Slip Line Field of Anisotropic Soil

1974 ◽  
Vol 41 (2) ◽  
pp. 453-458 ◽  
Author(s):  
J. Greenstein ◽  
M. Livneh
Keyword(s):  
Anisotropic Material ◽  
Yield Function ◽  
Isotropic Case ◽  
Two Dimensional ◽  
Equilibrium Equations ◽  
Line Field ◽  
Slip Line Field ◽  
Practical Applications ◽  
Perfectly Plastic ◽  
Anisotropic Soil

This paper is concerned with anisotropic material in the two-dimensional case. A general yield function is postulated, and it is shown that both the equilibrium equations and the velocity equations are hyperbolic. Moreover, in the perfectly plastic-rigid media the velocity characteristics coincide with the stress characteristics. Thus, for practical applications, once the parameters of the yield function have been found for the anisotropic material, the conventional method of the isotropic case may be adopted, using the relevant relationships along the characteristics. An illustrative example is given.

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.

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.

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.

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.

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.

Slip-Line Field Analysis for Orthogonal Machining Based upon Experimental Flow Fields

1972 ◽  
Vol 14 (2) ◽  
pp. 85-97 ◽  
Author(s):  
R. N. Roth ◽  
P. L. B. Oxley
Keyword(s):  
Flow Stress ◽  
Plastic Zone ◽  
Strain Hardening ◽  
Slip Line ◽  
Sufficient Information ◽  
Shear Strain Rate ◽  
Equilibrium Equations ◽  
Line Field ◽  
Slip Line Field ◽  
Stress Equilibrium

An experimental flow field for slow speed (0·5 in/min) orthogonal (plane strain) machining was analysed using slip-line field techniques. Although the experimental streamlines were not sufficiently accurate to determine a slip-line field directly by calculating the directions of maximum shear strain rate from the velocity gradients, they were found to give sufficient information together with the measured cutting forces for an approximate step-by-step method of constructing a slip-line field. In this way a slip-line field was constructed not only for the plastic zone in which the chip is formed but also for the plastic flow along the tool-chip interface. It is shown that for most of the flow the slip-line field is satisfactory for both stress and velocity. An interesting feature of the analysis is that at the start of plastic deformation where the work material enters the plastic zone in which the chip is formed the increase in flow stress caused by strain-hardening is appreciable and must be taken into account in analysing the stresses, that is, in the stress equilibrium equations. However, along the tool-chip interface where the material has been severely strained there is little strain hardening and the slip lines in this region are shown to be consistent with the Hencky stress equilibrium equations for a material of constant flow stress.

Slip-Line Field and Stress Distribution for Flat Rolling in Model Test

1985 ◽  
Vol 107 (3) ◽  
pp. 234-240
Author(s):  
T. Nishitani ◽  
A. Hasegawa
Keyword(s):  
Stress Distribution ◽  
Model Test ◽  
Slip Line ◽  
Experimental Investigations ◽  
Line Field ◽  
Slip Line Field ◽  
Perfectly Plastic ◽  
Roll Pressure ◽  
Flat Rolling ◽  
Stress States

In the flat rolling, there are many theoretical investigations for finding the slip-line field and the stress distribution under the condition of rigid-perfectly plastic strip or ideal work-hardening strip. However, the propriety of hypothesis used has been ascertained only partly. Though some experimental investigations have been performed to find the roll pressure and so on, the relations between their results and the corresponding actual stress states are not analyzed sufficiently. In the present paper, the proposed photoviscoplasticity is applied to analyze the slip-line field, stress states near the contact surface and the normal roll pressure of the strip in the model test of the flat rolling. As the results, the experimental slip-line field was remarkably different from the theoretical one. The normal roll pressure was appreciably affected by the deformation speed.

scholarly journals The numerical calculation of statically admissible slip-line field for plane strain compression of a three-layer symmetric strip between rigid plates

2021 ◽  
Vol 59 (1) ◽  
pp. 125
Author(s):  
Thanh Manh Nguyen ◽  
Kien Trung Nguyen ◽  
Sergei Alexandrov
Keyword(s):  
Slip Line ◽  
Material Interfaces ◽  
Line Field ◽  
Slip Line Field ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Shear Yield ◽  
Stress Boundary Conditions ◽  
Stress Boundary ◽  
Rigid Surfaces

This paper present a method to build up statically admissible slip-line field (the field of characteristics) and, as a result, the field of statically admissible stresses of the compression of a three-layer symmetric strip consisting of two different rigid perfectly plastic materials between rough, parallel, rigid plates (for the case: the shear yield  stress of the inner layer is greater than that of the outer layer). Under the conditions of sticking regime at bi-material interfaces and sliding occurs at rigid surfaces with maximum friction, the appropriate singularities on the boundary between the two materials have been assumed, then a standard numerical slip-line technique is supplemented with iterative procedure to calculate characteristic and stress fields that satisfy simultaneously the stress boundary conditions as well as the regime of sticking on the bi-material interfaces

Two-dimensional metal carbides and nitrides (MXenes): preparation, property, and applications in cancer therapy

Nanophotonics ◽  
2020 ◽  
Vol 9 (8) ◽  
pp. 2125-2145 ◽  
Author(s):  
Lu Ming Dong ◽  
Cui Ye ◽  
Lin Lin Zheng ◽  
Zhong Feng Gao ◽  
Fan Xia
Keyword(s):  
Cancer Therapy ◽  
Scientific Community ◽  
Critical Role ◽  
High Specific Surface Area ◽  
Future Perspective ◽  
Two Dimensional ◽  
Metal Carbides ◽  
Practical Applications ◽  
Two Dimensional Materials ◽  
Size And Morphology

AbstractTransition metal carbides and nitrides (MXenes), which comprise a rapidly growing family of two-dimensional materials, have attracted extensive attention of the scientific community, owing to its unique characteristics of high specific surface area, remarkable biocompatibility, and versatile applications. Exploring different methods to tune the size and morphology of MXenes plays a critical role in their practical applications. In recent years, MXenes have been demonstrated as promising nanomaterials for cancer therapy with substantial performances, which not only are helpful to clarify the mechanism between properties and morphologies but also bridge the gap between MXene nanotechnology and forward-looking applications. In this review, recent progress on the preparation and properties of MXenes are summarized. Further applications in cancer therapy are also discussed. Finally, the current opportunities and future perspective of MXenes are described.

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