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NASA NTRS1976

Plastic deformation of polycrystalline zirconium carbide

The compressive yield strength of arc-melted polycrystalline zirconium carbide has been found to vary from 77 kg per sq mm at 1200 C to 19 kg per sq mm at 1800 C. Yield drops were observed with plastic strain-rates greater than 0.003/sec but not with slower strain rates. Strain-rate change experiments yielded values for the strain-rate sensitivity parameter m which range from 6.5 at 1500 C to 3.8 at 1800 C, and the product dislocation velocity stress exponent times T was found to decrease linearly with increasing temperature. The deformation rate results are consistent with the Kelly-Rowcliffe model in which the diffusion of carbon assists the motion of dislocations.

Darolia, R.↗

NASA NTRS1988

Alterations in crack-tip deformation during variable-amplitude fatigue crack growth

Fatigue crack growth rate changes caused by single overloads and an overload followed by an underload have been studied in the high-strength aluminum alloy 7091. Crack-tip plasticity parameters were measured at each step in the loading sequence using the stereoimaging technique. Effective stress-intensity factor was measured with high resolution immediately at the crack tip both before an overload and during the subsequent growth rate retardation period. Crack-tip opening displacement and strain were altered in the same way as growth rate following the overload/underload events, and similitude with respect to crack-tip plasticity was preserved during the growth retardation period. Effective stress-intensity factor was found to correlate well with crack growth rate. Strains within the plastic zone were converted to stress at each step in load change. These stresses were then summed to determine the zone of residual stress caused by the overload. The region of compressive residual stress ahead of the crack tip was found to increase with overload severity but was limited to yield stress in magnitude. An underload shrank the spatial extent of the residual stresses caused by the overload.

Davidson, David L.↗

NASA NTRS1983

Effect of swaging on the 1000 C compressive slow plastic flow characteristics of the directionally solidified eutectic alloy gamma/gamma prime-alpha

Swaging between 750 and 1050 C has been investigated as a means to introduce work into the directionally solidified eutectic alloy gamma/gamma prime-alpha (Ni-32.3 wt percent Mo-6.3 wt percent Al) and increase the elevated temperature creep strength. The 1000 C slow plastic compressive flow stress-strain rate properties in air of as-grown, annealed, and worked nominally 10 and 25 percent materials have been determined. Swaging did not improve the slow plastic behavior. In fact large reductions tended to degrade the strength and produced a change in the deformation mechanism from uniform flow to one involving intense slip band formation. Comparison of 1000 C tensile and compressive strength-strain rate data reveals that deformation is independent of the stress state.

Whittenberger, J. D.↗

NASA NTRS1986

High temperature monotonic and cyclic deformation in a directionally solidified nickel-base superalloy

Directionally solidified (DS) MAR-M246+Hf was tested in tension and fatigue, at temperatures from 20 C to 1093 C. Tests were performed on (001) oriented specimens at strain rates of 50 % and 0.5 % per minute. In tension, the yield strength was constant up to 704 C, above which the strength dropped off rapidly. A strong dependence of strength on strain rate was seen at the higher temperatures. The deformation mode was observed to change from heterogeneous to homogeneous with increasing temperature. Low Cycle Fatigue tests were done using a fully reversed waveform and total strain control. For a given plastic strain range, lives increased with increasing temperature. For a given temperature strain rate had a strong effect on life. At 704 C, decreasing strain rates decreased life, while at the higher temperatures, decreasing strain rates increased life, for a given plastic strain range. These results could be explained through considerations of the deformation modes and stress levels. At the higher temperatures, marked coarsening caused beneficial stress reductions, but oxidation limited the life. The longitudinal grain boundaries were found to influence slip behavior. The degree of secondary slip adjacent to the boundaries was found to be related to the degree of misorientation between the grains.

Huron, Eric S.↗

NASA NTRS1996

Verification of Experimental Techniques for Flow Surface Determination

The concept of a yield surface is central to the mathematical formulation of a classical plasticity theory. However, at elevated temperatures, material response can be highly time-dependent, which is beyond the realm of classical plasticity. Viscoplastic theories have been developed for just such conditions. In viscoplastic theories, the flow law is given in terms of inelastic strain rate rather than the inelastic strain increment used in time-independent plasticity. Thus, surfaces of constant inelastic strain rate or flow surfaces are to viscoplastic theories what yield surfaces are to classical plasticity. The purpose of the work reported herein was to validate experimental procedures for determining flow surfaces at elevated temperatures. Since experimental procedures for determining yield surfaces in axial/torsional stress space are well established, they were employed -- except inelastic strain rates were used rather than total inelastic strains. In yield-surface determinations, the use of small-offset definitions of yield minimizes the change of material state and allows multiple loadings to be applied to a single specimen. The key to the experiments reported here was precise, decoupled measurement of axial and torsional strain. With this requirement in mind, the performance of a high-temperature multi-axial extensometer was evaluated by comparing its results with strain gauge results at room temperature. Both the extensometer and strain gauges gave nearly identical yield surfaces (both initial and subsequent) for type 316 stainless steel (316 SS). The extensometer also successfully determined flow surfaces for 316 SS at 650 C. Furthermore, to judge the applicability of the technique for composite materials, yield surfaces were determined for unidirectional tungsten/Kanthal (Fe-Cr-Al).

Lissenden, Cliff J.↗

NASA NTRS2010

Phase Transformation and Creep Behavior in Ti50Pd30Ni20 High Temperature Shape Memory Alloy in Compression

The creep behavior and the phase transformation of Ti50Pd30Ni20 High Temperature Shape Memory Alloy (HTSMA) is investigated by standard creep tests and thermomechanical tests. Ingots of the alloy are induction melted, extruded at high temperature, from which cylindrical specimens are cut and surface polished. A custom high temperature test setup is assembled to conduct the thermomechanical tests. Following preliminary monotonic tests, standard creep tests and thermally induced phase transformation tests are conducted on the specimen. The creep test results suggest that over the operating temperatures and stresses of this alloy, the microstructural mechanisms responsible for creep change. At lower stresses and temperatures, the primary creep mechanism is a mixture of dislocation glide and dislocation creep. As the stress and temperature increase, the mechanism shifts to predominantly dislocation creep. If the operational stress or temperature is raised even further, the mechanism shifts to diffusion creep. The thermally induced phase transformation tests show that actuator performance can be affected by rate independent irrecoverable strain (transformation induced plasticity + retained martensite) as well as creep. The rate of heating and cooling can adversely impact the actuators performance. While the rate independent irrecoverable strain is readily apparent early in the actuators life, viscoplastic strain continues to accumulate over the lifespan of the HTSMA. Thus, in order to get full actuation out of the HTSMA, the heating and cooling rates must be sufficiently high enough to avoid creep.

Kumar, Parikshith K.↗

NASA NTRS1985

On numerical integration and computer implementation of viscoplastic models

Due to the stringent design requirement for aerospace or nuclear structural components, considerable research interests have been generated on the development of constitutive models for representing the inelastic behavior of metals at elevated temperatures. In particular, a class of unified theories (or viscoplastic constitutive models) have been proposed to simulate material responses such as cyclic plasticity, rate sensitivity, creep deformations, strain hardening or softening, etc. This approach differs from the conventional creep and plasticity theory in that both the creep and plastic deformations are treated as unified time-dependent quantities. Although most of viscoplastic models give better material behavior representation, the associated constitutive differential equations have stiff regimes which present numerical difficulties in time-dependent analysis. In this connection, appropriate solution algorithm must be developed for viscoplastic analysis via finite element method.

Chang, T. Y.↗

NASA NTRS2004

Slip Analysis in a Ni-base Superalloy

A Ni-base superalloy single crystal with Gamma/Gamma' structure was tested at room temperature along the , <110> and <111> directions. Consistent with previously reported investigations, this alloy did not obey the Schmid law and the CRSS (critical resolved shear stress) was noticeably lower for the <111>-oriented samples. Furthermore, the strain hardening rate decreased and the degree of deformation localization increased in the order of <111>, and <110> orientations. The appearance and orientation of deformation traces were found to depend on the loading orientation as well as the amount of strain. In general, when Gamma'-particles were sheared, the traces followed the expected octahedral shear planes. It is demonstrated that the wavy deformation traces that do not follow the {111} planes are associated with changes in the gamma-channels width and the falling off of the gamma-particles. In this paper the evolution of deformation bands are discussed in terms of plastic localization at microscopic, mesoscopic and macroscopic levels.

Westbrooke, Eboni F.↗

NASA NTRS1990

Elevated temperature crack growth in aluminum alloys: Tensile deformation of 2618 and FVS0812 aluminum alloys

Understanding the damage tolerance of aluminum alloys at elevated temperatures is essential for safe applications of advanced materials. The objective of this project is to investigate the time dependent subcritical cracking behavior of powder metallurgy FVS0812 and ingot metallurgy 2618 aluminum alloys at elevated temperatures. The fracture mechanics approach was applied. Sidegrooved compact tension specimens were tested at 175, 250, and 316 C under constant load. Subcritical crack growth occurred in each alloy at applied stress intensity levels (K) of between about 14 and 25 MPa/m, well below K (sub IC). Measured load, crack opening displacement and displacement rate, and crack length and growth rate (da/dt) were analyzed with several continuum fracture parameters including, the C-integral, C (sub t), and K. Elevated temperature growth rate data suggest that K is a controlling parameter during time dependent cracking. For FVS0812, da/dt is highest at 175 C when rates are expressed as a function of K. While crack growth rate is not controlled by C (sub t) at 175 C, da/dt appears to better correlate with C (sub t) at higher temperatures. Creep brittle cracking at intermediate temperatures, and perhaps related to strain aging, is augmented by time dependent transient creep plasticity at higher temperatures. The C (sub t) analysis is, however, complicated by the necessity to measure small differences in the elastic crack growth and creep contributions to the crack opening displacement rate. A microstructural study indicates that 2618 and FVS0812 are likely to be creep brittle materials, consistent with the results obtained from the fracture mechanics study. Time dependent crack growth of 2618 at 175 C is characterized by mixed transgranular and intergranular fracture. Delamination along the ribbon powder particle boundaries occurs in FVS0812 at all temperatures. The fracture mode of FVS0812 changes with temperature. At 175 C, it is characterized as dimpled rupture, and at 316 C as mixed matrix superplastic rupture and matrix-dipersoid debonding.

Leng, Yang↗

NASA NTRS1988

The influence of grain size and composition on 1000 to 1400 K slow plastic flow properties of NiAl

The compressive slow plastic flow behavior of several B2 crystal structure NiAl intermetallics has been studied in air between 1000 and 1400 K. Small grain-sized Ni-48.25 at. pct Al (of about 10 microns) was found to be stronger than the previously studied 17 microns diameter material. While grain refinement improved the strength at all test temperatures, the exact mechanism is not clear. Experiments at lower temperature revealed that composition as well as grain size can be an important factor, since Ni-49.2Al was weaker than Ni-48.25Al. Pronounced yield points were found during slow strain-rate testing at 1000 K; however, continued deformation appears to take place by the same mechanism(s) as found at high temperatures. Small changes in thermomechanical processing (TMP) schedules to fabricate Ni-49.2Al indicated that basic deformation characteristics (stress exponent and activation energy) are not affected; however, the preexponential term could be modified if TMP alters the grain structure.

Whittenberger, J. Daniel↗

NASA NTRS1974

Finite elasto-plastic deformation. I - Theory and numerical examples

It is demonstrated that the problem of elasto-plastic finite deformation is governed by a quasi-linear model irrespective of deformation magnitude. This feature follows from the adoption of a rate viewpoint toward finite deformation analysis in an Eulerian reference frame. Objectivity of the formulation is preserved by introduction of a frame-invariant stress rate. Equations for piece-wise linear incremental finite element analysis are developed by application of the Galerkin method to the instantaneously linear governing differential equations of the quasi-linear model. Numerical solution capability has been established for problems of plane strain and plane stress. The accuracy of the numerical analysis is demonstrated by consideration of a number of problems of homogeneous finite deformation admitting comparative analytic solution. It is shown that accurate, objective numerical solutions can be obtained for problems involving dimensional changes of an order of magnitude and rotations of a full radian.

Osias, J. R.↗

NASA NTRS1994

Fracture mechanics validity limits

Fracture behavior is characteristics of a dramatic loss of strength compared to elastic deformation behavior. Fracture parameters have been developed and exhibit a range within which each is valid for predicting growth. Each is limited by the assumptions made in its development: all are defined within a specific context. For example, the stress intensity parameters, K, and the crack driving force, G, are derived using an assumption of linear elasticity. To use K or G, the zone of plasticity must be small as compared to the physical dimensions of the object being loaded. This insures an elastic response, and in this context, K and G will work well. Rice's J-integral has been used beyond the limits imposed on K and G. J requires an assumption of nonlinear elasticity, which is not characteristic of real material behavior, but is thought to be a reasonable approximation if unloading is kept to a minimum. As well, the constraint cannot change dramatically (typically, the crack extension is limited to ten-percent of the initial remaining ligament length). Rice, et al investigated the properties required of J-type parameters, J(sub x), and showed that the time rate, dJ(sub x)/dt, must not be a function of the crack extension rate, da/dt. Ernst devised the modified-J parameter, J(sub M), that meets this criterion. J(sub M) correlates fracture data to much higher crack growth than does J. Ultimately, a limit of the validity of J(sub M) is anticipated, and this has been estimated to be at a crack extension of about 40-percent of the initial remaining ligament length. None of the various parameters can be expected to describe fracture in an environment of gross plasticity, in which case the process is better described by deformation parameters, e.g., stress and strain. In the current study, various schemes to identify the onset of the plasticity-dominated behavior, i.e., the end of fracture mechanics validity, are presented. Each validity limit parameter is developed in detail, and then data is presented and the various schemes for establishing a limit of the validity are compared. The selected limiting parameter is applied to a set of fracture data showing the improvement of correlation gained.

Lambert, Dennis M.↗

NASA NTRS1987

Nonisothermal elasto-visco-plastic response of shell-type structures

A mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads is disussed. Among the system responses, which are associated with these load conditions, are thermal buckling and creep buckling. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and have been considered in the development of the mathematical model. Furthermore, this was accommodated in the solution procedures. A complete true ab-inito rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformation, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of the metric and curvature in two coordinate systems, a fixed (spatial) one and a convected (material) coordinate system. The relations between the time derivative and the covariant derivatives (gradients) have been developed for curved space and motion, so that the velocity components supply the connection between the equations of motion and the time rate of change of the metric and curvature tensors.

Simitses, G. J.↗

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 NTRS1947

Elastic Properties in Tension and Shear of High Strength Nonferrous Metals and Stainless Steel - Effect of Previous Deformation and Heat Treatment

A resume is given of an investigation of the influence of plastic deformation and of annealing temperature on the tensile and shear elastic properties of high strength nonferrous metals and stainless steels in the form of rods and tubes. The data were obtained from earlier technical reports and notes, and from unpublished work in this investigation. There are also included data obtained from published and unpublished work performed on an independent investigation. The rod materials, namely, nickel, monel, inconel, copper, 13:2 Cr-Ni steel, and 18:8 Cr-Ni steel, were tested in tension; 18:8 Cr-Ni steel tubes were tested in shear, and nickel, monel, aluminum-monel, and Inconel tubes were tested in both tension and shear. There are first described experiments on the relationship between hysteresis and creep, as obtained with repeated cyclic stressing of annealed stainless steel specimens over a constant load range. These tests, which preceded the measurements of elastic properties, assisted in devising the loading time schedule used in such measurements. From corrected stress-set curves are derived the five proof stresses used as indices of elastic or yield strength. From corrected stress-strain curves are derived the secant modulus and its variation with stress. The relationship between the forms of the stress-set and stress-strain curves and the values of the properties derived is discussed. Curves of variation of proof stress and modulus with prior extension, as obtained with single rod specimens, consist in wavelike basic curves with superposed oscillations due to differences of rest interval and extension spacing; the effects of these differences are studied. Oscillations of proof stress and modulus are generally opposite in manner. The use of a series of tubular specimens corresponding to different amounts of prior extension of cold reduction gave curves almost devoid of oscillation since the effects of variation of rest interval and extension spacing were removed. Comparison is also obtained between the variation of the several properties, as measured in tension and in shear. The rise of proof stress with extension is studied, and the work-hardening rates of the various metals evaluated. The ratio between the tensile and shear proof stresses for the various annealed and cold-worked tubular metals is likewise calculated. The influence of annealing or tempering temperature on the proof stresses and moduli for the cold-worked metals and for air-hardened 13:2 Cr-Ni steel is investigated. An improvement of elastic strength generally is obtained, without important loss of yield strength, by annealing at suitable temperature. The variation of the proof stress and modulus of elasticity with plastic deformation or annealing temperature is explained in terms of the relative dominance of three important factors: namely, (a) internal stress, (b) lattice-expansion or work-hardening, and (c) crystal reorientation. Effective values of Poisson's ratio were computed from tensile and shear moduli obtained on tubular specimens. The variation of Poisson's ratio with plastic deformation and annealing temperature is explained in terms of the degree of anisotropy produced by changes of (a) internal stress and (b) crystal orientation.

METALS - ELASTICITY↗