Showing papers on "Stress relaxation 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 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
TL;DR: In this article, a model of dynamic ductile and brittle fracture was developed for wave propagation in one-and two-dimensional geometries, and the model features were taken mainly from detailed observations of samples partially fractured during impacts, but the functional forms are consistent with theoretical results where applicable.
Abstract: Computational models of dynamic ductile and brittle fracture are developed for wave propagation in one‐ and two‐dimensional geometries. The model features have been taken mainly from detailed observations of samples partially fractured during impacts, but the functional forms are consistent with theoretical results where applicable. Basic features of the models are the nucleation and growth (hence, the acronym NAG for the models) of voids or cracks, and the stress relaxation resulting from the growing damage. The results of the calculations include number and sizes of cracks, voids, or fragments as a function of position in the material. The NAG analysis presents the nucleation law, determined from experiment, and two growth laws: both growth and nucleation are functions of stress and stress duration. Procedures for treating cracks with a range of sizes and orientation are presented with the method for computing the stress relaxation that accompanies growth of damage. Brittle fracture is essentially aniso...
350 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: In this paper, the grain-boundary sliding during superplastic flow of the Pb-Sn eutectic was observed and a threshold stress of 1.3×106N m−2 was observed for the onset of super-plastic deformation.
Abstract: Dynamic observations of grain-boundary sliding during superplastic flow of the Pb-Sn eutectic are reported. These observations confirm the postulate that the dominant deformation mode during superplastic flow is grain-boundary sliding with localized deformation necessary to maintain grain coherency. Extensive grain-boundary sliding is also observed when the strain-rate and/or grain size is outside the superplastic flow regime. Stress relaxation tests were also carried out on the Pb-Sn eutectic. These tests provide data on the activation energy (45±5 kJ mol−1), grain-size dependence (d−3), and stress dependence of superplastic flow in this alloy. A threshold stress of 1.3×106N m−2 for the onset of superplastic deformation is also observed.
92 citations
TL;DR: In this paper, the steady state values of the dislocation density in the subgrain interior (ρi) and of the sub-grain size were determined by means of transmission electron microscopy.
86 citations
TL;DR: In this paper, a new technique enabled the recording of force and displacement and determination of compaction energy at pressures as high as 7000 lb/in2 and a piston velocity of 13 in/s.
78 citations
TL;DR: In this paper, a model of nonlinear viscoelasticity with relaxation times which depend on the structure is compared with experimental results reported in the literature for a L.D. polyethylene.
Abstract: A model of non-linear viscoelasticity with relaxation times which depend on the structure is compared with experimental results reported in the literature for a L.D. polyethylene. The single parameter of the model is determined by comparison with steadystate shear results. The model is then used to interpret various transient data. These are: tangential and normal stress growth in shear, stress growth in elongation, normal stresses in shear creep. The comparison shows a good general agreement, thus supporting the suggestion of relating the change in time of the relaxation spectrum to structural variables.
59 citations
TL;DR: In this paper, the translational rule in a nonlinear, kinematic hardening model was modified to simulate cyclic loading and axial strain accumulation for asymetric stress cycle.
Abstract: By modifying the translational rule in a non-linear, kinematic hardening model, it is shown that some phenomena occuring during cyclic loading can be simulated: stress relaxation for cycles with prescribed strain amplitude superposed upon fixed strain, axial strain accumulation for asymetric stress cycle, cyclic hardening or softening. It is also shown that the variation of hardening modulus along the yield surface after plastic prestrain is fairly well described by the present model. The accumulation and relaxation phenomena depend on additional material function which can be determined from uniaxial loading-unloading or cyclic loading tests.
56 citations
TL;DR: In this article, stress reduction tests were performed during steady state tensile creep of Al-11 wt.% Zn at 523 K and constant stresses between 10 and 30 MPa.
54 citations
TL;DR: The creep of α-Fe in vacuum has been studied for the ranges of stress from 0.3 to 4.6 MN/m 2, of temperature from 758 to 1103 K (0.42 − 0.61 T m ), of intercept grain size from 32 to 102 μm and of test duration from 2 to 550 hr as mentioned in this paper.
TL;DR: In this paper, the authors analyzed the effect of activation volume on the effective stress σ ∗ (i.e., the difference between the applied and internal stress) through the relation νσ ∗ = ακT, where α is a constant, the value of which is between 6 and 12 depending on the type of flow and the material under study; α is the Boltzmann constant and T the absolute temperature.
TL;DR: In this paper, the activation volume of LD and HD polyethylene was found to satisfy the relation vσ* ≈ 10kT, where σ* is the effective stress, k is Boltzmann's constant, and T is the absolute temperature.
Abstract: Internal stress levels and values of the activation volume have been evaluated from the kinetics of stress relaxation in annealed samples of LD and HD polyethylene. The initial deformation of the samples was varied, the maximum values amounting to ca. 1%. The temperature of the experiments was 24°C for LDPE, and 24°, 50°, and 69°C for HDPE. The internal stress level was found to be approximately proportional to the initial deformation and independent of the temperature used. Such internal stresses appear to be introduced upon deformation, since permanent stresses had been removed by careful annealing. The activation volume (v) was found to satisfy the relation vσ* ≈ 10kT, where σ* is the effective stress, i.e., the difference between the applied and internal stress, k is Boltzmann's constant, and T is the absolute temperature. This is in good agreement with results reported elsewhere for a wide variety of materials. This relation applies primarily to the exponential flow portion of the relaxation curves, but by a simple transformation the power‐law region can also be encompassed. Copyright © 1976 John Wiley & Sons, Inc.
TL;DR: In this article, the force relaxation curves of deformed specimens of apples, pears and potatoes were studied in compression tests and it was found that ln all three commodities two relaxation curves could cross one another even if one of them started at conditions in which both the deformation and the initial force had higher values.
Abstract: The force relaxation curves of deformed specimens of apples, pears and potatoes were studied in compression tests. It was found that ln all three commodities two relaxation curves could cross one another even if one of them started at conditions in which both the deformation and the initial force had higher values. It was also noticed that for deformations bigger than about 5% the residual force was dependent on the rate at which the deformation had been reached. The values of the residual forces of samples deformed at a rate of 10 cm/min were smaller than the values of those samples which were deformed at 1 cm/min. These characteristics of the relaxation phenomenon could be explained by physical irreversible changes which occur during the deformation of the biological material. They could also be represented by a modified rheological model in which the number of active elements and their mode of mechanical response is a function of the deformation and its application rate.
TL;DR: In this paper, the authors point out that interpretations from stress changes alone during oriented crystallization have led to widely different proposed chain conformations and consequently very different crystallization mechanisms for strain-induced crystallization (SIC).
Abstract: This paper points out that interpretations from stress changes alone during oriented crystallization have led to widely different proposed chain conformations and consequently very different crystallization mechanisms for strain-induced crystallization (SIC). Many of the proposals, including the one by Keller and Machin which takes into account some electron microscopy and X-ray observations, show varying degrees of incompatibility with existing stress relaxation, kinetic or morphological data on SIC. Another problem lies in the difficulty with proper interpretation of observed morphology on samples which have been Subjected to additional thermally-induced crystallization (TIC) after SIC, especially, in the absence of prior characterization of SIC crystallites, the finding of a fibrillar-to-lamellar transformation in stretched polymers upon additional TIC (Part H) also indicates that the generally-observed oriented lamellar morphology has a much more subtle origin than-that depicted by most crystallization models. Part I discusses our previously published morphological data on the characteristics of SIC crystallites from the melt, which includes: (a) their melting point elevation, (Tm » T°m), (b) their nearly perfect crystalline orientation function (fc ∼ 1), (c) their fast rates of crystallization (t1/2 < 1 sec), and (d) their fibrillar morphology and limited dimensions along the fibrillar stretch axis (∼100A). Examples of morphology of SIC from the glass and from stirred solution are also included to show the overall similarity of fibrillar morphology brought about by stretching.
TL;DR: In this article, the effect of steady-state creep rate on applied stress sensitivity was investigated in three Zr-Nb alloys (0.5, 2.5 and 4.5 wt% Nb) in a temperature interval 350 to 550°C using transmission electron microscopy techniques.
TL;DR: In this article, the authors examined the effect of the variation of the mobile dislocation density during stress relaxation on the thermal activation parameters such as the dislocation velocity-stress exponent, m∗, athermal component of the flow stress.
TL;DR: In this paper, the authors compared the dynamic and static creep rates for a cyclic stress of 29.8 to 3.7 MPa over the temperature range of 302 K to 348 K and found that the dynamic creep rate increased with increasing strain and decreasing temperature.
Abstract: The creep of 99.999 pct pure aluminum subject to tension-tension cyclic stressing (dynamic creep) has been studied and compared to creep for the peak cyclic stress applied statically (static creep). The creep rate for a cyclic stress of 29.8 to 3.7 MPa was always found to be greater than the creep rate for static application of a stress of 29.8 MPa over the temperature range of 302 K to 348 K. The ratio of the dynamic creep rate to the static creep rate was found to increase with increasing strain and decreasing temperature. The apparent activation energy measured for dynamic creep was less than that measured for static creep. The substructure for dynamic creep is softer than for static creep and probably accounts for the accelerated creep rate and the lower observed activation energy.
TL;DR: In this paper, it was shown that the strain/time behavior following small stress decreases during steady-state creep of copper, α-brass and a two-phase copper-cobalt alloy cannot be accounted for in terms of a subgrain size dependence of creep but merely reflects the limited extent of recovery after a stress reduction.
Abstract: It has been shown that the strain/time behaviour following small stress decreases during steady-state creep of copper, α-brass and a two-phase copper-cobalt alloy cannot be accounted for in terms of a subgrain size dependence of creep but merely reflects the limited extent of recovery after a stress reduction.
TL;DR: In this article, the authors used diffracting X-rays at high Bragg angles from a filler consisting of crystalline particle or powders to measure tensile and compressive stresses in amorphous polymers.
Abstract: Experiments are described which show that stresses in amorphous polymers can be measured by diffracting X-rays at high Bragg angles from a filler consisting of crystalline particle or powders. The method is applicable, when calibrated, to both applied and residual stresses, to stress relaxation studies, to both tensile and compressive stresses, to both interior and surface positions in an object, and to composites of various types as well as to polymers that are substantially homogeneous. In the lower (Hookian) range, strains and stresses in metallic embedded particles increase linearly with applied stresses and strains in the matrix. When applied stresses exceed an apparent yield point, which correlates with the yield strength of the metallic filler, the elastic strains in the particles increase only slightly or even decrease as the matrix strains are increased, and with constant applied strain, the particles reveal changes due to relaxation. Strains in the particles are found to be smaller, and stresses higher, than in the matrix. Tests of graphite-fiber epoxy composites with embedded filings of silver or aluminum alloy show that compressive residual stresses from curing at 350°C and cooling to room temperature are registered in the particles as well as stresses externally applied to the cured composite. Precision of the order of 1000 psi (0.7 kg/mm2 or 6.9 M Pa) was obtained with measurements made and evaluated rapidly and simply; with more refined techniques, much higher precision would be possible.
TL;DR: In this article, the authors investigated the stress relaxation effect in an incompressible elastico-viscous fluid for the case of the lubrication of line-contact rollers and showed that a significant increase in the load capacity is obtained, owing to the relaxation time of the fluid.
Abstract: The stress relaxation effect in an incompressible elastico-viscous fluid is investigated for the case of the lubrication of line-contact rollers. Two extreme cases are considered: that of low pressures with rigid surfaces and constant viscosity and that of heavily loaded elasto-hydrodynamic lubrication. In order to solve this problem, a new invariant material time derivative is suggested. This derivative is referred to a co-ordinate system attached to the principal axes of the strain-rate tensor, while the former derivatives have been referred to the fluid particle. It is shown that, unlike the previous derivatives, the new one enables a separate parametric description of the stress relaxation process and the first normal-stress difference. The results show that a significant increase in the load capacity is obtained, owing to the relaxation time of the fluid. The investigation is for fluids with a relaxation time small compared with the transit time of the lubricant through the bearing.
Patent•
19 Nov 1976TL;DR: In this article, a process for providing copper base alloys with a combination of high strength and high strength to ductility characteristics is disclosed, where the alloys are hot worked, solution annealed and subjected to a controlled cooling to provide the desirable strength-ductility combinations.
Abstract: A process for providing copper base alloys with a combination of high strength and high strength to ductility characteristics is disclosed. The alloys should be those copper alloys which exhibit continuous, homogeneous precipitation of coherent particles such as spinodal decomposition upon precipitation hardening. The alloys are hot worked, solution annealed and subjected to a controlled cooling to provide the desirable strength-ductility combinations.
TL;DR: In this article, it was shown that such relations are not likely to exist when cast in terms of the common variables stress, strain, strain rate, and temperature, and introduced at least one evolutionary variable is necessary.
TL;DR: A deformation mechanism map, depicting the fields of stress and temperature in which modes of plastic flow are dominant (i provide the fastest strain rate) has been calculated for polycrystalline, stoichiometric galena for each of two grain sizes; namely, 10 and 103 μm as mentioned in this paper.
TL;DR: In this article, the effect of fast neutron flux at 570 K on the creep rate of specimens of zirconium-2.5 wt% niobium alloy taken from tubes in various metallurgical conditions, using both constant load tensile creep machines and bent-beam stress relaxation.
TL;DR: A theory is developed for the uniaxial viscoelastic behavior of rabbit skin tissue when small incremental strains are super-imposed on large constant deformation.
Abstract: Results of 58 biaxial and uniaxial stress-relaxation tests on flat specimens of abdominal rabbit skin are analyzed. It is shown that rabbit skin is a nonlinear viscoelastic material, i.e., the relaxation mode of each stress component depends on the strain (or alternatively on the initial stress). The dependence of the relaxation mode on the initial stress is investigated in terms of a modified power law with three parameters (Eq. (15)) which are functions of the initial stress. The differences and similarities between uniaxial and biaxial stress relaxation tests and the effect of the tissue “preconditioning” is discussed. On the basis of the results a theory is developed for the uniaxial viscoelastic behavior of rabbit skin tissue when small incremental strains are super-imposed on large constant deformation.
TL;DR: Arai and Niinomi as mentioned in this paper showed that the dependence of stress on λ could be described by the Mooney-Rivlin equation; the coefficients C1 and C2 were obtained from two linear plotting procedures.
Abstract: Relaxation of stress in simple extension of polyisobutylene (viscosity‐average molecular weight 2.3×106) has been measured at stretch ratios (λ) up to about 2. Data at 3, 25, and 50°C were reduced to 25°C. At any instant of reduced time, the dependence of stress on λ could be described by the Mooney‐Rivlin equation; the coefficients C1 and C2 were obtained from two linear plotting procedures. At short times, C1 decreased rapidly while C2 remained essentially constant. Two to three logarithmic decades of time later, C2 decreased. Thus, the terminal zone of viscoelastic behavior corresponds solely to the C2 contribution. This result confirms measurements by Arai and Niinomi (Kogyo Kagaku Zasshi, 74, 2525 (1971)) on polyisoprene and styrene‐butadiene rubber and measurements by Noordermeer and Ferry (J. Polym. Sci., (1976), in press) on 1,2‐polybutadiene. Tentative interpretations in terms of motions of entanglements are discussed. Similar measurements on a sample of polyisobutylene which had been heated with...