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NASA NTRS1978

Role of back stress in the creep behavior of particle strengthened alloys

Recent developments in the interpolation of high-temperature steady-state creep results have introduced the concept that the stress dependence of the creep rate should be in terms of the effective stress referred to as the applied stress minus a back stress. This paper reports on back stresses taken from data on a gamma-prime-strengthened wrought nickel-base superalloy, an oxide dispersion-strengthened ODS nickel-base solid solution alloy, and an ODS nickel-base superalloy. The effect of air versus vacuum environments and the effect of dynamic changes in the strengthening microstructures on the magnitude of the back stress are assessed. The role of modulus normalization and the back stress correction in determining the true creep activation energy are examined. It is shown that the high values of the apparent stress exponent 'n' of the steady-state creep equation can be easily explained through a relationship between n, the true stress exponent of steady-state creep, and the stress which when subtracted from the applied stress results in the effective driving stress acting on the mobile dislocations during creep.

Purushothaman, S.↗

NASA NTRS1984

Back stress in dislocation creep. Part 1: Basic concepts and measuring techniques

A theory is proposed whereby the plastic deformation of metal materials is determined by the difference between the applied stress and the back stress which characterizes the resistance of the material to plastic deformation. The back stress is usually equivalent to the internal stress or the friction stress and depends on the magnitude of the applied stress and temperature. The concept of back stress is applied to the case of the dislocation creep of precipitation-hardened or dispersion-strengthened metal materials. An additivity rule is formulated which can be useful in interpreting the creep behavior of such materials.

Cadek, J.↗

NASA NTRS1991

On the thermodynamics of stress rate in the evolution of back stress in viscoplasticity

A thermodynamic foundation using the concept of internal state variables is presented for the kinematic description of a viscoplastic material. Three different evolution equations for the back stress are considered. The first is that of classical, nonlinear, kinematic hardening. The other two include a contribution that is linear in stress rate. Choosing an appropriate change in variables can remove this stress rate dependence. As a result, one of these two models is shown to be equivalent to the classical, kinematic hardening model; while the other is a new model, one which seems to have favorable characteristics for representing ratchetting behavior. All three models are thermodynamically admissible.

Freed, Alan D.↗

NASA NTRS1993

Finite element analysis of structural engineering problems using a viscoplastic model incorporating two back stresses

The feasibility of a viscoplastic model incorporating two back stresses and a drag strength is investigated for performing nonlinear finite element analyses of structural engineering problems. To demonstrate suitability for nonlinear structural analyses, the model is implemented into a finite element program and analyses for several uniaxial and multiaxial problems are performed. Good agreement is shown between the results obtained using the finite element implementation and those obtained experimentally. The advantages of using advanced viscoplastic models for performing nonlinear finite element analyses of structural components are indicated.

Arya, Vinod K.↗

NASA NTRS1990

A crystallographic model for the tensile and fatigue response for Rene N4 at 982 C

An anisotropic constitutive model based on crystallographic slip theory was formulated for nickel-base single-crystal superalloys. The current equations include both drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments have been conducted to evaluate the existence of back stress in single crystals. The results showed that the back stress effect of reverse inelastic flow on the unloading stress is orientation-dependent, and a back stress state variable in the inelastic flow equation is necessary for predicting inelastic behavior. Model correlations and predictions of experimental data are presented for the single crystal superalloy Rene N4 at 982 C.

Sheh, M. Y.↗

NASA NTRS1988

Anisotropic constitutive modeling for nickel base single crystal superalloys using a crystallographic approach

A micromechanical model based on crystallographic slip theory was formulated for nickel-base single crystal superalloys. The current equations include both drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments have been conducted to evaluate the effect of back stress in single crystals. The results showed that (1) the back stress is orientation dependent; and (2) the back stress state variable in the inelastic flow equation is necessary for predicting anelastic behavior of the material. The model also demonstrated improved fatigue predictive capability. Model predictions and experimental data are presented for single crystal superalloy Rene N4 at 982 C.

Stouffer, D. C.↗

NASA NTRS1988

Anisotropic constitutive modeling for nickel-base single crystal superalloys

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.

Sheh, Michael Y.↗

NASA NTRS1993

Bounds on internal state variables in viscoplasticity

A typical viscoplastic model will introduce up to three types of internal state variables in order to properly describe transient material behavior; they are as follows: the back stress, the yield stress, and the drag strength. Different models employ different combinations of these internal variables--their selection and description of evolution being largely dependent on application and material selection. Under steady-state conditions, the internal variables cease to evolve and therefore become related to the external variables (stress and temperature) through simple functional relationships. A physically motivated hypothesis is presented that links the kinetic equation of viscoplasticity with that of creep under steady-state conditions. From this hypothesis one determines how the internal variables relate to one another at steady state, but most importantly, one obtains bounds on the magnitudes of stress and back stress, and on the yield stress and drag strength.

Freed, Alan D.↗

NASA NTRS1986

A Constitutive Model for the Inelastic Multiaxial Cyclic Response of a Nickel Base Superalloy Rene 80

The objective was to develop unified constitutive equations which can model a variety of nonlinear material phenomena observed in Rene 80 at elevated temperatures. A constitutive model was developed based on back stress and drag stress. The tensorial back stress was used to model directional effects; whereas, the scalar drag stress was used to model isotropic effects and cyclic hardening or softening. A flow equation and evolution equations for the state variables were developed in multiaxial form. Procedures were developed to generate the material parameters. The model predicted very well the monotonic tensile, cyclic, creep, and stress relaxation behavior of Rene 80 at 982 C. The model was then extended to 871, 760, and 538 C. It was shown that strain rate dependent behavior at high temperatures and strain rate independent behavior at the lower temperatures could be predicted very well. A large number of monotonic tensile, creep, stress relation, and cyclic experiments were predicted. The multiaxial capabilities of the model were verified extensively for combined tension/torsion experiments. The prediction of the model agreed very well for proportional, nonproportional, and pure shear cyclic loading conditions at 982 and 871 C.

Ramaswamy, V. G.↗

NASA NTRS1988

A constitutive model with damage for high temperature superalloys

A unified constitutive model is searched for that is applicable for high temperature superalloys used in modern gas turbines. Two unified inelastic state variable constitutive models were evaluated for use with the damage parameter proposed by Kachanov. The first is a model (Bodner, Partom) in which hardening is modeled through the use of a single state variable that is similar to drag stress. The other (Ramaswamy) employs both a drag stress and back stress. The extension was successful for predicting the tensile, creep, fatigue, torsional and nonproportional response of Rene' 80 at several temperatures. In both formulations, a cumulative damage parameter is introduced to model the changes in material properties due to the formation of microcracks and microvoids that ultimately produce a macroscopic crack. A back stress/drag stress/damage model was evaluated for Rene' 95 at 1200 F and is shown to predict the tensile, creep, and cyclic loading responses reasonably well.

Sherwood, J. A.↗

NASA NTRS1988

A viscoplastic theory applied to copper

A phenomenologically based viscoplastic model is derived for copper. The model is thermodynamically constrained by the condition of material dissipativity. Two internal state variables are considered. The back stress accounts for strain-induced anisotropy, or kinematic hardening. The drag stress accounts for isotropic hardening. Static and dynamic recovery terms are not coupled in either evolutionary equation. The evolution of drag stress depends on static recovery, while the evolution of back stress depends on dynamic recovery. The material constants are determined from isothermal data. Model predictions are compared with experimental data for thermomechanical test conditions. They are in good agreement at the hot end of the loading cycle, but the model overpredicts the stress response at the cold end of the cycle.

Freed, Alan D.↗

NASA NTRS1992

An investigation of the thermoviscoplastic behavior of a metal matrix composite at elevated temperatures

This research investigates the response of a fiberless 13 layer hot isostatically pressed Ti-15-3 laminate to creep, constant strain rate, and cyclic constant strain rate loading at temperatures ranging from 482C to 649C. Creep stresses from 48 to 260 MPa and strain rates of .0001 to .01 m/m/sec were used. Material parameters for three unified constitutive models (Bodner-Partom, Miller, and Walker models) were determined for Ti-15-3 from the experimental data. Each of the three models was subsequently incorporated into a rule of mixtures and evaluated for accuracy and ease of use in predicting the thermoviscoplastic response of unidirectional metal matrix composite laminates (both 0 and 90). The laminates were comprised of a Ti-15-3 matrix with 29 volume percent SCS6 fibers. The predicted values were compared to experimentally determined creep and constant strain rate data. It was found that all three models predicted the viscoplastic response of the 0 specimens reasonably well, but seriously underestimated the viscoplastic response of the 90 specimens. It is believed that this discrepancy is due to compliant and/or weak fiber-matrix interphase. In general, it was found that of the three models studied, the Bodner-Partom model was easiest to implement, primarily because this model does not require the use of cyclic constant strain rate tests to determine the material parameters involved. However, the version of the Bodner-Partom model used in this study does not include back stress as an internal state variable, and hence may not be suitable for use with materials which exhibit a pronounced Baushinger effect. The back stress is accounted for in both the Walker and Miller models; determination of the material parameters associated with the Walker model was somewhat easier than in the Miller model.

Rogacki, John R.↗

NASA NTRS2011

Monolithic Flexure Pre-Stressed Ultrasonic Horns

High-power ultrasonic actuators are generally assembled with a horn, backing, stress bolt, piezoelectric rings, and electrodes. The manufacturing process is complex, expensive, difficult, and time-consuming. The internal stress bolt needs to be insulated and presents a potential internal discharge point, which can decrease actuator life. Also, the introduction of a center hole for the bolt causes many failures, reducing the throughput of the manufactured actuators. A new design has been developed for producing ultrasonic horn actuators. This design consists of using flexures rather than stress bolts, allowing one to apply pre-load to the piezoelectric material. It also allows one to manufacture them from a single material/plate, rapid prototype them, or make an array in a plate or 3D structure. The actuator is easily assembled, and application of pre-stress greater than 25 MPa was demonstrated. The horn consists of external flexures that eliminate the need for the conventional stress bolt internal to the piezoelectric, and reduces the related complexity. The stress bolts are required in existing horns to provide prestress on piezoelectric stacks when driven at high power levels. In addition, the manufacturing process benefits from the amenability to produce horn structures with internal cavities. The removal of the pre-stress bolt removes a potential internal electric discharge point in the actuator. In addition, it significantly reduces the chances of mechanical failure in the piezoelectric stacks that result from the hole surface in conventional piezoelectric actuators. The novel features of this disclosure are: 1. A design that can be manufactured from a single piece of metal using EDM, precision machining, or rapid prototyping. 2. Increased electromechanical coupling of the horn actuator. 3. Higher energy density. 4. A monolithic structure of a horn that consists of an external flexure or flexures that can be used to pre-stress a solid piezoelectric structure rather than a bolt, which requires a through hole in the piezoelectric material. 5. A flexure system with low stiffness that accommodates mechanical creep with minor reduction in pre-stress.

Sherrit, Stewart↗

NASA NTRS1983

An uncoupled viscoplastic constitutive model for metals at elevated temperature

An uncoupled constitutive model for predicting the transient response of thermal and rate dependent, inelastic material behavior is presented. The uncoupled model assumes that there is a temperature below which the total strain consists essentially of elastic and rate insensitive inelastic strains only. Above this temperature, the rate dependent inelastic strain (creep) dominates. The rate insensitive inelastic strain component is modeled in an incremental form with a yield function, flow rule and hardening law. Revisions to the hardening rule permit the model to predict temperature-dependent kinematic-isotropic hardening behavior, cyclic saturation, asymmetric stress-strain response upon stress reversal, and variable Bauschinger effect. The rate dependent inelastic strain component is modeled using a rate equation in terms of back stress, drag stress and exponent n as functions of temperature and strain. A sequence of hysteresis loops and relaxation tests are utilized to define the rate dependent inelastic strain rate. Evaluation of the model is performed by comparison with experiments involving various thermal and mechanical load histories on 5086 aluminum alloy, 304 stainless steel and Hastelloy-X.

Haisler, W. E.↗

NASA NTRS1983

Development of constitutive models for cyclic plasticity and creep behavior of super alloys at high temperature

An uncoupled constitutive model for predicting the transient response of thermal and rate dependent, inelastic material behavior was developed. The uncoupled model assumes that there is a temperature below which the total strain consists essentially of elastic and rate insensitive inelastic strains only. Above this temperature, the rate dependent inelastic strain (creep) dominates. The rate insensitive inelastic strain component is modelled in an incremental form with a yield function, blow rule and hardening law. Revisions to the hardening rule permit the model to predict temperature-dependent kinematic-isotropic hardening behavior, cyclic saturation, asymmetric stress-strain response upon stress reversal, and variable Bauschinger effect. The rate dependent inelastic strain component is modelled using a rate equation in terms of back stress, drag stress and exponent n as functions of temperature and strain. A sequence of hysteresis loops and relaxation tests are utilized to define the rate dependent inelastic strain rate. Evaluation of the model has been performed by comparison with experiments involving various thermal and mechanical load histories on 5086 aluminum alloy, 304 stainless steel and Hastelloy X.

Haisler, W. E.↗

NASA NTRS1960

Criteria for Yielding of Dispersion-Strengthened Alloys

A dislocation model is presented in order to account for the yield behavior of alloys with a finely dispersed second-phase. The criteria for yielding used in the model, is that appreciable yielding occurs in these alloys when the shear stress due to piled-up groups of dislocations is sufficient to fracture or plastically deform the dispersed second-phase particles, relieving the back stress on the dislocation sources. Equations derived on the basis of this model, predict that the yield stress of the alloys varies as the reciprocal square root of the mean free path between dispersed particles. Experimental data is presented for several SAP-Type alloys, precipitation-hardened alloys and steels which are in good agreement with the yield strength variation as a function of dispersion spacing predicted by this theoretical treatment.

Ansell, G. S.↗

NASA NTRS2013

Low Temperature Creep of Hot-Extruded Near-Stoichiometric NiTi Shape Memory Alloy: Effect of Thermal Cycling - Part 2

This paper is the first report on the effect prior low temperature creep on the thermal cycling behavior of NiTi. The isothermal low temperature creep behavior of near-stoichiometric NiTi between 300 and 473 K was discussed in Part I. The effect of temperature cycling on its creep behavior is reported in the present paper (Part II). Temperature cycling tests were conducted between either 300 or 373 K and 473 K under a constant applied stress of either 250 or 350 MPa with hold times lasting at each temperature varying between 300 and 700 h. Each specimen was pre-crept either at 300 or at 473 K for several months under an identical applied stress as that used in the subsequent thermal cycling tests. Irrespective of the initial pre-crept microstructures, the specimens exhibited a considerable increase in strain with each thermal cycle so that the total strain continued to build-up to 15 to 20 percent after only 5 cycles. Creep strains were immeasurably small during the hold periods. It is demonstrated that the strains in the austenite and martensite are linearly correlated. Interestingly, the differential irrecoverable strain, in the material measured in either phase decreases with increasing number of cycles, similar to the well-known Manson-Coffin relation in low cycle fatigue. Both phases are shown to undergo strain hardening due to the development of residual stresses. Plots of true creep rate against absolute temperature showed distinct peaks and valleys during the cool-down and heat-up portions of the thermal cycles, respectively. Transformation temperatures determined from the creep data revealed that the austenitic start and finish temperatures were more sensitive to the pre-crept martensitic phase than to the pre-crept austenitic phase. The results are discussed in terms of a phenomenological model, where it is suggested that thermal cycling between the austenitic and martensitic phase temperatures or vice versa results in the deformation of the austenite and a corresponding development of a back stress due to a significant increase in the dislocation density during thermal cycling.

Raj, S. V.↗

NASA NTRS1985

Constitutive modeling and computational implementation for finite strain plasticity

This paper describes a simple alternate approach to the difficult problem of modeling material behavior. Starting from a general representation for a rate-tpe constitutive equation, it is shown by example how sets of test data may be used to derive restrictions on the scalar functions appearing in the representation. It is not possible to determine these functions from experimental data, but the aforementioned restrictions serve as a guide in their eventual definition. The implications are examined for hypo-elastic, isotropically hardening plastic, and kinematically hardening plastic materials. A simple model for the evolution of the 'back-stress,' in a kinematic-hardening plasticity theory, that is entirely analogous to a hypoelastic stress-strain relation is postulated and examined in detail in modeling finitely plastic tension-torsion test. The implementation of rate-type material models in finite element algorithms is also discussed.

Reed, K. W.↗