Slip-line field theory of plane plastic strain dealing with Mohr's criterion expressed by quadratic limiting curves

1988 ◽  
Vol 9 (2) ◽  
pp. 189-198
Author(s):  
Chen Qiang
Keyword(s):  
Field Theory ◽  
Plastic Strain ◽  
Slip Line ◽  
Line Field ◽  
Slip Line Field ◽  
Plane Plastic

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.

Prediction of earing in cups drawn from anisotropic sheet using slip-line field theory

1974 ◽  
Vol 9 (2) ◽  
pp. 102-108 ◽  
Author(s):  
R Sowerby ◽  
W Johnson
Keyword(s):  
Field Theory ◽  
Slip Line ◽  
Deep Drawing ◽  
Deformation Mode ◽  
Strain Theory ◽  
Material Anisotropy ◽  
Line Field ◽  
Anisotropic Parameter ◽  
Slip Line Field ◽  
Theoretical Predictions

Anisotropic slip-line fields have been developed in the flanges of drawn cups and used to predict the location of the ears and hollows at the onset of the drawing operation. The analysis is based on Hill's plane-strain theory of anisotropic metals. The material anisotropy is characterized by a lumped anisotropic parameter c. Deep-drawing tests were performed on circular blanks cut from anisotropic sheet and the actual deformation mode of particles in the flange was compared with the theoretical predictions. The correlation was found to be favourable.

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.

Unified Solutions to the Limit Load of Thick-Walled Vessels

2006 ◽  
Vol 129 (4) ◽  
pp. 670-675 ◽  
Author(s):  
Jun-hai Zhao ◽  
Yue Zhai ◽  
Lin Ji ◽  
Xue-ying Wei
Keyword(s):  
Field Theory ◽  
Shear Strength ◽  
Slip Line ◽  
Strength Criterion ◽  
Limit Load ◽  
Plastic Limit ◽  
Line Field ◽  
Slip Line Field ◽  
Von Mises ◽  
Coulomb Criterion

Unified solutions to the elastoplastic limit load of thick-walled cylindrical and spherical vessels under internal pressure are obtained in terms of the unified strength theory (UST) and the unified slip-line field theory (USLFT). The UST and the USLFT include or approximate an existing strength criterion or slip-line field theory by adopting a parameter b, which varies from 0 to 1. The theories can be used on pressure-sensitive materials, which have the strength difference (SD) effect. The solutions, based on the Tresca criterion, the von Mises criterion, the Mohr–Coulomb criterion, and the twin shear strength criterion, are special cases of the present unified solutions. The results based on the Mohr–Coulomb criterion (b=0) give the lower bound of the plastic limit load, while those according to the twin shear strength criterion (b=1) are the upper bound. The solution of the von Mises criterion is approximated by the linear function of the UST with a specific parameter (b≈0.5). Plastic limit solutions with respect to different yield criteria are illustrated and compared. The influences of the yield criterion as well as the ratio of the tensile strength to the compressive strength on the plastic limit loads are discussed.

Estimating the wax breaking force and wax removal efficiency of cup pig using orthogonal cutting and slip-line field theory

Fuel ◽  
2019 ◽  
Vol 236 ◽  
pp. 1529-1539 ◽  
Author(s):  
Weidong Li ◽  
Qiyu Huang ◽  
Wenda Wang ◽  
Xue Dong ◽  
Xuedong Gao ◽  
...  
Keyword(s):  
Field Theory ◽  
Removal Efficiency ◽  
Slip Line ◽  
Orthogonal Cutting ◽  
Breaking Force ◽  
Line Field ◽  
Slip Line Field ◽  
Wax Removal
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