Plane-Strain Plastic Flow of Strain-Rate Sensitive Materials

1974 ◽  
Vol 96 (3) ◽  
pp. 238-240 ◽  
Author(s):  
R. G. Fenton ◽  
B. Durai Swamy
Keyword(s):  
Flow Stress ◽  
Strain Rate ◽  
Plane Strain ◽  
Slip Line ◽  
Metal Flow ◽  
Stress Distributions ◽  
Line Field ◽  
Slip Line Field ◽  
Flow Problems ◽  
Iterative Calculation

A numerical method based on the modified Hencky and Geiringer equations is described for solving plane-strain metal flow problems of strain-rate sensitive materials. The slip-line field and flow-stress distributions are determined simultaneously using an iterative calculation.

Slip Line Field Analysis of a Simple Plane Strain Closed-Die Forging

1989 ◽  
Vol 203 (2) ◽  
pp. 91-99
Author(s):  
M V Srinivas ◽  
P Alva ◽  
S K Biswas
Keyword(s):  
Velocity Field ◽  
Plane Strain ◽  
Slip Line ◽  
Field Analysis ◽  
Line Field ◽  
Slip Line Field ◽  
Die Forging ◽  
Closed Die Forging ◽  
Cavity Filling ◽  
Single Cavity

A slip line field is proposed for symmetrical single-cavity closed-die forging by rough dies. A compatible velocity field is shown to exist. Experiments were conducted using lead workpiece and rough dies. Experimentally observed flow and load were used to validate the proposed slip line field. The slip line field was used to simulate the process in the computer with the objective of studying the influence of flash geometry on cavity filling.

Introduction

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Stress Distribution ◽  
Process Modeling ◽  
Slip Line ◽  
Metal Forming ◽  
Field Method ◽  
Stress Distributions ◽  
Line Field ◽  
Slip Line Field ◽  
Forming Technology ◽  
Computer Aided

In the late 1970s and early 1980s the use of computer-aided techniques (computer-aided engineering, design, and manufacturing) in the metal-forming industry increased considerably. The trend seems to be toward ever wider application of this technology for process simulation and process design. A goal in manufacturing research and development is to determine the optimum means of producing sound products. The optimization criteria may vary, depending on product requirements, but establishing an appropriate criterion requires thorough understanding of manufacturing processes. In metal-forming technology, proper design and control requires, among other things, the determination of deformation mechanics involved in the processes. Without the knowledge of the influences of variables such as friction conditions, material properties, and workpiece geometry on the process mechanics, it would not be possible to design the dies and the equipment adequately, or to predict and prevent the occurrence of defects. Thus, process modeling for computer simulation has been a major concern in modern metal-forming technology. Figure 1.1. indicates the role of process modeling in some detail. In the past a number of approximate methods of analysis have been developed and applied to various forming processes. The methods most well known are the slab method, the slip-line field method, the visioplasticity method, upper- (and lower-) bound techniques, Hill’s general method, and, more recently, the finite-element method (FEM). In the slab method, the workpiece being deformed is decomposed in several slabs. For each slab, simplifying assumptions are made mainly with respect to stress distributions. The resulting approximate equilibrium equations are solved with imposition of stress compatibility between slabs and boundary tractions. The final result is a reasonable load prediction with an approximate stress distribution. The slip-line field method is used in plane strain for perfectly plastic materials (constant yield stress) and uses the hyperbolic properties that the stress equations have in such cases. The construction of slip-line fields, although producing an “exact” stress distribution, is still quite limited in predicting results that give good correlations with experimental work. From the stress distributions, velocity fields can be calculated through plasticity equations.

Direct mapping of deformation in punch indentation and correlation with slip line fields

2009 ◽  
Vol 24 (3) ◽  
pp. 760-767 ◽  
Author(s):  
T.G. Murthy ◽  
J. Madariaga ◽  
S. Chandrasekar
Keyword(s):  
Strain Rate ◽  
Slip Line ◽  
Large Strain ◽  
Shear Bands ◽  
Indentation Hardness ◽  
Large Area ◽  
Line Field ◽  
Slip Line Field ◽  
Perfectly Plastic ◽  
Analysis Technique

Deformation field parameters in plane-strain indentation of a perfectly plastic solid with a punch have been mapped using particle image velocimetry, a correlation-based image analysis technique. Measurements of velocity and strain rate over a large area have shown that the deformation resembles that of the slip line field of Prandtl. A zone of dead metal is found to exist underneath the indenter adjoining which is a transition region of material flow similar to the centered-fan region in the slip line field. Shear bands demarcate the boundaries of these deformation regions. The observations suggest that a representative strain rate may be assigned to the indentation. By integrating the strain rate field along particle trajectories, the strains in the indentation region have been estimated. The strain values are seen to be large, 0.5 to 4, over a region extending to about twice the indenter half-width. A pocket of large strain, ∼4, is found to exist close to the edge of the indenter–specimen contact. Prandtl’s slip line field is modified based on the observations and used to estimate the strain field. The measurements of the deformation parameters are found to compare mostly favorably with the predictions of the slip line field and prior observations of indentation. The implications of these findings for analysis and interpretation of indentation hardness are briefly discussed.

Blank Development and Tooling Design for Drawn Parts Using a Modified Slip Line Field Based Approach

1989 ◽  
Vol 111 (4) ◽  
pp. 345-350 ◽  
Author(s):  
M. Karima
Keyword(s):  
Slip Line ◽  
Metal Flow ◽  
Deformation Path ◽  
Line Field ◽  
Slip Line Field ◽  
Starting Position ◽  
Novel Approach ◽  
Nodal Coordinates ◽  
Tooling Design ◽  
Incremental Form

Box shaped parts demonstrate unusual characteristics as opposed to the drawn cylindrical cups. A novel approach for blank development, based on the modified plane strain slip line field (SLF), is presented in this work. The approach is to balance the element volume between the final position in the wall and the starting position in the flat flange. The end result of this SLF based unfolding technique is a set of elements representing the deformation path of the part. By post-processing the information on the nodal coordinates and invoking the variational principle in its incremental form, the strain distribution in the flange and the wall stresses are determined. A methodology is also presented for understanding the implications of the metal flow lines for tooling design.

The Plane Strain Indentation of Anisotropic Aluminium Using a Frictionless Flat Rectangular Punch

1971 ◽  
Vol 13 (6) ◽  
pp. 416-428 ◽  
Author(s):  
R. Venter ◽  
W. Johnson ◽  
M. C. de Malherbe
Keyword(s):  
Plane Strain ◽  
Anisotropic Material ◽  
Slip Line ◽  
Line Field ◽  
Anisotropic Parameter ◽  
Slip Line Field

In Part 1, the slip-line field solutions and the associated load requirements necessary for the indentation of anisotropic solids are presented. The analysis is based on Hill's approach to the analysis of anisotropic material. All results are recorded in terms of a lumped anisotropic parameter, c. In Part 2, the results of an investigation to determine the anisotropic parameters of a commercially available aluminium are reported. Specimens machined from the aluminium at selected orientations to the anisotropic axes were indented using a nominally frictionless flat rectangular punch. A comparison between the theoretical and experimental indentation loads is given.

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