scholarly journals A quadratic viscous fluid law for ice deduced from Steinemann's uni-axial compression and torsion experiments

2021 ◽  
pp. 1-11
Author(s):  
R. Staroszczyk ◽  
L. W. Morland
Keyword(s):  
Viscous Fluid ◽  
Strain Rate ◽  
Axial Stress ◽  
Deviatoric Stress ◽  
Quadratic Term ◽  
Quadratic Relation ◽  
Stress And Strain Rate ◽  
Stress Invariant ◽  
Rate Formulation ◽  
Rule Out

Abstract The response of ice to applied stress on ice-sheet flow timescales is commonly described by a non-linear incompressible viscous fluid, for which the deviatoric stress has a quadratic relation in the strain rate with two response coefficient functions depending on two principal strain-rate invariants I2 and I3. Commonly, a coaxial (linear) relation between the deviatoric stress and strain rate, with dependence on one strain-rate invariant I2 in a stress formulation, equivalently dependence on one deviatoric stress invariant in a strain-rate formulation, is adopted. Glen's uni-axial stress experiments determined such a coaxial law for a strain-rate formulation. The criterion for both uni-axial and shear data to determine the same relation is determined. Here, we apply Steinemann's uni-axial stress and torsion data to determine the two stress response coefficients in a quadratic relation with dependence on a single invariant I2. There is a non-negligible quadratic term for some ranges of I2; that is, a coaxial relation with dependence on one invariant is not valid. The data does not, however, rule out a coaxial relation with dependence on two invariants.

scholarly journals Measurements and Characterization of Turbulence in the Tip Region of an Axial Compressor Rotor

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Yuanchao Li ◽  
Huang Chen ◽  
Joseph Katz
Keyword(s):  
Strain Rate ◽  
Shear Layer ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Suction Side ◽  
Stress And Strain ◽  
Spatial And Temporal Variability ◽  
Mean Flow ◽  
The Mean ◽  
Stress And Strain Rate

Modeling of turbulent flows in axial turbomachines is challenging due to the high spatial and temporal variability in the distribution of the strain rate components, especially in the tip region of rotor blades. High-resolution stereo-particle image velocimetry (SPIV) measurements performed in a refractive index-matched facility in a series of closely spaced planes provide a comprehensive database for determining all the terms in the Reynolds stress and strain rate tensors. Results are also used for calculating the turbulent kinetic energy (TKE) production rate and transport terms by mean flow and turbulence. They elucidate some but not all of the observed phenomena, such as the high anisotropy, high turbulence levels in the vicinity of the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side (SS) tip corner. The applicability of popular Reynolds stress models based on eddy viscosity is also evaluated by calculating it from the ratio between stress and strain rate components. Results vary substantially, depending on which components are involved, ranging from very large positive to negative values. In some areas, e.g., in the tip gap and around the TLV, the local stresses and strain rates do not appear to be correlated at all. In terms of effect on the mean flow, for most of the tip region, the mean advection terms are much higher than the Reynolds stress spatial gradients, i.e., the flow dynamics is dominated by pressure-driven transport. However, they are of similar magnitude in the shear layer, where modeling would be particularly challenging.

Thermoviscoplasticity Theory Incorporating the Third Deviatoric Stress Invariant

2015 ◽  
Vol 51 (1) ◽  
pp. 85-91 ◽  
Author(s):  
M. E. Babeshko ◽  
Yu. N. Shevchenko ◽  
N. N. Tormakhov
Keyword(s):  
Deviatoric Stress ◽  
The Third ◽  
Stress Invariant

Some Implications of a Nonlinear Viscoelastic Constitutive Theory Regarding Interrelationships Between Creep and Strength Behavior of Ice at Failure

1989 ◽  
Vol 111 (2) ◽  
pp. 144-148 ◽  
Author(s):  
B. D. Harper
Keyword(s):  
Strain Rate ◽  
Constant Strain Rate ◽  
Nonlinear Viscoelastic ◽  
Uniaxial Creep ◽  
Strength Behavior ◽  
Minimum Strain Rate ◽  
Strength Constant ◽  
Viscoelastic Constitutive Model ◽  
Stress And Strain Rate ◽  
Special Case

This study explores several possibilities for a correspondence in the behavior of ice at failure during uniaxial creep (constant stress) and strength (constant strain rate) experiments. The usual notion of failure in ice is employed (i.e., the occurrence of a minimum strain rate during a creep test and a peak or maximum stress during a strength test), and the behavior at failure is discussed in terms of a recently proposed nonlinear viscoelastic constitutive model for ice. It is demonstrated that no correspondence between creep and strength data can be expected in general; however, several approximate interrelationships do occur for the experimentally motivated special case of a constant (independent of stress and strain rate) failure strain.

Evaluation of Creep Constitutive Equations for Type 304 Stainless Steel Under Repeated Multiaxial Loading

1982 ◽  
Vol 104 (3) ◽  
pp. 159-164 ◽  
Author(s):  
Y. Ohashi ◽  
N. Ohno ◽  
M. Kawai
Keyword(s):  
Stainless Steel ◽  
Strain Rate ◽  
Strain Hardening ◽  
Deviatoric Stress ◽  
304 Stainless Steel ◽  
Multiaxial Loading ◽  
Mixed Hardening ◽  
Principal Axes ◽  
Type 304 ◽  
Type 304 Stainless Steel

Four kinds of creep constitutive models, i.e., strain-hardening, modified strain-hardening, kinematic-hardening, and mixed-hardening theory, are evaluated on the basis of creep-test results on type 304 stainless steel at 650°C under repeated multiaxial loading. The predictions of the four models are compared with the experimental results. It is shown that substantial differences appear among these predictions under large rotations of the principal axes of the deviatoric stress tensor, and that none of them can describe with sufficient accuracy the transient increase of strain-rate and the noncollinearity between the deviatoric stress and creep strain-rate vectors which are observed just after the stress-rotations.

A Theory of the Yield Point and the Transition Temperature of Mild Steel

1956 ◽  
Vol 23 (2) ◽  
pp. 219-224
Author(s):  
F. Forscher
Keyword(s):  
Transition Temperature ◽  
Mild Steel ◽  
Strain Rate ◽  
Yield Point ◽  
Structural Model ◽  
Yield Criterion ◽  
State Of Stress ◽  
Yield Point Phenomenon ◽  
Stress And Strain Rate ◽  
Temperature Strain

Abstract Experimental results indicate the dependence of the yield-point phenomenon of mild steel on temperature, strain rate, duration of stress, and stress state. This paper proposes a yield criterion which can account for these variables. The theory is developed on the basis of a “structural” model, by which the behavior of microscopic and submicroscopic elements is idealized. The theory postulates as yield criterion a critical number of relaxation centers (active Frank-Read sources) or, equivalently, a critical size of relaxation centers. The transition-temperature phenomenon is considered to be the result of an inhibition of yielding (upper yield point) by means of geometry, temperature and/or strain rate. A relation is given which expresses its dependence on the state of stress and strain rate.

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