A New Rock Salt Model with Drag Stress and Back Stress Hardening.
Abstract not provided.
Reedlunn, Benjamin↗
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A New Rock Salt Constitutive Model with Back Stress and Drag Stress Hardening.
Abstract not provided.
Reedlunn, Benjamin↗
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.↗
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.↗
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.↗
Back-Stress and Its Evolution during Primary Creep in Particle Strengthened Nickel Superalloys
According to Eshelby’s theory, inelastically inhomogeneous inclusions in a metallic matrix give rise to a distribution of internal stresses. In the case of particle strengthened materials, such as nickel base superalloys, the presence and evolution of this back-stress leads to various observable effects, such as primary creep, back-flow upon loading, and memory of prior deformation. This article presents the background of the concept of back-stress and how it applies to the scenario of creep. A derivation of an evolution equation for back-stress in the context of primary creep is also presented. The results from neutron diffraction with in-situ creep experiments on directionally solidified nickel superalloys are presented in order to demonstrate the validity of the proposed equation and the corollaries derived therefrom.
36 MATERIALS SCIENCE↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗
Investigation of twin growth mechanisms in precipitate hardened AZ91
Here, in this work, an elasto-viscoplastic fast-Fourier-transform (EVP-FFT) model with a dislocation-density (DD) based hardening law is employed to study the growth of a {10$\bar{1}$2} tensile twin that is blocked by basal-precipitates in precipitate-hardened AZ91 magnesium alloy. It is frequently reported that twin growth is hindered in precipitate-hardened Mg alloys; however, thick twin domains are often observed experimentally in these material systems. Detailed numerical investigation of deformation twinning starting from an early propagation stage, before twin growth, reveals that the stress fields that result from two sequentially propagated twins co-impinging on a precipitate relaxes the twin back stress locally and promotes twin growth at the twin-precipitate junction. Based on these findings, a two-step growth mechanism is proposed for twins arrested by precipitates. In the first step, the interaction of a twin tip with a precipitate develops a stress concentration on the other side of the precipitate, prompting the formation of a second twin. Subsequently, the back stresses associated with the first twin are relaxed by the formation of the second twin, allowing the first twin to grow at the twin-precipitate junction and eventually engulf the precipitate. This mechanism suggests that twin growth can be achieved locally with minimal additional external forces, explaining how relatively large twin domains can develop even in the presence of arrays of precipitates.
36 MATERIALS SCIENCE↗
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.↗
In-Situ Stress Measurements at the Utah Frontier Observatory for Research in Geothermal Energy (FORGE) Site
A scientific injection campaign was conducted at the Utah Frontier Observatory for Research in Geothermal Energy (FORGE) site in 2017 and 2019. The testing included pump-in/shut-in, pump-in/flowback, and step rate tests. Various methods have been employed to interpret the in-situ stress from the test dataset. This study focuses on methods to interpret the minimum in-situ stress from step rate, pump-in/extended shut-in tests data obtained during the stimulation of two zones in Well 58-32. This well was drilled in low-permeability granitoid. A temperature of 199 °C was recorded at the well’s total depth of 2297 m relative to the rotary Kelly bushing (RKB). The lower zone (Zone 1) consisted of 46 m of the openhole at the toe of the well. Fractures in the upper zone (Zone 2) were stimulated between 2123–2126 m measured depths (MD) behind the casing. The closure stress gradient variation depended on the depth and the injection chronology. The closure stress was found to increase with the pumping rate/volume. This stress variation could indicate that poroelastic effects (“back stress”) and the presence of adjacent natural fractures may play an important role in the interpretation of fracture closure stress. Further, progressively increasing local total stresses may, consequently, have practical applications when moderate volumes of fluid are injected in a naturally fractured or high-temperature reservoir. The alternative techniques that use pump-in/flowback tests and temperature signatures provide a valuable perspective view of the in-situ stress measurements.
15 GEOTHERMAL ENERGY↗
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↗