Strain Rate Relationship Research Articles

Squeezing flow of a highly viscous incompressible liquid pressed between slightly inclined lubricated wide plates

The theoretical force-height relationships of Newtonian and pseudo plastic liquids compressed between slightly tilted frictionless plates are compared with those produced when the plates are perfectly parallel. It is shown that a very small inclination angle can distort the flow curve to such an extent that a Newtonian liquid will appear as a pseudo plastic fluid, and a pseudo plastic liquid as having a flow index considerably smaller than its true one. The shape of the biaxial elongational viscosity vs biaxial strain rate relationship is also highly sensitive to the plates' inclination angle. Thus, if an experimental force-height relationship is used to determine a material's biaxial elongational viscosity, an unsuspected slight tilt will result in a considerable underestimate of the viscosity. A slight tilt will also produce an apparent strain rate dependency in a Newtonian liquid, which obviously does not exist. The mathematical model developed to reach these conclusions was tested with commercial mayonnaise, a self-lubricating fluid. A reasonable agreement was found between the predicted force-height relationships and those experimentally determined at tilts of 1°, 3°, and 5°.

Superplastic Characteristics of Ti-Alloy and Al-Alloy Sheets by Multi-Dome Forming Test

The present study evaluates the superplastic material characteristics of Ti-alloy “Ti–4.5Al–3V–2Fe–2Mo”, SP-700, and Al-alloy “A5083”, which have been obtained by utilizing a multi-dome forming test. First, the flow stress vs. strain rate relationship was established for certain strain rate range, from a single circular sheet containing four different domes, sized 35, 30, 25, and 20 mm diameter, respectively. The multi-dome forming experiments were conducted under constant pressure at a superplastic temperature of 800°C for Ti-alloy and of 530°C for Al-alloy. The bulge forming of domes was also simulated by finite element method (FEM) to verify the experimentally-obtained material characteristics. Then the material characteristics obtained through multi-dome forming test were compared to those obtained by tensile step strain rate tests. In contrast to the predictions of the tensile test, the multi-dome forming test’s predicted time of deformation was generally in reasonable agreement with the results of the FEM simulation. There was no great difference, however, between the multi-dome forming test and the tensile testing with regard to the predicted final thickness distribution.

Evaluation of Superplastic Material Characteristics Using Multi-Dome Forming Test

Superplastic characteristics of Ti-alloy Ti-4.5Al-3V-2Fe-2Mo have been evaluated by multi-domed single sheet forming instead of commonly used tensile test. The flow stress versus strain rate relationship was established from a circular sheet containing four different domes, with diameters of 20, 25, 30, and 35mm. Multi-dome forming experiments were conducted under constant pressure at a superplastic temperature of 800°C. Membrane theory was used to calculate the flow stress and the strain rate at the apex of each dome. Forming processes such as superplastic hemispherical and box forming were simulated by FEM using material characteristics obtained from multi-dome forming and tensile tests. Finally the results of estimated bulging time and final thickness distribution obtained from the simulation were compared to those of experiments. Material characteristics obtained from multi-dome forming experiments showed good agreements with the FEM simulation in the estimated bulging time, whereas the tensile tests had some discrepancies with regard to the estimated bulging time Almost the same final thickness distribution were obtained in the simulations by using two material characteristics, multi-dome forming and tensile jump test, but the one from multi-dome forming was more close to real experiments.

Superplastic Deformation Behavior of the Y-TZP Tested in Torsion

Constant torque torsional creep tests for 3Y-TZP have been conducted in an ambient atmosphere at 1623K to 1773K in the torque range of 0.53 to 1.51Nm. While there are no traces of primary and tertiary creeps, the creep-rate decreases with the increase in strain due to concurrent grain growth. In the shear stress versus shear strain-rate relations obtained in the present experimental range, there exist two regions; one in which m-value is 0.43 to 0.45 and the other in which m-value is 0.21 to 0.22 above and below the shear stress of around 14MPa, respectively. In the former, i.e., high m region, grain size exponent, p ≃ 2 and activation energy, Q=443KJ/mol, whereas in the latter, i.e., low m region, p ≃ 3 and Q=490KJ/mol. The former region corresponds to the superplastic region II. Regarding the latter region, it seems to be relating to the existence of threshold stress.

608 ねじり応力下における3Y-TZPの超塑性変形挙動(オーガナイズドセッション : 超成形・超塑性と材料)

Constant torque torsional creep tests for 3Y-TZP have been conducted in an ambient atmosphere at 1623K to 1773K in the torque range of 0.53 to 1.51Nm. While there are no traces of primary and tertiary creeps, the creep-rate decreases with the increase in strain due to concurrent grain growth. In the shear stress versus shear strain-rate relations obtained in the present experimental range, there exist two regions; one in which m-value is 0.43 to 0.45 and the other in which m-value is 0.21 to 0.22 above and below the shear stress of around 14MPa, respectively. In the former, i.e., high m region, grain size exponent, p ≃ 2 and activation energy, Q=443KJ/mol, whereas in the latter, i.e., low m region, p ≃ 3 and Q=490KJ/mol. The former region corresponds to the superplastic region II . Regarding the latter region, it seems to be relating to the existence of threshold stress.

Processing, microstructure, strength, and ductility relationships in ultrahigh carbon steel assessed by high strain rate torsion testing

The torsional ductility and strength of an unalloyed ultrahigh carbon steel containing 1·3%C (UHCS–1·3C) has been studied at high strain rates (0·2–26 s-1 ) and high temperatures (750–1200°C). The strength–strain rate relationships are in agreement with a diffusion controlled dislocation creep model, where power law creep is observed with a stress exponent n of ∼5. The results were compared with the high temperature ductility and strength of a medium carbon (0·3%C) high strength, low alloyed (HSLA) steel, 304 stainless steel, and an alloyed ultrahigh carbon steel (UHCS–1·8C–1·6Al–1·5Cr). It is shown that the UHCS–1·3C material is the most ductile of the four materials, and has the lowest stress for plastic flow. The results are explained by the high rate of iron lattice diffusion and by the high stacking fault energy in the UHCS–1·3C material. It is proposed that contemporary processing and manufacturing equipment can be used to make pearlitic structure ultrahigh carbon steels for high strength room temperature applications.

Rheological characterisation of almost intact and stirred yogurt by imperfect squeezing flow viscometry

Samples of plain yogurt of two national brands, almost intact and after stirring for 1 min by hand and with a domestic blender, were placed in a wide shallow TeflonR container. They were subsequently compressed with a wide TeflonR plate to induce imperfect lubricated ‘squeezing flow’. The recorded force versus height relationships were plotted on logarithmic co-ordinates. The resulting curves all had a clear linear part indicating the region where squeezing flow was dominant. Its slope was on the order of −1.2 to −1.3 in the almost intact specimens and −0.5 to −0.9 in the stirred samples. The test reproducibility, expressed in terms of the coefficient of variation (100σ/ x) was on the order of about 15% more than sufficient to detect textural differences between the two brands and to monitor textural changes caused by stirring. These were expressed in terms of the apparent compressive stress at two preselected heights (1 and 2 mm) and the residual stress after relaxation for two preselected times (60 and 120 s). The flowability of the stirred samples was also expressed in terms of apparent elongational viscosity versus biaxial elongational strain rate relationships. All these mechanical parameters had a modest dependence on the upper plate diameter but the latter had no effect on their sensitivity as measures of yogurt consistency. © 1999 Society of Chemical Industry

Rheological characterisation of almost intact and stirred yogurt by imperfect squeezing flow viscometry

Samples of plain yogurt of two national brands, almost intact and after stirring for 1 min by hand and with a domestic blender, were placed in a wide shallow TeflonR container. They were subsequently compressed with a wide TeflonR plate to induce imperfect lubricated ‘squeezing flow’. The recorded force versus height relationships were plotted on logarithmic co-ordinates. The resulting curves all had a clear linear part indicating the region where squeezing flow was dominant. Its slope was on the order of −1.2 to −1.3 in the almost intact specimens and −0.5 to −0.9 in the stirred samples. The test reproducibility, expressed in terms of the coefficient of variation (100σ/ x) was on the order of about 15% more than sufficient to detect textural differences between the two brands and to monitor textural changes caused by stirring. These were expressed in terms of the apparent compressive stress at two preselected heights (1 and 2 mm) and the residual stress after relaxation for two preselected times (60 and 120 s). The flowability of the stirred samples was also expressed in terms of apparent elongational viscosity versus biaxial elongational strain rate relationships. All these mechanical parameters had a modest dependence on the upper plate diameter but the latter had no effect on their sensitivity as measures of yogurt consistency. © 1999 Society of Chemical Industry

Grain Boundaries in Superplastic Ceramics

Superplastic flow in fine-grained materials takes place mainly by grain boundary sliding. Micrograin superplasticity has been discussed mainly from the analysis of flow stress against strain rate relationship to find an accommodation process for grain boundary sliding. The phenomenological analysis has commonly been used to make clear the general features on micrograin superplasticity and will also be a major approach for superplasticity research in the future. However, some experimental facts reported in recent years, particularly in ceramic materials, cannot be understood from this type of analysis. This paper aims to show that microscopic analysis on grain boundary structure, chemistry and local atomic bonding state is very effective to break through the limitation of phenomenological approach.

Wave Dispersion and Attenuation in Viscoelastic Split Hopkinson Pressure Bar

A viscoelastic split Hopkinson pressure bar intended for testing soft materials with low acoustic impedance is studied. Using one-dimensional linear viscoelastic wave propagation theory, the basic equations have been established for the determination of the stress—strain—strain rate relationship for the tested material. A method, based on the spectral analysis of wave motion and using measured wave signals along the split Hopkinson pressure bar, is developed for the correction of the dispersion and attenuation of viscoelastic waves. Computational simulations are performed to show the feasibility of the method.

Elaboration of an Inelastic Constitutive Model of Superplasticity and Extension to Multiaxial State of Stress.

Elaboration of a uniaxial constitutive model of superplasticity taking account of grain and cavity growth proposed by the present authors and its extension to a multiaxial form are discussed. First the expression of an inelastic strain-rate is improved by adopting the hyperbolic sine law proposed by Garofalo to represent the stress dependence of inelastic strain-rate. The evolution equation of cavity volume fraction is also improved by incorporating the strain-rare dependence of cavity growth induced by inelastic deformation. A multiaxial constitutive equation at finite deformation is established by using the flow theory of von Mises type. Comparison of the predictions with the corresponding monotonic tension experiments in literature shows that the proposed model can give much better predictions of the typical deformation behavior of superplasticity ; e.g. the S-curve in the stress versus strain-rate relation on a log scale, the strain-rate dependence of the slope of hardening curve, the strain-rate history dependence of flow stress in the presence of static grain growth, and the softening of flow stress due to cavity growth.

Stress and velocity fields in glaciers: Part I. Finite-difference schemes for higher-order glacier models

AbstractThe set of force equations and stress strain-rate relations for ice masses can be solved with the method of lines and shooting the stress-free conditions at the free surface. Single- and multiple-shooting schemes with fixed point or Newton iterations for solving the stress equations including the deviatoric stress gradients are described and their performances arc discussed. The single-shooting Newton iteration proved to be the fastest seheme for typical valley glaciers, although its horizontal grid limitation is restrictive. Grid resolution can be improved substantially with a multiple-shooting scheme but computation time and storage requirements increase substantially. The Newton iteration allows the handling of mixed basal boundary conditions, partly basal velocity and partly basal shear traction being prescribed. A stick slip free gravity flow illustrates the performance of the scheme.

Stress and velocity fields in glaciers: Part I. Finite-difference schemes for higher-order glacier models

AbstractThe set of force equations and stress strain-rate relations for ice masses can be solved with the method of lines and shooting the stress-free conditions at the free surface. Single- and multiple-shooting schemes with fixed point or Newton iterations for solving the stress equations including the deviatoric stress gradients are described and their performances arc discussed. The single-shooting Newton iteration proved to be the fastest seheme for typical valley glaciers, although its horizontal grid limitation is restrictive. Grid resolution can be improved substantially with a multiple-shooting scheme but computation time and storage requirements increase substantially. The Newton iteration allows the handling of mixed basal boundary conditions, partly basal velocity and partly basal shear traction being prescribed. A stick slip free gravity flow illustrates the performance of the scheme.

Imperfect lubricated squeezing flow viscometry for foods

Commercial mayonnaise and mustard samples placed in a wide, shallow Teflon container were compressed by a wide Teflon plate to induce an ‘imperfect’ lubricated squeezing flow. A dominant squeezing flow regime could be clearly identified as a linear region in the log F(t) vs log H(t) relationship, F(t) and H(t) being the momentary force and specimen height respectively. The slope of the relationship enabled the estimation of the flow index, n, and the consistency coefficient K. The n values of the mayonnaise were on the order of 0.6–0.85 and those of the mustard about 0.7. The corresponding K values were on the order of 6–13 and 4–5 kPasn respectively. Considering the crudeness of the array the measurements were highly reproducible and sensitive enough to detect differences (mayonnaise) or establish similarities (mustard) in products of different brands. The calculated flow index was practically independent of the plate's radius and of the consistency coefficient, which had a weak dependency on the latter. The calculated elongational viscosity vs biaxial strain rate relationship could also be used to compare the different products and brands. At 0.01 s−1 the elongational viscosity of the maynonnaise was on the order of 150 kPas, and of the mustard 60 kPas.

A predicted in vivo muscle force – velocity trajectory

The in vivo stress–strain and stress – strain rate relationships of the adductor muscle in a swimming scallop (Placopecten magellanicus) were predicted on the basis of detailed measured swimming movements and a recently developed dynamic model that integrates all important mechanical elements in the process. The in vivo behaviour of the muscle was found to be quite different than the in vitro properties measured on isolated muscle fibres, which suggests that in general the latter might not be directly used to predict the in vivo mechanical events.

A computational model for fixity of spud cans on stiff clay : H. P. Jostad, F. Nadim & K. H. Andersen, Publikasjon - Norges Geotekniske Institutt, 191, 1994, pp 151–171; reprinted from: BOSS'94, 7th international conference on the behaviour of offshore structures, Massachusetts, 1994, Vol. 1: Geotechnics, ed C. Chryssostomidis & others (Elsevier), 1994, pp 151–171

An integrated analysis of a jack-up platform and its soil foundation system may increase the overall bearing capacity and provide more favourable structural response compared to a conventional analysis based on pinned footing condition. A model for the cyclic force-displacement and moment-rotation relationships of a spud can on stiff clay is presented. The model takes into account the effects of the loading history (degradation during cyclic loading), strain rate, strength anisotropy and non-linear stress-strain relationship of the clay, and coupling between all force-displacement components. It is valid for all load levels, including the combination of the static vertical load due to the submerged weight of the platform and cyclic forces (due to waves, wind and current) that cause failure of the spud can. The model performance is illustrated by an analysis of a jack-up platform at a deep water site. The results are compared with those based on the pinned footing condition and a maximum lower bound solution of the overall bearing capacity of the platform.(

High temperature deformation behavior of physical vapor deposited Ti-6Al-4V

A detailed study has been conducted of the high temperature creep and microstructural evolution accompanying the creep deformation of an initially nanocrystalline Ti-6Al-4V alloy. For test temperatures of 600 and 680°C the alloy transformed from an ( α + α′) to a single phase α during creep testing and exhibited exceptionally low creep resistance. During testing between 760 and 900°C, the alloy transformed to a conventional ( α + β) microstructure and exhibited up to ten times the creep rates of conventional grain size (superplastic) Ti-6Al-4V. Creep models based on grain boundary sliding, dislocation and diffusional creep were combined with relationships for phase evolution and grain growth to predict stress—strain rate relationships at each test temperature. The analysis indicates that in the low temperature region dislocation accommodated GBS, in conjunction with diffusional flow, are responsible for creep whilst in the high temperature region diffusion accommodated GBS is the dominant mechanism.

Long-Term Consolidation Characteristic of Diluvial Clay in Osaka Bay

ABSTRACT On large-scale reclamation works, the consolidation settlement of diluvial clays which lie deep underground should be discussed. The diluvial clay in Osaka Bay is in a quasi-overconsolidated state by cementation bonding. The values of the compression index and the void ratio are very large in spite of the large overburden pressure. Therefore, its consolidation characteristic is considered to be different from that of the alluvial clay. In this paper, a series of long-term consolidation tests is carried out, and it is revealed that the value of coefficient of secondary compression (Cα) under a load in the quasi-overconsolidated region becomes to be that in the normally consolidated region as time elapses. Considering the effect of strain rate, this result shows that the yield stress is dependent on the strain rate. This also means that even if a clay behaves as an overconsolidated clay in the test, it might behave as a normally consolidated clay in the site. Therefore, it should be considered that the in-situ secondary compression settlement was underestimated if it was calculated by using Cα of the laboratory test. In addition, the settlements on two reclamation works in Osaka Bay are calculated by a proposed long-term settlement analyzing method using strain rate and time relationship, and the results are in good agreement with the observed settlement data at sites.

Rate-dependent plasticity of copper and stainless steel under shock compression

Experimental copper and stainless-steel particle velocity profiles are analyzed to determine the plastic strain, plastic strain rate, and deviatoric stress through the shock front. A steady-wave shock analysis is used, together with a numerical characteristics-code calculation to correct for reflections created when the steady wave passes through the sample-window interface. The results are well represented by power-law relations giving the plastic strain rate as powers of the deviatoric stress and plastic strain. The effects of the sample-window interface are found to be minor for windows closely matched in impedance to the sample. The effects of the window on the strain-rate relation are appreciable only near peak compression.

Application of an Internal Variable Constitutive Model to Predict Creep Response of an Aluminum Alloy Under Multiaxial Loading

This paper discusses the application of an internal variable, creep constitutive model, where the concept of piecewise linearity in the effective stress-creep strain rate relationship is utilized. Since the concept of piecewise linearity is assumed, an explicit functional form for creep strain rate at all levels of stress and temperature is not required. The aforementioned constitutive model is used to predict the creep response of an aluminum alloy (2618-T61) at 200°C and subjected to multiaxial loading. The results are compared with available experimental results. The model shows excellent agreement in the trend of creep response. The quantitative values also agree quite good with the experimental results.