Engineering topics

Freed, A. D.

Publications and source records attributed to Freed, A. D..

17 records

NASA NTRS2003

Algorithms for the Fractional Calculus: A Selection of Numerical Methods

Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

Diethelm, K.↗

NASA NTRS1999

A Phenomenological Description of Primary Creep in Class M Materials

Observations of creep microstructures in the primary creep region in class M materials show a remarkable similarity with those formed in the exponential creep regime. As a result, it is proposed that the constitutive creep law for normal primary creep is similar to that for the exponential creep regime. A phenomenological description is discussed to rationalize these microstructural observations in terms of a normalized strain rate vs. stress plot. The implications of this plot in describing different testing procedures, steady-state flow, and on the observed deviations from the universal creep law are discussed. The plot is also extended to explain the observed similarities in the transient creep behavior in pre-strained materials and in stress change experiments.

Raj, S. V.↗

NASA NTRS1995

Modeling the Role of Dislocation Substructure During Class M and Exponential Creep

The different substructures that form in the power-law and exponential creep regimes for single phase crystalline materials under various conditions of stress, temperature and strain are reviewed. The microstructure is correlated both qualitatively and quantitatively with power-law and exponential creep as well as with steady state and non-steady state deformation behavior. These observations suggest that creep is influenced by a complex interaction between several elements of the microstructure, such as dislocations, cells and subgrains. The stability of the creep substructure is examined in both of these creep regimes during stress and temperature change experiments. These observations are rationalized on the basis of a phenomenological model, where normal primary creep is interpreted as a series of constant structure exponential creep rate-stress relationships. The implications of this viewpoint on the magnitude of the stress exponent and steady state behavior are discussed. A theory is developed to predict the macroscopic creep behavior of a single phase material using quantitative microstructural data. In this technique the thermally activated deformation mechanisms proposed by dislocation physics are interlinked with a previously developed multiphase, three-dimensional. dislocation substructure creep model. This procedure leads to several coupled differential equations interrelating macroscopic creep plasticity with microstructural evolution.

Raj, S. V.↗

NASA NTRS1994

Algorithms For Integrating Nonlinear Differential Equations

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

Freed, A. D.↗

NASA NTRS1992

Stress versus temperature dependence of activation energies for creep

The activation energy for creep at low stresses and elevated temperatures is associated with lattice diffusion, where the rate controlling mechanism for deformation is dislocation climb. At higher stresses and intermediate temperatures, the rate controlling mechanism changes from dislocation climb to obstacle-controlled dislocation glide. Along with this change in deformation mechanism occurs a change in the activation energy. When the rate controlling mechanism for deformation is obstacle-controlled dislocation glide, it is shown that a temperature-dependent Gibbs free energy does better than a stress-dependent Gibbs free energy in correlating steady-state creep data for both copper and LiF-22mol percent CaF2 hypereutectic salt.

Freed, A. D.↗

NASA NTRS1992

A viscoplastic theory for anisotropic materials

The purpose of this work is the development of a unified, cyclic, viscoplastic model for anisotropic materials. The first part of the paper presents the foundations of the model in the framework of thermodynamics with internal variables. The second part considers the particular case of cubic symmetry, and addresses the cyclic behavior of a nickel-base single-crystal superalloy, CMSX-2, at high temperature (950 C).

Nouailhas, D.↗

NASA NTRS1991

Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equations

New methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist.

Walker, K. P.↗

NASA NTRS1991

A viscoplastic theory with thermodynamic considerations

A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity for initially isotropic materials. Three fundamental, internal, state variables are admitted; they are: a tensorial back stress for kinematic effects, and scalar drag and yield strengths for isotropic effects. All three are considered to evolve phenomenologically according to competitive processes between strain hardening, deformation-induced dynamic recovery, and thermally induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is proposed. The theory allows each of the three internal variables to be composed as a sum of independently evolving constituents. The evolution of internal state can also include terms that vary linearly with the external variable rates, whose presence affects the energy dissipation properties of a material.

Freed, A. D.↗

NASA NTRS1991

A viscoplastic theory with thermodynamic considerations

A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity for initially isotropic materials. Three, fundamental, internal, state variables are admitted; they are: a tensorial back stress for kinematic effects, and scalar drag and yield strengths for isotropic effects. All three are considered to evolve phenomenologically according to competitive processes between strain hardening, deformation induced dynamic recovery, and thermally induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is proposed. The theory allows each of the three internal variables to be composed as a sum of independently evolving constituents. The evolution of internal state can also include terms that vary linearly with the external variable rates, whose presence affects the energy dissipation properties of a material.

Freed, A. D.↗

NASA NTRS1990

Steady-state and transient Zener parameters in viscoplasticity: Drag strength versus yield strength

A hypothesis is put forth which enables the viscoplastician to formulate a theory of viscoplasticity that reduces, in closed form, to the classical theory of creep. This hypothesis is applied to a variety of drag and yield strength models. Because of two theoretical restrictions that are a consequence of this hypothesis, three different yield strength models and one drag strength model are shown to be theoretically admissible. One of these yield strength models is selected as being the most appropriate representation for isotropic hardening.

Freed, A. D.↗

NASA NTRS1990

A viscoplastic model with application to LiF-22 percent CaF2 hypereutectic salt

A viscoplastic model for class M (metal-like behavior) materials is presented. One novel feature is its use of internal variables to change the stress exponent of creep (where n is approximately = 5) to that of natural creep (where n = 3), in accordance with experimental observations. Another feature is the introduction of a coupling in the evolution equations of the kinematic and isotropic internal variables, making thermal recovery of the kinematic variable implicit. These features enable the viscoplastic model to reduce to that of steady-state creep in closed form. In addition, the hardening parameters associated with the two internal state variables (one scalar-valued, the other tensor-valued) are considered to be functions of state, instead of being taken as constant-valued. This feature enables each internal variable to represent a much wider spectrum of internal states for the material. The model is applied to a LiF-22 percent CaF2 hypereutectic salt, which is being considered as a thermal energy storage material for space-based solar dynamic power systems.

Freed, A. D.↗

NASA NTRS1990

Stress versus temperature dependent activation energies in creep

The activation energy for creep at low stresses and elevated temperatures is lattice diffusion, where the rate controlling mechanism for deformation is dislocation climb. At higher stresses and intermediate temperatures, the rate controlling mechanism changes from that of dislocation climb to one of obstacle-controlled dislocation glide. Along with this change, there occurs a change in the activation energy. It is shown that a temperature-dependent Gibbs free energy does a good job of correlating steady-state creep data, while a stress-dependent Gibbs free energy does a less desirable job of correlating the same data. Applications are made to copper and a LiF-22 mol. percent CaF2 hypereutectic salt.

Freed, A. D.↗

NASA NTRS1990

The isothermal fatigue behavior of a unidirectional SiC/Ti composite and the Ti alloy matrix

The high temperature fatigue behavior of a metal matrix composite (MMC) consisting of Ti-15V-3Cr-3Al-3Sn(Ti-15-3) matrix reinforced by 33 volume percent of continuous unidirectional SiC fibers was experimentally and analytically evaluated. Isothermal MMC fatigue tests with constant amplitude loading parallel to the fiber direction were performed at 300 and 550 C. Comparative fatigue tests of the Ti-15-3 matrix alloy were also performed. Composite fatigue behavior and the in situ stress state of the fiber and matrix were analyzed with a micromechanical model, the Concentric Cylinder Model (CCM). The cyclic stress-strain response of the composite was stable at 300 C. However, an increase in cyclic mean strain foreshortened MMC fatigue life at high strain ranges at 550 C. Fatigue tests of the matrix alloy and CCM analyses indicated this response was associated with stress relaxation of the matrix in the composite and subsequent load shedding to the fibers.

Gayda, John↗

NASA NTRS1989

Viscoplasticity: A thermodynamic formulation

A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity, as it applies to initially isotropic materials. Three fundamental internal state variables are admitted. They are: a tensor valued back stress for kinematic effects, and the scalar valued drag and yield strengths for isotropic effects. All three are considered to phenomenologically evolve according to competitive processes between strain hardening, strain induced dynamic recovery, and time induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is put forth. This theory allows each of the three fundamental internal variables to be composed as a sum of independently evolving constituents.

Freed, A. D.↗

NASA NTRS1989

Refinements in a viscoplastic model

A thermodynamically admissible theory of viscoplasticity with two internal variables (a back stress and a drag strength) is presented. Six material functions characterize a specific viscoplastic model. In the pursuit of compromise between accuracy and simplicity, a model is developed that is a hybrid of two existing viscoplastic models. A limited number of applications of the model to Al, Cu, and Ni are presented. A novel implicit integration method is also discussed. Applications are made to obtain solutions using this viscoplastic model.

Freed, A. D.↗

NASA NTRS1988

A theory of viscoplasticity accounting for internal damage

A constitutive theory for use in structural and durability analyses of high temperature isotropic alloys is presented. Constitutive equations based upon a potential function are determined from conditions of stability and physical considerations. The theory is self-consistent; terms are not added in an ad hoc manner. It extends a proven viscoplastic model by introducing the Kachanov-Rabotnov concept of net stress. Material degradation and inelastic deformation are unified; they evolve simultaneously and interactively. Both isotropic hardening and material degradation evolve with dissipated work which is the sum of inelastic work and internal work. Internal work is a continuum measure of the stored free energy resulting from inelastic deformation.

Freed, A. D.↗

NASA NTRS1986

The plastic compressibility of 7075-T651 aluminum-alloy plate

The change in volume, and therefore the change in mass density, of an aluminum alloy was measured in uniaxial tension using clip-on extensometers. The experimental data do not agree with the assumption of plastic incompressibility found in the classical theories of plasticity. In fact, the elastic and plastic volume changes are of the same order of magnitude. Plastic anisotropy is thought to be the prime cause of this plastic compressibility.

Freed, A. D.↗