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Conceptual theory proposes that cyclic hardening due to non-uniform strain and stress amplitudes during testing, especially during the initial application of stress to a specimen, may correlate positively with the ultimate strength of the specimen under test.
Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.
A simplified inelastic analysis computer program was developed for predicting the stress-strain history of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a simulated plasticity hardening model. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, and different materials and plasticity models. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.
For crystal plasticity formulation neglecting the strain gradients at the dislocation scale, backstresses are necessary to satisfy the mesoscopic stress equilibrium and strain compatibility requirements. Backstresses in a material point and those between neighboring points are treated separately. Physically backstresses can dynamically induce either hardening or softening effects to adjust the dislocation hardening of slip systems, whereas the sum of the stresses resulting in backstresses in the representative volume element (RVE) is zero. Backstress hardening suppresses certain slip activities, while backstress softening triggers excess dislocations. A two-phase brass is studied. Backstresses make the hard phase deform smaller and the soft phase deform more than those without employing backstresses in a model. In the former, more homogeneous lattice strain and higher yield stress are obtained. Backstress has limited effects on the evolution of the critical resolved shear stress and crystallographic texture. Furthermore, it is a major cause of the banded structures featuring sharp crystallographic contrasts which are not parallel to the slip planes. Tests indicate that backstress induces a serrated behavior at the early stages of deformation and induces the geometrically necessary bands (GNBs), which are parallel to the macroscopic axes.
Compression tests are conducted on NiAl-1Hf to assess the elevated-temperature creep behavior of this precipitation-hardened aluminide. While the strength is high under fast strain rates (more than 10 exp -5/s), under slower conditions the alloy is weak. Thus, it is unlikely that effective creep resistance can be obtained in NiAl through small Hf additions.
The multiaxial deformation behavior of the Ni-based alloy B1900 + Hf has been studied at elevated temperatures in the range of 649-982 C. Combined tension/torsion cyclic tests were performed on thin-wall tubular specimens under both in-phase and out-of-phase strain-controlled loading cycles. Both straining conditions resulted in stress loci of comparable magnitude, exhibiting no difference in cyclic hardening response. A phase angle was observed between the deviatoric stress and the incremental plastic strain vectors during 90-deg out-of-phase strain cycling, and nonproportional stress relaxation occurred under biaxial strain hold. The overall results have been used to assess the flow law, the hardening equations, and the applicability of the J2-based, elastic-viscoplastic model of Bodner-Partom (1979) for multiaxial loading conditions. The overall agreement between theory and experiment is good. Discrepancies are discussed in relation to micromechanical considerations.
A 304L-VAR stainless steel is mechanically characterized in tension over a full range of strain rates from low, intermediate, to high using a variety of apparatuses. While low- and high-strain-rate tests are conducted with a conventional Instron and a Kolsky tension bar, the tensile tests at intermediate strain rates are conducted with a fast MTS and a Drop-Hopkinson bar. The fast MTS used in this study is able to obtain reliable tensile response at the strain rates up to 150 s -1 , whereas the lower limit for the Drop-Hopkinson bar is 100 s -1 . Combining the fast MTS and the Drop-Hopkinson bar closes the gap within the intermediate strain rate regime. Using these four apparatuses, the tensile stress-strain curves of the 304L-VAR stainless steel are obtained at strain rates on each order of magnitude ranging from 0.0001 to 2580 s -1 . All tensile stress-strain curves exhibit linear elasticity followed by significant work hardening prior to necking. After necking occurrs, the specimen load decreases, and the deformation becomes highly localized until fracture. The tensile stress-strain response of the 304L-VAR stainless steel exhibits strain rate dependence. The flow stress increases with increasing strain rate and is described with a power law. The strain-rate sensitivity is also strain-dependent, possibly due to thermosoftening caused by adiabatic heating at high strain rates. The 304L-VAR stainless steel shows significant ductility. The true strains at the onset of necking and at failure are determined. The results show that the true strains at both onset of necking and failure decrease with increasing strain rate. The true failure strains are approximately 200% at low strain rates but are significantly lower (~100%) at high strain rates. The transition of true failure strain occurs within the intermediate strain rate range between 10 -2 and 10 2 s -1 . A Boltzmann description is used to present the effect of nominal strain rate on true failure strain.
We characterize primary (shape-change) and secondary (friction) deformation, and associated temperature fields, in metal cutting and forming processes, using in situ imaging and simulation. The experimental configurations enable access to the deformation zones and die contact-interfaces, for measuring deformation, temperature, and frictional drag. Infra-red thermography reveals that the plastic strain-rate field is an excellent proxy for the deformation-induced heat sources. Both spatially confined and diffuse strain-rate fields occur, depending on the initial workpiece deformation state. When the strain rate is confined, as in pre-hardened material, the temperature modeling is much simplified, as the heat source is also now localized. However complex, microstructure-driven deformation modes, like sinuous flow in annealed metals, result in spatially diffuse strain-rate and body heat sources, more challenging to analyze. Furthermore, our unified measurements should be of value for accurately estimating the fraction of plastic dissipation that is converted into heat in large-strain deformation processes.
A formulation for a dimensionless coefficient c b is derived that represents a scale of microstructural softening for alloys which follow Kocks-Mecking (K-M) work hardening behavior. The variation of the true plastic strain ε p between the proportional limit σ y and the strength σ u at the instability is determined using the Considère criterion. Parameterization of the model is limited to variables expressly measured within tensile experiments. Further development is now made for the softening factor c bi through the individual and sequential stages 3 and 4 of plastic deformation during K-M work hardening Q behavior. Application is shown for tensile test results of Ti-6Al-4V made by different additively manufactured (AM) processes. It is found that the variation in plastic strain as a function of c bi produces a continuous curve representative of the alloy system. The results of data analysis indicate that Θ o3 and c b3 increase, while Θ o4 and c b4 decrease, as the total plastic strain ε p increases. Furthermore, formulations derived for K-M stages 3 and 4 enable the evaluation of other material parameters such as the activation volume ν* for the onset of plastic deformation. This activation volume is found to be near constant, at a ν*-value of 0.353±0.036 nm 3 as computed using a strain-rate sensitivity of strength exponent m of 0.014, irrespective of the AM method used to produce the Ti-6Al-4V alloy.
Alloys based on the intermetallic compound NiAl are considered potential replacements for Ni and Co-based superalloys in high temperature structural applications due to their excellent oxidation resistance, low densities, high thermal conductivities, and increased melting points. Unfortunately, NiAl exhibits low tensile ductility at room temperature and low strengths at elevated temperatures which have combined to hinder its development. Recent efforts, have revealed that NiAl in the presence of sufficient solute levels, is subject to the phenomenon of strain aging which manifests itself as: sharp yield points, abnormally low strain rate sensitivities (SRS), plateaus or peaks in yield stress and work hardening rate as a function of temperature, flow stress transients upon an upward change in strain rate, reduced tensile elongations at elevated temperatures, and serrated stress-strain curves. Though recent efforts via either alloying or the removal of interstitial impurities, have resulted in consistent room-temperature tensile elongations exceeding 5% and the elimination of serrated flow, the effects of particular substitutional and interstitial elements and the mechanisms by which they might enhance or hinder the mechanical properties remain unknown. Consequently, the purpose of the present paper is to provide a preliminary assessment of the influence of common substitutional and interstitial impurities on the deformation behavior of NiAl. To accomplish this goal a series of NiAl single crystal alloys containing various interstitial solutes were prepared and their mechanical properties were evaluated between 77 and 1100 K. Because Si is a common impurity in conventional purity single crystals grown by the Bridgman method, Si concentrations were also varied in order to determine the influence of this element.
Transmission electron microscopy and X-ray diffraction observations of substructure and elastic strains in cold worked and annealed dispersion strengthened alloys
A room-temperature experimental program was conducted on AISI type 316 stainless steel to determine the effect of wall thickness on the cyclic deformation behavior and fatigue life of thin-wall, tubular, axial-torsional fatigue specimens. The following experimental variables were examined in this study: the depth of the surface work-hardened layer produced in specimen machining, and the effects of strain range and axial-torsional strain phasing. Tubular fatigue specimens were fabricated with wall thicknesses of 1.5, 2.0, and 2.5 mm. One as-fabricated specimen from each wall thickness was sectioned for microstructural examination and microhardness measurement. A specimen of each wall thickness was tested at each of three conditions - high strain range in-phase, low strain range in-phase, and low strain range out-of-phase - for a total of nine axial-torsional fatigue experiments. The machining-induced work-hardened zone, as a percentage of the gage section material, was found to have a minimal effect on both deformation behavior and fatigue life. Also, little or no variation in fatigue life or deformation behavior as a function of wall thickness was observed. Out-of-phase fatigue tests displayed shorter fatigue lives and more cyclic hardening than in-phase tests.
The predictive performance of a multimechanism GVIPS model with saturating hardening function is assessed against a set of high temperature cyclic experiments under both strain-control and stress-control at varying rates of loading as well as several complex interrupted cyclic responses. The material specimens were composed of the titanium alloy, TIMETAL 21S, and tested at 650oC, see Lissenden et al., 2007. The model did a very good job of predicting the variety of tests, particularly given the fact that only monotonic loading tests (tensile, creep, relaxation) and a single fully reversed cycle was used for characterization. It was particularly interesting that the model was capable of reasonably capturing the rate of accumulated strain during ratchetting under tensile mean stress. Given complex interrupted cyclic response, the model was able to both qualitatively and even quantitatively predict reasonably well both the cyclic and associated relaxation periods (in all quadrants of the stress-strain space) thus confirming the validity of the chosen functional forms for both hardening and thermal recovery. The quantitative inaccuracy is associated with the fact that the material specimens tested by Lissenden et al., 2007 was significantly “softer” than those tested by Castelli in Saleeb et al., 1994 which were used for characterization of the GVIPS model parameters.
The predictive performance of a multimechanism GVIPS model with saturating hardening function is assessed against a set of high temperature cyclic experiments under both strain-control and stress-control at varying rates of loading as well as several complex interrupted cyclic responses. The material specimens were composed of the titanium alloy, TIMETAL 21S, and tested at 650 °C, see Lissenden et al., 2007. The model did a very good job of predicting the variety of tests, particularly given the fact that only monotonic loading tests (tensile, creep, relaxation) and a single fully reversed cycle was used for characterization. It was particularly interesting that the model was capable of reasonably capturing the rate of accumulated strain during ratchetting under tensile mean stress. Given complex interrupted cyclic response, the model was able to both qualitatively and even quantitatively predict reasonably well both the cyclic and associated relaxation periods (in all quadrants of the stress-strain space) thus confirming the validity of the chosen functional forms for both hardening and thermal recovery. The quantitative inaccuracy is associated with the fact that the material specimens tested by Lissenden et al., 2007 was significantly “softer” than those tested by Castelli in Saleeb et al., 1994 which were used for characterization of the GVIPS model parameters.
An anisotropic constitutive model was developed based on crystallographic slip theory for nickel base single crystal superalloys. The constitutive equations developed utilizes drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments were conducted to evaluate the existence of back stress in single crystal superalloy Rene N4 at 982 C. The results suggest that: (1) the back stress is orientation dependent; and (2) the back stress state variable is required for the current model to predict material anelastic recovery behavior. The model was evaluated for its predictive capability on single crystal material behavior including orientation dependent stress-strain response, tension/compression asymmetry, strain rate sensitivity, anelastic recovery behavior, cyclic hardening and softening, stress relaxation, creep and associated crystal lattice rotation. Limitation and future development needs are discussed.
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.
The object of this study was to investigate the micro-structural response of DP 600 subjected to high strain rate, ballistic impact tests. The ballistic tests were conducted using normal impact of a hardened steel penetrator into a 2 mm thick sheet of DP 600. The average strain rates produced from this test method are on the order of 10(exp 5)/s. Electron microscopy was used to investigate the microstructure before and after high strain rate deformation. A variation in material response was observed between tests conducted at 0.8 x 105 and 25 x 10(exp 5)/s.
The resistance to dislocation glide associated with slip systems {110}<111> and {112}<111> in single phase FeCrAl alloy is measured via micromechanical testing in a scanning electronic microscopy at room temperature. Two important factors, the shape and orientation of a pillar, are discussed with respect to the glide resistance and stress-strain response. Maximizing Schmid factor of one specific slip system while minimizing others is recommended in order to diminish obvious dislocations-induced hardening during in-situ testing. Apparent Schmid factor analysis is conducted to select grains with preferred orientations. Two types of pillars with conventional cylindrical shape or dog-bone shape are tested under compression to estimate the resistance to dislocation glide and evaluate the effect of pillar shape on the compression stress-strain response. One dog-bone pillar is tested under tension to check the tension-compression isotropy of dislocation slip. We discover that the shape of a pillar to a smaller extent affects the measured resistance but strongly influences the stress strain response. Cylindrical pillars exhibit apparent hardening associated with early yielding due to stress or strain concentration at contact region, while dog-bone pillars show an obvious yielding and continuous shearing without hardening. The resistance is 220 MPa for slip system {110}<111> and 230 MPa for slip system {112}<111>. Finite element analysis is performed to account for the influence of pillar shape and contact condition on mechanical response.