Stress-strain Rate Relationship Research Articles

Ice flow at low deviatoric stress

AbstractThe effective viscosity of ice depends upon many factors, including temperature, deviatoric stress, crystal orientation and impurities. A flow law that includes these factors and is simple to implement is a requirement for numerically efficient ice-flow models. The dominant microscale flow mechanism changes as temperature, deviatoric stress or grain-size changes. For both anisotropic and isotropic constitutive relations, this shift in dominant flow mechanism is expressed as a change in the stress exponent. We study the effects of this shift in stress exponent on ice flow using a two-term flow law for isotropic ice. Our stress–strain-rate relationship does not explicitly describe the microscale processes of ice deformation; however, it encompasses a range of deformation behaviors with a simple law. In terrestrial ice, a flow-mechanism shift may occur in low-deviatoric-stress regions near ice divides, resulting in a near-linear constitutive relationship for ice flow. Compared to a non-linear (Glen) divide, a divide dominated by a near-linear flow mechanism has vertical-velocity profiles that are similar at divide and flank sites, internal layers that do not develop a Raymond bump, and a steady-state surface profile that is more rounded near the divide.

FE simulation of rectangular box forming using material characteristics from the multi-dome forming test

The finite element (FE) simulation of superplastic rectangular box forming process was conducted to examine the validity of the material characteristics, stress–strain rate relationship, strain rate sensitivity, m, and strength coefficient, K, which have been obtained by utilising a multi-dome test. The simulation results were then compared with those obtained with material characteristics from the tensile jump test. The material characteristics m and K were included as variable parameters and a function of the strain rate in a special subroutine. The subroutine was linked to the FE simulation in order to investigate the correctness of the superplastic material characteristics. The influence of die shape factor (length-to-width-to-depth ratio) and die friction on the deformation behaviour and on the final thickness distribution was also demonstrated. The results of rectangular box forming simulation revealed that the multi-dome test can be used not only in simple processes (such as free bulge-forming) but also in more complex situations such as rectangular box forming process and with consideration of the friction between the sheet metal and the die surface.

Comparative study of a high-strain-rate superplastic Al-4.4Cu-1.5Mg/21SiCW sheet under uniaxial and equibiaxial tension

In this paper, the strain rate sensitivity exponent and the cavitation behavior of a high-strain-rate superplastic Al-4.4Cu-1.5Mg/21SiCW sheet were examined under uniaxial and equibiaxial tension at the optimal temperature of 793 K. A maximum elongation of about 335% was obtained at the initial strain rate of 0.17 s−1. It was found that the strain rate sensitivity of the composite under uniaxial and equibiaxial tension was 0.34 and 0.36, respectively. The reasons for a large discrepancy between uniaxial and equibiaxial stress versus strain rate curves were analyzed. It was concluded that the flow stress–strain rate relationship determined from uniaxial tension could be used for forming processes subject to complex stress states after proper adjustment. The amount of cavity was found to increase with increasing strain and the amount of cavity obtained under equibiaxial tension was slightly larger than that under uniaxial tension at the same effective strain rate. A slightly higher cavity growth rate parameter was also observed under equibiaxial tension. The experimental results revealed that the cavity growth was essentially plastic-controlled. It was suggested that the presence of liquid phase was beneficial to nucleation at the interfaces and limited the cavity growth rate.

Diffusional Creep: Stresses and Strain Rates in Thin Films and Multilayers

AbstractIn this article, we discuss creep deformation as it relates to thin films and multilayer foils. We begin by reviewing experimental techniques for studying creep deformation in thin-film geometries, listing the pros and cons of each; then we discuss the use of deformation-mechanism maps for recording and understanding observed creep behavior. We include a number of cautionary remarks regarding the impact of microstructural stability, zero-creep stresses, and transient-creep strains on stress–strain rate relationships, and we finish by reviewing the current state of knowledge for creep deformation in thin films. This includes both thin films that are heated on substrates as well as multilayer films that are tested as freestanding foils.

An experimental investigation of a superplastic constitutive equation in Al–Mg–Si alloy composites reinforced with Si3N4 whiskers

Superplastic properties at 818 K were investigated by tensile tests for Al–Mg–Si alloy composites reinforced with Si3N4 whiskers whose volume fractions were 0–30%. The 20 and 30 vol.% composites exhibited large elongation of 615 and 285% at a high strain rate of 2×10−1 s−1, respectively. High strain rate superplasticity of the composites is attributed to the very small grain size of less than 3 μm. The stress–strain rate relation for the composites was almost the same as that of the alloy, taking into consideration the influences of threshold stress and grain size, and the relation was independent of the volume fraction of whisker. This is probably because grain boundary sliding was not hampered by the whiskers due to the presence of liquid phase for the composites.

The role of solution chemistry in the stability and detachment of cohesive kaolinite particles

The effect of solution chemistry on the behavior of kaolinite in three different situations was investigated: (1) the detachment of kaolinite from glass beads in a fluidized bed, (2) the erosion of kaolinite deposits in a laboratory flume and (3) the determination of the stress-strain rate relationship of concentrated suspensions in a rheometer. The experimental results from these three different approaches could be explained in terms of changes in mode of particle associations which in turn could be characterized in terms of a micromechanical force model which predicts the effect of solution chemistry on the interaction force between adjacent particle surfaces. Understanding the relationship between solution and surface chemistry on the structure, mechanical strength and mechanism of erosion of cohesive sediment deposits is an important step towards developing predictive models of a number of processes including erosion of cohesive sediments in streams and estuaries, and detachment of particles from granular media during filtration and filter backwashing.

High Temperature Deformation of a Yttria-Stabilized Tetragonal Zirconia

The creep behavior of a high-purity tetragonal zirconia polycrystal containing 3 mol% yttria (3Y-TZP) is characterized with a stress exponent of n∼2.7 and a grain size exponent of p∼2.0-3.0 in a high stress region, and with n∼1.3 and p∼2.0 in a low stress region. These regions are connected with a transition region with n≥5, and accordingly the creep stress-strain rate relationship as a whole exhibits a sigmoidal feature. The apparent activation energy in the high and the low stress regions is the same, 580 kJ/mol, which corresponds to a value reported for lattice diffusion of cations. In the high stress region, evidence of intragranular dislocations revealed by TEM suggests that the motion of intragranular dislocations would contribute to the accommodation process of grain boundary sliding. In the low stress region where such dislocations were not observed, the combination of n∼1.3 and p∼2.0 suggests an intervention of lattice diffusion creep.

Fuzzy algorithm for calculating roll speed variation based on roll separating force in hot rolling

Thickness control of hot-rolled strips has become an important issue in recent years because of the need for improving the quality of the hot-rolled strip. For this purpose, various thickness control systems such as finishing mill set-up (FSU), automatic gauge control (AGC), and looper control system, have been developed at steel works. Although these systems have greatly improved the quality of the strip thickness, there still exists a small amount of thickness deviation. It is difficult to adequately control by applying conventional thickness control techniques since hot rolling process is a highly nonlinear system in which many process parameters are coupled. In this study, a fuzzy algorithm to calculate the roll speed variations was developed in order to improve the thickness uniformity of hot-rolled strips. Since the strip thickness is mostly affected by the magnitude of roll separating force depending on the roll speed, the strip thickness deviation between the desired and actual thicknesses can be reduced by controlling roll speed. In order to carry out this investigation, slab analysis was carried out to determine the relation between roll separating force and roll speed for various process parameters such as roll speed, reduction ratio, strip entry thickness, and front and back tensions. From the production data, the effective stress-strain rate relations of the materials used in slab analyses were acquired. Based on the analytical results, the relation between roll separating force and roll speed was approximated by a log function. A fuzzy algorithm was developed to determine variations in roll speed according to variations of roll separating force, depending on various ranges of rolling temperature, reduction ratio, front and back tensions, and strip thickness. In addition, simulations to predict roll speed variations for a small amount of thickness deviation were carried out at continuous finishing mills consisting of seven stands and the calculated roll speed variations were found to be reasonable. Thus, the developed fuzzy algorithm might be useful in reducing the thickness deviation in the actual hot rolling mills.

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.

High-temperature tensile ductility in WC-Co cemented carbides

High-temperature tensile deformation in WC-Co was investigated at temperatures between 1150 °C and 1250 °C. The flow stress is sensitive to temperature, strain rate, volume fraction of binder, and the addition of other carbides. The stress-strain rate relationship is divided into three regions at each temperature as in superplastic metals. A large tensile elongation over 100 pct was first obtained in WC-6Co and WC-13Co (wt pct) at temperatures of 1200 °C. Contrary to superplastic metals, the largest tensile elongation is not obtained in region II but on the border of regions I and II. The failure mode changes from necking in region I to sharp cracking in region II.

エラータ : 流動粉粒体 (粗大粒子) の応力と歪み速度の関係

エラータ : 流動粉粒体 (粗大粒子) の応力と歪み速度の関係

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流動粉粒体（粗大粒子）の応力と歪み速度の関係 離散要素法と実験による導出

流動粉粒体（粗大粒子）の応力と歪み速度の関係 離散要素法と実験による導出

Determination of a Dynamic Constitutive Equation of Hard Steels Based on a Bending Test.

The dynamic and static stress-strain curves of steels (SCM3, SUJ2, S55C, SK3) hardened by heat treatment from HV360 to HV820 were determined by means of a three-point bending test under various strain rates. For convenience, an instrumented Charpy impact bending was used at high strain rates, and a previously proposed constitutive equation was applied to these curves. Results agreed well with the experimental values and their applicability to hard steels was shown. The experimental constants included in the equation for the present materials were closely concerned with the hardness. Therefore, the calculated curves of the stress-strain rate relation at a given strain using constants expressed by the hardness were compared with the experimental ones and showed good agreement.

Stress-Strain Rate Relationship during Hot Compression of SiCp-2024Al Superplastic Composites

Stress-Strain Rate Relationship during Hot Compression of SiCp-2024Al Superplastic Composites

High temperature deformation of NbTiAl alloys with σ + γ microstructure

The deformation behavior of an alloy with composition 27Nb33Ti40Al was evaluated at 1000 °C using compression and creep testing. In this alloy, σ-Nb 2Al + γ-TiAl duplex microstructures with different degrees of coarseness and morphology but similar volume fractions of the phases were obtained through suitable aging treatments. The compressive flow curves of both microstructures revealed flow softening, which has been attributed to dynamic recrystallization of the γ phase. During deformation, the σ phase underwent a fragmentation process by which it broke up into smaller particles. The degree of fragmentation increased with decreases in strain rate and σ phase particle size. The main mechanism involved in the fragmentation process has been identified as grain boundary sliding. The coarser microstructure exhibited microcracking at high strain rates and large applied strains. The stress-strain rate relationship for both compression and creep tests followed a power law. For the specimen with a fine microstructure, the stress exponents were 1.9 and 3.1 while for the specimens with a coarse microstructure they were 3.2 and 4.5 for creep and compression testing respectively. These results are consistent with observation of grain boundary sliding in the σ phase and dislocation glide and twinning of the σ phase on deformation.

The finite deformation of nonlinear composite materials—I. Instantaneous constitutive relations

This work deals with the development of effective constitutive models for two-phase nonlinearly viscous and rigid-perfectly plastic composites subjected to finite deformations. The main new feature of the model is the ability to account approximately for the evolution of the microstructure resulting from the finite changes in geometry during a given deformation process. The model is formulated in terms of instantaneous constitutive relations for the composites, which depend on appropriate variables characterizing the state of the microstructure, together with evolution equations for these state variables. This first part of the work is concerned with the development of the instantaneous constitutive relations for classes of microstructures that are sufficiently broad to capture the changes in microstructure associated with general triaxial finite-deformation histories. Simple formulae are given for the effective potentials and stress-strain rate relations of power-law viscous composites made of aligned ellipsoidal inclusions of one phase dispersed in a matrix of a second phase. In addition, effective yield surfaces are computed for the special case of two-phase rigid-perfectly plastic composites with aligned spheroidal inclusions. The effects of the phase volume fractions, inclusion shape and yield strength ratio on these effective yield surfaces are considered. These effects will turn out to be important in the understanding of the effective response of the composites with evolving microstructures, which is considered in Part II of this work.

The finite deformation of nonlinear composite materials—II. Evolution of the microstructure

This work deals with the development of constitutive models for two-phase nonlinearly viscous and rigid-perfectly plastic composites with evolving microstructures. Part I of the work was concerned with the estimation of instantaneous constitutive relations for the class of particulate microstructures with aligned ellipsoidal inclusions. This second part deals with the identification of appropriate variables characterizing the state of the microstructure, and with the development of evolution equations for these variables. Under the assumption of triaxial loading conditions, it is argued that aligned ellipsoidal inclusions deform—in some average sense—into ellipsoidal inclusions with different size and shape. The appropriate state variables are thus the current values of the volume fractions of the phases and the aspect ratios of the inclusions. The pertinent evolution laws then follow from well-known kinematical relations, together with appropriate estimates for the average strain rate in the inclusion and matrix phase. The resulting constitutive models take the form of standard homogenized stress-strain rate relations, supplemented by evolution equations for the above-mentioned state variables. Although the ultimate goal of this study is to be able to model complex forming processes, illustrative results are given here only for axisymmetric and plane strain deformations of composites with rigid-perfectly plastic phases. The main conclusion is that effective behavior of these composites will not be perfectly plastic, but may exhibit hardening, or even softening, depending on the specific nature of the applied loading conditions.