A matrix technique for constructing slip‐line field solutions to a class of plane strain plasticity problems

Abstract

A procedure is described for solving plane strain rigid perfect‐plasticity problems which lead to linear integral equations. The problem of finding the initial characteristic (slip‐line), from which the complete field can be constructed, is reduced to a simple matrix inversion. Although the form of this matrix will depend on the particular problem concerned, it will be expressible in terms of a few fundamental matrices which occur in all problems of this type. The properties of these basic matrices and FORTRAN subroutines for assimilating them and for performing the corresponding linear transformations are given in detail. In illustration the procedure is applied to a drawing and to a strip rolling problem.

Slip-line metal cutting model with negative rake angle

“…Mathematical formulation of the model was done based on basic matrix algorithm of Dewhurst and Collins (1973).…”

“…The matrix algorithm developed by Dewhurst and Collins (1973) in order to solve slip line problems is used in this study. This algorithm is being applied to solve plain friction limited slip line problems.…”

“…Fang (2005) used an analytical model of the chip formation for the solution. In this work, the mathematical formulation of the model was established based on Dewhurst and Collins's (1973) matrix technique for numerically solving slip-line field model. Kıta et al (1981) investigated the influence of the cutting speed on the shape of the stagnant region of material produced ahead of the tool face.…”

The Evaluation of Analytical Models for Orthogonal Cutting Process

“…The slip line models [19][20][21][22][23][24][25][26][27] Depends only on material properties and not to the experimental data. These models predict the Mechanical response and temperature distribution and are consistent with stretching, the stretch rate and temperature-dependent models.…”

Slip Line Field Solution for Second Pass in Lubricated 4-High Reversing Cold Rolling Sheet Mill

“…Dewhurst and Collins [10] suggested a matrix technique for the construction of slip line fields and illustrated the technique with reference to strip rolling and drawing. However, there is lack of information on slip line field solutions to subsequent passes after the first pass in cold rolling mills which will be quite relevant in the cold rolling firm.…”