Creep Behavior Of Materials Research Articles

Long-term creep of copper at cryogenic temperatures

The equipment designed and used in this study basically consists of a constant load lever arm creep machine, a vacuum thermally isolated cryostat that is cooled by a low rate of cryogen flow, and a testing to transmit the load onto the specimen. Briefly, Figure i shows the tensile testing insert and the cryostat schematically. The tensile testing insert consists of the pull rod, the compression tube, and the specimen grips. The temperature of the specimen can be controlled with an accuracy of +l°K. The strain of the specimen was measured directly using a strain gage technique, which is capable of resolving +1 uc on the specimen. Typical creep results at 77K and 34.5 MPa initial applied stress are given in Figure 2. There is no indication of the exhaustion of creep strain when the test was terminated at i00 hours. Indeed, a steady-state creep behavior rather than a logarithmic creep claimed in another study of copper (8) was observed. The derivative of the creep curve, i.e., strain rate versus time, is also plotted in Figure 2. The onset of the steady-state region, as shown by the minimum creep rate, was determined to occur at 75 hours. The steady-state creep rate was 4 x 10 -11 sec -I. From these results, it can be concluded that long-term creep testing (about 100 hours) is necessary to study the creep behavior of materials at very low temperatures. With the current ability of conducting long-term cryogenic creep tests, more creep data will be generated to systematically investigate the long-term low temperature creep behavior of OFHC copper and other materials at the 77 K range and at 4.2K. Acknowledgments The authors wish to thank the International Copper Research Association (INCRA) and Dr. L.M. Schetky, the Technical Director, for supporting this program. We also are grate

Superplasticity in Rapidly Solidified White Cast Irons

Superplastic properties of three different composition white cast irons were investigated in the temperature range of 630 to 725 °C. Fine structures consisting of 1 to 2 μm ferrite grains were developed in these materials by consolidation of rapidly solidified powders at intermediate temperatures below the A1 critical temperature. Tensile elongations of 1410 pct were found for a 3.0 pct C + 1.5 pct Cr white cast iron, 940 pct for a 3.0 pct C white cast iron, and 480 pct for a 2.4 pct C white cast iron when tested at 700 °C and at a strain rate of 1 pct per minute. The superplastic white cast irons exhibited a high strain rate sensitivity exponent,m, of 0.5 and activation energies for plastic flow were found to be nearly equal to the activation energy for grain boundary self-diffusion in iron. These observations are in agreement with the creep behavior of superplastic materials controlled by grain boundary diffusion.

Phenomenological description of high temperature transient creep for non-stationary loading conditions

The paper deals with the application of Garofalo's equation to the description of creep behavior of materials subjected to stress or temperature ramp loading. The analysis assumes that: (i) the steady state strain rate ϵ s is proportional to a power function of the effective stress σ c ( t) = σ − σ i ( t); (ii) the mean internal stress σ i is a function of time and applied stress σ; (iii) σ i approaches a stationary value irrespective of loading conditions. It is shown that for stationary creep, at otherwise unchanged conditions the acceleration at t = 0, \\ ̈ ge(0) will decrease with increasing σ and T, respectively. Similarly, for σ- and T-ramp loading, \\ ̈ ge(0) increases with increasing rates gs(0), T of the respective ramps at t = 0. Creep curves are calculated by means of Garofalo's equation choosing for σ i ( t) the particular form. These are qualitatively compared to experimental ones.

A Physically Consistent Method for the Prediction of Creep Behavior of Metals

A physically consistent method, which considers the deformation mechanisms, the active and latent hardening in single crystals, and their transient and steady creep, is proposed to predict the creep behavior of polycrystalline materials. This method consists of two steps: first, the material constants of single crystals are determined from the tensile creep data of the polycrystal, and then these constants are used to predict the creep properties of the same polycrystal under required loading conditions. This method simultaneously satisfies the requirements of equilibrium and compatibility over the grain boundaries, and is self-consistent. The proposed method was applied to calculate the creep strains of a 2618-T61 Aluminum alloy under pure shear, combined stress and nonradial loading; the results obtained were in good agreement with the test data.

Apparatus for i n s i t u creep testing during irradiation with high-energy neutrons from a planar neutron source

An apparatus is described for investigating the in situ creep behavior of materials during irradiation with neutrons having a spectrum similar to that of a fusion power reactor. Techniques are discussed for remote, high-vacuum creep testing during irradiation with high-energy neutrons from a planar Be(d,n) source used on the 1.93-m Isochronous Cyclotron at the University of California at Davis. Significant effects of radiation damage on the creep of niobium at a flux of 2 x 10(16) n.m(-2) s(-1) are reported.

Determination of tensile and compressive creep behaviour of ceramic materials from bend tests

We have developed equations that permit the determination of individual compressive and tensile creep rates from four-point bend test measurements made on trapezoidal bars. The equations developed are for the general stress dependence case. Finnie first proposed this type of analysis and solved the equations for the case of linear stress dependence. We present graphs that show solutions to the equations for the stress squared case. Creep measurements were performed on trapezoidal HS-130 Si3 N 4 bars to determine the ratio of compressive to tensile creep (β). The values determined on four separate tests using two different temperatures and beam dimension ratios b 2/b 1 gave fairly consistent results. The β′s for previously unstrained material are: 0.24, 0.14, 0.17, and 0.17 with the average value of β=0.18. For the case of prestrained Si3N4, β is 0.48. To further test the usefulness of this analysis, data from a conventional (rectangular bars) four-point bend test were taken from the literature and analysed using the equations developed in this paper and the average determined value of β. The individual tensile and compressive creep rates determined in this manner were found to agree very closely with other literature data measured in direct tension and compression tests.

Prediction of Creep Behavior from Stress Relaxation Data for Nonlinearly Viscoelastic Materials

Abstract The stress relaxation behavior of many polymeric materials can be expressed in a very simple fashion, because the logarithm of nominal stress fi(t) (based upon the undeformed cross-sectional area of the sample) plotted against the logarithm of time, t, is a straight line. Furthermore, these lines are often parallel, and with linearly viscoelastic materials, one obtains a straight line for the stress-relaxation modulus E(t)=fi(t)/εi, independent of the strain level. Thus, the linear stress-relaxation modulus can be expressed as: Ei(t)=Ei0·t−m, with Ei0 the modulus at t=1 s and m the slope of the straight line in the double logarithmic plot. Most polymers are, of course, nonlinearly viscoelastic (except for infinitesimal deformations); that is, the stress-relaxation modulus is a function of both time and strain. These time and strain effects can be factored out, if the log fi(t) versus log t curves are parallel: Ei(t,εi)=Ei0·t−mϕ(ε), where ϕ(ε), the strain function, is a measure of the nonlinearity of the viscoelastic response. It has been shown elsewhere that Ei0/ϕ(ε) is approximately identical to the modulus observed in the stress-strain measurement. With many polymers, creep experiments also yield approximately straight lines of slope n, when the logarithm of strain εi(t) is plotted against the logarithm of time. With nonlinearly viscoelastic materials, one generally does not obtain a set of parallel lines, when the stress fi, is changed. Therefore, it is not possible to separate the influence of time and stress on the creep compliance Di(t)=εi(t)/fi, as was the case for stress relaxation. It has been shown previously that the creep behavior can be predicted from stress-relaxation data with the help of the convolution integral. The numerical method involved is very laborious, however. It has been shown that the rate of creep may be predicted from the slope of stress-relaxation curves and the shape of the stress-strain curve. The purpose of this paper is to present a method by which the creep behavior of nonlinearly viscoelastic materials can be predicted in a simple fashion from stress-relaxation data. The theoretical predictions have been tested with the stress-relaxation and creep data of a block copolymer.

Cyclic Creep Behavior and Unstable Fracture under True Stress Controlled Cyclic Condition

Cyclic creep behaviors of material have generally been studied by the load controlled tension-compression low-cycle fatigue tests. The results obtained by the load controlled tests include the effect of the increase of the maximum tensile stress due to the progress of axial strain, in addition to the effect of cyclic softening of the material. To separate the two effects clearly, true-stress controlled cyclic tension-compression tests are made with brass and the results obtained are compared with those by the load controlled tests. Cyclic creep curves under true-stress controlled condition are found to consist mainly of the primary transient and the secondary steady stages, with lack of the tertiary accelerating stage. Cyclic creep characteristics are formulated as a function of the maximum cyclic stress and the number of cycles. A criterion of the unstable fracture under cyclic creep is also given.

Cyclic creep-type fracture and fatigue-type fracture in the constant-load low cycle fatigue tests

An approximate method of calculating cyclic creep deformation is proposed based on the cyclic creep behaviour of materials. The calculated values of the number of cycles and the maximum tensile strain at the starting point of unstable cyclic deformation were compared with some experimental results and fairly good agreement obtained between them. Combining this result with the authors' previous study on fatigue-type fracture in low-cycle fatigue, the number of cycles at the transition from cyclic creep-type fracture to fatigue-type fracture can be estimated quantitatively for each cyclic loading condition with a given stress ratio. The adequacy of this estimation for determining a limit of cyclic creep-type fracture was verified with experimental data.

Reference stresses and temperatures for cylinders and spheres under internal pressure with a steady heat flow in the radial direction

The paper examines the creep behavior of thick cylinders and spheres subjected to internal pressure and a negative temperature gradient in the radial direction. It is found that at stationary state the rate of radial displacement of the vessel wall is simply proportional to the material creep behavior associated with a single stress and temperature. Such “reference stresses” and “reference temperatures” are defined for spheres and cylinders of varying wall thicknesses. These reference stresses and reference temperatures are valid for any creep problem where the material behavior may be characterized by a function of the form ε _. ' = Kf(t) exp (γT)σ m . The extension of these results to variable pressure and temperature loading cases is discussed.

The influence of polycrystal grain size on several mechanical properties of materials

The ductile-brittle transition, hardness, fatigue, and creep behavior of polycrystalline materials are known to be influenced under certain conditions by the polycrystal grain size. These properties have been correlated, historically, with the material stress-strain behavior. The (Hall-Petch) stress-grain size relations are useful for describing the complete stress-strain behavior for polycrystals and, therefore, these relations provide a reference for understanding the manner in which these other properties should also depend on the grain size. In some cases, the grain size dependence of a particular property follows directly from this connection.

Creep and fatigue of engineering materials

Summary The creep behaviour of materials used in nuclear reactors, gas turbines and in electrical power plant is discussed in terms of the underlying physical processes. Our understanding of fatigue is less good, but it is possible to give qualitative reasons for particular fatigue characteristics of various engineering materials. Finally, the development of new materials is mentioned.

Yield Points and Delay Times in Single Crystals

Stress-strain curves and transient creep curves for single crystals are obtained from calculations based on the observed behavior of dislocations in LiF, and the strain rate equation, ε̇=bnv. The pronounced yield drops and apparent ``delay times'' predicted by the calculations are observed experimentally. This agreement between calculation and experiment implies that further consideration of the calculations may give some insight into the yield point and transient creep behavior of single crystals. Several parameters are varied in the calculation in order to determine the effect of such things as testing machine speed, machine hardness, rate of dislocation multiplication, work-hardening rate, number of mobile dislocations initially present, and the dependence of dislocation velocity on stress. The parameter that most strongly influences the yield points and transient creep behavior of a given material is n0, the number of mobile dislocations initially present. The wide range of observed yield point and transient creep behavior of various materials can be rationalized in terms of how dislocation velocity varies with stress; the less sensitive is the velocity to the applied stress, the more pronounced will be the yield drop or delay time. The calculation is applicable only when n0≠0; and the yield points and yield drops develop continuously and relatively gradually as dislocation motion and multiplication begin before the upper yield point is reached. The upper yield stress is not closely related to the stress required to unpin dislocations. It is necessary to distinguish between this type of yield point, which is commonly observed, and the Cottrell type of yield point in which dislocation motion begins at the upper yield stress, and in which the upper yield stress is related to the unpinning stress.

Analysis of compressibility in creep by the nonlinear elastic analogue

An elementary device for including compressibility effects on the creep behavior of materials is presented. A hollow sphere subjected to uniform pressures is analyzed to illustrate these effects. The stress solution is presented in closed parametric form.