On the Simulation of Microhardness at Large Strains Using a Gradient Theory of Plasticity

2001 ◽  
Vol 4 (3-4) ◽  
pp. 413-430 ◽  
Author(s):  
Thomas Svedberg ◽  
Kenneth Runesson
Keyword(s):  
Large Strains ◽  
Gradient Theory ◽  
Theory Of Plasticity

A Comparative Study of Two Types of Gradient Theory of Plasticity

2011 ◽  
Vol 145 ◽  
pp. 485-488
Author(s):  
Sergei Alexandrov ◽  
Yeau Ren Jeng
Keyword(s):  
Strain Rate ◽  
Hollow Sphere ◽  
Strain Gradient ◽  
Strain Gradient Theory ◽  
Large Strains ◽  
Gradient Theory ◽  
Theory Of Plasticity ◽  
Gradient Theories ◽  
General Physical ◽  
Rate Gradient

The objective of the present paper is to show that predictions of the conventional strain gradient theories do not coincide with some general physical expectations when large strains and geometry changes should be considered. As an alternative, it is proposed to use strain rate gradient theories of plasticity. One possible theory of this type is formulated as a formal modification of a strain gradient theory of plasticity. The problem of hollow sphere expansion at large strains is solved for both the strain gradient and strain rate gradient theories of plasticity. Comparison of these solutions reveals advantages of the strain rate gradient theory of plasticity for a class of problems.

A Strain-Rate Gradient Theory of Plasticity and its Comparison with Strain Gradient Theories

2013 ◽  
Vol 284-287 ◽  
pp. 8-12
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeau Ren Jeng
Keyword(s):  
Strain Rate ◽  
Strain Gradient ◽  
Strain Gradient Theory ◽  
Laplacian Operator ◽  
Gradient Theory ◽  
Qualitative Behavior ◽  
Theory Of Plasticity ◽  
Gradient Theories ◽  
Derivatives Of ◽  
Rate Gradient

Gradient theories of plasticity play an important role in the description of inelastic behavior of materials. Usually, these theories involve space derivatives of stress or strain. On the other hand, conventional theories of plasticity can be divided into two groups, flow and deformation theories. Each of these groups has its own area of applications. The main conceptual difference between the theories belonging to the different groups is that the primary kinematics variables in deformation theories are displacements (or strains) whereas in flow theories velocities (or strain rates). Therefore, it is of interest to propose a gradient theory of plasticity involving space derivatives of a measure of strain rate (strain-rate gradient theory of plasticity) and to compare qualitative behavior of solutions for the strain-rate gradient theory of plasticity and an existing strain gradient theory of plasticity. One possible strain-rate gradient theory of plasticity is proposed in the present paper. The equivalent strain rate (second invariant of the strain rate tensor) is used as a measure of strain rate. The Laplacian operator is adopted to introduce the gradient term. An analytic solution for expansion of a hollow sphere is given for two strain-rate gradient theories of plasticity and one strain gradient theory. Comparison of the solutions shows that some qualitative features of the solutions for the strain-rate gradient theories are in better agreement with general physical expectations than those for the strain gradient theory.

scholarly journals Mechanical properties of superionic ceramics based on (Cu1–xAgx)7GeSe5I solid solutions

2021 ◽  
Vol 24 (04) ◽  
pp. 372-377
Author(s):  
V.S. Bilanych ◽  
◽  
M.I. Babilya ◽  
D.M. Korovska ◽  
V.I. Studenyak ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Solid Solutions ◽  
Size Effects ◽  
Copper Content ◽  
Microstructural Analysis ◽  
Gradient Theory ◽  
Indentation Method ◽  
Ceramic Samples ◽  
Theory Of Plasticity ◽  
Cationic Substitution

Cu1–xAgx)7GeSe5I-based ceramics were prepared by pressing and sintering from the micro- and nanopowders. The ceramic samples were investigated using microstructural analysis. The microhardness was measured applying the indentation method with use of the Vickers pyramid. It has been shown that the microhardness of (Cu1–xAgx)7GeSe5I-based ceramics decreases with copper content decrease at Cu+→Ag+cationic substitution. The compositional dependences and size effects of microhardness inherent to (Cu1–xAgx)7GeSe5I-based ceramics have been analyzed. The size effects of microindentation have been interpreted within the framework of the gradient theory of plasticity.

The mensuration of interfaces

1992 ◽  
Vol 50 (1) ◽  
pp. 216-217
Author(s):  
W.M. Stobbs
Keyword(s):  
Electron Microscopy ◽  
50Th Anniversary ◽  
Numerical Data ◽  
Industrial Applications ◽  
Dynamical Theory ◽  
Large Strains ◽  
Reasonable Approach ◽  
Lattice Resolution ◽  
Analogue To Digital ◽  
The Way

I do not have access to the abstracts of the first meeting of EMSA but at this, the 50th Anniversary meeting of the Electron Microscopy Society of America, I have an excuse to consider the historical origins of the approaches we take to the use of electron microscopy for the characterisation of materials. I have myself been actively involved in the use of TEM for the characterisation of heterogeneities for little more than half of that period. My own view is that it was between the 3rd International Meeting at London, and the 1956 Stockholm meeting, the first of the European series , that the foundations of the approaches we now take to the characterisation of a material using the TEM were laid down. (This was 10 years before I took dynamical theory to be etched in stone.) It was at the 1956 meeting that Menter showed lattice resolution images of sodium faujasite and Hirsch, Home and Whelan showed images of dislocations in the XlVth session on “metallography and other industrial applications”. I have always incidentally been delighted by the way the latter authors misinterpreted astonishingly clear thickness fringes in a beaten (”) foil of Al as being contrast due to “large strains”, an error which they corrected with admirable rapidity as the theory developed. At the London meeting the research described covered a broad range of approaches, including many that are only now being rediscovered as worth further effort: however such is the power of “the image” to persuade that the above two papers set trends which influence, perhaps too strongly, the approaches we take now. Menter was clear that the way the planes in his image tended to be curved was associated with the imaging conditions rather than with lattice strains, and yet it now seems to be common practice to assume that the dots in an “atomic resolution image” can faithfully represent the variations in atomic spacing at a localised defect. Even when the more reasonable approach is taken of matching the image details with a computed simulation for an assumed model, the non-uniqueness of the interpreted fit seems to be rather rarely appreciated. Hirsch et al., on the other hand, made a point of using their images to get numerical data on characteristics of the specimen they examined, such as its dislocation density, which would not be expected to be influenced by uncertainties in the contrast. Nonetheless the trends were set with microscope manufacturers producing higher and higher resolution microscopes, while the blind faith of the users in the image produced as being a near directly interpretable representation of reality seems to have increased rather than been generally questioned. But if we want to test structural models we need numbers and it is the analogue to digital conversion of the information in the image which is required.

Transition alpha structure in beta-isomorphous Nb-Hf alloys

1987 ◽  
Vol 45 ◽  
pp. 232-233
Author(s):  
R.W. Carpenter ◽  
Changhai Li ◽  
David J. Smith
Keyword(s):  
Solid Solution ◽  
Solution Phase ◽  
Miscibility Gap ◽  
Large Strains ◽  
Solid Solution Phase ◽  
Two Phase ◽  
Diffuse Intensity ◽  
Metastable Form ◽  
The Matrix ◽  
Equilibrium Morphology

Binary Nb-Hf alloys exhibit a wide bcc solid solution phase field at temperatures above the Hfα→ß transition (2023K) and a two phase bcc+hcp field at lower temperatures. The β solvus exhibits a small slope above about 1500K, suggesting the possible existence of a miscibility gap. An earlier investigation showed that two morphological forms of precipitate occur during the bcc→hcp transformation. The equilibrium morphology is rod-type with axes along <113> bcc. The crystallographic habit of the rod precipitate follows the Burgers relations: {110}||{0001}, <112> || <1010>. The earlier metastable form, transition α, occurs as thin discs with {100} habit. The {100} discs induce large strains in the matrix. Selected area diffraction examination of regions ∼2 microns in diameter containing many disc precipitates showed that, a diffuse intensity distribution whose symmetry resembled the distribution of equilibrium α Bragg spots was associated with the disc precipitate.

A Numerical Description of a Liquid-Vapor Interface Based on the Second Gradient Theory

1995 ◽  
Vol 22 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Didier Jamet ◽  
Olivier Lebaigue ◽  
Jean-Marc Delhaye ◽  
N. Coutris
Keyword(s):  
Gradient Theory ◽  
Vapor Interface ◽  
Second Gradient ◽  
Liquid Vapor
Sign in / Sign up

Export Citation Format

Share Document