The strain dependence of postdynamic recrystallization in 304 H stainless steel

Using double-hit hot compression tests, the softening behavior of 304 H stainless steel was studied during unloading. The prestrains used were associated with the initiation of dynamic recrystallization (DRX) (ε _c), the peak strain (ε _p), 1/2 (ε _c+ε _p), the strain at maximum softening rate (ε _i), and the onset of steady state flow (ε _s). The following conditions of deformation were used: T=1000 °C, 1050 °C, and 1100 °C, =0.01 and 0.1 s⁻¹, and delay times of 0.3 to 1000 seconds. To define the above important strains, single-hit hot compression tests were performed over a wider range of deformation conditions than the double-hit ones—i.e., 900 °C to 1100 °C and =0.01 to 1 s⁻¹. The results show that a transition strain (ε*) separates the strain-dependent range of postdynamic softening from the strain-independent range. At strains between ε _c and ε*, both metadynamic and static recrystallization contribute to interhit softening. The value of ε* obtained in this work was ε*=4/3 ε _p. It was also found that the strain hardening rate was identical at all the critical strains (ε*) and took the value −22 MPa.     

The high temperature creep and fracture behavior of 70-30 alpha-brass

Constant stress creep tests have been carried out over a range of stresses at 324°, 413°, 503°, and 550°C. In all cases, over almost the entire creep curve, the time dependence of the true creep strain, ∈, can be described accurately as where ∈₀ is the instantaneous strain on loading, ∈_T the transient creep strain,m a parameter relating to the rate of exhaustion of transient creep, the steady creep rate, ∈_L andP are tertiary creep parameters, andt _t is the time to the onset of tertiary creep. A number of relationships exist between the transient and tertiary parameters in this equation and the steady creep rate, which suggests that the same basic deformation process operates throughout almost the entire creep life. Transient creep ends after a time,t _s, such thatmt _s is a constant (≃4). Similarly, the duration of tertiary creep (t _f – t_t), wheret _f is the time to fracture, depends on the parameter,p, asp (t_f − t_t) is a constant (≃4.5). The time to fracture is found to be related to the parametersm andp asmt _s +pt _f − t_s) =constant (−12) independent of stress and temperature. Formerly Research Student, University College     

Characterization and modeling of the high temperature flow behavior of aluminum alloy 2024

Isothermal flow curves were determined for aluminum alloy 2024-0 at temperatures of 145 to 482 °C and at constant true-strain rates of 10^-3 to 12.5 s^-1 using compression tests of cylindrical specimens. The average pressure was corrected for friction and for deformation heating to determine the flow stress. At 250 °C and above, the isothermal flow curves usually exhibited a peak followed by flow softening. At 145 °C the flow curves exhibited strain hardening. For 250 °C≦ T<= 482 °C, 10^-3 s^-1 ≦ ≦ 12.5 s^-1, and ε ≦ 0.6 the flow behavior was represented by the constitutive equation σ =K (T, ε) where logK andm are simple functions of temperature and strain. The as-deformed microstructures generally supported the idea that flow softening in Al 2024-0 is caused by dynamic recovery. At the higher temperatures and strain rates, however, fine recrystallized grains were observed in local areas near second phase particles and at as-annealed grain boundaries. At 482 °C, there was evidence of re-dissolution of the CuMgAl₂ precipitate. Formerly Visiting Associate Professor, Wright State University, Dayton, OH 45435 Formerly a Mechanical Systems Engineering Student at Wright State University Formerly a Materials Engineering Student at Wright State University Formerly Director, Metallurgy Program, National Science Foundation, Washington, DC     

Creep lifetime prediction of oxide-dispersion-strengthened nickel-base superalloys: A micromechanically based approach

The high-temperature creep behavior of the oxide-dispersion-strengthened (ODS) nickel-base superalloys MA 754 and MA 6000 has been investigated at temperatures up to 1273 K and lifetimes of approximately 4000 hours using monotonic creep tests at constant true stressσ, as well as true constant extension rate tests (CERTs) at . The derivation of creep rupture-lifetime diagrams is usually performed with conventional engineering parametric methods, according to Sherby and Dorn or Larson and Miller. In contrast, an alternative method is presented that is based on a more microstructural approach. In order to describe creep, the effective stress model takes into account the hardening contributionσ _p caused by the presence of second-phase particles, as well as the classical Taylor back-stressσ _p caused by dislocations. The modeled strain rate-stress dependence can be transferred directly into creep-rupture stress-lifetime diagrams using a modified Monkman-Grant (MG) relationship, which adequately describes the interrelation between representing dislocation motion, and lifetimet _f representing creep failure. The comparison with measured creep-rupture data proves the validity of the proposed micromechanical concept.     

Effect of quenching,tempering, and cold rolling on creep deformation behavior of a tempered martensitic 9Cr-1W steel

The effect of quenching, tempering, cold-rolling, and aging treatments, which produce different dislocation substructures and different carbide distributions, on the creep-deformation behavior is investigated for a tempered martensitic 9Cr-1W steel at 873 K, mainly. The creep rate vs time curves indicate transient creep, where the creep rate decreases with time, and accelerating creep, where the creep rate increases with time. The minimum creep rate is closely correlated with the onset time of acceleration creep and is inversely proportional to the duration of the transient creep region. The onset of acceleration creep shifts to shorter times for the specimens subjected to the quenching, 20-hour tempering (long-term tempering) at 1023 K, and cold-rolling treatments than that for the specimen subjected to the standard quenching and tempering (QT) treatment. The onset of acceleration creep is closely correlated with the migration of lath or subgrain boundaries, causing the coarsening of laths or subgrains. Dislocation cells produced by cold rolling are free of M₂₃C₆ carbides. The migration and recovery of dislocation cells significantly promote the onset of acceleration creep. The preferential distribution of M₂₃C₆ carbides along lath boundaries is effective for the retardation of the onset of acceleration creep for up to longer times by the stabilization of lath boundaries. In the acceleration creep region, after reaching a minimum creep rate, the logarithm of the creep rate increases linearly with strain for a wide range of strains. The time to rupture (tr) is inversely proportional to the minimum creep rate times the acceleration of the creep rate (d ln /dε) in the acceleration creep region, but is not proportional to only the minimum creep rate, as given by

High temperature creep of alpha iron in terms of effective stress and dislocation dynamics

The dynamics of dislocations in both steady state and transient creep in alpha iron of about 99.5 pct purity was investigated in the temperature interval 773 to 923 K, and the applied stress range 24.5 to 220.5 MN m⁻². The applied stress sensitivity parameter of the steady state creep rate m∲ = (∂ In ε/∂ In σ) _T increased linearly with increasing applied stress σ from about 5 at σ = 24.5 MN m⁻² to about 12 at σ = 196 MN m⁻². The apparent activation energy of steady state creep rate was found to decrease linearly with stress from 89 K cal mol⁻¹ at σ = 98 MN m⁻² to 81 K cal mol⁻¹ at a = 147 MN m⁻². Measurements of the mean effective stress σ^* by the strain transient dip test technique led to a nonlinear relation between σ^* and σ, indicating a dependence of the ratio σ*/σ on the applied stress. The effective stress sensitivity parameter was lower than m′.However, the apparent activation energy was equal toQ. Using the stress sensitivity technique, the relation between transient creep rate and effective stress at various constant internal stresses and temperatures was obtained. The effective stress sensitivity of transient creep rate was found to be lessthan that of steady creep rate.     

Effect of stress and temperature on the creep and rupture behavior of a 1.25 Pct chromium—0.5 Pct molybdenum steel

The creep and stress rupture behavior of a normalized 1.25 pct chromium-0.5 pct molybdenum steel has been investigated over a temperature (T) range of 510 to 620°C and a stress(σ) range of 65 to 425 MN/m². The creep rate ( ) and time to rupture (t _r ) data have been analyzed in terms of the general expression ort _r -A σⁿ exp (Q/RT), whereA is a constant,n is the power exponent of stress,Q is an empirical activation energy for the rate controlling process andR is the universal gas constant. At each temperature, the logarithmic plots of creep rate and time to rupture as functions of stress consist of two linear segments, separating the data into low stress and high stress regimes. The stress exponent has approximate values of 4 and 10 in the low stress and high stress regimes respectively in the appropriate expressions for both creep rate and for time to rupture. The activation energy has values of 367 and 420 kJ/mole in the low stress regime for time to rupture and creep rate respectively. In the high stress regime, the respective values of activation energy are 581 and 670 kJ/mole. Fractographic observations show that the changes from low stress to high stress behavior in creep rate and time to rupture approximately coincide with the transition in fracture mode from intergranular to transgranular cracking as well as with the transition in the rupture ductility from a region of linear variation with stress to one of constant ductility. These observations suggest that the transition from low stress to high stress behavior may be associated with a change in deformation mode from predominantly grain boundary sliding at low stress to transgranular matrix deformation at high stress. Analysis of the creep rate data based on this premise enables calculation of the ratio of the contributions of the grain boundary sliding mode to the total deformation (ε _gb /ε _T ) at various values of stress and temperature. Results of this analysis are consistent with numerous experimental observations reported in the literature.     

The high-temperature creep behavior of nickel-rich Ni-W solid solutions

The steady-state creep behavior of four nickel-rich Ni-W solid solutions (1, 2, 4, and 6 wt pct W) was investigated in the temperature range 850° to 1050°C. Constant stress tensile creep tests were performed in vacuum in the stress range 3000 to 7000 psi. Activation energies for creep were observed to be 71.4 ± 2.0, 74.4 ± 3.0, and 75.8 ±2.0 kcal per mole, after correcting temperature dependence of the elastic modulus, for alloys containing 2,4, and 6 pct W respectively. These values closely approximate the activation energies for the weighted diffusion coefficient, =D _Ni D _W/(X _W D _Ni) whereX _Ni andX _w are the atom fractions of nickel and tungsten respectively, andD _Ni andD _w are the diffusion coefficients of nickel and tungsten in the alloy. The steady-state creep rates exhibit a power law stress dependence with an exponent,n, equal to 4.8 ±0.2 for all of the alloys studied. For tests conducted at temperatures and stresses such that both the diffusivity, , and the ratio of the applied stress to the elastic modulus, σ/E, are. held constant, the steady-state creep rate, , was found to vary with the stacking fault energy, γ, according to the empirical relation ∼ γ^{4 2±4} over the range of creep rates studied. W. R. Johnson, formerly Graduate Student, Stanford Univeristy, Stanford, Calif.     

Solid solution creep behavior of Sn-xBi alloys

This study details the steady-state creep properties of Sn-1 wt pct Bi, Sn-2 wt pct Bi, and Sn-5 wt pct Bi as a function of stress and temperature. All data, including previous work on pure Sn, are described by the following empirical equation:

Elevated-temperature deformation at forming rates of 10−2 to 102 s−1

In the hot working at constant strain rate ( ) of Al and α Fe alloys at 0.5 to 0.9 T _M (absolute melting temperature), steady-state deformation is achieved in similarity to creep, which is usually at constant stress. After an initial strain-hardening transient, the flow stress becomes constant in association with a substructure which remainsequiaxed and constant in the spacing of sub-boundaries and of dislocations in both walls and subgrains. All these spacings become larger at higher temperature (T) and lower values as well as with lower stress, being fully consistent with the relationships established in creep. Because hot working can proceed to a much higher true strain in torsion (∼100) and compression (∼2) as well as in extrusion (∼20) and rolling (∼5), it is possible to confirm that grains continue to elongate while the subgrains within them remain equiaxed and constant in size. When the thickness of grains reaches about 2 subgrain diameters (d _s), the grain boundaries with serrations (∼d _s) begin to impinge and the grains pinch off, becoming somewhat indistinguishable from the subgrains; this has been called geometric dynamic recrystallization (DRX). In polycrystals as at 20 °C, deformation bands form and rotate during hot working according to the Taylor theory, developing textures very similar to those in cold working. In metals of lower dynamic recoverability such as Cu, Ni, and γ Fe, new grains nucleate and grow (discontinuous DRX), leading to a steady state related to frequently renewed equiaxed grains, containing an equiaxed substructure that develops to a constant character and defines the flow stress. This article is based on a presentation made in the workshop entitled “Mechanisms of Elevated Temperature Plasticity and Fracture,” which was held June 27–29, 2001, in San Diego, CA, concurrent with the 2001 Joint Applied Mechanics and Materials Summer Conference. The workshop was sponsored by Basic Energy Sciences of the United States Department of Energy.     

Modeling creep and fatigue of copper alloys

This article reviews expressions to quantify the thermal creep and fatigue lifetime for four copper alloys: Cu-Ag-P, Cu-Cr-Zr, Cu-Ni-Be, and Cu-Al₂O₃. These property models are needed to simulate the mechanical behavior of structures with copper components, which are subjected to high heat-flux and fatigue loading conditions, such as molds for the continuous casting of steel and the first wall in a fusion reactor. Then, measurements of four-point bending fatigue tests were conducted on two-layered specimens of copper alloy and stainless steel, and thermal ratchetting behavior was observed at 250 °C. The test specimens were modeled with a two-dimensional elastic-plastic-creep finite-element model using the ABAQUS software. To match the measurements, a primary thermal-creep law was developed for Cu-0.28 pct Al₂O₃ for stress levels up to 500 MPa and strain rates from 10⁻⁸ to 10⁻² s⁻¹. Specifically, (s⁻¹)=1.43×10¹⁰ exp (−197,000/8.31 T(K)) (σ(MPa))^2.5 (t(s))^−0.9.     

Quasi-steady-state creep crack growth in a 3.5NiCrMoV steel

Creep crack growth rate ( ) is usually characterized in terms of macroscopic load parameters, such as C*, C _t and C(t), through the constant load test. However, load parameters are continuously changing during the test, and so is . Here, by conducting constant C _t and constant tests, quasi-steady-state crack growth was obtained where remained almost constant. Results indicate the ∼[C _t ]^0.76 correlation, which differ from the ∼[C _t ]^0.96 correlation of the constant load test. Discrepancies can be ascribed to the inclusion of the stage II data, which showed no correlation between and C _p in the constant load analysis. Finally, the crack growth rate was well predicted using the Monkmam-Grant analysis in creep crack growth.     

Structural superplasticity at higher strain rates of hypereutectoid Fe-5.5Al-1Sn-1Cr-1.3C steel

A fine-grained ultra-high-carbon steel—UHC steel—containing 1.35 wt pct carbon, 5.5 wt pct aluminum, 1 wt pct tin, and 1 wt pct chromium exhibits fine-structure superplasticity in the temperature regime between 775 °C and 900 °C at higher strain rates up to 10⁻² s⁻¹. Thermomechanical processing was performed in order to achieve a fine-grained equiaxed microstructure consisting of κ-carbides of about 0.7 to 2.5 μm in size finely distributed within the ferritic Fe(Al, Sn, Cr) solid solution matrix with a linear intercept grain size of 3 to 5 μm. Superplasticity occurred in the strain rate regime of 10⁻⁴<- ≤10⁻² s⁻¹ with m values of 0.5 to 0.6 (stress exponent n=1.6 to 2). Tensile elongations of more than 900 pct were recorded. From thermal activation analysis, activation energies of Q=230 to 243 kJ/mole were determined, which clearly reveal a contribution of the alloying elements Al and Sn to the lattice diffusion of iron. The governing deformation mechanism is grain boundary sliding accommodated by dislocation climb controlled by lattice diffusion sustained by chemical diffusion. At very high strain rates of ≳2 · 10⁻² s⁻¹, the strain-rate-sensitivity exponent decreases to about 0.2≤m≤0.27, which indicates class II solid solution behavior of this material.     

Grain-growth-inhibiting effects of primary inclusion particles of ZrO2 and MgO in Fe-10 mass pct Ni alloy

Grain-growth inhibition in an Fe-10 mass pct Ni alloy, which was continuously cooled from a melt, was studied at 1673 K in the presence of primary deoxidation products of ZrO₂ or MgO particles. The mean grain size and grain-size distribution in a cross section were measured as a function of holding time for up to 240 minutes. The grain growth was strongly inhibited by the inclusion particles and was influenced by the dissolved Zr. In the Zr deoxidation, the number of particles per unit area (N _A) ranged from 80 to 650 mm⁻², the ZrO₂ particle size ( ) varied from 1.1 to 1.6 μm, and the dissolved Zr level was below 1800 mass ppm. In the Mg deoxidation, the particle-number density was 90 to 270 mm⁻², the MgO particle size was 1.1 to 1.7 μm, and the dissolved Mg level was below 20 mass ppm. In a logarithmic plot of the ratio of limiting mean grain diameter ( ) to the mean particle diameter ( ) against the volume fraction of particles (f _V), both the value for a given f _V value, which ranged from 0.014 to 0.074 pct, and the slope were significantly lower than that predicted from the two-dimensional relation =(4/π) · f _V ^/−1 , i.e., Zener’s limit. This discrepancy is discussed in light of the fraction of particles at the grain boundaries measured experimentally. Normal grain growth was confirmed from the grain-size distribution observed as a function of holding time, which was best described by the log-normal distribution.     

Elevated temperature deformation behavior of a dispersion-strengthened Al-Fe,V,Si alloy

The deformation behavior of a rapidly solidified, dispersion-strengthened Al alloy containing 11.7 pct Fe, 1.2 pct V, and 2.4 pct Si was studied at test temperatures up to 450 °C using constantstress creep and constnt strain-rate tensile tests. Apparent stress exponents (n) up to ∼24 and an activation energy of 360 kJ/mol were obtained with the standard Arrhenius type power-law creep equation, which also suggested a change in behavior at ∼300 °C. Substructure-invariant and dislocation/dispersoid interaction models were found to be inadequate for explaining the behavior. When the data were replotted as vs σ, two regimes were found between 350 °C and 450 °C. A model with a pseudothreshold stress (σ _Th′ ) for the higher stress regime resulted inn ∼3, indicating solute drag in this regime. Transmission electron microscopy (TEM) showed departureside pinning of dislocations at higher stresses. In the lower stress regime, TEM showed dislocation subgrain structures. Here, the model resulted in a stress exponent of ∼4.5 indicating the dislocation climb mechanism. At temperatures below ∼300 °C, a single regime was found along with lower activation energies and a stress dependence of ∼3. Dislocation pipe diffusion is proposed to explain the lower activation energy. The origin ofσ _Th′ has been tied to dislocation generation at the grain boundaries.     

Prediction of dendrite arm spacings in unsteady-and steady-state heat flow of unidirectionally solidified binary alloys

Various theoretical dendrite and cell spacing formulas have been tested against experimental data obtained in unsteady- and steady-state heat flow conditions. An iterative assessment strategy satisfactorily overcomes the circumstances that certain constitutive parameters are inadequately established and/or highly variable and that many of the data sets, in terms of gradients, velocities, and/or cooling rates, are unreliable. The accessed unsteady- and steady-state observations on near-terminal binary alloys for primary and secondary spacings were first examined within conventional power law representations, the deduced exponents and confidence limits for each alloy being tabularly recorded. Through this analysis, it became clear that to achieve predictive generality the many constitutive parameters must be included in a rational way, this being achievable only through extant or new theoretical formulations. However, in the case of primary spacings, all formulas, including our own, failed within the unsteady heat flow algorithm while performing adequately within their steady-state context. An earlier untested, heuristically derived steady-state formula after modification,

β brass bicrystal stress-strain relations

The stress-strain relations of three isoaxial and one nonisoaxial bicrystal whose grain boundaries are parallel to the stress axis have been studied. From one set of isoaxial bicrystals it has been possible, for a given strain, to determine the average stress in the grain boundary deformation zone from the relationship where σ _T is the applied stress, σ _b is the single crystal flow stress for the given strain, andV _gb is the volume fraction of grain boundary deformation zone. was determined from measured values of σ _T , σ _b , andV _gb . From these data and it was possible to extrapolate to the grain boundary to obtain σ _gb , the grain boundary stress. From the nonisoaxial bicrystal series containing a hard and a soft component, it was possible to determine at a given strain the stresses in each component and therefore the stress-strain relations from the relationship where and are the average stress in the hard and soft components respectively, andV _H andV _S are the corresponding volume fractions. The remaining two isoaxial bicrystal series were used to evaluate strengthening effects of bicrystal boundaries. YII-DER CHUANG, formerly Graduate Student, Department of Metallurgy and Materials Sciences, School of Engineering, New York University, Bronx, N. Y. 10453 This paper is based on a thesis submitted by Yii-der Chuang in partial fulfillment of the requirements for the Ph.D. degree in metallurgy at New York University, New York, N. Y.     

High-strain-rate superplastic behavior of equal-channel angular-pressed 5083 Al-0.2 wt pct Sc

Tensile tests were carried out at temperatures of 673 to 773 K and strain rates of 1×10⁻³ to 1 s⁻¹ on an ultrafine-grained (UFG) 5083 Al alloy containing 0.2 wt pct Sc fabricated by equal-channel angular pressing, in order to examine its high-strain-rate superplastic characteristics. The mechanical data for the alloy at 723 and 773 K exhibited a sigmoidal behavior in a double logarithmic plot of the maximum true stress vs true strain rate. The strain-rate sensitivity was 0.25 to 0.3 in the low-( <5×10⁻³ s⁻¹) and high- ( >5×10⁻² s⁻¹) strain-rate regions, and ∼0.5 in the intermediate-strain-rate region (5×10⁻³ s⁻¹< <5 × 10⁻² s⁻¹). The maximum elongation to failure of ∼740 pct was obtained at 1×10⁻² s⁻¹ and 773 K. By contrast, no sigmoidal behavior was observed at 673 K. Instead, the strain-rate sensitivity of 0.3 was measured in both intermediate-and low-strain-rate regions, but it was about 0.25 in the high-strain-rate region. High-strain-rate superplasticity (HSRS) in the intermediate-strain-rate region at 723 and 773 K was dominated by grain-boundary sliding (GBS) associated with continuous recrystallization and preservation of fine recrystallized grains by second-phase particles. However, the activation energy for HSRS of the present alloy was lower than that predicted for any standard high-temperature deformation mechanism. The low activation energy was likely the result of the not-fully equilibrated microstructure due to the prior severe plastic deformation (SPD). For 673 K, the mechanical data and the microstructural examination revealed that viscous glide was a dominant deformation mechanism in the intermediate- and low-strain-rate regions. Deformation in the high-strain-rate region at all testing temperatures was attributed to dislocation breakaway from solute atmospheres.     

Phase transformation of Zn-4Al-3Cu alloy during heat treatment

The phase transformation in Zn-4 Al-3 Cu alloy employing various solution-treatment temperatures (230 °C to 325 °C) was studied by means of microhardness, scanning electron microscopy (SEM), electron probe microanalysis (EPMA), transmission electron microscopy (TEM), and X-ray diffraction (XRD). The starting microstructure of the as-cast Zn-4Al-3Cu alloy consists of an α phase (aluminum-rich, fcc structure) in the η matrix (zinc-rich, h.c.p. structure) prior to solution-treatment. A platelike ε phase with 3-μm length and 0.5-μm thickness was found in the η phase matrix after solution-treating the as-cast material at 240 °C for 1 hour. The ε phase was then dissolved gradually back into the η matrix above that temperature. A four-phase transformation, α + ε → T′ + η, was observed from the temperature 250 °C to 310 °C, wherein the T′ phase formed at the interface of ε platelet and η phase matrix. This T′ phase was further identified as a rhombohedral structure. As the solution-treatment temperature was increased to above 310 °C, the ε phase was completely dissolved back into the η matrix and numerous β phase particles were distributed uniformly in the η matrix. The β phase subsequently decomposed at room temperature to a fine α phase embedded in the η matrix. For the materials solution-treated above 250 °C, the microhardness of the η matrix increased in 40 minutes during natural aging, which was associated with the formation of fine ε phase of 0.15-μm diameter. The orientation relationship between this fine ε phase and η phase was determined as .     

Epsilon carbide precipitation during tempering of plain carbon martensite

Epsilon carbide precipitation in steel martensite has been investigated by means of transmission electron microscopy. The first stage of tempering initiates with the nucleation of very fine ε-carbide particles on the closely spaced parallel line defects, the morphology being so-called “cross-hatched” ε-carbide needles. The ε-carbide particles which produce the well-defined dif-fraction patterns are related to the martensite matrix with a Pitsch and Schrader orientation relationship.^[32] These particles subsequently grow into rods elongated in the direction parallel to the within the matrix. The final reaction in the first stage is the rearrangement of ε-carbide rods into a disklike morphology. The e-carbide rods elongated in the 〈100〉_ε di-rections coalesce on planes in a raftlike manner, as in the case of those formed in the quench-aged low-carbon ferrite, the tetragonality of martensite being completely lost. Although the deviation from hexagonal symmetry about the [0001]_ε axis exists, no evidence of orthorhombic η-carbide formation was obtained.