A Numerical Method for Computing Plane Plastic Slip-Line Fields

1976 ◽  
Vol 43 (1) ◽  
pp. 97-101 ◽  
Author(s):  
B. I. Bachrach ◽  
S. K. Samanta
Keyword(s):  
Numerical Method ◽  
Slip Line ◽  
Optimization Problems ◽  
Plastic Material ◽  
Field Analysis ◽  
Line Field ◽  
Entrance Angle ◽  
Perfectly Plastic ◽  
Plane Plastic ◽  
The Mean

A numerical method for slip-line field analysis of rigid perfectly plastic material is presented. The method formulates the analysis of metal forming operations as constrained optimization problems. As an example extrusion through curved dies with zero exit angle and nonzero entrance angle is solved using the proposed method. Slip-line fields, hodograph, and flow field are illustrated, and the mean extrusion pressure as a function of reduction ratio is computed.

Plane-Strain Problems

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element ◽  
Plastic Flow ◽  
Slip Line ◽  
Field Analysis ◽  
Valuable Insight ◽  
Line Field ◽  
Slip Line Field ◽  
Perfectly Plastic ◽  
Nonsteady State ◽  
Plane Plastic

This chapter is concerned with the formulations and solutions for plane plastic flow. In plane plastic flow, velocities of all points occur in planes parallel to a certain plane, say the (x, y) plane, and are independent of the distance from that plane. The Cartesian components of the velocity vector u are ux(x, y), uy(x, y), and uz = 0. For analyzing the deformation of rigid-perfectly plastic and rate-insensitive materials, a mathematically sound slip-line field theory was established (see the books on metal forming listed in Chap. 1). The solution techniques have been well developed, and the collection of slip-line solutions now available is large. Although these slip-line solutions provide valuable insight into deformation modes and forming loads, slip-line field analysis becomes unwieldy for nonsteady-state problems where the field has to be updated as deformation proceeds to account for changes in material boundaries. Furthermore, the neglect of work-hardening, strain-rate, and temperature effects is inappropriate for certain types of problems. Many investigators, notably Oxley and his co-workers, have attempted to account for some of these effects in the construction of slip-line fields. However, by so doing, the problem becomes analytically difficult, and recourse is made to experimental determination of velocity fields, similarly to the visioplasticity method. Some of this work is summarized in Reference [2]. The applications of the finite-element method are particularly effective to the problems for which the slip-line solutions are difficult to obtain. The finite-element formulation specific to plane flow is recapitulated here.

scholarly journals A Slip-Line Field Analysis of the Deformation at the Confluence of two Glacier Streams

1970 ◽  
Vol 9 (56) ◽  
pp. 169-193 ◽  
Author(s):  
I. F. Collins
Keyword(s):  
Slip Line ◽  
Plastic Material ◽  
Yukon Territory ◽  
Field Analysis ◽  
Main Stream ◽  
Line Field ◽  
Perfectly Plastic ◽  
Line Theory ◽  
Intense Shear ◽  
The Ideal

The deformation and state of stress at the confluence of two glacier streams are analysed using the techniques of slip-line theory. The valley walls are taken to be vertical parallel planes and the deformation is supposed independent of depth. The mechanical behavior of ice is modeled by the ideal rigid/perfectly plastic material.Detailed solutions are presented for the deformation at the confluence of one or more tributaries with a main stream and of two main streams. Attention is concentrated on predicting the number, position and magnitude of the bands of intense shear which emanate from some of the junction corners. The predictions of this idealized theory are compared with field data from a confluence on the Kaskawulsh Glacier, Yukon Territory, Canada.

scholarly journals A Slip-Line Field Analysis of the Deformation at the Confluence of two Glacier Streams

1970 ◽  
Vol 9 (56) ◽  
pp. 169-193 ◽  
Author(s):  
I. F. Collins
Keyword(s):  
Slip Line ◽  
Plastic Material ◽  
Yukon Territory ◽  
Field Analysis ◽  
Main Stream ◽  
Line Field ◽  
Perfectly Plastic ◽  
Line Theory ◽  
Intense Shear ◽  
The Ideal

The deformation and state of stress at the confluence of two glacier streams are analysed using the techniques of slip-line theory. The valley walls are taken to be vertical parallel planes and the deformation is supposed independent of depth. The mechanical behavior of ice is modeled by the ideal rigid/perfectly plastic material.Detailed solutions are presented for the deformation at the confluence of one or more tributaries with a main stream and of two main streams. Attention is concentrated on predicting the number, position and magnitude of the bands of intense shear which emanate from some of the junction corners. The predictions of this idealized theory are compared with field data from a confluence on the Kaskawulsh Glacier, Yukon Territory, Canada.

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.

Effects of Strain Hardening on Rock / Bit-Tooth Interaction

1979 ◽  
Vol 101 (1) ◽  
pp. 53-58
Author(s):  
R. B. Pan ◽  
J. B. Cheatham
Keyword(s):  
Pressure Distribution ◽  
Strain Hardening ◽  
Slip Line ◽  
Confining Pressure ◽  
Line Field ◽  
Slip Line Field ◽  
Perfectly Plastic ◽  
High Confining Pressure ◽  
Rock Bit ◽  
Interaction Problem

The rock/bit-tooth interaction problem has been approximated previously by plasticity analysis of a wedge indenting a half-space. In the previous work the rock, under high confining pressure, was assumed to be perfectly plastic. In the present paper, an approximate method is presented for including the effects of strain hardening of the rock on the pressure distribution at the rock bit-tooth interface. The slip-line field for the perfectly plastic solution is used as a basis for applying corrections for the strain-hardening effect.

Identification of Friction Factors for Chamfered and Honed Tools Through Slip-Line Field Analysis

2006 ◽  
Author(s):  
Yigˇit Karpat ◽  
Tugˇrul O¨zel
Keyword(s):  
Slip Line ◽  
Metal Cutting ◽  
Orthogonal Cutting ◽  
Cutting Edge ◽  
Material Behavior ◽  
Field Analysis ◽  
Machining Performance ◽  
Line Field ◽  
Slip Line Field ◽  
Friction Factors

Analysis of tool-chip friction for tools with edge design in metal cutting helps to understand the complex material behavior around the cutting edge of the tool. The results of this analysis can be used to identify optimum tool edge design to achieve the most desirable machining performance. In this study, slip-line field analysis approach is used to investigate the average friction factor at the tool-chip interface and the dead metal zone phenomenon in orthogonal cutting for chamfered and honed tools. In an experimental set-up, an orthogonal cutting test of AISI 4340 steel is performed. Measured forces are utilized in identifying the friction factors at the tool-interface for both chamfered and honed tools for varying feed rates. Comparison of predicted and measured forces indicates good agreements. The results of this study can be utilized in designing friction at tool-chip interface for Finite Element simulations of machining with edge design tools. This study can also be extended to waterfall hone tools to identify the most optimum cutting edge geometry.

An Interpretation of Slip-Line Field Patterns in Plane Plastic Flow

1963 ◽  
Vol 30 (4) ◽  
pp. 625-627
Author(s):  
M. J. Hillier
Keyword(s):  
Plastic Flow ◽  
Slip Line ◽  
Horizontal Displacement ◽  
Field Pattern ◽  
Line Field ◽  
Slip Line Field ◽  
Contour Maps ◽  
Field Patterns ◽  
Comparison With Experiment ◽  
Plane Plastic

A method of interpretation of slip-line field solutions is proposed. Contour maps showing lines joining points of equal vertical or horizontal displacement velocity are plotted superimposed on the slip-line field pattern for a number of known solutions. The method has the advantage of emphasizing the nature of the theoretical characteristic curves and suggests a method of comparison with experiment.

An Abrasive Wear Model of Fractal Surfaces Based on the Slip–Line Theory of Plasticity

2009 ◽  
Author(s):  
X. Yin ◽  
K. Komvopoulos
Keyword(s):  
Abrasive Wear ◽  
Slip Line ◽  
Interfacial Adhesion ◽  
Plastic Material ◽  
Normal Load ◽  
Wear Particle ◽  
Wear Coefficient ◽  
Wear Model ◽  
Line Field ◽  
Fractal Surfaces

A generalized abrasive wear model of a three-dimensional rough (fractal) surface sliding against a relatively softer material is presented. The model is based on a slip-line field of a rigid spherical asperity (or spherical wear particle) that plows through a soft surface, resulting in material removal by a microcutting process. The analysis yields a relationship of the abrasive wear coefficient in terms of the interfacial adhesion characteristics of the interacting surfaces, topography (fractal) parameters, elastic-plastic material properties, and applied normal load. Numerical results illustrate the effects of surface roughness and interfacial adhesion (lubrication effect) on the abrasive wear coefficient of fractal surfaces.

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