Activation Energy For Steady State Creep Research Articles

Tomographic method for evaluation of apparent activation energy of steady-state creep

A new method for the evaluation of the apparent activation energy of steady-state creep in metals is presented. It is based on in situ monitoring by microtomography the geometry of a specimen subjected to uniaxial load and inhomogeneous temperature distribution. It is shown that microtomography acting as a three dimensional extensometer enables the evaluation of local strain-rates of small material volumes and is an adequate tool for characterization of inhomogeneously deforming specimens. Activation energies obtained with the new method for stainless steel agree within an error of 5% with values obtained according to the classical procedure.

Primary Creep in Sn-3.8Ag-0.7Cu Solder, Part II: Constitutive Creep Model Development and Finite Element Analysis

A constitutive creep model is presented for Sn-3.8Ag-0.7Cu that incorporates both transient and steady-state creep to provide agreement for both creep and stress relaxation data with a single set of eight coefficients. The model utilizes both temperature-compensated time and strain rate to normalize minimum strain rate and saturated transient creep strain, thereby establishing equivalence between decreased temperature and increased strain rate. The apparent activation energy of steady-state creep, 83.6 kJ/mol, was indicative of both dislocation core and bulk lattice diffusion. A saturation threshold was defined that distinguishes whether transient or steady-state creep is dominant under either static or variable loading.

In situ tomographic investigation of brass during high-temperature creep

Microstructure evolution during high-temperature creep of a CuZn40Pb2 brass alloy was characterized in situ by synchrotron microtomography. It is shown that tomographic data are sufficiently accurate for local material characterization. Imposing a constant temperature gradient along the gauge length of the sample allows the apparent activation energy of steady-state creep to be evaluated for a single specimen.

A framework for modeling creep in pure metals

The process of creep in pure metals is modeled as the cooperative interaction of three phenomena: the thermally activated, force-dependent release of dislocation segments from obstacles; the substructural refinement of the microstructure due to plastic deformation; and the diffusion-controlled coarsening of the substructure. Key parameters are given as approximate generic values which can be varied. It is shown that for a wide range of parameters, the model reproduces the key features of the creep of pure metals: a steady-state stress exponent near 5 is recovered, and the key microstructural-length scale is related by a power law close to the reciprocal of stress (this dependence is not a strong function of temperature at a given stress). In addition, the activation energy of steady-state creep is nearly that of self-diffusion. Thus, the model reproduces the well-known phenomenology of puremetal steady-state creep. However, the present model is based on separate microstructural phenomena, which can be independently refined and studied.

Creep of CdZnTe at high homologous temperatures

The creep behavior of single-crystal Zn-doped CdTe was examined in the small strain regime. Specimens from two different sources, with tensile axes [110] and [112], were deformed at 1073 and 1173 K. Strain rates were of order 10−6 to 10−7 s−1. A laser interferometer was constructed to measure the small sample displacement. Cadmium overpressure was used to inhibit sublimation of test specimens at elevated temperatures. Some tests showed a transition from secondary to tertiary creep at low levels of strain. An activation energy for steady-state creep was calculated as QC = 1.46 eV, and the creep exponent was found to be approximately n = 4.2. These results, coupled with reported activation energies for self-diffusion of Cd in Cd(Zn)Te, indicate a dislocation creep mechanism. Etch pit density was measured before and after deformation and approached a common level regardless of initial etch pit density.

The Creep Behaviour of 310-Type Stainless Steel

Abstract The primary and steady-state creep behaviour of 310-type stainless steel has been investigated over the temperature range 500–700°C (0.46–0.58 Tm ). The steady-state stress exponent, n, increased slightly with increasing grain size, d, from n= 5.9 at d = 40 μm to n = 6.4 at d = 100 μm at a test temperature T = 600°C. The activation energy for steady-state creep, Q c, determined at σ = 300 MPa was 250±6.4 kJ mol−1 for d = 40 μm. This value of Q c is approximately equal to that for the volume self-diffusion of iron (280 kJ mol−1). The activation energy determined for primary creep is almost the same as that for secondary creep. The grain diameter parameter, m, in the equation ec = Aσn d m exp (− Q c/RT) was determined to be –1.67 for σ = 300 MPa and T = 600°C. This value is slightly different from a previously published value of m= −2, which was obtained at a lower applied stress. Using the strain-time data obtained in these tests, constitutive equations have been developed to describe both the pri...

Effect of Creep Damage on the Tensile Creep Behavior of a Siliconized Silicon Carbide

The tensile creep behavior of a siliconized silicon carbide was investigated in air, under applied stresses of 103 to 172 MPa for the temperature range of 1100° to 1200°C. At 1100°C, the steady‐state stress exponent for creep was approximately 4 under applied stresses less than the threshold for creep damage (132 MPa). At applied stresses greater than the threshold stress for creep damage, the stress exponent increased to approximately 10. The activation energy for steady‐state creep at 103 MPa was approximately 175 kJ/mol for the temperature range of 1100° to 1200°C. Under applied stresses of 137 and 172 MPa, the activation energy for creep increased to 210 and 350 kJ/mol, respectively, for the same temperature range. Creep deformation in the siliconized silicon carbide below the threshold stress for creep damage was determined to be controlled by dislocation processes in the silicon phase. At applied stresses above the threshold stress for creep damage, creep damage enhanced the rate of deformation, resulting in an increased stress exponent and activation energy for creep. The contribution of creep damage to the deformation process was shown to increase the stress exponent from 4 to 10.

中間温度域（０．２５‐０．３６Ｔ／Ｔｍ）における実用タングステン線材の変形特性

Tensile tests, creep tests and SEM observation of fractured surfaces are made to investigate deformation characteristics of sintered tungsten wires of 1.0 mm in diameter at intermediate temperatures. The failure occurs with no cup-and-cone fracture because of the chisel-edge type failure of individual fibers, giving several microcracks running along the separated fibers in the radial directions at the temperature range of 600 to 800 K. The number of microcracks decreases with increasing temperature and the double cupped fracture is observed at 1300 K. Typical curves are obtained from creep tests and the stress exponent of steady-state creep rate is about 7 characteristic of the sintered materials in which subgrains do not form during creep. The ratio of the activation energy for steady-state creep to the lattice diffusion energy is then calculated to be less than 0.5, which may result from the active short-circuit diffusion through many boundaries of fibers in the present material.

The stress and temperature dependence of steady-state flow at intermediate temperatures for pure polycrystalline aluminum

Torsion tests to large strains (ϵ = 3–10) in the intermediate temperature range (0.2−0.6 T m where T m is the melting temperature in degrees absolute) have been performed on high purity aluminum. Steady-state was reached at all temperatures except for 0.2 T m . Between 0.29 and 0.48 T m ä the activation energy for steady-state creep ( Q ss ) was found to be equal to about 87 kj mole −1 which corresponds quiteclosely to the activation energy for dislocation pipe diffusion as measured by Volin, Lie and Balluffi using a void shrinkage analysis. The relation between stress, σ ss, and strain rate, ϵ ss , in steady-state has been analyzed using an effective diffusion coefficient, D eff , for creep data over the temperature range 0.21-0.93 T m . The D heff utilized is based on all published diffusion data, namely two different additive lattice self-diffusion coefficients and one dislocation pipe diffusion coefficient. Over 21 orders of magnitude in ϵ ss / D eff , the data fit the equation ϵ ss D eff = B[ sinh(α σ ss E )] n , where α B and n are constants and E is the dynamic unrelaxed average Young's modulus. This Garofalo-type hyperbolic-sine equation is therefore a good representation of the steady-state behavior of pure polycrystalline aluminum. The activation energy for transient deformation, Q trans , was found to be dependent upon the method of testing. Q trans was greater than Q ss when calculated from temperature-change tests but less than Q ss when calculated from constant temperature tensile tests.

The effect of solute additions on the steady-state creep behavior of dispersion-strengthened aluminum

The effect of solute additions on the steady-state creep behavior of coarse-grained dispersionstrengthened aluminum alloys was studied. Recrystallized dispersion-strengthened solid solutions were found to have stress and temperature sensitivities quite unlike those observed in single-phase solid solutions having the same composition and grain size. The addition of magnesium or copper to the matrix of a recrystallized dispersion-strengthened aluminum causes a decrease in the steady-state creep rate which is much smaller than that caused by similar amounts of solute in single-phase solid solutions. All alloys exhibited essentially a 4.0 power stress exponent in agreement with the model of Ansell and Weertman. This was observed even in alloys whose matrix shows a much lower stress exponent when tested as a single-phase solid solution. The activation energy for steady-state creep in dispersion-strengthened Al−Mg alloys, as well as the stress dependence, was in agreement with the physical model of dislocation climb over the dispersed particles. For the dispersion-strengthened Al−Cu alloys, the activation energy for steady-state creep suggested that the kinetics of dislocation climb may be related to the mobility of copper'atoms in the matrix. Electron microscopic examination of the dislocation structure present after steady-state creep had been reached suggested that few mobile dislocations are involved in the steady-state creep process at the stress levels employed in this investigation.

Creep of Dispersions of Ultrafine Amorphous Silica in Ice

A technique was developed to produce ice containing a fine uniform dispersion of amorphous silica particles. Rates of creep in tension of dispersions with ½- and 1-volume % silica in ice were measured in the temperature range of −22 to −2°C and in the stress range of 4.64–17.8 bar and compared with those of pure ice. The silica dispersion strongly decreases creep in ice, resulting in steady-state creep rates in a 1-volume % dispersion 10–30 times slower than in pure ice. The activation energy for steady-state creep in dispersion-strengthened ice calculated from the temperature dependence of the creep rate is stress dependent with an average value of 97 kcal/mole, 6–7 times that for self-diffusion in pure ice. The steady-state creep rate increases exponentially with stress. This behavior differs from that of metallic coarse-grained dispersion-strengthened materials, in which the creep rate is proportional to a power of the stress and the activation energy is stress independent and equal to that for the self-diffusivity of the matrix metal. It is suggested that this unexpected behavior is due to particle-matrix decohesion in the ice-silica system, which interferes with the normal blockage of dislocation motion by second-phase particles during creep.

Creep of polycrystalline lithium fluoride

Abstract The creep behaviour of polycrystalline lithium fluoride under conditions of constant stress was investigated over the temperature range from 300°C to 550°C and found to be essentially similar to that observed in pure metals. The measured activation energy for steady-state creep was of the anticipated magnitude for diffusion of the fluorine ion, and the results suggest that the rate-controlling mechanism is some form of dislocation motion rather than the stress-directed diffusion of vacancies.

Investigation of the physical parameters of long-time fracture of pure polycrystalline nickel at temperatures above 0.45 Tm (where Tm is the melting point)

Parameters of long-time fracture of high-purity nickel at temperatures above 0.45 Tm and stresses higher than 3 kg/mm2 were studied. Our own and published experimental data was used to postulate an integration of the physical meaning of the coefficientβ and of the activation energy for steady-state creep and long-time fracture. A graphical method of determining the activation energy for creep was developed, in which the temperature dependence of elastic constants is taken into account.

Annealing and Creep of Dispersion-Strengthened Ni-Al<SUB>2</SUB>O<SUB>3</SUB> Alloys

Changes in the hardness and structure of dispersion-strengthened Ni-Al2O3 alloys (1∼5 wt% Al2O3) were observed by vacuum annealing at 1200°C for 5 hr. According to the result, the Ni-1%Al2O3 alloy showed the disappearance of the fiber texture and a slight change in hardness by further annealing. Hence the alloy was selected as a material suitable for the study of the steady-state creep mechanism, and creep tests were carried out at 650°∼800°C under a stress of 2∼6 kg/mm2.The results of the creep tests were compared with those theoretically obtained by assuming the fittest parameter values n and Q in the equation \dotε=Aσnexp(−Q⁄kT), where \dotε is the steady-state creep rate and Q is the activation energy, as proposed by Ansell et al.The values obtained by the authors are n=4.3–6.5 and Q=34.0–71.7 kcal/mol which are approximate to the theoretical ones on the assumption that dislocation climb is the rate-determining process. Moreover, it has been established that the activation energy for steady-state creep decreases with increasing applied stress.The values of the shear modulus μ, calculated from the theoretical formula \dotε=(2πλ2)⁄(hμ3kT)σ4D0exp(−Q⁄kT) by use of the experimental values, \dotε and Q, are in the range of 1012 dyne/cm2 which is comparable with those of nickel.

フェライト系Fe-Cr合金の定常クリープ速度と磁気変態温度との関連性

Tensile creep tests have been carried out with ferritic iron-chromium alloys (15, 20 and 25 wt%Cr) at temperatures ranging from 600° to 800°C and stresses up to 5 kg/mm2. The temperature and stress dependences of the steady-state creep rate have been studied with special reference to the magnetic transformation. The results obtained are as follows: (1) The greatest activation energy for steady-state creep is obtained at the magnetic transformation temperature. The activation energy at the higher temperatures does not seem to depend on stress and is higher than the activation energy for self-diffusion. Besides, at the lower temperatures a gradual decrease is found as the stress increases. These values are comparatively higher than the activation energies obtained above the magnetic transformation temperatures. (2) The stress exponent does not seem to depend on the temperatures. Transitional decrease in the activation volume occurred with increasing stress and two activation volumes for steady-state creep are obtained at each testing temperature. Both values are much larger than the atomic volume and increase as the temperature rises. (3) The experimental evidence seems to be governed to some extent by the diffusion-controlled mechanisms, partly by the climbing of edge dislocations and partly by the non-conservative movement of jogged screw dislocations. The models based on the viscous motion of dislocations due to dragging of solute atmosphere and diffusional flow of vacancies without accompanying the motion of dislocations will not be operative.