The Pattern of Plastic Deformation in a Deeply Notched Bar With Semicircular Roots

1956 ◽  
Vol 23 (1) ◽  
pp. 56-58
Author(s):  
L. Garr ◽  
E. H. Lee ◽  
A. J. Wang
Keyword(s):  
Plastic Deformation ◽  
Free Surface ◽  
Velocity Field ◽  
Plastic Strain ◽  
Plane Strain ◽  
Cross Section ◽  
Finite Deformation ◽  
Large Plastic Strain ◽  
Step Method ◽  
Square Grid

Abstract The plastic deformation in a notched bar with deep semicircular roots pulled in plane strain is determined theoretically. The finite deformation is analyzed according to plastic-rigid theory. The motion is unsteady, and the velocity field at any instant is given in terms of the current geometry of the deformed free surface. A graphical step-by-step method is used to determine the deformation of a square grid scribed on the undeformed cross section. The deformed pattern details the regions of large plastic strain, and may be useful in considering the initiation of fracture cracks.

Magnetohydrodynamic flow due to the discharge of an electric current in a hemispherical container

1976 ◽  
Vol 73 (4) ◽  
pp. 641-650 ◽  
Author(s):  
C. Sozou ◽  
W. M. Pickering
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Flow Field ◽  
Electric Current ◽  
Cross Section ◽  
Analytic Solution ◽  
Closed Loops ◽  
Slow Viscous Flow ◽  
Axial Cross Section ◽  
Section Form

In this paper we consider the flow field induced in an incompressible viscous conducting fluid in a hemispherical bowl by a symmetric discharge of electric current from a point source at the centre of the plane end of the hemisphere. This plane end is a free surface. We construct an analytic solution for the slow viscous flow and a numeriacl solution for the nonlinear problem. The streamlines in an axial cross-section form two sets of closed loops, one on either side of the axis. Our computations indicate that, for a given fluid, when the discharged current reaches a certain magnitude the velocity field breaks down. This breakdown probably originates at the vertex of the hemispherical container.

Mechanical Properties of Aluminium Processed by ECAP

2006 ◽  
Vol 114 ◽  
pp. 39-44
Author(s):  
Rafal M. Molak ◽  
Zbigniew Pakiela
Keyword(s):  
Mechanical Properties ◽  
Plastic Deformation ◽  
Plastic Strain ◽  
Room Temperature ◽  
Tensile Tests ◽  
Large Plastic Strain ◽  
Angular Pressing ◽  
Purity Aluminium ◽  
High Purity Aluminium ◽  
The Relationship

The aim of this study was to investigate the influence of large plastic strain on the microstructure and mechanical properties of aluminium processed by severe plastic deformation (SPD) by the Equal Channel Angular Pressing (ECAP) method. Polycrystalline high purity aluminium (99,99%) was pressed at room temperature to produce samples subjected to 4, 8 and 12 ECAP passes. The microstructure of aluminium was examined using a light polarized microscope. Microhardness measurements and tensile tests were undertaken to determine the mechanical properties of the material processed by ECAP. The results obtained show the relationship between the microstructure and the mechanical properties of the material.

Velocity field and strain-rates in plastic deformation

1967 ◽  
Vol 2 (3) ◽  
pp. 196-206 ◽  
Author(s):  
T C Hsu
Keyword(s):  
Plastic Deformation ◽  
Steady State ◽  
Velocity Field ◽  
Finite Deformation ◽  
Finite Deformations ◽  
The Other ◽  
Strain Rates ◽  
Steady State Flow ◽  
Quantitative Results ◽  
The One

Grid lines have often been scribed, printed or photographed on metal surfaces for studying plastic deformation. Hitherto, most of them have been used only for qualitative results. It has been shown in a previous paper (2)∗ how quantitative results on finite deformations can be derived from a deformed grid. As a sequel to that paper, a method is presented here for deriving the rates of deformation from deformed grids. The relation between the velocity field on the one hand and the strain-rates and rotations on the other is first discussed. The theory thus developed is then applied to the cases of steady-state and non-steady-state flow, with practical example for the former. The connection between finite deformation and rate of deformation is also explained.

Crossed patch arrangements of linear triangular elements for upper bound finite-element analysis of plane strain deformation problems

2010 ◽  
Vol 225 (2) ◽  
pp. 280-291 ◽  
Author(s):  
C C Chang
Keyword(s):  
Finite Element Analysis ◽  
Plastic Deformation ◽  
Finite Element ◽  
Velocity Field ◽  
Plane Strain ◽  
Element Analysis ◽  
Quadrilateral Elements ◽  
Plane Strain Deformation ◽  
Incompressibility Constraint ◽  
Triangular Elements

In standard linear finite-element formulations, volumetric locking because of the incompressibility constraint that may occur in computational plasticity is often encountered. This study uses crossed patch arrangements of triangles to form quadrilateral elements in order to overcome the locking in the upper bound finite-element analysis of plane strain deformation problems. The velocity field is described in terms of linear triangular elements, while the incompressibility constraint is imposed by quadrilateral elements. Rigid, perfectly plastic materials, and strain hardening materials that form the von Mises model have been considered. The velocity formulation is presented and has been implemented in a finite-element code. Several examples, some benchmarks problems, are presented to illustrate the applicability of the approach for predicting the load, strain, and velocity field during the plastic deformation. Numerical results show that the crossed patch arrangements of linear triangular elements are free of volumetric locking and achieve well-defined limit loads. This study shows that the presented method can be used to simulate large plastic deformation under plane strain conditions.

Plastic Deformation in Microtomed Sections

1971 ◽  
Vol 29 ◽  
pp. 458-459
Author(s):  
J. Temple Black
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Applied Stress ◽  
Elastic Strain ◽  
High Strain ◽  
Tool Material ◽  
Cutting Edge ◽  
Material Structure ◽  
Geometrical Constraints

The output of the ultramicrotomy process with its high strain levels is dependent upon the input, ie., the nature of the material being machined. Apart from the geometrical constraints offered by the rake and clearance faces of the tool, each material is free to deform in whatever manner necessary to satisfy its material structure and interatomic constraints. Noncrystalline materials appear to survive the process undamaged when observed in the TEM. As has been demonstrated however microtomed plastics do in fact suffer damage to the top and bottom surfaces of the section regardless of the sharpness of the cutting edge or the tool material. The energy required to seperate the section from the block is not easily propogated through the section because the material is amorphous in nature and has no preferred crystalline planes upon which defects can move large distances to relieve the applied stress. Thus, the cutting stresses are supported elastically in the internal or bulk and plastically in the surfaces. The elastic strain can be recovered while the plastic strain is not reversible and will remain in the section after cutting is complete.

scholarly journals Fractal-induced 2D flexible net undulation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Michael Joon Seng Goh ◽  
Yeong Shiong Chiew ◽  
Ji Jinn Foo
Keyword(s):  
3D Reconstruction ◽  
Cross Section ◽  
Channel Cross Section ◽  
Time Varying ◽  
Blockage Ratio ◽  
Transient Time ◽  
Cross Sectional ◽  
Velocity Fluctuations ◽  
Square Grid ◽  
Multilength Scale

AbstractA net immersed in fractal-induced turbulence exhibit a transient time-varying deformation. The anisotropic, inhomogeneous square fractal grid (SFG) generated flow interacts with the flexible net to manifest as visible cross-sectional undulations. We hypothesize that the net’s response may provide a surrogate in expressing local turbulent strength. This is analysed as root-mean-squared velocity fluctuations in the net, displaying intensity patterns dependent on the grid conformation and grid-net separation. The net’s fluctuation strength is found to increase closer to the turbulator with higher thickness ratio while presenting stronger fluctuations compared to regular-square-grid (RSG) of equivalent blockage-ratio, σ. Our findings demonstrate a novel application where 3D-reconstruction of submerged nets is used to experimentally contrast the turbulence generated by RSG and multilength scale SFGs across the channel cross-section. The net’s response shows the unique turbulence developed from SFGs can induce 9 × higher average excitation to a net when compared against RSG of similar σ.

Radial Flow Velocity Field for Predicting Upper-Bound Solutions for Plane Strain Extrusion

1968 ◽  
Vol 90 (1) ◽  
pp. 45-50
Author(s):  
R. G. Fenton
Keyword(s):  
Velocity Field ◽  
Flow Field ◽  
Flow Velocity ◽  
Plane Strain ◽  
Upper Bound ◽  
Radial Flow ◽  
Flow Velocity Field ◽  
Wide Range ◽  
Ram Pressure ◽  
Considerable Range

The upper bound of the average ram pressure, based on an assumed radial flow velocity field, is derived for plane strain extrusion. Ram pressures are calculated for a complete range of reduction ratios and die angles, considering a wide range of frictional conditions. Results are compared with upper-bound ram pressures obtained by considering velocity fields other than the radial flow field, and it is shown that for a considerable range of reduction ratios and die angles, the radial flow field yields better upper bounds for the average ram pressure.

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