scholarly journals The Behavior of Melts with Vanishing Viscosity in the Cone-and-Plate Rheometer

2019 ◽  
Vol 10 (1) ◽  
pp. 172
Author(s):  
Lihui Lang ◽  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Van Manh Dinh
Keyword(s):  
Strain Rate ◽  
Shear Strain ◽  
Constitutive Equations ◽  
Material Flow ◽  
Analytic Solution ◽  
Theoretical Solution ◽  
Qualitative Behavior ◽  
Strain Rate Tensor ◽  
Shear Strain Rate ◽  
Vanishing Viscosity

A semi-analytic solution for material flow in the cone-and-plate rheometer is presented. It is assumed that the viscosity is solely a function of the second invariant of the strain rate tensor. A distinguishing feature of the constitutive equations used is that the viscosity is vanishing as the shear strain rate approaches infinity. This feature of the constitutive equations affects the qualitative behavior of the solution. Asymptotic analysis is carried out near the surface of the cone to reveal these features. It is shown that the regime of sliding must occur and the shear strain rate approaches infinity under certain conditions. It is also shown that the asymptotic behavior of the viscosity as the shear strain rate approaches infinity controls these qualitative features of the theoretical solution. Some of these features are feasible for experimental verification. An interpretation of the theoretical solution found is proposed.

scholarly journals 3D Muscle Deformation Mapping at Submaximal Isometric Contractions: Applications to Aging Muscle

2020 ◽  
Vol 11 ◽  
Author(s):  
Vadim Malis ◽  
Usha Sinha ◽  
Shantanu Sinha
Keyword(s):  
Extracellular Matrix ◽  
Strain Rate ◽  
Shear Strain ◽  
Compressive Strain ◽  
Strain Tensor ◽  
Medial Gastrocnemius ◽  
Strain Rate Tensor ◽  
Shear Strain Rate ◽  
Velocity Mapping ◽  
Lateral Transmission

3D strain or strain rate tensor mapping comprehensively captures regional muscle deformation. While compressive strain along the muscle fiber is a potential measure of the force generated, radial strains in the fiber cross-section may provide information on the material properties of the extracellular matrix. Additionally, shear strain may potentially inform on the shearing of the extracellular matrix; the latter has been hypothesized as the mechanism of lateral transmission of force. Here, we implement a novel fast MR method for velocity mapping to acquire multi-slice images at different % maximum voluntary contraction (MVC) for 3D strain mapping to explore deformation in the plantar-flexors under isometric contraction in a cohort of young and senior subjects. 3D strain rate and strain tensors were computed and eigenvalues and two invariants (maximum shear and volumetric strain) were extracted. Strain and strain rate indices (contractile and in-plane strain/strain rate, shear strain/strain rate) changed significantly with %MVC (30 and 60% MVC) and contractile and shear strain with age in the medial gastrocnemius. In the soleus, significant differences with age in contractile and shear strain were seen. Univariate regression revealed weak but significant correlation of in-plane and shear strain and shear strain rate indices to %MVC and correlation of contractile and shear strain indices to force. The ability to map strain tensor components provides unique insights into muscle physiology: with contractile strain providing an index of the force generated by the muscle fibers while the shear strain could potentially be a marker of lateral transmission of force.

Physical constitutive equations for plastic deformation of FCC metals subjected to high strain rate loading

2015 ◽  
Vol 232 (2) ◽  
pp. 106-120 ◽  
Author(s):  
E Etemadi ◽  
J Zamani ◽  
M Jafarzadeh
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Entropy Generation ◽  
Constitutive Equations ◽  
High Strain ◽  
Velocity Shear ◽  
Viscous Drag ◽  
Shear Strain Rate ◽  
Face Centered Cubic ◽  
Fcc Metals

This paper develops a new physically based model to investigate face centered cubic (FCC) metals and alloys under high strain rate loadings (\gt104 s−1) which includes kinematics and constitutive equations for the propagation of elastic and steady plastic waves. The model’s formulations are based on the rate of the conservation energy law that includes the rate of the input energy, internal energy, and entropy generation. This formulation is obtained by incorporating the viscous drag effects and associating the entropy generation to the generation, glide, and annihilation of dislocations. The model is used for 6061-T6 aluminum alloys and the results are verified with the published theoretical models and experimental tests. Also, the effect of different parameters, such as the particle velocity, shear flow stress, shear strain rate and temperature are investigated. As a result, the presented model shows good capability in describing the mentioned parameters.

High shear strain rate rheometry of polymer melts

2009 ◽  
Vol 114 (2) ◽  
pp. 864-873 ◽  
Author(s):  
A. L. Kelly ◽  
T. Gough ◽  
B. R. Whiteside ◽  
P. D. Coates
Keyword(s):  
Strain Rate ◽  
Shear Strain ◽  
Polymer Melts ◽  
Shear Strain Rate ◽  
High Shear

Rheology of colloids

Surfactants ◽  
2019 ◽  
pp. 400-424
Author(s):  
Bob Aveyard
Keyword(s):  
Strain Rate ◽  
Shear Strain ◽  
Shear Thickening ◽  
Rheological Behaviour ◽  
Maxwell Model ◽  
Colloidal Dispersions ◽  
Shear Strain Rate ◽  
Plastic Behaviour ◽  
Shear Thickening Fluids ◽  
External Forces

Lyophobic colloidal dispersions, aggregated surfactant systems, and polymer solutions, as well as foams and emulsions, can all be deformed by weak external forces; rheology is the study of deformation and flow of materials. Various rheological quantities arising from the response of a material to shear are defined. For liquids the stress, τ‎, applied is related to the rate of deformation, that is, the shear strain rate, γ̇. For Newtonian fluids τ‎ and γ̇ are linearly related and τ‎ / γ̇ is the viscosity, η‎. Other nonlinear relationships correspond to shear thinning and shear thickening fluids and to plastic behaviour in which there is a yield stress. Viscoelastic systems exhibit both viscous and elastic properties; such behaviour is often treated using the simple Maxwell model. Some illustrative experimentally observed rheological behaviour is presented.

scholarly journals Erebus Glacier Tongue, Mcmurdo Sound, Antarctica

1974 ◽  
Vol 13 (67) ◽  
pp. 27-35 ◽  
Author(s):  
G. Holdsworth
Keyword(s):  
Shear Stress ◽  
Strain Rate ◽  
Shear Strain ◽  
Longitudinal Strain ◽  
Strain Rates ◽  
Shear Strain Rate ◽  
Mcmurdo Sound ◽  
Glacier Tongue ◽  
The Past ◽  
Image Position

Examination of the past and present behaviour of the Erebus Glacier tongue over the last 60 years indicates that a major calving from the tongue appears to be imminent. Calculations of the regime of the tongue indicate that bottom melt rates may exceed 1 m a−1. By successive mapping of the ice tongue between the years 1947 and 1970, longitudinal strain-rates were determined using the change in distance between a set of 15 teeth, which are a prominent marginal feature of the tongue. Assuming a flow law for ice of the form where τ is the effective shear stress and is the effective shear strain-rate, values of the exponent n = 3 and B = 1 × 108 N m−2 are determined. These are in fair agreement with published values.

scholarly journals Deformation in the Vicinity of Ice Divides

1983 ◽  
Vol 29 (103) ◽  
pp. 357-373 ◽  
Author(s):  
Charles F. Raymond
Keyword(s):  
Finite Elements ◽  
Laminar Flow ◽  
Velocity Profile ◽  
Strain Rate ◽  
Shear Strain ◽  
Vertical Velocity ◽  
Flow Theory ◽  
Numerical Calculations ◽  
Shear Strain Rate ◽  
Horizontal Shear

AbstractNumerical calculations by finite elements show that the variation of horizontal velocity with depth in the vicinity of a symmetric, isothermal, non-slipping ice ridge deforming on a flat bed is approximately consistent with prediction from laminar flow theory except in a zone within about four ice thicknesses of the divide. Within this near-divide zone horizontal shear strain-rate is less concentrated near the bottom and downward velocity is less rapid in comparison to the flanks. The profiles over depth of horizontal and vertical velocity approach being linear and parabolic respectively. Calculations for various surface elevation profiles show these velocity profile shapes are insensitive to the ice-sheet geometry.

scholarly journals The theory of plane plastic strain for anisotropic metals

1949 ◽  
Vol 198 (1054) ◽  
pp. 428-437 ◽  
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Shear Strain ◽  
Plane Strain ◽  
Yield Criterion ◽  
Elliptic Functions ◽  
Shear Strain Rate ◽  
Maximum Shear Strain ◽  
Geometrical Properties ◽  
Plane Plastic

A yield criterion and plastic stress-strain relations are formulated for anisotropic metals deformed under conditions of plane strain. The equations are shown to be hyperbolic, the characteristics coinciding with the directions of maximum shear strain-rate. When the anisotropy is uniformly distributed, the variation of the stresses along the characteristics is expressed in terms of elliptic functions, and geometrical properties of the field of characteristics are established. The theory is applied to the problem of indentation by a flat die.

scholarly journals Plastometric tests for plasticine as physical modelling material

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Łukasz Wójcik ◽  
Konrad Lis ◽  
Zbigniew Pater
Keyword(s):  
Strain Rate ◽  
Temperature Change ◽  
Compression Test ◽  
Constitutive Equations ◽  
Metal Forming ◽  
Material Flow ◽  
Physical Modelling ◽  
Flow Curves ◽  
Black And White ◽  
White Colour

Abstract This paper presents results of plastometric tests for plasticine, used as material for physical modelling of metal forming processes. The test was conducted by means of compressing by flat dies of cylindrical billets at various temperatures. The aim of the conducted research was comparison of yield stresses and course of material flow curves. Tests were made for plasticine in black and white colour. On the basis of the obtained experimental results, the influence of forming parameters change on flow curves course was determined. Sensitivity of yield stresses change in function of material deformation, caused by forging temperature change within the scope of 0&C ÷ 20&C and differentiation of strain rate for ˙ɛ = 0.563; ˙ɛ = 0.0563; ˙ɛ = 0.0056s−1,was evaluated. Experimental curves obtained in compression test were described by constitutive equations. On the basis of the obtained results the function which most favourably describes flow curves was chosen.

scholarly journals Deformation in the Vicinity of Ice Divides

1983 ◽  
Vol 29 (103) ◽  
pp. 357-373 ◽  
Author(s):  
Charles F. Raymond
Keyword(s):  
Finite Elements ◽  
Laminar Flow ◽  
Velocity Profile ◽  
Strain Rate ◽  
Shear Strain ◽  
Vertical Velocity ◽  
Flow Theory ◽  
Numerical Calculations ◽  
Shear Strain Rate ◽  
Horizontal Shear

AbstractNumerical calculations by finite elements show that the variation of horizontal velocity with depth in the vicinity of a symmetric, isothermal, non-slipping ice ridge deforming on a flat bed is approximately consistent with prediction from laminar flow theory except in a zone within about four ice thicknesses of the divide. Within this near-divide zone horizontal shear strain-rate is less concentrated near the bottom and downward velocity is less rapid in comparison to the flanks. The profiles over depth of horizontal and vertical velocity approach being linear and parabolic respectively. Calculations for various surface elevation profiles show these velocity profile shapes are insensitive to the ice-sheet geometry.

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