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.

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.

A New Approach to Plasticity and Its Application to Blunt Two Dimensional Indenters

1970 ◽  
Vol 92 (2) ◽  
pp. 469-479 ◽  
Author(s):  
M. C. Shaw ◽  
G. J. DeSalvo
Keyword(s):  
Residual Stresses ◽  
Plastic Flow ◽  
Slip Line ◽  
New Method ◽  
Two Dimensional ◽  
Constraint Factor ◽  
Line Field ◽  
New Approach ◽  
Slip Line Field ◽  
First Time

The classical slip line field solution for a two-dimensional punch is found to give a constraint factor (2.57) which is too small when the specimen beneath the punch is extensive. A new approach based on elasticity provides a constraint factor of 2.75. The new method of analysis also enables residual stresses to be estimated and indicates that plastic flow occurs not only when the specimen is loaded, but also when it is unloaded. Several details concerning the performance of hardness indenters are explained by the new theory for the first time.

Plastic Deformation when Cutting into an Inclined Plane

1967 ◽  
Vol 9 (1) ◽  
pp. 1-10 ◽  
Author(s):  
W. B. Palmer
Keyword(s):  
Plastic Deformation ◽  
Plastic Flow ◽  
Work Hardening ◽  
Slip Line ◽  
Inclined Plane ◽  
Line Field ◽  
Hardening Material ◽  
Slip Line Field ◽  
Theory Of Plasticity

Plastic flow and tool forces were observed as an orthogonal tool cut slowly into an inclined plane of En 9 steel. A slip-line field is constructed which represents the observed flow, and on the basis of the theory of plasticity for work-hardening material estimates of stress are consistent with observed tool forces.

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.

The Relation Between the Friction of Lubricated Rough Surfaces and Apparent Normal Pressure

1989 ◽  
Vol 111 (2) ◽  
pp. 260-264 ◽  
Author(s):  
P. Lacey ◽  
A. A. Torrance ◽  
J. A. Fitzpatrick
Keyword(s):  
Surface Roughness ◽  
Friction Coefficient ◽  
Boundary Lubrication ◽  
Slip Line ◽  
Field Model ◽  
Rough Surfaces ◽  
Normal Pressure ◽  
Line Field ◽  
Slip Line Field ◽  
Asperity Contacts

Most previous studies of boundary lubrication have ignored the contribution of surface roughness to friction. However, recent work by Moalic et al. (1987) has shown that when asperity contacts can be modelled by a slip line field, there is a precise relation between the friction coefficient and the asperity slope. Here, it is shown that there is also a relation between the friction coefficient and the normal pressure for rough surfaces which can be predicted from a development of the slip line field model.

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