specimens of a cast nickel base alloy, B19000+Hf. Initial results comparing computed and test results for tensile and cyclic straining for temperature from ambient to 982 C and strain rates from 10(exp-7) 10(exp-3) s(exp-1) are given. Some preliminary date correlations are presented also for highly non-proportional biaxial loading which demonstrate an increase in biaxial cyclic hardening rate over uniaxial or proportional loading conditions. Initial work has begun on the implementation of both constitutive models in the MARC finite element computer code

Constitutive modeling for isotropic materials (HOST)

The results of the third year of work on a program which is part of the NASA Hot Section Technology program (HOST) are presented. The goals of this program are: (1) the development of unified constitutive models for rate dependent isotropic materials; and (2) the demonstration of the use of unified models in structural analyses of hot section components of gas turbine engines. The unified models selected for development and evaluation are those of Bodner-Partom and of Walker. A test procedure was developed for assisting the generation of a data base for the Bodner-Partom model using a relatively small number of specimens. This test procedure involved performing a tensile test at a temperature of interest that involves a succession of strain-rate changes. The results for B1900+Hf indicate that material constants related to hardening and thermal recovery can be obtained on the basis of such a procedure. Strain aging, thermal recovery, and unexpected material variations, however, preluded an accurate determination of the strain-rate sensitivity parameter is this exercise. The effects of casting grain size on the constitutive behavior of B1900+Hf were studied and no particular grain size effect was observed. A systematic procedure was also developed for determining the material constants in the Bodner-Partom model. Both the new test procedure and the method for determining material constants were applied to the alternate material, Mar-M247 . Test data including tensile, creep, cyclic and nonproportional biaxial (tension/torsion) loading were collected. Good correlations were obtained between the Bodner-Partom model and experiments. A literature survey was conducted to assess the effects of thermal history on the constitutive behavior of metals. Thermal history effects are expected to be present at temperature regimes where strain aging and change of microstructure are important. Possible modifications to the Bodner-Partom model to account for these effects are outlined. The use of a unified constitutive model for hot section component analyses was demonstrated by applying the Walker model and the MARC finite-element code to a B1900+Hf airfoil problem

What Does it Mean to Design? A Qualitative Investigation of Design Professionals' Experiences

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95041/1/j.2168-9830.2012.tb00048.x.pd

Nonlinear elastic-viscoplastic constitutive equations for aging facial tissues

This paper reports on the initial stages of a project to simulate the nonlinear mechanical behavior of an aging human face. A cross-section of the facial structure is considered to consist of a multilayered composite of tissues with differing mechanical behavior. The constitutive properties of these tissues are incorporated into a finite element model of the three-dimensional facial geometry. Relatively short time (elastic-viscoplastic) behavior is governed by equations previously developed which are consistent with mechanical tests. The long time response is controlled by the aging elastic components of the tissues. An aging function is introduced which, in a simplified manner, captures the observed loss of stiffness of these aging elastic components due to the history of straining as well as other physiological and environmental influences. Calculations have been performed for 30years of exposure to gravitational forces. Progressive gravimetric soft tissue descent is simulated, which is regarded as the main indication of facial aging. Results are presented for the deformations and stress distributions in the layers of the soft tissue

Gauging the Heisenberg algebra of special quaternionic manifolds

We show that in N=2 supergravity, with a special quaternionic manifold of (quaternionic) dimension h_1+1 and in the presence of h_2 vector multiplets, a h_2+1 dimensional abelian algebra, intersecting the 2h_1+3 dimensional Heisenberg algebra of quaternionic isometries, can be gauged provided the h_2+1 symplectic charge--vectors V_I, have vanishing symplectic invariant scalar product V_I X V_J=0. For compactifications on Calabi--Yau three--folds with Hodge numbers (h_1,h_2) such condition generalizes the half--flatness condition as used in the recent literature. We also discuss non--abelian extensions of the above gaugings and their consistency conditions.Comment: 9 pages, LaTe

N=2 Supersymmetric Scalar-Tensor Couplings

We determine the general coupling of a system of scalars and antisymmetric tensors, with at most two derivatives and undeformed gauge transformations, for both rigid and local N=2 supersymmetry in four-dimensional spacetime. Our results cover interactions of hyper, tensor and double-tensor multiplets and apply among others to Calabi-Yau threefold compactifications of Type II supergravities. As an example, we give the complete Lagrangian and supersymmetry transformation rules of the double-tensor multiplet dual to the universal hypermultiplet.Comment: 23 pages, LaTeX2e with amsmath.sty; v2: corrected typos and added referenc