Showing papers on "Creep published in 1976"
TL;DR: In this article, the true stress-strain curves of polycrystalline aluminum, copper, and stainless steel are shown to be adequately represented by an exponential approach to a saturation stress over a significant range.
Abstract: The true stress-strain curves of polycrystalline aluminum, copper, and stainless steel are shown to be adequately represented by an exponential approach to a saturation stress over a significant range. This empirical law, which was first proposed by Voce, is expanded to describe the temperature and strain-rate dependence, and is put on a physical foundation in the framework of dislocation storage and dynamic recovery rates. The formalism can be applied to the steady-state limit of creep in the same range of temperatures and strain rates; the stress exponent of the creep rate must, as a consequence, be strongly temperature dependent, the activation energy weakly stress dependent. Near half the melting temperature, where available work-hardening data and available creep data overlap, they match. Extrapolation of the proposed law to higher temperatures suggests that no new mechanisms may be necessary to describe high-temperature creep. A new differential equation for transient creep also follows from the empirical work-hardening law.
1,357 citations
TL;DR: In this paper, the roles of grain-boundary sliding (GBS) and of other creep mechanisms in creep and fine-grain superplasticity are presented in relation to a model based on the division of grains into their central cores and peripheral “mantles.
Abstract: The roles of grain-boundary sliding (GBS) and of other creep mechanisms in creep and fine-grain superplasticity are presented in relation to a model based on the division of grains into their central “cores“ and peripheral “mantles”; GBS and its accommodation is limited to the latter, which changes with the mode of accommodation,viz by fold formation, dislocation motion in the mantle or pure diffusion. This description is used to adapt from the literature or develop equations for creep rate based on dislocation or vacancy mechanisms, which are then combined to give plots of the various regimes of superplastic (or creep) behavior, all of which involve GBS in a quantitatively defined manner. The predictions of these equations are compared with a number of results in the literature and with those of a lead-thallium alloy of grain sizes intermediate between superplastic behavior and normal creep. Some preliminary comparisons of measured GBS are also made with the predictions of the model. Agreement is good.
570 citations
TL;DR: In this article, a fracture mechanics approach was used to study high-temperature creep crack propagation, and crack growth rates were correlated with the C*-parameter which is an energy rate line integral.
Abstract: A fracture mechanics approach was used to study high-temperature creep crack propagation. Crack growth rates were correlated with the C*-parameter which is an energy rate line integral. For materials conforming to a nonlinear stress and strain rate relationship in the steady-state creep range, specifically, those which can be properly idealized as purely viscous (negligible elastic and transient creep effects), C* characterizes the crack tip stress and strain rate fields. Crack growth rate tests were conducted in the creep range on a discaloy superalloy at 1200°F (920 K). Two specimen geometries were tested, a center cracked panel and a compact geometry, to establish the geometry independence of this approach. The results showed that crack growth rate correlated with the C*-integral, while other parameters (K and nominal stress) failed to adequately characterize crack growth rate.
355 citations
343 citations
296 citations
TL;DR: In this article, the role of various alloying elements on the carbide dispersion is examined, and the effects of other metallurgical variables on the banded dispersions are discussed, including factors which influence the dispersion stability.
Abstract: This paper is concerned with the direct transformation of austenite at high temperatures to form ferrite and alloy carbide dispersions. The ferrite/austenite interfaces vary from high energy random boundaries to low energy planar boundaries which grow by step propagation, while the alloy carbide morphologies include a pearlitic form, fine fibers and fine banded arrays of particles. It is shown that these morphologies are closely related to the mode of growth of the ferritic matrix. The role of various alloying elements on the carbide dispersion is examined, and the effects of other metallurgical variables on the banded dispersions are discussed, including factors which influence the dispersion stability. The mechanical properties of directly transformed alloy steels are shown to depend largely on the ferrite grain size and the state of the carbide dispersion. Micro-alloyed steels subjected to controlled rolling provide an excellent example of the achievement of high strength and toughness levels by control of these variables. The paper finally attempts to show how such benefits can be achieved in low and medium alloy steels, and in particular where resistance to creep failure at elevated temperatures is an important property.
293 citations
TL;DR: In this article, the authors identified two processes which produce stick-slip instability in the frictional slliding of rock and identified the Bowden and Tabor adhesion theory to predict frictional behavior of rock when brittle fracture of asperities is inhibited.
289 citations
TL;DR: In this article, it is shown that a constraint on growth rate can occur in polycrystals because creep cavities are inhomogeneously distributed amongst the various grain boundaries, and that the rate of unconstrained cavity growth is directly proportional to the maximum principal tensile stress, whereas constrained growth is proportional to nth power of the octahedral shear stress.
Abstract: There have been a number of rate equations proposed in the literature for the growth of grain-boundary cavities during creep. Implicit in all these analyses is the assumption that growth occurs freely and that no constraints exist that would attenuate the predicted rates. It is shown that a constraint on growth rate can occur in polycrystals because creep cavities are inhomogeneously distributed amongst the various grain boundaries. This attenuation of growth rate is predicted to be greatest when high-strength alloys with large cavity populations are deformed slowly and least when pure metals with low cavity populations are deformed quickly. The application of these ideas to multiaxial stress states and extrapolation procedures is discussed in the knowledge that the rate of unconstrained cavity growth is directly proportional to the maximum principal tensile stress, whereas constrained growth is proportional to the nth power of the octahedral shear stress.
283 citations
TL;DR: In this article, a creep theory for precipitation-hardened alloys has been described, leading to a relationship of the type έ = A(έ-έp)4, where έp represents a back stress due to the particle dispersion.
Abstract: Recent experimental data of the stress/creep rate relationship for precipitation-hardened alloys have been surveyed. These materials display typically a higher stress-sensitivity of the creep rate than is observed for pure metals, and solid solutions. Furthermore, their stress/creep rate curves show pronounced breaks, with a stress-sensitivity of the creep rate, ∂ ln έ/∂ ln σ, of ∼4 below the break. The precipitation dispersion affects the creep rate such that it reaches a minimum at an intermediate interparticle spacing, with higher rates for both larger and smaller spacings. Based on the principles of recovery creep, a creep theory for precipitation-hardened alloys has been described, leading to a relationship of the type έ= A(έ-έp)4, where έp represents a back stress due to the particle dispersion. At high creep stresses έp is constant and defined by the stress to operate a particle-cutting mechanism or the Orowan mechanism. At lower stresses the dislocations are able to bypass the particles, s...
264 citations
TL;DR: The high temperature creep properties of single crystals of Ni-20Cr-2ThO 2 have been investigated in the temperature range 650-1300°C in this article, where single crystal tensile specimens were cut from plates having a large elongated grain structure and constant stress vacuum creep tests were conducted at various stresses and temperatures.
250 citations
TL;DR: In this paper, the authors compare the conditions under which hole growth without vacancy condensation is faster than hole growth by diffusion and show that low values of the ratio σ/e, where σ is stress and e is the strain rate, as well as large voids favour the strain process.
Abstract: In a creeping solid holes may grow by vacancy condensation or by the action of the applied stress producing strains at the surface of the hole which cause it to grow. The latter mechanism does not involve a vacancy flux to the hole. A comparison of the two processes indicates the conditions under which hole growth without vacancy condensation is faster than hole growth by diffusion. Low values of the ratio σ/e, where σ is stress and e is the strain rate, as well as large voids favour the strain process. Such conditions usually arise in tertiary creep but may also occur earlier in the creep life. Experimental examples of cavitation in which vacancy condensation is shown to be the minor process are given, and the relevance of such a mechanism to hole growth in grain-boundary sliding and regions of localized flow is indicated.
TL;DR: In this paper, the intrinsic time model for concretes is extended to concrete and it is demonstrated that the proposed model predicts quite closely: (1) stress-strain diagrams for concrete of different strength; (2)uniaxial, biaxial and triaxial stressstrain diagram and failure envelopes; (3) failure envelopes for combined torsion and compression; (4) lateral strains and volume expansion in uniaxia and biaaxial tests; (5) the behavior of spirally confined concrete; (6)
Abstract: A gradual accumulation of inelastic strain can be most conveniently described in terms of the so-called intrinsic time, whose increment depends on the time increment as well as the strain increments, and was previously developed for metals and is extended herein to concrete. It is demonstrated that the proposed model predicts quite closely: (1)Stress-strain diagrams for concretes of different strength; (2)uniaxial, biaxial, and triaxial stress-strain diagrams and failure envelopes; (3)failure envelopes for combined torsion and compression; (4)lateral strains and volume expansion in uniaxial and biaxial tests; (5)the behavior of spirally confined concrete; (6) hysteresis loops for repeated high compression; (7)cyclic creep up to 10 6 cycles; (8)the strain rate effect; (9)the decrease of long time strength; and (10)the increase of short-time strength due to low stress creep.
TL;DR: In this article, the creep process due to atmosphere dragging-controlled glide and climb of dislocations has been modelled and the resulting dislocation density and creep rate at the steady-state showed fair agreement with the experimental results on Class I alloys.
TL;DR: In this paper, a mathematical solution for the steady, quasi-static, plane strain advance of a shear fault in a fluid-infiltrated elastic porous material is developed.
Abstract: A mathematical solution is developed for the steady, quasi-static, plane strain advance of a shear fault in a fluid-infiltrated elastic porous material. As revealed through analysis of some elementary fracture mechanics models, the coupled deformation-diffusion effects in such a material lead to a required ‘force’ to drive the fault that increases continuously with fault velocity up to a maximum value. The nominal fault tip energy release rate required for spreading at this maximum is greater than that for very slow speeds by a factor approaching (1 - v)2/(1 - vu)2, where v andvu are the elastic Poisson's ratios under ‘drained’ and ‘undrained’ conditions, respectively. The effect is numerically significant and provides a mechanism by which a spreading shear fault can, within limits, be stabilized against catastrophic (seismic) propagation. Predictions of the model are compared to data representative of creep events on the San Andreas system. It is concluded that the speeds and slipping lengths of the observed events are consistent with their being stabilized by the effect discussed, and hence the model would seem to provide a viable mechanism for fault creep. Similar effects may be operative also in setting the time scale of progressive landslide failures in overconsolidated clay soils, in which rupture occurs by propagation of a narrow slip surface.
TL;DR: In this article, the authors showed that the creep strength of the Ni-Ti-Al alloy is at least comparable with that of the nickel-base superailoy MARM-200 for values ofT/T m in the range 0.68 to 0.82.
Abstract: Creep experiments have been made on a Ni-Ti-Al alloy, which has a microstructure consisting of a distribution of semi-coherent NiAl(β) precipitates with a Ni2AlTi(β′) Heusler phase matrix. The creep strength of this bcc type structure alloy is at least comparable with that of the nickel-base superailoy MARM-200 for values ofT/T
m in the range 0.68 to 0.82. Quantitative electron microscope experiments show that both undissociated α0〈110〉 dislocations, and paired α0〈100〉 dislocations coupled by a sublattice A.P.B. exist within the β′ phase;α
0 is the lattice parameter of a bcc cell of which the large Ni2AlTi unit-cell is composed. The sublattice A.P.B. is a crystallographic fault created by wrong bonds between atoms on the Al-Ti sublattice. Theoretically the energy γ of a sublattice A.P.B. is shown to be minimum on {100}, and the experimental value for γ on {100} is ~40 mJ/m2.
TL;DR: In this article, the double power law is extended by introducing the age dependence, which enhances the reliability in long-term extrapolation of creep data and also yields the correct age dependance of the conventional elastic modulus, E.
Abstract: The dependence of creep on load duration (t−t′) as well as age at loading t′ is described by the law [1+ϕ1t′-m(t-t′)n]/E0 in which m, n,ϕ1 E0=material parameters which are determined from test data by optimization techniques. The law is limited to basic creep, but with different values of material parameters it can also describe drying creep up to a certain time. The previous formulations are extended by introducing the age dependence. This also enhances the reliability in long-term extrapolation of creep data. Substituting t−t′=0.001 day, the law also yields the correct age dependance of the conventional elastic modulus, E. If E0, which is much larger than E, were replaced by E (as implied by previous power laws without age dependence), the age dependence of creep curves obtained by data analysis would be more scattered, the age dependence of E would have to be described by a separate formula, and more material parameters would be necessary to fit test data. The simplicity of the double power law is a major advantage for statistical evaluation of test data.
TL;DR: In this article, the number of cavities per unit volume was a function of the shear strain and independent of the stress state, and the results are compatible with the hypothesis that cavities are produced by grain interior slip and stabilized by plastic deformation induced internal tensile stresses.
Abstract: Submicrometre grain boundary cavities are produced in Nimonic 80A when plastic deformation in any of three different stress states is followed by a short anneal. Tension, torsion and compression specimens were plastically strained in a systematic manner and then annealed for 2 h at 750 °C. Detailed quantitative observations with a 1 MV microscope showed that the number of cavities per unit volume was a function of the shear strain and independent of the stress state. Furthermore the measurements revealed the surprising result that most cavities were on those grain boundaries which were parallel to the maximum principal stress axis. However, Preferential cavity growth occurred during subsequent tensile creep and cavities on these parallel boundaries either remained constant in size or diminished while those on boundaries which were orthogonal to the applied stress axis grew relatively quickly, thus producing the usual appearance of cavitated tensile samples. Plastic strain was more detrimental to torsional creep ductility when the direction of torque between plastic deformation and creep was reversed which is in accordance with the anisotropic cavitated boundary distribution. The results are compatible with the hypothesis that cavities are produced by grain interior slip and stabilized by plastic deformation induced internal tensile stresses.
TL;DR: The observed viscoelastic phenomena are discussed in terms of the structure of the collagenous tissue, and the advantages of the creep T -jump technique for the study of biological polymers are also discussed.
TL;DR: In this article, the authors analyzed the growth rate of creep crack on double cantilever beam (DCB) specimens for aluminium alloy RR58 and a chromium-molybdenum-vanadium steel.
Abstract: Creep crack growth tests, conducted on contoured double cantilever beam (DCB) specimens are described for aluminium alloy RR58 and a chromium-molybdenum-vanadium steel. The results are analyzed in terms of J, the rate equivalent of the J contour integral, which is a nonlinear fracture mechanics parameter. Direct proportionality is found between crack growth rate, ˙a and j. The treatment is shown to reveal a unification of the linear elastic fracture mechanics and net section or reference stress descriptions of creep cracking.
TL;DR: In this paper, twelve different combinations of hot die forging and heat treatment, in the α+β and β phase regions, were investigated, and the resulting heat treated forgings were classified into four distinct categories based on their microstructural appearance.
Abstract: To establish correlations between microstructure and mechanical properties for the Till alloy, twelve different combinations of hot die forging and heat treatment, in the α+β and β phase regions, were investigated. The resulting heat treated forgings were classified into four distinct categories based on their microstructural appearance. The room temperature tensile, post-creep tensile, fracture toughness and fatigue crack propagation properties were measured along with creep and low cycle fatigue at 566°C. The creep, tensile, fatigue crack propagation and fracture toughness properties, grouped in a manner similar to the microstructural categories. The fracture appearance and behavior of the cracks during propagation in fatigue and in fracture toughness tests were examined, and correlations with the microstructure discussed. In the case of the fully transformed acicular microstructure, it was found that the size and the orientation of colonies of similarly aligned α needles are dominant factors in the crack behavior.
TL;DR: In this article, the authors show that the mechanism associated with low n-values is probably the active one in many geological situations involving flow in fine-grained carbonates and corresponds to superplastic phenomena known to occur in finegrained metals.
TL;DR: In this paper, the authors investigated the effect of heat treatment on the creep strength of Si bearing Ti alloys and found that the highest creep strength was obtained by using a heat treatment which retained the maximum amount of silicon in solution.
Abstract: Operative creep mechanisms in laboratory melts of Ti-5Zr-0.5Si and Ti-5Al-5Zr-0.5Si have been investigated as a function of microstructure, creep stress, and temperature. From creep rate data and transmission electron microscopy results, it has been shown that an important creep strengthening mechanism at 811 K in Si bearing Ti alloys is clustering of solute atoms on dislocations. All of the alloys investigated showed anomalously high apparent activation energies and areas for creep, and a high exponent (n) in the Dorn equation. In addition, the effect of heat treatment was investigated and it is shown that the highest creep strength was obtained by using a heat treatment which retained the maximum amount of silicon in solution. This is consistent with the proposed creep strengthening mechanism. An investigation of the creep behavior of several other Si containing alloys including two commercial alloys, Ti-11 and IMI-685 indicated similar results.
TL;DR: In this paper, it was shown that the general applicability of the expression with p ≃ 3.5 is confirmed on a variety of nickel and iron-base alloys encompassing a range of microstructures commonly found in engineering materials.
Abstract: It has previously been shown that, during creep deformation, secondary creep rates (es) can be related to stress (σ) by the equationes = A*(σ−σ0)p exp (−Qc*/RT).The exponent p ≃ 4, Qc*≃an activation energy for diffusion (usually self-diffusion), and σ0 is a friction stress. The parameter A* is material-dependent so that creep data for a variety of materials appear as a set of parallel lines on a log es/log (σ−σ0) graph. In the present paper, the general applicability of the expression with p ≃ 3.5 is confirmed on a variety of nickel- and iron-base alloys encompassing a range of microstructures commonly found in engineering materials. Further, a single universal equation to describe the creep behaviour of the various materials has been developed. It involves normalization of the effective stress (σ−σ0) by the proof (σ0.05) or yield (σy) stress of the alloy at the appropriate creep temperature, resulting in the expressiones = B(σ−σ0/σ0.05)3.5with B independent of material, crystal lattice, microstru...
TL;DR: In this article, a ternary alloy of polycrystalline Ni2AlTi of stoichiometric composition was proposed for improving the high temperature creep strength of β-NiAl by a terneary addition giving rise to an additional degree of order.
Abstract: A specific method for improving the high temperature creep strength of β-NiAl by a ternary addition giving rise to an additional degree of order is examined. The ternary alloy thus formed has theA
2BC or Heusler type structure, and the present study is devoted to the creep behavior of polycrystalline Ni2AlTi of stoichiometric composition. Possible slip modes are predicted on the basis of the hard sphere model, and quantitative transmission electron microscopy is used to verify these predictions. All intracellular dislocations, and network dislocations have a α0〈110〉 type Burgers vector; α0 is the lattice parameter of a bcc cell of which the large Ni2AlTi unit cell is composed. The creep strength of this alloy is ∼ 3 times that of NiAl in its most creep resistant form, na mely [100] axis single crystals.
TL;DR: It is postulated that the coherence and elastic modulus of the fine ligated clot are largely due to steric blocking of long protofibrils with a high flexural stiffness.
01 Nov 1976
TL;DR: In this paper, a general model for high-temperature recovery-controlled creep is proposed, where cross slip of screw dislocations is introduced on an equal footing with climb of edge dislocation as a recovery process: cross slip and climb operate as two parallel concurrent mechanisms controlling the creep rate.
Abstract: A general model for high-temperature recovery-controlled creep is proposed. Cross slip of screw dislocations is introduced on an equal footing with climb of edge dislocations as a recovery process : cross slip and climb operate as two parallel concurrent mechanisms controlling the creep rate. A constitutive equation is derived from simple assumptions : Climb and cross slip are dominant in different domains of T and σ according to the relative magnitudes of the activation energies for self-diffusion QSD and cross slip Q CS(σ). The stress dependence of ἐ does not follow a power law except when climb is dominant, and intermediate values of apparent stress exponents are attributed to the existence of a transition domain. The published experimental evidence is compatible with this model ; the case of copper is reviewed as an example and it is shown that the low activation energy domain can be controlled by cross slip. The present approach is relevant to such problems as the influence of the stacking-fault energy on the creep rate or the creep of solid-solution alloys.
TL;DR: In this article, the results of using several of these techniques in structural studies on injection mouldings of glass fibre-reinforced grades of polypropylene and polyamide 66 are presented.
Abstract: Techniques which are readily available, and which may be considered suitable for the qualitative or quantitative assessment of fibre orientation distribution in short glass fibre-reinforced thermoplastics are reviewed. The results of using several of these techniques in structural studies on injection mouldings of glass fibre-reinforced grades of polypropylene and polyamide 66 are presented. Uniaxial tensile creep tests were carried out on specimens cut from the mouldings and the anisotropy of stiffness of each moulding is compared with that predicted from the structural studies. Certain of the structural techniques are considered to be unreliable or of restricted applicability and it is concluded that the technique of contact micro-radiography is the most versatile; being capable of yielding reliable qualitative or quantitative information on fibre orientation distribution. Detailed structural studies on edge-gated injection moulded discs, using the technique of contact micro-radiography, show that the fibre orientation distribution varies dramatically through the thickness of the mouldings, even in cases where uniaxial tensile creep tests suggest isotropy of stiffness in the plane of the moulding. Care must therefore be taken when seeking to relate flexural data to tensile data and strength data to stiffness data.
TL;DR: It is inferred that, although both primary and tertiary creep may be important in certain regions, large-scale ductile deformation in the Earth’s crust must be governed by secondary creep (steady state), which involves plastic deformation resulting from dislocation motion and diffusion.
Abstract: It is inferred that, although both primary and tertiary creep may be important in certain regions, large-scale ductile deformation in the Earth’s crust must be governed by secondary creep (steady state). This flow involves plastic deformation resulting from dislocation motion and diffusion. Geological, geophysical and geochemical observations constrain the temperature ( T ), strain rate (i), and stress difference (cr) for rocks undergoing secondary creep to: — 30-800 °C, 10_7-10-15 s-1, and up to 300 MPa (3 kbar). The actual conditions of secondary creep are strongly dependent on rock type and depth of deformation. Useful laboratory data on rocks obtained over wide ranges of T, e and cr are limited to ice, halite, marble, dolomite, quartzite and dunite. Steady-state flow results are available for both wet and dry rocks; H2O strongly affects the behaviour of both quartzite and dunite, but has a negligible effect on halite and marble. Secondary creep data for each rock are well fitted by exp ( ) crn, where Q is an activation energy for creep (diffusion) and A, R, n are constants. Comparison between those rocks expected in the deep crust indicates that at the highest T and at e of 10~12-10-15 s_1, cr is largest for dry dunite and dolomite, followed by dry quartzite, marble and wet quartzite. Equivalent viscosities ( ) range from 1018-1022 Pa s (1019-1023 P). At intermediate depths (at T = 300-500 °G), o9 in dolomite is slightly greater than dry quartzite; both are much stronger than marble. In the shallow crust, secondary creep is expected only in marble >250 °C) and in halite (T >2 5 °C). The y of halite at 25-250 °C, range from 1021—1017 Pas. At the surface and at e of 10~7—10_1° s-1 (glacier flow), of ice would be 1015 to 1012 Pa s between — 30 and 0 °C. Values of y for all rocks examined appear insensitive to T except wet quartzite and all dunite.
TL;DR: In this paper, a series of triaxial tests, using both these loading regimes, was carried out on reconstituted samples of a silty clay in order to quantify this similarity in terms of the relationship between stress and plastic strain.
Abstract: Previous investigations have indicated a similarity in the behaviour of clay under repeated loading compared with that under creep loading. A series of triaxial tests, using both these loading regimes, was carried out on reconstituted samples of a silty clay in order to quantify this similarity in terms of the relationship between stress and plastic strain. The samples were consolidated isotropically in the triaxial cell and brought to various overconsolidation ratios between 4 and 10. Undrained creep and repeated load tests were carried out using servo-hydraulic test equipment. The repeated load tests involved sinusoidal variation of deviator stress at a frequency of 10 Hz and constant confining stress. The development of plastic strain and mean pore-pressure in both types of test was shown to be similar. The results were expressed in terms of plastic strain rate as a function of time, applied deviator stress and stress history. The sinusoidal stress pulse was approximated by a step function which allowe...